1,1,57,45,0.041626,"\int x^m (A+B x) \left(b x+c x^2\right) \, dx","Integrate[x^m*(A + B*x)*(b*x + c*x^2),x]","\frac{x^{m+2} (A (m+4) (b (m+3)+c (m+2) x)+B (m+2) x (b (m+4)+c (m+3) x))}{(m+2) (m+3) (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,"(x^(2 + m)*(A*(4 + m)*(b*(3 + m) + c*(2 + m)*x) + B*(2 + m)*x*(b*(4 + m) + c*(3 + m)*x)))/((2 + m)*(3 + m)*(4 + m))","A",1
2,1,33,33,0.0061588,"\int x^3 (A+B x) \left(b x+c x^2\right) \, dx","Integrate[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",1
3,1,33,33,0.0046747,"\int x^2 (A+B x) \left(b x+c x^2\right) \, dx","Integrate[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",1
4,1,33,33,0.0045391,"\int x (A+B x) \left(b x+c x^2\right) \, dx","Integrate[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",1
5,1,29,33,0.0047253,"\int (A+B x) \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(b*x + c*x^2),x]","\frac{1}{12} x^2 (A (6 b+4 c x)+B x (4 b+3 c x))","\frac{1}{3} x^3 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{4} B c x^4",1,"(x^2*(B*x*(4*b + 3*c*x) + A*(6*b + 4*c*x)))/12","A",1
6,1,28,28,0.0045367,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x} \, dx","Integrate[((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",1
7,1,24,24,0.0054714,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^2} \, dx","Integrate[((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",1
8,1,22,22,0.0086284,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^3} \, dx","Integrate[((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",1
9,1,28,27,0.0101801,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^4} \, dx","Integrate[((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,"-1/2*(A*b)/x^2 + (-(b*B) - A*c)/x + B*c*Log[x]","A",1
10,1,28,31,0.0096077,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^5} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/x^5,x]","-\frac{A (2 b+3 c x)+3 B x (b+2 c x)}{6 x^3}","-\frac{A c+b B}{2 x^2}-\frac{A b}{3 x^3}-\frac{B c}{x}",1,"-1/6*(3*B*x*(b + 2*c*x) + A*(2*b + 3*c*x))/x^3","A",1
11,1,29,33,0.0077304,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^6} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/x^6,x]","-\frac{3 A b+4 A c x+4 b B x+6 B c x^2}{12 x^4}","-\frac{A c+b B}{3 x^3}-\frac{A b}{4 x^4}-\frac{B c}{2 x^2}",1,"-1/12*(3*A*b + 4*b*B*x + 4*A*c*x + 6*B*c*x^2)/x^4","A",1
12,1,31,33,0.0098446,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^7} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/x^7,x]","-\frac{3 A (4 b+5 c x)+5 B x (3 b+4 c x)}{60 x^5}","-\frac{A c+b B}{4 x^4}-\frac{A b}{5 x^5}-\frac{B c}{3 x^3}",1,"-1/60*(5*B*x*(3*b + 4*c*x) + 3*A*(4*b + 5*c*x))/x^5","A",1
13,1,31,33,0.009059,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^8} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/x^8,x]","-\frac{2 A (5 b+6 c x)+3 B x (4 b+5 c x)}{60 x^6}","-\frac{A c+b B}{5 x^5}-\frac{A b}{6 x^6}-\frac{B c}{4 x^4}",1,"-1/60*(3*B*x*(4*b + 5*c*x) + 2*A*(5*b + 6*c*x))/x^6","A",1
14,1,71,71,0.0956135,"\int x^m (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[x^m*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{x^{m+3} \left(\left(\frac{b^2}{m+3}+\frac{2 b c x}{m+4}+\frac{c^2 x^2}{m+5}\right) (A c (m+6)-b B (m+3))+B (b+c x)^3\right)}{c (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,"(x^(3 + m)*(B*(b + c*x)^3 + (-(b*B*(3 + m)) + A*c*(6 + m))*(b^2/(3 + m) + (2*b*c*x)/(4 + m) + (c^2*x^2)/(5 + m))))/(c*(6 + m))","A",1
15,1,55,55,0.0099621,"\int x^3 (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[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",1
16,1,55,55,0.008906,"\int x^2 (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[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",1
17,1,55,55,0.0079367,"\int x (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[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",1
18,1,49,55,0.0112183,"\int (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(b*x + c*x^2)^2,x]","\frac{1}{60} x^3 \left(20 A b^2+12 c x^2 (A c+2 b B)+15 b x (2 A c+b B)+10 B c^2 x^3\right)","\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,"(x^3*(20*A*b^2 + 15*b*(b*B + 2*A*c)*x + 12*c*(2*b*B + A*c)*x^2 + 10*B*c^2*x^3))/60","A",1
19,1,49,55,0.0102833,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x,x]","\frac{1}{60} x^2 \left(30 A b^2+15 c x^2 (A c+2 b B)+20 b x (2 A c+b B)+12 B c^2 x^3\right)","\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,"(x^2*(30*A*b^2 + 20*b*(b*B + 2*A*c)*x + 15*c*(2*b*B + A*c)*x^2 + 12*B*c^2*x^3))/60","A",1
20,1,47,38,0.0103725,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^2} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^2,x]","\frac{1}{12} x \left(12 A b^2+4 c x^2 (A c+2 b B)+6 b x (2 A c+b B)+3 B c^2 x^3\right)","\frac{B (b+c x)^4}{4 c^2}-\frac{(b+c x)^3 (b B-A c)}{3 c^2}",1,"(x*(12*A*b^2 + 6*b*(b*B + 2*A*c)*x + 4*c*(2*b*B + A*c)*x^2 + 3*B*c^2*x^3))/12","A",1
21,1,43,46,0.0147137,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^3} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^3,x]","A b^2 \log (x)+b c x (2 A+B x)+\frac{1}{6} c^2 x^2 (3 A+2 B x)+b^2 B 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",1,"b^2*B*x + b*c*x*(2*A + B*x) + (c^2*x^2*(3*A + 2*B*x))/6 + A*b^2*Log[x]","A",1
22,1,43,44,0.0284835,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^4} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^4,x]","A \left(c^2 x-\frac{b^2}{x}\right)+b \log (x) (2 A c+b B)+\frac{1}{2} B c x (4 b+c 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",1,"(B*c*x*(4*b + c*x))/2 + A*(-(b^2/x) + c^2*x) + b*(b*B + 2*A*c)*Log[x]","A",1
23,1,44,44,0.0254922,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^5} \, dx","Integrate[((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,"-1/2*(A*b^2)/x^2 - (b*(b*B + 2*A*c))/x + B*c^2*x + c*(2*b*B + A*c)*Log[x]","A",1
24,1,47,49,0.0248427,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^6} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^6,x]","B c^2 \log (x)-\frac{2 A \left(b^2+3 b c x+3 c^2 x^2\right)+3 b B x (b+4 c x)}{6 x^3}","-\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,"-1/6*(3*b*B*x*(b + 4*c*x) + 2*A*(b^2 + 3*b*c*x + 3*c^2*x^2))/x^3 + B*c^2*Log[x]","A",1
25,1,50,53,0.0140066,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^7} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^7,x]","-\frac{A \left(3 b^2+8 b c x+6 c^2 x^2\right)+4 B x \left(b^2+3 b c x+3 c^2 x^2\right)}{12 x^4}","-\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,"-1/12*(4*B*x*(b^2 + 3*b*c*x + 3*c^2*x^2) + A*(3*b^2 + 8*b*c*x + 6*c^2*x^2))/x^4","A",1
26,1,53,55,0.0143405,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^8} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^8,x]","-\frac{2 A \left(6 b^2+15 b c x+10 c^2 x^2\right)+5 B x \left(3 b^2+8 b c x+6 c^2 x^2\right)}{60 x^5}","-\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,"-1/60*(5*B*x*(3*b^2 + 8*b*c*x + 6*c^2*x^2) + 2*A*(6*b^2 + 15*b*c*x + 10*c^2*x^2))/x^5","A",1
27,1,87,96,0.1059027,"\int x^m (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[x^m*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{x^{m+4} \left(\left(\frac{b^3}{m+4}+\frac{3 b^2 c x}{m+5}+\frac{3 b c^2 x^2}{m+6}+\frac{c^3 x^3}{m+7}\right) (A c (m+8)-b B (m+4))+B (b+c x)^4\right)}{c (m+8)}","\frac{A b^3 x^{m+4}}{m+4}+\frac{b^2 x^{m+5} (3 A c+b B)}{m+5}+\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,"(x^(4 + m)*(B*(b + c*x)^4 + (-(b*B*(4 + m)) + A*c*(8 + m))*(b^3/(4 + m) + (3*b^2*c*x)/(5 + m) + (3*b*c^2*x^2)/(6 + m) + (c^3*x^3)/(7 + m))))/(c*(8 + m))","A",1
28,1,75,75,0.0131117,"\int x^3 (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[x^3*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{7} A b^3 x^7+\frac{1}{8} b^2 x^8 (3 A c+b B)+\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}{7} A b^3 x^7+\frac{1}{8} b^2 x^8 (3 A c+b B)+\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",1
29,1,75,75,0.0113716,"\int x^2 (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[x^2*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{6} A b^3 x^6+\frac{1}{7} b^2 x^7 (3 A c+b B)+\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}{6} A b^3 x^6+\frac{1}{7} b^2 x^7 (3 A c+b B)+\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",1
30,1,75,75,0.0113653,"\int x (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[x*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{5} A b^3 x^5+\frac{1}{6} b^2 x^6 (3 A c+b B)+\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}{5} A b^3 x^5+\frac{1}{6} b^2 x^6 (3 A c+b B)+\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",1
31,1,75,75,0.0101408,"\int (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{4} A b^3 x^4+\frac{1}{5} b^2 x^5 (3 A c+b B)+\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}{4} A b^3 x^4+\frac{1}{5} b^2 x^5 (3 A c+b B)+\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",1
32,1,75,75,0.0098869,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x,x]","\frac{1}{3} A b^3 x^3+\frac{1}{4} b^2 x^4 (3 A c+b B)+\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}{3} A b^3 x^3+\frac{1}{4} b^2 x^4 (3 A c+b B)+\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",1
33,1,67,62,0.0143345,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^2} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^2,x]","\frac{1}{60} x^2 \left(30 A b^3+20 b^2 x (3 A c+b B)+12 c^2 x^3 (A c+3 b B)+45 b c x^2 (A c+b B)+10 B c^3 x^4\right)","-\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,"(x^2*(30*A*b^3 + 20*b^2*(b*B + 3*A*c)*x + 45*b*c*(b*B + A*c)*x^2 + 12*c^2*(3*b*B + A*c)*x^3 + 10*B*c^3*x^4))/60","A",1
34,1,67,38,0.0083983,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^3} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^3,x]","A b^3 x+\frac{1}{2} b^2 x^2 (3 A c+b B)+\frac{1}{4} c^2 x^4 (A c+3 b B)+b c x^3 (A c+b B)+\frac{1}{5} B c^3 x^5","\frac{B (b+c x)^5}{5 c^2}-\frac{(b+c x)^4 (b B-A c)}{4 c^2}",1,"A*b^3*x + (b^2*(b*B + 3*A*c)*x^2)/2 + b*c*(b*B + A*c)*x^3 + (c^2*(3*b*B + A*c)*x^4)/4 + (B*c^3*x^5)/5","A",1
35,1,63,66,0.0246853,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^4} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^4,x]","A b^3 \log (x)+\frac{1}{12} x \left(18 b^2 c (2 A+B x)+6 b c^2 x (3 A+2 B x)+c^3 x^2 (4 A+3 B x)+12 b^3 B\right)","A b^3 \log (x)+b^2 x (3 A c+b B)+\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,"(x*(12*b^3*B + 18*b^2*c*(2*A + B*x) + 6*b*c^2*x*(3*A + 2*B*x) + c^3*x^2*(4*A + 3*B*x)))/12 + A*b^3*Log[x]","A",1
36,1,67,65,0.0336182,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^5} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^5,x]","-\frac{A b^3}{x}+\log (x) \left(3 A b^2 c+b^3 B\right)+\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","-\frac{A b^3}{x}+b^2 \log (x) (3 A c+b B)+\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^3*B + 3*A*b^2*c)*Log[x]","A",1
37,1,71,65,0.0198928,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^6} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^6,x]","-\frac{A b^3}{2 x^2}+3 \log (x) \left(A b c^2+b^2 B c\right)+\frac{b^3 (-B)-3 A b^2 c}{x}+c^2 x (A c+3 b B)+\frac{1}{2} B c^3 x^2","-\frac{A b^3}{2 x^2}-\frac{b^2 (3 A c+b B)}{x}+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,"-1/2*(A*b^3)/x^2 + (-(b^3*B) - 3*A*b^2*c)/x + c^2*(3*b*B + A*c)*x + (B*c^3*x^2)/2 + 3*(b^2*B*c + A*b*c^2)*Log[x]","A",1
38,1,73,64,0.0331071,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^7} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^7,x]","-\frac{A b^3}{3 x^3}-\frac{3 \left(A b c^2+b^2 B c\right)}{x}+\frac{b^3 (-B)-3 A b^2 c}{2 x^2}+\log (x) \left(A c^3+3 b B c^2\right)+B c^3 x","-\frac{A b^3}{3 x^3}-\frac{b^2 (3 A c+b B)}{2 x^2}+c^2 \log (x) (A c+3 b B)-\frac{3 b c (A c+b B)}{x}+B c^3 x",1,"-1/3*(A*b^3)/x^3 + (-(b^3*B) - 3*A*b^2*c)/(2*x^2) - (3*(b^2*B*c + A*b*c^2))/x + B*c^3*x + (3*b*B*c^2 + A*c^3)*Log[x]","A",1
39,1,71,69,0.0309927,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^8} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^8,x]","B c^3 \log (x)-\frac{3 A \left(b^3+4 b^2 c x+6 b c^2 x^2+4 c^3 x^3\right)+2 b B x \left(2 b^2+9 b c x+18 c^2 x^2\right)}{12 x^4}","-\frac{A b^3}{4 x^4}-\frac{b^2 (3 A c+b B)}{3 x^3}-\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,"-1/12*(2*b*B*x*(2*b^2 + 9*b*c*x + 18*c^2*x^2) + 3*A*(b^3 + 4*b^2*c*x + 6*b*c^2*x^2 + 4*c^3*x^3))/x^4 + B*c^3*Log[x]","A",1
40,1,72,71,0.0187528,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^9} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^9,x]","-\frac{A \left(4 b^3+15 b^2 c x+20 b c^2 x^2+10 c^3 x^3\right)+5 B x \left(b^3+4 b^2 c x+6 b c^2 x^2+4 c^3 x^3\right)}{20 x^5}","-\frac{A b^3}{5 x^5}-\frac{b^2 (3 A c+b B)}{4 x^4}-\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,"-1/20*(5*B*x*(b^3 + 4*b^2*c*x + 6*b*c^2*x^2 + 4*c^3*x^3) + A*(4*b^3 + 15*b^2*c*x + 20*b*c^2*x^2 + 10*c^3*x^3))/x^5","A",1
41,1,74,75,0.0189006,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{10}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^10,x]","-\frac{A \left(10 b^3+36 b^2 c x+45 b c^2 x^2+20 c^3 x^3\right)+3 B x \left(4 b^3+15 b^2 c x+20 b c^2 x^2+10 c^3 x^3\right)}{60 x^6}","-\frac{A b^3}{6 x^6}-\frac{b^2 (3 A c+b B)}{5 x^5}-\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,"-1/60*(3*B*x*(4*b^3 + 15*b^2*c*x + 20*b*c^2*x^2 + 10*c^3*x^3) + A*(10*b^3 + 36*b^2*c*x + 45*b*c^2*x^2 + 20*c^3*x^3))/x^6","A",1
42,1,75,75,0.0183374,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{11}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^11,x]","-\frac{3 A \left(20 b^3+70 b^2 c x+84 b c^2 x^2+35 c^3 x^3\right)+7 B x \left(10 b^3+36 b^2 c x+45 b c^2 x^2+20 c^3 x^3\right)}{420 x^7}","-\frac{A b^3}{7 x^7}-\frac{b^2 (3 A c+b B)}{6 x^6}-\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,"-1/420*(7*B*x*(10*b^3 + 36*b^2*c*x + 45*b*c^2*x^2 + 20*c^3*x^3) + 3*A*(20*b^3 + 70*b^2*c*x + 84*b*c^2*x^2 + 35*c^3*x^3))/x^7","A",1
43,1,80,87,0.0298103,"\int \frac{x^4 (d+e x)}{b x+c x^2} \, dx","Integrate[(x^4*(d + e*x))/(b*x + c*x^2),x]","\frac{12 b^3 (b e-c d) \log (b+c x)+c x \left(-12 b^3 e+6 b^2 c (2 d+e x)-2 b c^2 x (3 d+2 e x)+c^3 x^2 (4 d+3 e x)\right)}{12 c^5}","-\frac{b^3 (c d-b e) \log (b+c x)}{c^5}+\frac{b^2 x (c d-b e)}{c^4}-\frac{b x^2 (c d-b e)}{2 c^3}+\frac{x^3 (c d-b e)}{3 c^2}+\frac{e x^4}{4 c}",1,"(c*x*(-12*b^3*e + 6*b^2*c*(2*d + e*x) - 2*b*c^2*x*(3*d + 2*e*x) + c^3*x^2*(4*d + 3*e*x)) + 12*b^3*(-(c*d) + b*e)*Log[b + c*x])/(12*c^5)","A",1
44,1,61,66,0.0199527,"\int \frac{x^3 (d+e x)}{b x+c x^2} \, dx","Integrate[(x^3*(d + e*x))/(b*x + c*x^2),x]","\frac{c x \left(6 b^2 e-3 b c (2 d+e x)+c^2 x (3 d+2 e x)\right)+6 b^2 (c d-b e) \log (b+c x)}{6 c^4}","\frac{b^2 (c d-b e) \log (b+c x)}{c^4}-\frac{b x (c d-b e)}{c^3}+\frac{x^2 (c d-b e)}{2 c^2}+\frac{e x^3}{3 c}",1,"(c*x*(6*b^2*e - 3*b*c*(2*d + e*x) + c^2*x*(3*d + 2*e*x)) + 6*b^2*(c*d - b*e)*Log[b + c*x])/(6*c^4)","A",1
45,1,41,45,0.012668,"\int \frac{x^2 (d+e x)}{b x+c x^2} \, dx","Integrate[(x^2*(d + e*x))/(b*x + c*x^2),x]","\frac{c x (-2 b e+2 c d+c e x)+2 b (b e-c d) \log (b+c x)}{2 c^3}","-\frac{b (c d-b e) \log (b+c x)}{c^3}+\frac{x (c d-b e)}{c^2}+\frac{e x^2}{2 c}",1,"(c*x*(2*c*d - 2*b*e + c*e*x) + 2*b*(-(c*d) + b*e)*Log[b + c*x])/(2*c^3)","A",1
46,1,25,25,0.0071994,"\int \frac{x (d+e x)}{b x+c x^2} \, dx","Integrate[(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",1
47,1,29,30,0.0090239,"\int \frac{d+e x}{b x+c x^2} \, dx","Integrate[(d + e*x)/(b*x + c*x^2),x]","\frac{(b e-c d) \log (b+c x)}{b c}+\frac{d \log (x)}{b}","\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",1
48,1,42,43,0.0172005,"\int \frac{d+e x}{x \left(b x+c x^2\right)} \, dx","Integrate[(d + e*x)/(x*(b*x + c*x^2)),x]","\frac{\log (x) (b e-c d)}{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",1
49,1,58,62,0.0313066,"\int \frac{d+e x}{x^2 \left(b x+c x^2\right)} \, dx","Integrate[(d + e*x)/(x^2*(b*x + c*x^2)),x]","\frac{-\frac{b (b d+2 b e x-2 c d x)}{x^2}+2 c \log (x) (c d-b e)+2 c (b e-c d) \log (b+c x)}{2 b^3}","\frac{c \log (x) (c d-b e)}{b^3}-\frac{c (c d-b e) \log (b+c x)}{b^3}+\frac{c d-b e}{b^2 x}-\frac{d}{2 b x^2}",1,"(-((b*(b*d - 2*c*d*x + 2*b*e*x))/x^2) + 2*c*(c*d - b*e)*Log[x] + 2*c*(-(c*d) + b*e)*Log[b + c*x])/(2*b^3)","A",1
50,1,81,86,0.0482534,"\int \frac{d+e x}{x^3 \left(b x+c x^2\right)} \, dx","Integrate[(d + e*x)/(x^3*(b*x + c*x^2)),x]","\frac{\frac{b \left(-\left(b^2 (2 d+3 e x)\right)+3 b c x (d+2 e x)-6 c^2 d x^2\right)}{x^3}+6 c^2 \log (x) (b e-c d)+6 c^2 (c d-b e) \log (b+c x)}{6 b^4}","-\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 (c d-b e)}{b^3 x}+\frac{c d-b e}{2 b^2 x^2}-\frac{d}{3 b x^3}",1,"((b*(-6*c^2*d*x^2 + 3*b*c*x*(d + 2*e*x) - b^2*(2*d + 3*e*x)))/x^3 + 6*c^2*(-(c*d) + b*e)*Log[x] + 6*c^2*(c*d - b*e)*Log[b + c*x])/(6*b^4)","A",1
51,1,87,90,0.0526078,"\int \frac{x^5 (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(x^5*(d + e*x))/(b*x + c*x^2)^2,x]","\frac{\frac{6 b^3 (c d-b e)}{b+c x}+6 b^2 (3 c d-4 b e) \log (b+c x)+3 c^2 x^2 (c d-2 b e)+6 b c x (3 b e-2 c d)+2 c^3 e x^3}{6 c^5}","\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{b x (2 c d-3 b e)}{c^4}+\frac{x^2 (c d-2 b e)}{2 c^3}+\frac{e x^3}{3 c^2}",1,"(6*b*c*(-2*c*d + 3*b*e)*x + 3*c^2*(c*d - 2*b*e)*x^2 + 2*c^3*e*x^3 + (6*b^3*(c*d - b*e))/(b + c*x) + 6*b^2*(3*c*d - 4*b*e)*Log[b + c*x])/(6*c^5)","A",1
52,1,66,69,0.0502792,"\int \frac{x^4 (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(x^4*(d + e*x))/(b*x + c*x^2)^2,x]","\frac{\frac{2 b^2 (b e-c d)}{b+c x}+2 c x (c d-2 b e)+2 b (3 b e-2 c d) \log (b+c x)+c^2 e x^2}{2 c^4}","-\frac{b^2 (c d-b e)}{c^4 (b+c x)}-\frac{b (2 c d-3 b e) \log (b+c x)}{c^4}+\frac{x (c d-2 b e)}{c^3}+\frac{e x^2}{2 c^2}",1,"(2*c*(c*d - 2*b*e)*x + c^2*e*x^2 + (2*b^2*(-(c*d) + b*e))/(b + c*x) + 2*b*(-2*c*d + 3*b*e)*Log[b + c*x])/(2*c^4)","A",1
53,1,41,45,0.0232706,"\int \frac{x^3 (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(x^3*(d + e*x))/(b*x + c*x^2)^2,x]","\frac{\frac{b (c d-b e)}{b+c x}+(c d-2 b e) \log (b+c x)+c e x}{c^3}","\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,"(c*e*x + (b*(c*d - b*e))/(b + c*x) + (c*d - 2*b*e)*Log[b + c*x])/c^3","A",1
54,1,31,32,0.010235,"\int \frac{x^2 (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(x^2*(d + e*x))/(b*x + c*x^2)^2,x]","\frac{b e-c d}{c^2 (b+c x)}+\frac{e \log (b+c x)}{c^2}","\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",1
55,1,38,42,0.0245244,"\int \frac{x (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(x*(d + e*x))/(b*x + c*x^2)^2,x]","\frac{\frac{b (c d-b e)}{c (b+c x)}-d \log (b+c x)+d \log (x)}{b^2}","-\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,"((b*(c*d - b*e))/(c*(b + c*x)) + d*Log[x] - d*Log[b + c*x])/b^2","A",1
56,1,56,65,0.0370062,"\int \frac{d+e x}{\left(b x+c x^2\right)^2} \, dx","Integrate[(d + e*x)/(b*x + c*x^2)^2,x]","\frac{\frac{b (b e-c d)}{b+c x}+\log (x) (b e-2 c d)+(2 c d-b e) \log (b+c x)-\frac{b d}{x}}{b^3}","-\frac{\log (x) (2 c d-b e)}{b^3}+\frac{(2 c d-b e) \log (b+c x)}{b^3}-\frac{c d-b e}{b^2 (b+c x)}-\frac{d}{b^2 x}",1,"(-((b*d)/x) + (b*(-(c*d) + b*e))/(b + c*x) + (-2*c*d + b*e)*Log[x] + (2*c*d - b*e)*Log[b + c*x])/b^3","A",1
57,1,85,85,0.0657096,"\int \frac{d+e x}{x \left(b x+c x^2\right)^2} \, dx","Integrate[(d + e*x)/(x*(b*x + c*x^2)^2),x]","\frac{-\frac{b \left(b^2 (d+2 e x)+b c x (4 e x-3 d)-6 c^2 d x^2\right)}{x^2 (b+c x)}+2 c \log (x) (3 c d-2 b e)+2 c (2 b e-3 c d) \log (b+c x)}{2 b^4}","\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{2 c d-b e}{b^3 x}+\frac{c (c d-b e)}{b^3 (b+c x)}-\frac{d}{2 b^2 x^2}",1,"(-((b*(-6*c^2*d*x^2 + b^2*(d + 2*e*x) + b*c*x*(-3*d + 4*e*x)))/(x^2*(b + c*x))) + 2*c*(3*c*d - 2*b*e)*Log[x] + 2*c*(-3*c*d + 2*b*e)*Log[b + c*x])/(2*b^4)","A",1
58,1,106,113,0.0815394,"\int \frac{d+e x}{x^2 \left(b x+c x^2\right)^2} \, dx","Integrate[(d + e*x)/(x^2*(b*x + c*x^2)^2),x]","\frac{-\frac{2 b^3 d}{x^3}-\frac{3 b^2 (b e-2 c d)}{x^2}+\frac{6 b c^2 (b e-c d)}{b+c x}+6 c^2 \log (x) (3 b e-4 c d)+6 c^2 (4 c d-3 b e) \log (b+c x)+\frac{6 b c (2 b e-3 c d)}{x}}{6 b^5}","-\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{c^2 (c d-b e)}{b^4 (b+c x)}-\frac{c (3 c d-2 b e)}{b^4 x}+\frac{2 c d-b e}{2 b^3 x^2}-\frac{d}{3 b^2 x^3}",1,"((-2*b^3*d)/x^3 - (3*b^2*(-2*c*d + b*e))/x^2 + (6*b*c*(-3*c*d + 2*b*e))/x + (6*b*c^2*(-(c*d) + b*e))/(b + c*x) + 6*c^2*(-4*c*d + 3*b*e)*Log[x] + 6*c^2*(4*c*d - 3*b*e)*Log[b + c*x])/(6*b^5)","A",1
59,1,86,94,0.0524725,"\int \frac{x^6 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^6*(d + e*x))/(b*x + c*x^2)^3,x]","\frac{\frac{b^3 (c d-b e)}{(b+c x)^2}+\frac{2 b^2 (4 b e-3 c d)}{b+c x}+2 c x (c d-3 b e)+6 b (2 b e-c d) \log (b+c x)+c^2 e x^2}{2 c^5}","\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{3 b (c d-2 b e) \log (b+c x)}{c^5}+\frac{x (c d-3 b e)}{c^4}+\frac{e x^2}{2 c^3}",1,"(2*c*(c*d - 3*b*e)*x + c^2*e*x^2 + (b^3*(c*d - b*e))/(b + c*x)^2 + (2*b^2*(-3*c*d + 4*b*e))/(b + c*x) + 6*b*(-(c*d) + 2*b*e)*Log[b + c*x])/(2*c^5)","A",1
60,1,75,71,0.0273661,"\int \frac{x^5 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^5*(d + e*x))/(b*x + c*x^2)^3,x]","\frac{2 b c d-3 b^2 e}{c^4 (b+c x)}+\frac{b^3 e-b^2 c d}{2 c^4 (b+c x)^2}+\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^3*e)/(2*c^4*(b + c*x)^2) + (2*b*c*d - 3*b^2*e)/(c^4*(b + c*x)) + ((c*d - 3*b*e)*Log[b + c*x])/c^4","A",1
61,1,54,55,0.0163588,"\int \frac{x^4 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^4*(d + e*x))/(b*x + c*x^2)^3,x]","\frac{3 b^2 e-b c (d-4 e x)+2 e (b+c x)^2 \log (b+c x)-2 c^2 d x}{2 c^3 (b+c x)^2}","-\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,"(3*b^2*e - 2*c^2*d*x - b*c*(d - 4*e*x) + 2*e*(b + c*x)^2*Log[b + c*x])/(2*c^3*(b + c*x)^2)","A",1
62,1,26,36,0.0086551,"\int \frac{x^3 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^3*(d + e*x))/(b*x + c*x^2)^3,x]","-\frac{b e+c (d+2 e x)}{2 c^2 (b+c x)^2}","-\frac{c d-b e}{2 c^2 (b+c x)^2}-\frac{e}{c^2 (b+c x)}",1,"-1/2*(b*e + c*(d + 2*e*x))/(c^2*(b + c*x)^2)","A",1
63,1,53,57,0.0401692,"\int \frac{x^2 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^2*(d + e*x))/(b*x + c*x^2)^3,x]","\frac{\frac{b \left(b^2 (-e)+3 b c d+2 c^2 d x\right)}{c (b+c x)^2}-2 d \log (b+c x)+2 d \log (x)}{2 b^3}","-\frac{d \log (b+c x)}{b^3}+\frac{d \log (x)}{b^3}+\frac{d}{b^2 (b+c x)}+\frac{c d-b e}{2 b c (b+c x)^2}",1,"((b*(3*b*c*d - b^2*e + 2*c^2*d*x))/(c*(b + c*x)^2) + 2*d*Log[x] - 2*d*Log[b + c*x])/(2*b^3)","A",1
64,1,81,88,0.0476985,"\int \frac{x (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x*(d + e*x))/(b*x + c*x^2)^3,x]","\frac{\frac{b^2 (b e-c d)}{(b+c x)^2}+\frac{2 b (b e-2 c d)}{b+c x}+2 \log (x) (b e-3 c d)+2 (3 c d-b e) \log (b+c x)-\frac{2 b d}{x}}{2 b^4}","-\frac{\log (x) (3 c d-b e)}{b^4}+\frac{(3 c d-b e) \log (b+c x)}{b^4}-\frac{2 c d-b e}{b^3 (b+c x)}-\frac{d}{b^3 x}-\frac{c d-b e}{2 b^2 (b+c x)^2}",1,"((-2*b*d)/x + (b^2*(-(c*d) + b*e))/(b + c*x)^2 + (2*b*(-2*c*d + b*e))/(b + c*x) + 2*(-3*c*d + b*e)*Log[x] + 2*(3*c*d - b*e)*Log[b + c*x])/(2*b^4)","A",1
65,1,102,110,0.0754114,"\int \frac{d+e x}{\left(b x+c x^2\right)^3} \, dx","Integrate[(d + e*x)/(b*x + c*x^2)^3,x]","\frac{-\frac{b \left(b^3 (d+2 e x)+b^2 c x (9 e x-4 d)+6 b c^2 x^2 (e x-3 d)-12 c^3 d x^3\right)}{x^2 (b+c x)^2}+6 c \log (x) (2 c d-b e)+6 c (b e-2 c d) \log (b+c x)}{2 b^5}","\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{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{d}{2 b^3 x^2}",1,"(-((b*(-12*c^3*d*x^3 + 6*b*c^2*x^2*(-3*d + e*x) + b^3*(d + 2*e*x) + b^2*c*x*(-4*d + 9*e*x)))/(x^2*(b + c*x)^2)) + 6*c*(2*c*d - b*e)*Log[x] + 6*c*(-2*c*d + b*e)*Log[b + c*x])/(2*b^5)","A",1
66,1,129,140,0.117341,"\int \frac{d+e x}{x \left(b x+c x^2\right)^3} \, dx","Integrate[(d + e*x)/(x*(b*x + c*x^2)^3),x]","\frac{\frac{b \left(-\left(b^4 (2 d+3 e x)\right)+b^3 c x (5 d+12 e x)+2 b^2 c^2 x^2 (27 e x-10 d)+18 b c^3 x^3 (2 e x-5 d)-60 c^4 d x^4\right)}{x^3 (b+c x)^2}+12 c^2 \log (x) (3 b e-5 c d)+12 c^2 (5 c d-3 b e) \log (b+c x)}{6 b^6}","-\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{c^2 (4 c d-3 b e)}{b^5 (b+c x)}-\frac{3 c (2 c d-b e)}{b^5 x}-\frac{c^2 (c d-b e)}{2 b^4 (b+c x)^2}+\frac{3 c d-b e}{2 b^4 x^2}-\frac{d}{3 b^3 x^3}",1,"((b*(-60*c^4*d*x^4 + 18*b*c^3*x^3*(-5*d + 2*e*x) - b^4*(2*d + 3*e*x) + b^3*c*x*(5*d + 12*e*x) + 2*b^2*c^2*x^2*(-10*d + 27*e*x)))/(x^3*(b + c*x)^2) + 12*c^2*(-5*c*d + 3*b*e)*Log[x] + 12*c^2*(5*c*d - 3*b*e)*Log[b + c*x])/(6*b^6)","A",1
67,1,166,200,0.2818721,"\int x^3 (A+B x) \sqrt{b x+c x^2} \, dx","Integrate[x^3*(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(-210 b^4 c (2 A+B x)+56 b^3 c^2 x (5 A+3 B x)-16 b^2 c^3 x^2 (14 A+9 B x)+64 b c^4 x^3 (3 A+2 B x)+256 c^5 x^4 (6 A+5 B x)+315 b^5 B\right)-\frac{105 b^{9/2} (3 b B-4 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{7680 c^{11/2}}","-\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^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 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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(315*b^5*B - 210*b^4*c*(2*A + B*x) + 64*b*c^4*x^3*(3*A + 2*B*x) + 56*b^3*c^2*x*(5*A + 3*B*x) + 256*c^5*x^4*(6*A + 5*B*x) - 16*b^2*c^3*x^2*(14*A + 9*B*x)) - (105*b^(9/2)*(3*b*B - 4*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(7680*c^(11/2))","A",1
68,1,148,165,0.2519523,"\int x^2 (A+B x) \sqrt{b x+c x^2} \, dx","Integrate[x^2*(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\frac{15 b^{7/2} (7 b B-10 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(10 b^3 c (15 A+7 B x)-4 b^2 c^2 x (25 A+14 B x)+16 b c^3 x^2 (5 A+3 B x)+96 c^4 x^3 (5 A+4 B x)-105 b^4 B\right)\right)}{1920 c^{9/2}}","\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^2 (b+2 c x) \sqrt{b x+c x^2} (7 b B-10 A c)}{128 c^4}+\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-105*b^4*B + 16*b*c^3*x^2*(5*A + 3*B*x) + 96*c^4*x^3*(5*A + 4*B*x) + 10*b^3*c*(15*A + 7*B*x) - 4*b^2*c^2*x*(25*A + 14*B*x)) + (15*b^(7/2)*(7*b*B - 10*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(1920*c^(9/2))","A",1
69,1,128,113,0.2143478,"\int x (A+B x) \sqrt{b x+c x^2} \, dx","Integrate[x*(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(-2 b^2 c (12 A+5 B x)+8 b c^2 x (2 A+B x)+16 c^3 x^2 (4 A+3 B x)+15 b^3 B\right)-\frac{3 b^{5/2} (5 b B-8 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{192 c^{7/2}}","-\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(15*b^3*B + 8*b*c^2*x*(2*A + B*x) + 16*c^3*x^2*(4*A + 3*B*x) - 2*b^2*c*(12*A + 5*B*x)) - (3*b^(5/2)*(5*b*B - 8*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(192*c^(7/2))","A",1
70,1,108,97,0.1802608,"\int (A+B x) \sqrt{b x+c x^2} \, dx","Integrate[(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\frac{3 b^{3/2} (b B-2 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(2 b c (3 A+B x)+4 c^2 x (3 A+2 B x)-3 b^2 B\right)\right)}{24 c^{5/2}}","\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-3*b^2*B + 2*b*c*(3*A + B*x) + 4*c^2*x*(3*A + 2*B*x)) + (3*b^(3/2)*(b*B - 2*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(24*c^(5/2))","A",1
71,1,89,92,0.1439415,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x,x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} (4 A c+b B+2 B c x)-\frac{\sqrt{b} (b B-4 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{4 c^{3/2}}","-\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(b*B + 4*A*c + 2*B*c*x) - (Sqrt[b]*(b*B - 4*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(4*c^(3/2))","A",1
72,1,75,83,0.140255,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^2} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^2,x]","\frac{\sqrt{x (b+c x)} \left(\frac{\sqrt{x} (2 A c+b B) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{c} \sqrt{\frac{c x}{b}+1}}-2 A+B x\right)}{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}",1,"(Sqrt[x*(b + c*x)]*(-2*A + B*x + ((b*B + 2*A*c)*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b])))/x","A",1
73,1,86,73,0.0626241,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^3} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^3,x]","\frac{2 \sqrt{x (b+c x)} \left((b+c x) \sqrt{\frac{c x}{b}+1} (b B-A c)-b^2 B \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{c x}{b}\right)\right)}{3 b c x^2 \sqrt{\frac{c x}{b}+1}}","-\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*Sqrt[x*(b + c*x)]*((b*B - A*c)*(b + c*x)*Sqrt[1 + (c*x)/b] - b^2*B*Hypergeometric2F1[-3/2, -3/2, -1/2, -((c*x)/b)]))/(3*b*c*x^2*Sqrt[1 + (c*x)/b])","C",1
74,1,36,57,0.0131752,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^4} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^4,x]","-\frac{2 (x (b+c x))^{3/2} (3 A b-2 A c x+5 b B x)}{15 b^2 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*(x*(b + c*x))^(3/2)*(3*A*b + 5*b*B*x - 2*A*c*x))/(15*b^2*x^4)","A",1
75,1,56,90,0.0305292,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^5} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^5,x]","-\frac{2 (x (b+c x))^{3/2} \left(A \left(15 b^2-12 b c x+8 c^2 x^2\right)+7 b B x (3 b-2 c x)\right)}{105 b^3 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*(x*(b + c*x))^(3/2)*(7*b*B*x*(3*b - 2*c*x) + A*(15*b^2 - 12*b*c*x + 8*c^2*x^2)))/(105*b^3*x^5)","A",1
76,1,78,125,0.0309227,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^6} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^6,x]","-\frac{2 (x (b+c x))^{3/2} \left(A \left(35 b^3-30 b^2 c x+24 b c^2 x^2-16 c^3 x^3\right)+3 b B x \left(15 b^2-12 b c x+8 c^2 x^2\right)\right)}{315 b^4 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*(x*(b + c*x))^(3/2)*(3*b*B*x*(15*b^2 - 12*b*c*x + 8*c^2*x^2) + A*(35*b^3 - 30*b^2*c*x + 24*b*c^2*x^2 - 16*c^3*x^3)))/(315*b^4*x^6)","A",1
77,1,100,160,0.0451923,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^7} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^7,x]","-\frac{2 (x (b+c x))^{3/2} \left(A \left(315 b^4-280 b^3 c x+240 b^2 c^2 x^2-192 b c^3 x^3+128 c^4 x^4\right)+11 b B x \left(35 b^3-30 b^2 c x+24 b c^2 x^2-16 c^3 x^3\right)\right)}{3465 b^5 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*(x*(b + c*x))^(3/2)*(11*b*B*x*(35*b^3 - 30*b^2*c*x + 24*b*c^2*x^2 - 16*c^3*x^3) + A*(315*b^4 - 280*b^3*c*x + 240*b^2*c^2*x^2 - 192*b*c^3*x^3 + 128*c^4*x^4)))/(3465*b^5*x^7)","A",1
78,1,123,195,0.0426339,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^8} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^8,x]","-\frac{2 (x (b+c x))^{3/2} \left(5 A \left(693 b^5-630 b^4 c x+560 b^3 c^2 x^2-480 b^2 c^3 x^3+384 b c^4 x^4-256 c^5 x^5\right)+13 b B x \left(315 b^4-280 b^3 c x+240 b^2 c^2 x^2-192 b c^3 x^3+128 c^4 x^4\right)\right)}{45045 b^6 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*(x*(b + c*x))^(3/2)*(13*b*B*x*(315*b^4 - 280*b^3*c*x + 240*b^2*c^2*x^2 - 192*b*c^3*x^3 + 128*c^4*x^4) + 5*A*(693*b^5 - 630*b^4*c*x + 560*b^3*c^2*x^2 - 480*b^2*c^3*x^3 + 384*b*c^4*x^4 - 256*c^5*x^5)))/(45045*b^6*x^8)","A",1
79,1,179,238,0.4334714,"\int x^3 (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Integrate[x^3*(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{x^5 \sqrt{x (b+c x)} \left(\frac{11 (11 b B-16 A c) \left(315 b^{13/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)-\sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \left(315 b^6-210 b^5 c x+168 b^4 c^2 x^2-144 b^3 c^3 x^3+128 b^2 c^4 x^4+6400 b c^5 x^5+5120 c^6 x^6\right)\right)}{71680 c^{11/2} x^{11/2} \sqrt{\frac{c x}{b}+1}}+11 B (b+c x)^2\right)}{88 c}","\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{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{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,"(x^5*Sqrt[x*(b + c*x)]*(11*B*(b + c*x)^2 + (11*(11*b*B - 16*A*c)*(-(Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*(315*b^6 - 210*b^5*c*x + 168*b^4*c^2*x^2 - 144*b^3*c^3*x^3 + 128*b^2*c^4*x^4 + 6400*b*c^5*x^5 + 5120*c^6*x^6)) + 315*b^(13/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(71680*c^(11/2)*x^(11/2)*Sqrt[1 + (c*x)/b])))/(88*c)","A",1
80,1,167,203,0.3374728,"\int x^2 (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Integrate[x^2*(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{x^4 \sqrt{x (b+c x)} \left(9 B (b+c x)^2-\frac{3 (9 b B-14 A c) \left(105 b^{11/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)+\sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \left(-105 b^5+70 b^4 c x-56 b^3 c^2 x^2+48 b^2 c^3 x^3+1664 b c^4 x^4+1280 c^5 x^5\right)\right)}{5120 c^{9/2} x^{9/2} \sqrt{\frac{c x}{b}+1}}\right)}{63 c}","-\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^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 \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,"(x^4*Sqrt[x*(b + c*x)]*(9*B*(b + c*x)^2 - (3*(9*b*B - 14*A*c)*(Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*(-105*b^5 + 70*b^4*c*x - 56*b^3*c^2*x^2 + 48*b^2*c^3*x^3 + 1664*b*c^4*x^4 + 1280*c^5*x^5) + 105*b^(11/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(5120*c^(9/2)*x^(9/2)*Sqrt[1 + (c*x)/b])))/(63*c)","A",1
81,1,166,151,0.2913243,"\int x (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Integrate[x*(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{\sqrt{x (b+c x)} \left(\frac{15 b^{9/2} (7 b B-12 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(10 b^4 c (18 A+7 B x)-8 b^3 c^2 x (15 A+7 B x)+48 b^2 c^3 x^2 (2 A+B x)+64 b c^4 x^3 (33 A+26 B x)+256 c^5 x^4 (6 A+5 B x)-105 b^5 B\right)\right)}{7680 c^{9/2}}","\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^3 (b+2 c x) \sqrt{b x+c x^2} (7 b B-12 A c)}{512 c^4}+\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-105*b^5*B + 48*b^2*c^3*x^2*(2*A + B*x) + 256*c^5*x^4*(6*A + 5*B*x) - 8*b^3*c^2*x*(15*A + 7*B*x) + 10*b^4*c*(18*A + 7*B*x) + 64*b*c^4*x^3*(33*A + 26*B*x)) + (15*b^(9/2)*(7*b*B - 12*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(7680*c^(9/2))","A",1
82,1,146,134,0.252175,"\int (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(-10 b^3 c (3 A+B x)+4 b^2 c^2 x (5 A+2 B x)+16 b c^3 x^2 (15 A+11 B x)+32 c^4 x^3 (5 A+4 B x)+15 b^4 B\right)-\frac{15 b^{7/2} (b B-2 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{640 c^{7/2}}","-\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{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{128 c^3}-\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(15*b^4*B - 10*b^3*c*(3*A + B*x) + 4*b^2*c^2*x*(5*A + 2*B*x) + 32*c^4*x^3*(5*A + 4*B*x) + 16*b*c^3*x^2*(15*A + 11*B*x)) - (15*b^(7/2)*(b*B - 2*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(640*c^(7/2))","A",1
83,1,128,132,0.2204762,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x,x]","\frac{\sqrt{x (b+c x)} \left(\frac{3 b^{5/2} (3 b B-8 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(6 b^2 c (4 A+B x)+8 b c^2 x (14 A+9 B x)+16 c^3 x^2 (4 A+3 B x)-9 b^3 B\right)\right)}{192 c^{5/2}}","\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-9*b^3*B + 6*b^2*c*(4*A + B*x) + 16*c^3*x^2*(4*A + 3*B*x) + 8*b*c^2*x*(14*A + 9*B*x)) + (3*b^(5/2)*(3*b*B - 8*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(192*c^(5/2))","A",1
84,1,109,126,0.1863807,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^2} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^2,x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(2 b c (15 A+7 B x)+4 c^2 x (3 A+2 B x)+3 b^2 B\right)-\frac{3 b^{3/2} (b B-6 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{24 c^{3/2}}","-\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(3*b^2*B + 4*c^2*x*(3*A + 2*B*x) + 2*b*c*(15*A + 7*B*x)) - (3*b^(3/2)*(b*B - 6*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(24*c^(3/2))","A",1
85,1,94,118,0.1700997,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^3} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^3,x]","\frac{\sqrt{x (b+c x)} \left(\frac{3 \sqrt{b} \sqrt{x} (4 A c+b B) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{c} \sqrt{\frac{c x}{b}+1}}+A (4 c x-8 b)+B x (5 b+2 c x)\right)}{4 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}",1,"(Sqrt[x*(b + c*x)]*(B*x*(5*b + 2*c*x) + A*(-8*b + 4*c*x) + (3*Sqrt[b]*(b*B + 4*A*c)*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[c]*Sqrt[1 + (c*x)/b])))/(4*x)","A",1
86,1,84,120,0.0437517,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^4} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^4,x]","-\frac{2 \sqrt{x (b+c x)} \left(b x (2 A c+3 b B) \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{c x}{b}\right)+A \sqrt{\frac{c x}{b}+1} (b+c x)^2\right)}{3 b x^2 \sqrt{\frac{c x}{b}+1}}","-\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,"(-2*Sqrt[x*(b + c*x)]*(A*(b + c*x)^2*Sqrt[1 + (c*x)/b] + b*(3*b*B + 2*A*c)*x*Hypergeometric2F1[-3/2, -1/2, 1/2, -((c*x)/b)]))/(3*b*x^2*Sqrt[1 + (c*x)/b])","C",1
87,1,88,95,0.0782518,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^5} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^5,x]","\frac{2 \sqrt{x (b+c x)} \left((b+c x)^2 \sqrt{\frac{c x}{b}+1} (b B-A c)-b^3 B \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};-\frac{c x}{b}\right)\right)}{5 b c x^3 \sqrt{\frac{c x}{b}+1}}","-\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 c \sqrt{b x+c x^2}}{x}-\frac{2 B \left(b x+c x^2\right)^{3/2}}{3 x^3}",1,"(2*Sqrt[x*(b + c*x)]*((b*B - A*c)*(b + c*x)^2*Sqrt[1 + (c*x)/b] - b^3*B*Hypergeometric2F1[-5/2, -5/2, -3/2, -((c*x)/b)]))/(5*b*c*x^3*Sqrt[1 + (c*x)/b])","C",1
88,1,36,57,0.0181427,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^6} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^6,x]","-\frac{2 (x (b+c x))^{5/2} (5 A b-2 A c x+7 b B x)}{35 b^2 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*(x*(b + c*x))^(5/2)*(5*A*b + 7*b*B*x - 2*A*c*x))/(35*b^2*x^6)","A",1
89,1,56,90,0.0269498,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^7} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^7,x]","\frac{2 (x (b+c x))^{5/2} \left(A \left(-35 b^2+20 b c x-8 c^2 x^2\right)+9 b B x (2 c x-5 b)\right)}{315 b^3 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*(x*(b + c*x))^(5/2)*(9*b*B*x*(-5*b + 2*c*x) + A*(-35*b^2 + 20*b*c*x - 8*c^2*x^2)))/(315*b^3*x^7)","A",1
90,1,79,125,0.0342396,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^8} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^8,x]","-\frac{2 (x (b+c x))^{5/2} \left(3 A \left(105 b^3-70 b^2 c x+40 b c^2 x^2-16 c^3 x^3\right)+11 b B x \left(35 b^2-20 b c x+8 c^2 x^2\right)\right)}{3465 b^4 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*(x*(b + c*x))^(5/2)*(11*b*B*x*(35*b^2 - 20*b*c*x + 8*c^2*x^2) + 3*A*(105*b^3 - 70*b^2*c*x + 40*b*c^2*x^2 - 16*c^3*x^3)))/(3465*b^4*x^8)","A",1
91,1,100,160,0.0386195,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^9} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^9,x]","\frac{2 (x (b+c x))^{5/2} \left(A \left(-1155 b^4+840 b^3 c x-560 b^2 c^2 x^2+320 b c^3 x^3-128 c^4 x^4\right)+13 b B x \left(-105 b^3+70 b^2 c x-40 b c^2 x^2+16 c^3 x^3\right)\right)}{15015 b^5 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*(x*(b + c*x))^(5/2)*(13*b*B*x*(-105*b^3 + 70*b^2*c*x - 40*b*c^2*x^2 + 16*c^3*x^3) + A*(-1155*b^4 + 840*b^3*c*x - 560*b^2*c^2*x^2 + 320*b*c^3*x^3 - 128*c^4*x^4)))/(15015*b^5*x^9)","A",1
92,1,122,195,0.0425896,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{10}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^10,x]","-\frac{2 (x (b+c x))^{5/2} \left(A \left(3003 b^5-2310 b^4 c x+1680 b^3 c^2 x^2-1120 b^2 c^3 x^3+640 b c^4 x^4-256 c^5 x^5\right)+3 b B x \left(1155 b^4-840 b^3 c x+560 b^2 c^2 x^2-320 b c^3 x^3+128 c^4 x^4\right)\right)}{45045 b^6 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*(x*(b + c*x))^(5/2)*(3*b*B*x*(1155*b^4 - 840*b^3*c*x + 560*b^2*c^2*x^2 - 320*b*c^3*x^3 + 128*c^4*x^4) + A*(3003*b^5 - 2310*b^4*c*x + 1680*b^3*c^2*x^2 - 1120*b^2*c^3*x^3 + 640*b*c^4*x^4 - 256*c^5*x^5)))/(45045*b^6*x^10)","A",1
93,1,207,276,0.3564915,"\int x^3 (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Integrate[x^3*(A + B*x)*(b*x + c*x^2)^(5/2),x]","\frac{x^4 (x (b+c x))^{5/2} \left(13 B (b+c x)^3-\frac{13 (13 b B-20 A c) \left(3465 b^{17/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)+\sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \left(-3465 b^8+2310 b^7 c x-1848 b^6 c^2 x^2+1584 b^5 c^3 x^3-1408 b^4 c^4 x^4+1280 b^3 c^5 x^5+316416 b^2 c^6 x^6+530432 b c^7 x^7+229376 c^8 x^8\right)\right)}{4128768 c^{13/2} x^{13/2} \sqrt{\frac{c x}{b}+1}}\right)}{130 c (b+c x)^2}","-\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^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 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,"(x^4*(x*(b + c*x))^(5/2)*(13*B*(b + c*x)^3 - (13*(13*b*B - 20*A*c)*(Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*(-3465*b^8 + 2310*b^7*c*x - 1848*b^6*c^2*x^2 + 1584*b^5*c^3*x^3 - 1408*b^4*c^4*x^4 + 1280*b^3*c^5*x^5 + 316416*b^2*c^6*x^6 + 530432*b*c^7*x^7 + 229376*c^8*x^8) + 3465*b^(17/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(4128768*c^(13/2)*x^(13/2)*Sqrt[1 + (c*x)/b])))/(130*c*(b + c*x)^2)","A",1
94,1,197,241,0.3960376,"\int x^2 (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Integrate[x^2*(A + B*x)*(b*x + c*x^2)^(5/2),x]","\frac{x^3 (x (b+c x))^{5/2} \left(\frac{11 (11 b B-18 A c) \left(315 b^{15/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)-\sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \left(315 b^7-210 b^6 c x+168 b^5 c^2 x^2-144 b^4 c^3 x^3+128 b^3 c^4 x^4+20736 b^2 c^5 x^5+33792 b c^6 x^6+14336 c^7 x^7\right)\right)}{229376 c^{11/2} x^{11/2} \sqrt{\frac{c x}{b}+1}}+11 B (b+c x)^3\right)}{99 c (b+c x)^2}","\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{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{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,"(x^3*(x*(b + c*x))^(5/2)*(11*B*(b + c*x)^3 + (11*(11*b*B - 18*A*c)*(-(Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*(315*b^7 - 210*b^6*c*x + 168*b^5*c^2*x^2 - 144*b^4*c^3*x^3 + 128*b^3*c^4*x^4 + 20736*b^2*c^5*x^5 + 33792*b*c^6*x^6 + 14336*c^7*x^7)) + 315*b^(15/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(229376*c^(11/2)*x^(11/2)*Sqrt[1 + (c*x)/b])))/(99*c*(b + c*x)^2)","A",1
95,1,182,189,0.40632,"\int x (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Integrate[x*(A + B*x)*(b*x + c*x^2)^(5/2),x]","\frac{(x (b+c x))^{9/2} \left(9 B (b+c x)^3-\frac{3 (9 b B-16 A c) \left(105 b^{13/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)+\sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \left(-105 b^6+70 b^5 c x-56 b^4 c^2 x^2+48 b^3 c^3 x^3+4736 b^2 c^4 x^4+7424 b c^5 x^5+3072 c^6 x^6\right)\right)}{14336 c^{9/2} x^{9/2} \sqrt{\frac{c x}{b}+1}}\right)}{72 c (b+c x)^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{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{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,"((x*(b + c*x))^(9/2)*(9*B*(b + c*x)^3 - (3*(9*b*B - 16*A*c)*(Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*(-105*b^6 + 70*b^5*c*x - 56*b^4*c^2*x^2 + 48*b^3*c^3*x^3 + 4736*b^2*c^4*x^4 + 7424*b*c^5*x^5 + 3072*c^6*x^6) + 105*b^(13/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(14336*c^(9/2)*x^(9/2)*Sqrt[1 + (c*x)/b])))/(72*c*(b + c*x)^4)","A",1
96,1,171,171,0.3885003,"\int (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(b*x + c*x^2)^(5/2),x]","\frac{(x (b+c x))^{7/2} \left(\frac{49 (b B-2 A c) \left(15 b^{11/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)-\sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \left(15 b^5-10 b^4 c x+8 b^3 c^2 x^2+432 b^2 c^3 x^3+640 b c^4 x^4+256 c^5 x^5\right)\right)}{3072 c^{7/2} x^{7/2} \sqrt{\frac{c x}{b}+1}}+7 B (b+c x)^3\right)}{49 c (b+c x)^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{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{(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,"((x*(b + c*x))^(7/2)*(7*B*(b + c*x)^3 + (49*(b*B - 2*A*c)*(-(Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*(15*b^5 - 10*b^4*c*x + 8*b^3*c^2*x^2 + 432*b^2*c^3*x^3 + 640*b*c^4*x^4 + 256*c^5*x^5)) + 15*b^(11/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(3072*c^(7/2)*x^(7/2)*Sqrt[1 + (c*x)/b])))/(49*c*(b + c*x)^3)","A",1
97,1,166,170,0.2907192,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x,x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(-10 b^4 c (18 A+5 B x)+40 b^3 c^2 x (3 A+B x)+48 b^2 c^3 x^2 (62 A+45 B x)+64 b c^4 x^3 (63 A+50 B x)+256 c^5 x^4 (6 A+5 B x)+75 b^5 B\right)-\frac{15 b^{9/2} (5 b B-12 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{7680 c^{7/2}}","-\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^3 (b+2 c x) \sqrt{b x+c x^2} (5 b B-12 A c)}{512 c^3}-\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(75*b^5*B + 40*b^3*c^2*x*(3*A + B*x) + 256*c^5*x^4*(6*A + 5*B*x) - 10*b^4*c*(18*A + 5*B*x) + 48*b^2*c^3*x^2*(62*A + 45*B*x) + 64*b*c^4*x^3*(63*A + 50*B*x)) - (15*b^(9/2)*(5*b*B - 12*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(7680*c^(7/2))","A",1
98,1,147,169,0.2574225,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^2} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^2,x]","\frac{\sqrt{x (b+c x)} \left(\frac{15 b^{7/2} (3 b B-10 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(30 b^3 c (5 A+B x)+4 b^2 c^2 x (295 A+186 B x)+16 b c^3 x^2 (85 A+63 B x)+96 c^4 x^3 (5 A+4 B x)-45 b^4 B\right)\right)}{1920 c^{5/2}}","\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 (b+2 c x) \sqrt{b x+c x^2} (3 b B-10 A c)}{128 c^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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-45*b^4*B + 30*b^3*c*(5*A + B*x) + 96*c^4*x^3*(5*A + 4*B*x) + 16*b*c^3*x^2*(85*A + 63*B*x) + 4*b^2*c^2*x*(295*A + 186*B*x)) + (15*b^(7/2)*(3*b*B - 10*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(1920*c^(5/2))","A",1
99,1,128,155,0.2242383,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^3} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^3,x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(2 b^2 c (132 A+59 B x)+8 b c^2 x (26 A+17 B x)+16 c^3 x^2 (4 A+3 B x)+15 b^3 B\right)-\frac{15 b^{5/2} (b B-8 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{192 c^{3/2}}","-\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(15*b^3*B + 16*c^3*x^2*(4*A + 3*B*x) + 8*b*c^2*x*(26*A + 17*B*x) + 2*b^2*c*(132*A + 59*B*x)) - (15*b^(5/2)*(b*B - 8*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(192*c^(3/2))","A",1
100,1,117,153,0.206208,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^4} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^4,x]","\frac{\sqrt{x (b+c x)} \left(\frac{15 b^{3/2} \sqrt{x} (6 A c+b B) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{c} \sqrt{\frac{c x}{b}+1}}-6 A \left(8 b^2-9 b c x-2 c^2 x^2\right)+B x \left(33 b^2+26 b c x+8 c^2 x^2\right)\right)}{24 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}",1,"(Sqrt[x*(b + c*x)]*(-6*A*(8*b^2 - 9*b*c*x - 2*c^2*x^2) + B*x*(33*b^2 + 26*b*c*x + 8*c^2*x^2) + (15*b^(3/2)*(b*B + 6*A*c)*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[c]*Sqrt[1 + (c*x)/b])))/(24*x)","A",1
101,1,86,157,0.0525279,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^5} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^5,x]","-\frac{2 \sqrt{x (b+c x)} \left(b^2 x (4 A c+3 b B) \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{c x}{b}\right)+A \sqrt{\frac{c x}{b}+1} (b+c x)^3\right)}{3 b x^2 \sqrt{\frac{c x}{b}+1}}","\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 \left(b x+c x^2\right)^{5/2} (4 A c+3 b B)}{3 b x^3}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{3 b x^5}",1,"(-2*Sqrt[x*(b + c*x)]*(A*(b + c*x)^3*Sqrt[1 + (c*x)/b] + b^2*(3*b*B + 4*A*c)*x*Hypergeometric2F1[-5/2, -1/2, 1/2, -((c*x)/b)]))/(3*b*x^2*Sqrt[1 + (c*x)/b])","C",1
102,1,87,155,0.0518908,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^6} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^6,x]","-\frac{2 \sqrt{x (b+c x)} \left(b^2 x (2 A c+5 b B) \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{c x}{b}\right)+3 A \sqrt{\frac{c x}{b}+1} (b+c x)^3\right)}{15 b x^3 \sqrt{\frac{c x}{b}+1}}","c^{3/2} (2 A c+5 b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)+\frac{c^2 \sqrt{b x+c x^2} (2 A c+5 b B)}{b}-\frac{2 c \left(b x+c x^2\right)^{3/2} (2 A c+5 b B)}{3 b x^2}-\frac{2 \left(b x+c x^2\right)^{5/2} (2 A c+5 b B)}{15 b x^4}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{5 b x^6}",1,"(-2*Sqrt[x*(b + c*x)]*(3*A*(b + c*x)^3*Sqrt[1 + (c*x)/b] + b^2*(5*b*B + 2*A*c)*x*Hypergeometric2F1[-5/2, -3/2, -1/2, -((c*x)/b)]))/(15*b*x^3*Sqrt[1 + (c*x)/b])","C",1
103,1,83,119,0.0592953,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^7} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^7,x]","\frac{2 (x (b+c x))^{5/2} \left((b+c x)^3 (b B-A c)-\frac{b^4 B \, _2F_1\left(-\frac{7}{2},-\frac{7}{2};-\frac{5}{2};-\frac{c x}{b}\right)}{\sqrt{\frac{c x}{b}+1}}\right)}{7 b c x^6 (b+c x)^2}","-\frac{2 A \left(b x+c x^2\right)^{7/2}}{7 b x^7}+2 B c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 B c^2 \sqrt{b x+c x^2}}{x}-\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*(x*(b + c*x))^(5/2)*((b*B - A*c)*(b + c*x)^3 - (b^4*B*Hypergeometric2F1[-7/2, -7/2, -5/2, -((c*x)/b)])/Sqrt[1 + (c*x)/b]))/(7*b*c*x^6*(b + c*x)^2)","C",1
104,1,43,57,0.0154478,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^8} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^8,x]","-\frac{2 (b+c x)^3 \sqrt{x (b+c x)} (7 A b-2 A c x+9 b B x)}{63 b^2 x^5}","-\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*(b + c*x)^3*Sqrt[x*(b + c*x)]*(7*A*b + 9*b*B*x - 2*A*c*x))/(63*b^2*x^5)","A",1
105,1,63,90,0.023933,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^9} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^9,x]","\frac{2 (b+c x)^3 \sqrt{x (b+c x)} \left(A \left(-63 b^2+28 b c x-8 c^2 x^2\right)+11 b B x (2 c x-7 b)\right)}{693 b^3 x^6}","\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*(b + c*x)^3*Sqrt[x*(b + c*x)]*(11*b*B*x*(-7*b + 2*c*x) + A*(-63*b^2 + 28*b*c*x - 8*c^2*x^2)))/(693*b^3*x^6)","A",1
106,1,86,125,0.0292402,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{10}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^10,x]","-\frac{2 (b+c x)^3 \sqrt{x (b+c x)} \left(3 A \left(231 b^3-126 b^2 c x+56 b c^2 x^2-16 c^3 x^3\right)+13 b B x \left(63 b^2-28 b c x+8 c^2 x^2\right)\right)}{9009 b^4 x^7}","-\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*(b + c*x)^3*Sqrt[x*(b + c*x)]*(13*b*B*x*(63*b^2 - 28*b*c*x + 8*c^2*x^2) + 3*A*(231*b^3 - 126*b^2*c*x + 56*b*c^2*x^2 - 16*c^3*x^3)))/(9009*b^4*x^7)","A",1
107,1,107,160,0.0336791,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{11}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^11,x]","\frac{2 (b+c x)^3 \sqrt{x (b+c x)} \left(A \left(-3003 b^4+1848 b^3 c x-1008 b^2 c^2 x^2+448 b c^3 x^3-128 c^4 x^4\right)+15 b B x \left(-231 b^3+126 b^2 c x-56 b c^2 x^2+16 c^3 x^3\right)\right)}{45045 b^5 x^8}","\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*(b + c*x)^3*Sqrt[x*(b + c*x)]*(15*b*B*x*(-231*b^3 + 126*b^2*c*x - 56*b*c^2*x^2 + 16*c^3*x^3) + A*(-3003*b^4 + 1848*b^3*c*x - 1008*b^2*c^2*x^2 + 448*b*c^3*x^3 - 128*c^4*x^4)))/(45045*b^5*x^8)","A",1
108,1,130,195,0.0382795,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{12}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^12,x]","-\frac{2 (b+c x)^3 \sqrt{x (b+c x)} \left(5 A \left(9009 b^5-6006 b^4 c x+3696 b^3 c^2 x^2-2016 b^2 c^3 x^3+896 b c^4 x^4-256 c^5 x^5\right)+17 b B x \left(3003 b^4-1848 b^3 c x+1008 b^2 c^2 x^2-448 b c^3 x^3+128 c^4 x^4\right)\right)}{765765 b^6 x^9}","-\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*(b + c*x)^3*Sqrt[x*(b + c*x)]*(17*b*B*x*(3003*b^4 - 1848*b^3*c*x + 1008*b^2*c^2*x^2 - 448*b*c^3*x^3 + 128*c^4*x^4) + 5*A*(9009*b^5 - 6006*b^4*c*x + 3696*b^3*c^2*x^2 - 2016*b^2*c^3*x^3 + 896*b*c^4*x^4 - 256*c^5*x^5)))/(765765*b^6*x^9)","A",1
109,1,133,197,0.3459806,"\int \frac{x^4 (A+B x)}{\sqrt{b x+c x^2}} \, dx","Integrate[(x^4*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\frac{(9 b B-10 A c) \left(c x \sqrt{\frac{c x}{b}+1} \left(105 b^3-70 b^2 c x+56 b c^2 x^2-48 c^3 x^3\right)-105 b^{7/2} \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)\right)}{\sqrt{\frac{c x}{b}+1}}+384 B c^5 x^5\right)}{1920 c^6 x}","-\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^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 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,"(Sqrt[x*(b + c*x)]*(384*B*c^5*x^5 + ((9*b*B - 10*A*c)*(c*x*Sqrt[1 + (c*x)/b]*(105*b^3 - 70*b^2*c*x + 56*b*c^2*x^2 - 48*c^3*x^3) - 105*b^(7/2)*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/Sqrt[1 + (c*x)/b]))/(1920*c^6*x)","A",1
110,1,129,162,0.3285612,"\int \frac{x^3 (A+B x)}{\sqrt{b x+c x^2}} \, dx","Integrate[(x^3*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\frac{15 b^{5/2} (7 b B-8 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(10 b^2 c (12 A+7 B x)-8 b c^2 x (10 A+7 B x)+16 c^3 x^2 (4 A+3 B x)-105 b^3 B\right)\right)}{192 c^{9/2}}","\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^2 \sqrt{b x+c x^2} (7 b B-8 A c)}{64 c^4}+\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-105*b^3*B + 16*c^3*x^2*(4*A + 3*B*x) - 8*b*c^2*x*(10*A + 7*B*x) + 10*b^2*c*(12*A + 7*B*x)) + (15*b^(5/2)*(7*b*B - 8*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(192*c^(9/2))","A",1
111,1,116,127,0.0828633,"\int \frac{x^2 (A+B x)}{\sqrt{b x+c x^2}} \, dx","Integrate[(x^2*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{c} x (b+c x) \left(-2 b c (9 A+5 B x)+4 c^2 x (3 A+2 B x)+15 b^2 B\right)-3 b^{5/2} \sqrt{x} \sqrt{\frac{c x}{b}+1} (5 b B-6 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{24 c^{7/2} \sqrt{x (b+c 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}",1,"(Sqrt[c]*x*(b + c*x)*(15*b^2*B + 4*c^2*x*(3*A + 2*B*x) - 2*b*c*(9*A + 5*B*x)) - 3*b^(5/2)*(5*b*B - 6*A*c)*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(24*c^(7/2)*Sqrt[x*(b + c*x)])","A",1
112,1,96,75,0.0712776,"\int \frac{x (A+B x)}{\sqrt{b x+c x^2}} \, dx","Integrate[(x*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{b^{3/2} \sqrt{x} \sqrt{\frac{c x}{b}+1} (3 b B-4 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)+\sqrt{c} x (b+c x) (4 A c-3 b B+2 B c x)}{4 c^{5/2} \sqrt{x (b+c 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}",1,"(Sqrt[c]*x*(b + c*x)*(-3*b*B + 4*A*c + 2*B*c*x) + b^(3/2)*(3*b*B - 4*A*c)*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*c^(5/2)*Sqrt[x*(b + c*x)])","A",1
113,1,80,55,0.0583497,"\int \frac{A+B x}{\sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/Sqrt[b*x + c*x^2],x]","\frac{B \sqrt{c} x (b+c x)-\sqrt{b} \sqrt{x} \sqrt{\frac{c x}{b}+1} (b B-2 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{3/2} \sqrt{x (b+c 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}}",1,"(B*Sqrt[c]*x*(b + c*x) - Sqrt[b]*(b*B - 2*A*c)*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(c^(3/2)*Sqrt[x*(b + c*x)])","A",1
114,1,69,52,0.1479006,"\int \frac{A+B x}{x \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(x*Sqrt[b*x + c*x^2]),x]","\frac{2 \sqrt{x (b+c x)} \left(\frac{\sqrt{b} B \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{c} \sqrt{\frac{c x}{b}+1}}-A\right)}{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*Sqrt[x*(b + c*x)]*(-A + (Sqrt[b]*B*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[c]*Sqrt[1 + (c*x)/b])))/(b*x)","A",1
115,1,35,57,0.0194575,"\int \frac{A+B x}{x^2 \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^2*Sqrt[b*x + c*x^2]),x]","-\frac{2 \sqrt{x (b+c x)} (A (b-2 c x)+3 b B x)}{3 b^2 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*Sqrt[x*(b + c*x)]*(3*b*B*x + A*(b - 2*c*x)))/(3*b^2*x^2)","A",1
116,1,54,90,0.028217,"\int \frac{A+B x}{x^3 \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^3*Sqrt[b*x + c*x^2]),x]","-\frac{2 \sqrt{x (b+c x)} \left(A \left(3 b^2-4 b c x+8 c^2 x^2\right)+5 b B x (b-2 c x)\right)}{15 b^3 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*Sqrt[x*(b + c*x)]*(5*b*B*x*(b - 2*c*x) + A*(3*b^2 - 4*b*c*x + 8*c^2*x^2)))/(15*b^3*x^3)","A",1
117,1,79,125,0.0295446,"\int \frac{A+B x}{x^4 \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^4*Sqrt[b*x + c*x^2]),x]","-\frac{2 \sqrt{x (b+c x)} \left(3 A \left(5 b^3-6 b^2 c x+8 b c^2 x^2-16 c^3 x^3\right)+7 b B x \left(3 b^2-4 b c x+8 c^2 x^2\right)\right)}{105 b^4 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*Sqrt[x*(b + c*x)]*(7*b*B*x*(3*b^2 - 4*b*c*x + 8*c^2*x^2) + 3*A*(5*b^3 - 6*b^2*c*x + 8*b*c^2*x^2 - 16*c^3*x^3)))/(105*b^4*x^4)","A",1
118,1,100,160,0.046853,"\int \frac{A+B x}{x^5 \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^5*Sqrt[b*x + c*x^2]),x]","-\frac{2 \sqrt{x (b+c x)} \left(A \left(35 b^4-40 b^3 c x+48 b^2 c^2 x^2-64 b c^3 x^3+128 c^4 x^4\right)+9 b B x \left(5 b^3-6 b^2 c x+8 b c^2 x^2-16 c^3 x^3\right)\right)}{315 b^5 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*Sqrt[x*(b + c*x)]*(9*b*B*x*(5*b^3 - 6*b^2*c*x + 8*b*c^2*x^2 - 16*c^3*x^3) + A*(35*b^4 - 40*b^3*c*x + 48*b^2*c^2*x^2 - 64*b*c^3*x^3 + 128*c^4*x^4)))/(315*b^5*x^5)","A",1
119,1,123,195,0.0394952,"\int \frac{A+B x}{x^6 \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^6*Sqrt[b*x + c*x^2]),x]","-\frac{2 \sqrt{x (b+c x)} \left(5 A \left(63 b^5-70 b^4 c x+80 b^3 c^2 x^2-96 b^2 c^3 x^3+128 b c^4 x^4-256 c^5 x^5\right)+11 b B x \left(35 b^4-40 b^3 c x+48 b^2 c^2 x^2-64 b c^3 x^3+128 c^4 x^4\right)\right)}{3465 b^6 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*Sqrt[x*(b + c*x)]*(11*b*B*x*(35*b^4 - 40*b^3*c*x + 48*b^2*c^2*x^2 - 64*b*c^3*x^3 + 128*c^4*x^4) + 5*A*(63*b^5 - 70*b^4*c*x + 80*b^3*c^2*x^2 - 96*b^2*c^3*x^3 + 128*b*c^4*x^4 - 256*c^5*x^5)))/(3465*b^6*x^6)","A",1
120,1,137,170,0.2155882,"\int \frac{x^4 (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^4*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{\frac{(b+c x) (7 b B-6 A c) \left(c x \sqrt{\frac{c x}{b}+1} \left(15 b^2-10 b c x+8 c^2 x^2\right)-15 b^{5/2} \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)\right)}{3 \sqrt{\frac{c x}{b}+1}}+16 c^4 x^4 (A c-b B)}{8 b c^5 \sqrt{x (b+c 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{5 b \sqrt{b x+c x^2} (7 b B-6 A c)}{8 c^4}-\frac{5 x \sqrt{b x+c x^2} (7 b B-6 A c)}{12 c^3}+\frac{x^2 \sqrt{b x+c x^2} (7 b B-6 A c)}{3 b c^2}-\frac{2 x^4 (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(16*c^4*(-(b*B) + A*c)*x^4 + ((7*b*B - 6*A*c)*(b + c*x)*(c*x*Sqrt[1 + (c*x)/b]*(15*b^2 - 10*b*c*x + 8*c^2*x^2) - 15*b^(5/2)*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(3*Sqrt[1 + (c*x)/b]))/(8*b*c^5*Sqrt[x*(b + c*x)])","A",1
121,1,109,135,0.0927988,"\int \frac{x^3 (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^3*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{3 b^{3/2} \sqrt{x} \sqrt{\frac{c x}{b}+1} (5 b B-4 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)+\sqrt{c} x \left(b c (12 A-5 B x)+2 c^2 x (2 A+B x)-15 b^2 B\right)}{4 c^{7/2} \sqrt{x (b+c x)}}","\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{3 \sqrt{b x+c x^2} (5 b B-4 A c)}{4 c^3}+\frac{x \sqrt{b x+c x^2} (5 b B-4 A c)}{2 b c^2}-\frac{2 x^3 (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(Sqrt[c]*x*(-15*b^2*B + b*c*(12*A - 5*B*x) + 2*c^2*x*(2*A + B*x)) + 3*b^(3/2)*(5*b*B - 4*A*c)*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*c^(7/2)*Sqrt[x*(b + c*x)])","A",1
122,1,88,99,0.0829578,"\int \frac{x^2 (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^2*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{\sqrt{c} x (-2 A c+3 b B+B c x)-\sqrt{b} \sqrt{x} \sqrt{\frac{c x}{b}+1} (3 b B-2 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{5/2} \sqrt{x (b+c x)}}","-\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{\sqrt{b x+c x^2} (3 b B-2 A c)}{b c^2}-\frac{2 x^2 (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(Sqrt[c]*x*(3*b*B - 2*A*c + B*c*x) - Sqrt[b]*(3*b*B - 2*A*c)*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(c^(5/2)*Sqrt[x*(b + c*x)])","A",1
123,1,79,60,0.0655131,"\int \frac{x (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(x*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{c} x (A c-b B)+2 b^{3/2} B \sqrt{x} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b c^{3/2} \sqrt{x (b+c 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}}",1,"(2*Sqrt[c]*(-(b*B) + A*c)*x + 2*b^(3/2)*B*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(b*c^(3/2)*Sqrt[x*(b + c*x)])","A",1
124,1,30,33,0.0126458,"\int \frac{A+B x}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(b*x + c*x^2)^(3/2),x]","\frac{2 b B x-2 A (b+2 c x)}{b^2 \sqrt{x (b+c x)}}","-\frac{2 (A b-x (b B-2 A c))}{b^2 \sqrt{b x+c x^2}}",1,"(2*b*B*x - 2*A*(b + 2*c*x))/(b^2*Sqrt[x*(b + c*x)])","A",1
125,1,52,60,0.0203693,"\int \frac{A+B x}{x \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x*(b*x + c*x^2)^(3/2)),x]","-\frac{2 \left(A \left(b^2-4 b c x-8 c^2 x^2\right)+3 b B x (b+2 c x)\right)}{3 b^3 x \sqrt{x (b+c 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}}",1,"(-2*(3*b*B*x*(b + 2*c*x) + A*(b^2 - 4*b*c*x - 8*c^2*x^2)))/(3*b^3*x*Sqrt[x*(b + c*x)])","A",1
126,1,75,93,0.0253816,"\int \frac{A+B x}{x^2 \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^2*(b*x + c*x^2)^(3/2)),x]","-\frac{2 \left(3 A \left(b^3-2 b^2 c x+8 b c^2 x^2+16 c^3 x^3\right)+5 b B x \left(b^2-4 b c x-8 c^2 x^2\right)\right)}{15 b^4 x^2 \sqrt{x (b+c 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}}",1,"(-2*(5*b*B*x*(b^2 - 4*b*c*x - 8*c^2*x^2) + 3*A*(b^3 - 2*b^2*c*x + 8*b*c^2*x^2 + 16*c^3*x^3)))/(15*b^4*x^2*Sqrt[x*(b + c*x)])","A",1
127,1,98,128,0.0298081,"\int \frac{A+B x}{x^3 \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^3*(b*x + c*x^2)^(3/2)),x]","-\frac{2 \left(A \left(5 b^4-8 b^3 c x+16 b^2 c^2 x^2-64 b c^3 x^3-128 c^4 x^4\right)+7 b B x \left(b^3-2 b^2 c x+8 b c^2 x^2+16 c^3 x^3\right)\right)}{35 b^5 x^3 \sqrt{x (b+c 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}}",1,"(-2*(7*b*B*x*(b^3 - 2*b^2*c*x + 8*b*c^2*x^2 + 16*c^3*x^3) + A*(5*b^4 - 8*b^3*c*x + 16*b^2*c^2*x^2 - 64*b*c^3*x^3 - 128*c^4*x^4)))/(35*b^5*x^3*Sqrt[x*(b + c*x)])","A",1
128,1,123,163,0.0345381,"\int \frac{A+B x}{x^4 \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^4*(b*x + c*x^2)^(3/2)),x]","-\frac{2 \left(5 A \left(7 b^5-10 b^4 c x+16 b^3 c^2 x^2-32 b^2 c^3 x^3+128 b c^4 x^4+256 c^5 x^5\right)+9 b B x \left(5 b^4-8 b^3 c x+16 b^2 c^2 x^2-64 b c^3 x^3-128 c^4 x^4\right)\right)}{315 b^6 x^4 \sqrt{x (b+c 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}}",1,"(-2*(9*b*B*x*(5*b^4 - 8*b^3*c*x + 16*b^2*c^2*x^2 - 64*b*c^3*x^3 - 128*c^4*x^4) + 5*A*(7*b^5 - 10*b^4*c*x + 16*b^3*c^2*x^2 - 32*b^2*c^3*x^3 + 128*b*c^4*x^4 + 256*c^5*x^5)))/(315*b^6*x^4*Sqrt[x*(b + c*x)])","A",1
129,1,80,172,0.0585221,"\int \frac{x^5 (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^5*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x^5 \left((b+c x) \sqrt{\frac{c x}{b}+1} (7 b B-4 A c) \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};-\frac{c x}{b}\right)+7 b (A c-b B)\right)}{21 b^2 c (x (b+c x))^{3/2}}","\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{5 \sqrt{b x+c x^2} (7 b B-4 A c)}{4 c^4}+\frac{5 x \sqrt{b x+c x^2} (7 b B-4 A c)}{6 b c^3}-\frac{2 x^3 (7 b B-4 A c)}{3 b c^2 \sqrt{b x+c x^2}}-\frac{2 x^5 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(2*x^5*(7*b*(-(b*B) + A*c) + (7*b*B - 4*A*c)*(b + c*x)*Sqrt[1 + (c*x)/b]*Hypergeometric2F1[3/2, 7/2, 9/2, -((c*x)/b)]))/(21*b^2*c*(x*(b + c*x))^(3/2))","C",1
130,1,80,136,0.0559067,"\int \frac{x^4 (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^4*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x^4 \left((b+c x) \sqrt{\frac{c x}{b}+1} (5 b B-2 A c) \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{c x}{b}\right)+5 b (A c-b B)\right)}{15 b^2 c (x (b+c x))^{3/2}}","-\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{\sqrt{b x+c x^2} (5 b B-2 A c)}{b c^3}-\frac{2 x^2 (5 b B-2 A c)}{3 b c^2 \sqrt{b x+c x^2}}-\frac{2 x^4 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(2*x^4*(5*b*(-(b*B) + A*c) + (5*b*B - 2*A*c)*(b + c*x)*Sqrt[1 + (c*x)/b]*Hypergeometric2F1[3/2, 5/2, 7/2, -((c*x)/b)]))/(15*b^2*c*(x*(b + c*x))^(3/2))","C",1
131,1,99,84,0.0945469,"\int \frac{x^3 (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^3*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{x \left(2 \sqrt{c} x \left(A c^2 x-3 b^2 B-4 b B c x\right)+6 b^{3/2} B \sqrt{x} (b+c x) \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)\right)}{3 b c^{5/2} (x (b+c x))^{3/2}}","-\frac{2 x^3 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}-\frac{2 B x}{c^2 \sqrt{b x+c x^2}}",1,"(x*(2*Sqrt[c]*x*(-3*b^2*B - 4*b*B*c*x + A*c^2*x) + 6*b^(3/2)*B*Sqrt[x]*(b + c*x)*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(3*b*c^(5/2)*(x*(b + c*x))^(3/2))","A",1
132,1,35,67,0.0152424,"\int \frac{x^2 (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^2*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x^2 (3 A b+2 A c x+b B x)}{3 b^2 (x (b+c x))^{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*x^2*(3*A*b + b*B*x + 2*A*c*x))/(3*b^2*(x*(b + c*x))^(3/2))","A",1
133,1,55,70,0.0239387,"\int \frac{x (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{x \left(2 b B x (3 b+2 c x)-2 A \left(3 b^2+12 b c x+8 c^2 x^2\right)\right)}{3 b^3 (x (b+c x))^{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,"(x*(2*b*B*x*(3*b + 2*c*x) - 2*A*(3*b^2 + 12*b*c*x + 8*c^2*x^2)))/(3*b^3*(x*(b + c*x))^(3/2))","A",1
134,1,72,70,0.0279517,"\int \frac{A+B x}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(b*x + c*x^2)^(5/2),x]","-\frac{2 \left(A \left(b^3-6 b^2 c x-24 b c^2 x^2-16 c^3 x^3\right)+b B x \left(3 b^2+12 b c x+8 c^2 x^2\right)\right)}{3 b^4 (x (b+c x))^{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*(b*B*x*(3*b^2 + 12*b*c*x + 8*c^2*x^2) + A*(b^3 - 6*b^2*c*x - 24*b*c^2*x^2 - 16*c^3*x^3)))/(3*b^4*(x*(b + c*x))^(3/2))","A",1
135,1,98,96,0.0323715,"\int \frac{A+B x}{x \left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x*(b*x + c*x^2)^(5/2)),x]","-\frac{2 \left(A \left(3 b^4-8 b^3 c x+48 b^2 c^2 x^2+192 b c^3 x^3+128 c^4 x^4\right)+5 b B x \left(b^3-6 b^2 c x-24 b c^2 x^2-16 c^3 x^3\right)\right)}{15 b^5 x (x (b+c x))^{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*(5*b*B*x*(b^3 - 6*b^2*c*x - 24*b*c^2*x^2 - 16*c^3*x^3) + A*(3*b^4 - 8*b^3*c*x + 48*b^2*c^2*x^2 + 192*b*c^3*x^3 + 128*c^4*x^4)))/(15*b^5*x*(x*(b + c*x))^(3/2))","A",1
136,1,123,131,0.0370798,"\int \frac{A+B x}{x^2 \left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^2*(b*x + c*x^2)^(5/2)),x]","-\frac{2 \left(5 A \left(3 b^5-6 b^4 c x+16 b^3 c^2 x^2-96 b^2 c^3 x^3-384 b c^4 x^4-256 c^5 x^5\right)+7 b B x \left(3 b^4-8 b^3 c x+48 b^2 c^2 x^2+192 b c^3 x^3+128 c^4 x^4\right)\right)}{105 b^6 x^2 (x (b+c x))^{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*(7*b*B*x*(3*b^4 - 8*b^3*c*x + 48*b^2*c^2*x^2 + 192*b*c^3*x^3 + 128*c^4*x^4) + 5*A*(3*b^5 - 6*b^4*c*x + 16*b^3*c^2*x^2 - 96*b^2*c^3*x^3 - 384*b*c^4*x^4 - 256*c^5*x^5)))/(105*b^6*x^2*(x*(b + c*x))^(3/2))","A",1
137,1,145,166,0.046963,"\int \frac{A+B x}{x^3 \left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^3*(b*x + c*x^2)^(5/2)),x]","\frac{6 b B x \left(-3 b^5+6 b^4 c x-16 b^3 c^2 x^2+96 b^2 c^3 x^3+384 b c^4 x^4+256 c^5 x^5\right)-2 A \left(7 b^6-12 b^5 c x+24 b^4 c^2 x^2-64 b^3 c^3 x^3+384 b^2 c^4 x^4+1536 b c^5 x^5+1024 c^6 x^6\right)}{63 b^7 x^3 (x (b+c x))^{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,"(6*b*B*x*(-3*b^5 + 6*b^4*c*x - 16*b^3*c^2*x^2 + 96*b^2*c^3*x^3 + 384*b*c^4*x^4 + 256*c^5*x^5) - 2*A*(7*b^6 - 12*b^5*c*x + 24*b^4*c^2*x^2 - 64*b^3*c^3*x^3 + 384*b^2*c^4*x^4 + 1536*b*c^5*x^5 + 1024*c^6*x^6))/(63*b^7*x^3*(x*(b + c*x))^(3/2))","A",1
138,1,105,107,0.0424124,"\int \frac{d+e x}{\left(b x+c x^2\right)^{7/2}} \, dx","Integrate[(d + e*x)/(b*x + c*x^2)^(7/2),x]","-\frac{2 \left(b^5 (3 d+5 e x)-10 b^4 c x (d+4 e x)+80 b^3 c^2 x^2 (d-3 e x)+160 b^2 c^3 x^3 (3 d-2 e x)-128 b c^4 x^4 (e x-5 d)+256 c^5 d x^5\right)}{15 b^6 (x (b+c x))^{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*(256*c^5*d*x^5 + 80*b^3*c^2*x^2*(d - 3*e*x) + 160*b^2*c^3*x^3*(3*d - 2*e*x) - 128*b*c^4*x^4*(-5*d + e*x) - 10*b^4*c*x*(d + 4*e*x) + b^5*(3*d + 5*e*x)))/(15*b^6*(x*(b + c*x))^(5/2))","A",1
139,1,150,145,0.0569774,"\int \frac{d+e x}{\left(b x+c x^2\right)^{9/2}} \, dx","Integrate[(d + e*x)/(b*x + c*x^2)^(9/2),x]","-\frac{2 \sqrt{x (b+c x)} \left(b^7 (5 d+7 e x)-14 b^6 c x (d+2 e x)+56 b^5 c^2 x^2 (d+5 e x)-560 b^4 c^3 x^3 (d-4 e x)+4480 b^3 c^4 x^4 (e x-d)+1792 b^2 c^5 x^5 (2 e x-5 d)+1024 b c^6 x^6 (e x-7 d)-2048 c^7 d x^7\right)}{35 b^8 x^4 (b+c x)^4}","\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*Sqrt[x*(b + c*x)]*(-2048*c^7*d*x^7 - 560*b^4*c^3*x^3*(d - 4*e*x) + 1024*b*c^6*x^6*(-7*d + e*x) + 4480*b^3*c^4*x^4*(-d + e*x) + 1792*b^2*c^5*x^5*(-5*d + 2*e*x) - 14*b^6*c*x*(d + 2*e*x) + 56*b^5*c^2*x^2*(d + 5*e*x) + b^7*(5*d + 7*e*x)))/(35*b^8*x^4*(b + c*x)^4)","A",1
140,1,33,39,0.0104362,"\int x^{7/2} (A+B x) \left(b x+c x^2\right) \, dx","Integrate[x^(7/2)*(A + B*x)*(b*x + c*x^2),x]","\frac{2 x^{11/2} (15 A (13 b+11 c x)+11 B x (15 b+13 c x))}{2145}","\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*x^(11/2)*(15*A*(13*b + 11*c*x) + 11*B*x*(15*b + 13*c*x)))/2145","A",1
141,1,33,39,0.0112317,"\int x^{5/2} (A+B x) \left(b x+c x^2\right) \, dx","Integrate[x^(5/2)*(A + B*x)*(b*x + c*x^2),x]","\frac{2 x^{9/2} (13 A (11 b+9 c x)+9 B x (13 b+11 c x))}{1287}","\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*x^(9/2)*(13*A*(11*b + 9*c*x) + 9*B*x*(13*b + 11*c*x)))/1287","A",1
142,1,33,39,0.0087788,"\int x^{3/2} (A+B x) \left(b x+c x^2\right) \, dx","Integrate[x^(3/2)*(A + B*x)*(b*x + c*x^2),x]","\frac{2}{693} x^{7/2} (11 A (9 b+7 c x)+7 B x (11 b+9 c 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}",1,"(2*x^(7/2)*(11*A*(9*b + 7*c*x) + 7*B*x*(11*b + 9*c*x)))/693","A",1
143,1,33,39,0.0110132,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right) \, dx","Integrate[Sqrt[x]*(A + B*x)*(b*x + c*x^2),x]","\frac{2}{315} x^{5/2} (9 A (7 b+5 c x)+5 B x (9 b+7 c 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}",1,"(2*x^(5/2)*(9*A*(7*b + 5*c*x) + 5*B*x*(9*b + 7*c*x)))/315","A",1
144,1,33,39,0.010527,"\int \frac{(A+B x) \left(b x+c x^2\right)}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/Sqrt[x],x]","\frac{2}{105} x^{3/2} (7 A (5 b+3 c x)+3 B x (7 b+5 c 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}",1,"(2*x^(3/2)*(7*A*(5*b + 3*c*x) + 3*B*x*(7*b + 5*c*x)))/105","A",1
145,1,31,37,0.0108158,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^{3/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/x^(3/2),x]","\frac{2}{15} \sqrt{x} (5 A (3 b+c x)+B x (5 b+3 c x))","\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*Sqrt[x]*(5*A*(3*b + c*x) + B*x*(5*b + 3*c*x)))/15","A",1
146,1,29,35,0.0117517,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^{5/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/x^(5/2),x]","\frac{2 (B x (3 b+c x)-3 A (b-c x))}{3 \sqrt{x}}","2 \sqrt{x} (A c+b B)-\frac{2 A b}{\sqrt{x}}+\frac{2}{3} B c x^{3/2}",1,"(2*(-3*A*(b - c*x) + B*x*(3*b + c*x)))/(3*Sqrt[x])","A",1
147,1,28,35,0.0099516,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^{7/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/x^(7/2),x]","-\frac{2 (A (b+3 c x)+3 B x (b-c x))}{3 x^{3/2}}","-\frac{2 (A c+b B)}{\sqrt{x}}-\frac{2 A b}{3 x^{3/2}}+2 B c \sqrt{x}",1,"(-2*(3*B*x*(b - c*x) + A*(b + 3*c*x)))/(3*x^(3/2))","A",1
148,1,30,37,0.0105309,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^{9/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/x^(9/2),x]","-\frac{2 (A (3 b+5 c x)+5 B x (b+3 c x))}{15 x^{5/2}}","-\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*(5*B*x*(b + 3*c*x) + A*(3*b + 5*c*x)))/(15*x^(5/2))","A",1
149,1,55,63,0.0185448,"\int x^{7/2} (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[x^(7/2)*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{2 x^{13/2} \left(19 A \left(255 b^2+442 b c x+195 c^2 x^2\right)+13 B x \left(323 b^2+570 b c x+255 c^2 x^2\right)\right)}{62985}","\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*x^(13/2)*(19*A*(255*b^2 + 442*b*c*x + 195*c^2*x^2) + 13*B*x*(323*b^2 + 570*b*c*x + 255*c^2*x^2)))/62985","A",1
150,1,55,63,0.0170526,"\int x^{5/2} (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[x^(5/2)*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{2 x^{11/2} \left(17 A \left(195 b^2+330 b c x+143 c^2 x^2\right)+11 B x \left(255 b^2+442 b c x+195 c^2 x^2\right)\right)}{36465}","\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*x^(11/2)*(17*A*(195*b^2 + 330*b*c*x + 143*c^2*x^2) + 11*B*x*(255*b^2 + 442*b*c*x + 195*c^2*x^2)))/36465","A",1
151,1,55,63,0.0164944,"\int x^{3/2} (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[x^(3/2)*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{2 x^{9/2} \left(5 A \left(143 b^2+234 b c x+99 c^2 x^2\right)+3 B x \left(195 b^2+330 b c x+143 c^2 x^2\right)\right)}{6435}","\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*x^(9/2)*(5*A*(143*b^2 + 234*b*c*x + 99*c^2*x^2) + 3*B*x*(195*b^2 + 330*b*c*x + 143*c^2*x^2)))/6435","A",1
152,1,55,63,0.0176144,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[Sqrt[x]*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{2 x^{7/2} \left(13 A \left(99 b^2+154 b c x+63 c^2 x^2\right)+7 B x \left(143 b^2+234 b c x+99 c^2 x^2\right)\right)}{9009}","\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*x^(7/2)*(13*A*(99*b^2 + 154*b*c*x + 63*c^2*x^2) + 7*B*x*(143*b^2 + 234*b*c*x + 99*c^2*x^2)))/9009","A",1
153,1,55,63,0.0165454,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/Sqrt[x],x]","\frac{2 x^{5/2} \left(11 A \left(63 b^2+90 b c x+35 c^2 x^2\right)+5 B x \left(99 b^2+154 b c x+63 c^2 x^2\right)\right)}{3465}","\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*x^(5/2)*(11*A*(63*b^2 + 90*b*c*x + 35*c^2*x^2) + 5*B*x*(99*b^2 + 154*b*c*x + 63*c^2*x^2)))/3465","A",1
154,1,54,63,0.0161804,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^{3/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^(3/2),x]","\frac{2}{315} x^{3/2} \left(3 A \left(35 b^2+42 b c x+15 c^2 x^2\right)+B x \left(63 b^2+90 b c x+35 c^2 x^2\right)\right)","\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*x^(3/2)*(3*A*(35*b^2 + 42*b*c*x + 15*c^2*x^2) + B*x*(63*b^2 + 90*b*c*x + 35*c^2*x^2)))/315","A",1
155,1,54,61,0.0160905,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^{5/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^(5/2),x]","\frac{2}{105} \sqrt{x} \left(7 A \left(15 b^2+10 b c x+3 c^2 x^2\right)+B x \left(35 b^2+42 b c x+15 c^2 x^2\right)\right)","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*Sqrt[x]*(7*A*(15*b^2 + 10*b*c*x + 3*c^2*x^2) + B*x*(35*b^2 + 42*b*c*x + 15*c^2*x^2)))/105","A",1
156,1,54,59,0.0160122,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^{7/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^(7/2),x]","\frac{10 A \left(-3 b^2+6 b c x+c^2 x^2\right)+2 B x \left(15 b^2+10 b c x+3 c^2 x^2\right)}{15 \sqrt{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}",1,"(10*A*(-3*b^2 + 6*b*c*x + c^2*x^2) + 2*B*x*(15*b^2 + 10*b*c*x + 3*c^2*x^2))/(15*Sqrt[x])","A",1
157,1,52,59,0.016243,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^{9/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^(9/2),x]","\frac{2 B x \left(-3 b^2+6 b c x+c^2 x^2\right)-2 A \left(b^2+6 b c x-3 c^2 x^2\right)}{3 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 + 6*b*c*x - 3*c^2*x^2) + 2*B*x*(-3*b^2 + 6*b*c*x + c^2*x^2))/(3*x^(3/2))","A",1
158,1,70,85,0.0462261,"\int x^{7/2} (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[x^(7/2)*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{2 \left(B x^{15/2} (b+c x)^4-\frac{x^{15/2} \left(2261 b^3+5985 b^2 c x+5355 b c^2 x^2+1615 c^3 x^3\right) (15 b B-23 A c)}{33915}\right)}{23 c}","\frac{2}{15} A b^3 x^{15/2}+\frac{2}{17} b^2 x^{17/2} (3 A c+b B)+\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*(B*x^(15/2)*(b + c*x)^4 - ((15*b*B - 23*A*c)*x^(15/2)*(2261*b^3 + 5985*b^2*c*x + 5355*b*c^2*x^2 + 1615*c^3*x^3))/33915))/(23*c)","A",1
159,1,70,85,0.0453646,"\int x^{5/2} (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[x^(5/2)*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{2 \left(B x^{13/2} (b+c x)^4-\frac{x^{13/2} \left(1615 b^3+4199 b^2 c x+3705 b c^2 x^2+1105 c^3 x^3\right) (13 b B-21 A c)}{20995}\right)}{21 c}","\frac{2}{13} A b^3 x^{13/2}+\frac{2}{15} b^2 x^{15/2} (3 A c+b B)+\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*(B*x^(13/2)*(b + c*x)^4 - ((13*b*B - 21*A*c)*x^(13/2)*(1615*b^3 + 4199*b^2*c*x + 3705*b*c^2*x^2 + 1105*c^3*x^3))/20995))/(21*c)","A",1
160,1,70,85,0.0439229,"\int x^{3/2} (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[x^(3/2)*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{2 \left(B x^{11/2} (b+c x)^4-\frac{x^{11/2} \left(1105 b^3+2805 b^2 c x+2431 b c^2 x^2+715 c^3 x^3\right) (11 b B-19 A c)}{12155}\right)}{19 c}","\frac{2}{11} A b^3 x^{11/2}+\frac{2}{13} b^2 x^{13/2} (3 A c+b B)+\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*(B*x^(11/2)*(b + c*x)^4 - ((11*b*B - 19*A*c)*x^(11/2)*(1105*b^3 + 2805*b^2*c*x + 2431*b*c^2*x^2 + 715*c^3*x^3))/12155))/(19*c)","A",1
161,1,70,85,0.0450276,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[Sqrt[x]*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{2 \left(B x^{9/2} (b+c x)^4-\frac{x^{9/2} \left(715 b^3+1755 b^2 c x+1485 b c^2 x^2+429 c^3 x^3\right) (9 b B-17 A c)}{6435}\right)}{17 c}","\frac{2}{9} A b^3 x^{9/2}+\frac{2}{11} b^2 x^{11/2} (3 A c+b B)+\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*(B*x^(9/2)*(b + c*x)^4 - ((9*b*B - 17*A*c)*x^(9/2)*(715*b^3 + 1755*b^2*c*x + 1485*b*c^2*x^2 + 429*c^3*x^3))/6435))/(17*c)","A",1
162,1,70,85,0.0465003,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/Sqrt[x],x]","\frac{2 \left(B x^{7/2} (b+c x)^4-\frac{x^{7/2} \left(429 b^3+1001 b^2 c x+819 b c^2 x^2+231 c^3 x^3\right) (7 b B-15 A c)}{3003}\right)}{15 c}","\frac{2}{7} A b^3 x^{7/2}+\frac{2}{9} b^2 x^{9/2} (3 A c+b B)+\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*(B*x^(7/2)*(b + c*x)^4 - ((7*b*B - 15*A*c)*x^(7/2)*(429*b^3 + 1001*b^2*c*x + 819*b*c^2*x^2 + 231*c^3*x^3))/3003))/(15*c)","A",1
163,1,70,85,0.0452547,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{3/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^(3/2),x]","\frac{2 \left(B x^{5/2} (b+c x)^4-\frac{x^{5/2} \left(231 b^3+495 b^2 c x+385 b c^2 x^2+105 c^3 x^3\right) (5 b B-13 A c)}{1155}\right)}{13 c}","\frac{2}{5} A b^3 x^{5/2}+\frac{2}{7} b^2 x^{7/2} (3 A c+b B)+\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*(B*x^(5/2)*(b + c*x)^4 - ((5*b*B - 13*A*c)*x^(5/2)*(231*b^3 + 495*b^2*c*x + 385*b*c^2*x^2 + 105*c^3*x^3))/1155))/(13*c)","A",1
164,1,70,85,0.0419328,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{5/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^(5/2),x]","\frac{2 \left(B x^{3/2} (b+c x)^4-\frac{1}{315} x^{3/2} \left(105 b^3+189 b^2 c x+135 b c^2 x^2+35 c^3 x^3\right) (3 b B-11 A c)\right)}{11 c}","\frac{2}{3} A b^3 x^{3/2}+\frac{2}{5} b^2 x^{5/2} (3 A c+b B)+\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*(B*x^(3/2)*(b + c*x)^4 - ((3*b*B - 11*A*c)*x^(3/2)*(105*b^3 + 189*b^2*c*x + 135*b*c^2*x^2 + 35*c^3*x^3))/315))/(11*c)","A",1
165,1,63,83,0.0429356,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{7/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^(7/2),x]","\frac{2 \sqrt{x} \left(35 B (b+c x)^4-\left(35 b^3+35 b^2 c x+21 b c^2 x^2+5 c^3 x^3\right) (b B-9 A c)\right)}{315 c}","2 A b^3 \sqrt{x}+\frac{2}{3} b^2 x^{3/2} (3 A c+b B)+\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*Sqrt[x]*(35*B*(b + c*x)^4 - (b*B - 9*A*c)*(35*b^3 + 35*b^2*c*x + 21*b*c^2*x^2 + 5*c^3*x^3)))/(315*c)","A",1
166,1,75,79,0.0229112,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{9/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^(9/2),x]","\frac{2 \left(7 A \left(-5 b^3+15 b^2 c x+5 b c^2 x^2+c^3 x^3\right)+B x \left(35 b^3+35 b^2 c x+21 b c^2 x^2+5 c^3 x^3\right)\right)}{35 \sqrt{x}}","-\frac{2 A b^3}{\sqrt{x}}+2 b^2 \sqrt{x} (3 A c+b B)+\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*(7*A*(-5*b^3 + 15*b^2*c*x + 5*b*c^2*x^2 + c^3*x^3) + B*x*(35*b^3 + 35*b^2*c*x + 21*b*c^2*x^2 + 5*c^3*x^3)))/(35*Sqrt[x])","A",1
167,1,74,81,0.0228377,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{11/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^(11/2),x]","\frac{6 B x \left(-5 b^3+15 b^2 c x+5 b c^2 x^2+c^3 x^3\right)-10 A \left(b^3+9 b^2 c x-9 b c^2 x^2-c^3 x^3\right)}{15 x^{3/2}}","-\frac{2 A b^3}{3 x^{3/2}}-\frac{2 b^2 (3 A c+b B)}{\sqrt{x}}+\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,"(-10*A*(b^3 + 9*b^2*c*x - 9*b*c^2*x^2 - c^3*x^3) + 6*B*x*(-5*b^3 + 15*b^2*c*x + 5*b*c^2*x^2 + c^3*x^3))/(15*x^(3/2))","A",1
168,1,101,113,0.0634301,"\int \frac{x^{7/2} (A+B x)}{b x+c x^2} \, dx","Integrate[(x^(7/2)*(A + B*x))/(b*x + c*x^2),x]","\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 \sqrt{x} \left(35 b^2 c (3 A+B x)-7 b c^2 x (5 A+3 B x)+3 c^3 x^2 (7 A+5 B x)-105 b^3 B\right)}{105 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 b^2 \sqrt{x} (b B-A c)}{c^4}+\frac{2 b x^{3/2} (b B-A c)}{3 c^3}-\frac{2 x^{5/2} (b B-A c)}{5 c^2}+\frac{2 B x^{7/2}}{7 c}",1,"(2*Sqrt[x]*(-105*b^3*B + 35*b^2*c*(3*A + B*x) - 7*b*c^2*x*(5*A + 3*B*x) + 3*c^3*x^2*(7*A + 5*B*x)))/(105*c^4) + (2*b^(5/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(9/2)","A",1
169,1,81,90,0.0589295,"\int \frac{x^{5/2} (A+B x)}{b x+c x^2} \, dx","Integrate[(x^(5/2)*(A + B*x))/(b*x + c*x^2),x]","\frac{2 \sqrt{x} \left(-5 b c (3 A+B x)+c^2 x (5 A+3 B x)+15 b^2 B\right)}{15 c^3}-\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 b^{3/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{7/2}}+\frac{2 b \sqrt{x} (b B-A c)}{c^3}-\frac{2 x^{3/2} (b B-A c)}{3 c^2}+\frac{2 B x^{5/2}}{5 c}",1,"(2*Sqrt[x]*(15*b^2*B - 5*b*c*(3*A + B*x) + c^2*x*(5*A + 3*B*x)))/(15*c^3) - (2*b^(3/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(7/2)","A",1
170,1,63,69,0.0319967,"\int \frac{x^{3/2} (A+B x)}{b x+c x^2} \, dx","Integrate[(x^(3/2)*(A + B*x))/(b*x + c*x^2),x]","\frac{2 \sqrt{b} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{5/2}}+\frac{2 \sqrt{x} (3 A c-3 b B+B c x)}{3 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 \sqrt{x} (b B-A c)}{c^2}+\frac{2 B x^{3/2}}{3 c}",1,"(2*Sqrt[x]*(-3*b*B + 3*A*c + B*c*x))/(3*c^2) + (2*Sqrt[b]*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(5/2)","A",1
171,1,49,49,0.0264756,"\int \frac{\sqrt{x} (A+B x)}{b x+c x^2} \, dx","Integrate[(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",1
172,1,49,49,0.0315452,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)} \, dx","Integrate[(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",1
173,1,44,69,0.0137458,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(3/2)*(b*x + c*x^2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{c x}{b}\right) (6 A c x-6 b B x)-2 A b}{3 b^2 x^{3/2}}","-\frac{2 \sqrt{c} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{5/2}}-\frac{2 (b B-A c)}{b^2 \sqrt{x}}-\frac{2 A}{3 b x^{3/2}}",1,"(-2*A*b + (-6*b*B*x + 6*A*c*x)*Hypergeometric2F1[-1/2, 1, 1/2, -((c*x)/b)])/(3*b^2*x^(3/2))","C",1
174,1,43,90,0.0161568,"\int \frac{A+B x}{x^{5/2} \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(5/2)*(b*x + c*x^2)),x]","\frac{-10 x (b B-A c) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{c x}{b}\right)-6 A b}{15 b^2 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 c (b B-A c)}{b^3 \sqrt{x}}-\frac{2 (b B-A c)}{3 b^2 x^{3/2}}-\frac{2 A}{5 b x^{5/2}}",1,"(-6*A*b - 10*(b*B - A*c)*x*Hypergeometric2F1[-3/2, 1, -1/2, -((c*x)/b)])/(15*b^2*x^(5/2))","C",1
175,1,44,113,0.0146153,"\int \frac{A+B x}{x^{7/2} \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(7/2)*(b*x + c*x^2)),x]","\frac{2 \left(\, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{c x}{b}\right) (7 A c x-7 b B x)-5 A b\right)}{35 b^2 x^{7/2}}","-\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^2 (b B-A c)}{b^4 \sqrt{x}}+\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*(-5*A*b + (-7*b*B*x + 7*A*c*x)*Hypergeometric2F1[-5/2, 1, -3/2, -((c*x)/b)]))/(35*b^2*x^(7/2))","C",1
176,1,44,136,0.0144488,"\int \frac{A+B x}{x^{9/2} \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(9/2)*(b*x + c*x^2)),x]","\frac{2 \left(\, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};-\frac{c x}{b}\right) (9 A c x-9 b B x)-7 A b\right)}{63 b^2 x^{9/2}}","\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^3 (b B-A c)}{b^5 \sqrt{x}}-\frac{2 c^2 (b B-A c)}{3 b^4 x^{3/2}}+\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*(-7*A*b + (-9*b*B*x + 9*A*c*x)*Hypergeometric2F1[-7/2, 1, -5/2, -((c*x)/b)]))/(63*b^2*x^(9/2))","C",1
177,1,110,131,0.0696745,"\int \frac{x^{9/2} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(x^(9/2)*(A + B*x))/(b*x + c*x^2)^2,x]","\frac{\sqrt{x} \left(b^2 (70 B c x-75 A c)-2 b c^2 x (25 A+7 B x)+2 c^3 x^2 (5 A+3 B x)+105 b^3 B\right)}{15 c^4 (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{b^{3/2} (7 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{9/2}}+\frac{b \sqrt{x} (7 b B-5 A c)}{c^4}-\frac{x^{3/2} (7 b B-5 A c)}{3 c^3}+\frac{x^{5/2} (7 b B-5 A c)}{5 b c^2}-\frac{x^{7/2} (b B-A c)}{b c (b+c x)}",1,"(Sqrt[x]*(105*b^3*B + 2*c^3*x^2*(5*A + 3*B*x) - 2*b*c^2*x*(25*A + 7*B*x) + b^2*(-75*A*c + 70*B*c*x)))/(15*c^4*(b + c*x)) - (b^(3/2)*(7*b*B - 5*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(9/2)","A",1
178,1,88,109,0.0574767,"\int \frac{x^{7/2} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(x^(7/2)*(A + B*x))/(b*x + c*x^2)^2,x]","\frac{\sqrt{x} \left(b c (9 A-10 B x)+2 c^2 x (3 A+B x)-15 b^2 B\right)}{3 c^3 (b+c x)}+\frac{\sqrt{b} (5 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{7/2}}","\frac{\sqrt{b} (5 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{7/2}}-\frac{\sqrt{x} (5 b B-3 A c)}{c^3}+\frac{x^{3/2} (5 b B-3 A c)}{3 b c^2}-\frac{x^{5/2} (b B-A c)}{b c (b+c x)}",1,"(Sqrt[x]*(-15*b^2*B + b*c*(9*A - 10*B*x) + 2*c^2*x*(3*A + B*x)))/(3*c^3*(b + c*x)) + (Sqrt[b]*(5*b*B - 3*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(7/2)","A",1
179,1,69,88,0.0411339,"\int \frac{x^{5/2} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(x^(5/2)*(A + B*x))/(b*x + c*x^2)^2,x]","\frac{\sqrt{x} (-A c+3 b B+2 B c x)}{c^2 (b+c x)}-\frac{(3 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} c^{5/2}}","-\frac{(3 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} c^{5/2}}+\frac{\sqrt{x} (3 b B-A c)}{b c^2}-\frac{x^{3/2} (b B-A c)}{b c (b+c x)}",1,"(Sqrt[x]*(3*b*B - A*c + 2*B*c*x))/(c^2*(b + c*x)) - ((3*b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*c^(5/2))","A",1
180,1,63,64,0.0358573,"\int \frac{x^{3/2} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(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} (A c-b B)}{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",1
181,1,59,85,0.0173056,"\int \frac{\sqrt{x} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(b*x + c*x^2)^2,x]","\frac{(b+c x) (b B-3 A c) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{c x}{b}\right)+b (A c-b B)}{b^2 c \sqrt{x} (b+c 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-3 A c}{b^2 c \sqrt{x}}-\frac{b B-A c}{b c \sqrt{x} (b+c x)}",1,"(b*(-(b*B) + A*c) + (b*B - 3*A*c)*(b + c*x)*Hypergeometric2F1[-1/2, 1, 1/2, -((c*x)/b)])/(b^2*c*Sqrt[x]*(b + c*x))","C",1
182,1,64,110,0.0197638,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(b*x + c*x^2)^2),x]","\frac{(b+c x) (3 b B-5 A c) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{c x}{b}\right)+3 b (A c-b B)}{3 b^2 c x^{3/2} (b+c 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{3 b B-5 A c}{b^3 \sqrt{x}}+\frac{3 b B-5 A c}{3 b^2 c x^{3/2}}-\frac{b B-A c}{b c x^{3/2} (b+c x)}",1,"(3*b*(-(b*B) + A*c) + (3*b*B - 5*A*c)*(b + c*x)*Hypergeometric2F1[-3/2, 1, -1/2, -((c*x)/b)])/(3*b^2*c*x^(3/2)*(b + c*x))","C",1
183,1,64,130,0.0182615,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^(3/2)*(b*x + c*x^2)^2),x]","\frac{(b+c x) (5 b B-7 A c) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{c x}{b}\right)+5 b (A c-b B)}{5 b^2 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{c (5 b B-7 A c)}{b^4 \sqrt{x}}-\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{b B-A c}{b c x^{5/2} (b+c x)}",1,"(5*b*(-(b*B) + A*c) + (5*b*B - 7*A*c)*(b + c*x)*Hypergeometric2F1[-5/2, 1, -3/2, -((c*x)/b)])/(5*b^2*c*x^(5/2)*(b + c*x))","C",1
184,1,64,156,0.0177349,"\int \frac{A+B x}{x^{5/2} \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^(5/2)*(b*x + c*x^2)^2),x]","\frac{(b+c x) (7 b B-9 A c) \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};-\frac{c x}{b}\right)+7 b (A c-b B)}{7 b^2 c x^{7/2} (b+c 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^2 (7 b B-9 A c)}{b^5 \sqrt{x}}+\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*B) + A*c) + (7*b*B - 9*A*c)*(b + c*x)*Hypergeometric2F1[-7/2, 1, -5/2, -((c*x)/b)])/(7*b^2*c*x^(7/2)*(b + c*x))","C",1
185,1,61,169,0.0230992,"\int \frac{x^{13/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^(13/2)*(A + B*x))/(b*x + c*x^2)^3,x]","\frac{x^{9/2} \left(\frac{9 b^2 (A c-b B)}{(b+c x)^2}+(9 b B-5 A c) \, _2F_1\left(2,\frac{9}{2};\frac{11}{2};-\frac{c x}{b}\right)\right)}{18 b^3 c}","-\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{7 b \sqrt{x} (9 b B-5 A c)}{4 c^5}-\frac{7 x^{3/2} (9 b B-5 A c)}{12 c^4}+\frac{7 x^{5/2} (9 b B-5 A c)}{20 b c^3}-\frac{x^{7/2} (9 b B-5 A c)}{4 b c^2 (b+c x)}-\frac{x^{9/2} (b B-A c)}{2 b c (b+c x)^2}",1,"(x^(9/2)*((9*b^2*(-(b*B) + A*c))/(b + c*x)^2 + (9*b*B - 5*A*c)*Hypergeometric2F1[2, 9/2, 11/2, -((c*x)/b)]))/(18*b^3*c)","C",1
186,1,61,147,0.0219279,"\int \frac{x^{11/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^(11/2)*(A + B*x))/(b*x + c*x^2)^3,x]","\frac{x^{7/2} \left(\frac{7 b^2 (A c-b B)}{(b+c x)^2}+(7 b B-3 A c) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{c x}{b}\right)\right)}{14 b^3 c}","\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{5 \sqrt{x} (7 b B-3 A c)}{4 c^4}+\frac{5 x^{3/2} (7 b B-3 A c)}{12 b c^3}-\frac{x^{5/2} (7 b B-3 A c)}{4 b c^2 (b+c x)}-\frac{x^{7/2} (b B-A c)}{2 b c (b+c x)^2}",1,"(x^(7/2)*((7*b^2*(-(b*B) + A*c))/(b + c*x)^2 + (7*b*B - 3*A*c)*Hypergeometric2F1[2, 7/2, 9/2, -((c*x)/b)]))/(14*b^3*c)","C",1
187,1,61,126,0.0220506,"\int \frac{x^{9/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^(9/2)*(A + B*x))/(b*x + c*x^2)^3,x]","\frac{x^{5/2} \left(\frac{5 b^2 (A c-b B)}{(b+c x)^2}+(5 b B-A c) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};-\frac{c x}{b}\right)\right)}{10 b^3 c}","-\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{3 \sqrt{x} (5 b B-A c)}{4 b c^3}-\frac{x^{3/2} (5 b B-A c)}{4 b c^2 (b+c x)}-\frac{x^{5/2} (b B-A c)}{2 b c (b+c x)^2}",1,"(x^(5/2)*((5*b^2*(-(b*B) + A*c))/(b + c*x)^2 + (5*b*B - A*c)*Hypergeometric2F1[2, 5/2, 7/2, -((c*x)/b)]))/(10*b^3*c)","C",1
188,1,85,100,0.0622177,"\int \frac{x^{7/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(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} \left(-b c (A+5 B x)+A c^2 x-3 b^2 B\right)}{4 b c^2 (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,"(Sqrt[x]*(-3*b^2*B + A*c^2*x - b*c*(A + 5*B*x)))/(4*b*c^2*(b + c*x)^2) + ((3*b*B + A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*b^(3/2)*c^(5/2))","A",1
189,1,91,100,0.0976908,"\int \frac{x^{5/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^(5/2)*(A + B*x))/(b*x + c*x^2)^3,x]","\frac{\sqrt{x} \left(\frac{b^2 (A c-b B)}{(b+c x)^2}-\frac{1}{2} (-3 A c-b B) \left(\frac{b}{b+c x}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{c} \sqrt{x}}\right)\right)}{2 b^3 c}","\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,"(Sqrt[x]*((b^2*(-(b*B) + A*c))/(b + c*x)^2 - ((-(b*B) - 3*A*c)*(b/(b + c*x) + (Sqrt[b]*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[c]*Sqrt[x])))/2))/(2*b^3*c)","A",1
190,1,59,123,0.0222271,"\int \frac{x^{3/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(x^(3/2)*(A + B*x))/(b*x + c*x^2)^3,x]","\frac{\frac{b^2 (A c-b B)}{(b+c x)^2}+(b B-5 A c) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{c x}{b}\right)}{2 b^3 c \sqrt{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{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{b B-A c}{2 b c \sqrt{x} (b+c x)^2}",1,"((b^2*(-(b*B) + A*c))/(b + c*x)^2 + (b*B - 5*A*c)*Hypergeometric2F1[-1/2, 2, 1/2, -((c*x)/b)])/(2*b^3*c*Sqrt[x])","C",1
191,1,61,147,0.023085,"\int \frac{\sqrt{x} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(b*x + c*x^2)^3,x]","\frac{\frac{3 b^2 (A c-b B)}{(b+c x)^2}+(3 b B-7 A c) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\frac{c x}{b}\right)}{6 b^3 c x^{3/2}}","-\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{5 (3 b B-7 A c)}{4 b^4 \sqrt{x}}+\frac{5 (3 b B-7 A c)}{12 b^3 c x^{3/2}}-\frac{3 b B-7 A c}{4 b^2 c x^{3/2} (b+c x)}-\frac{b B-A c}{2 b c x^{3/2} (b+c x)^2}",1,"((3*b^2*(-(b*B) + A*c))/(b + c*x)^2 + (3*b*B - 7*A*c)*Hypergeometric2F1[-3/2, 2, -1/2, -((c*x)/b)])/(6*b^3*c*x^(3/2))","C",1
192,1,61,169,0.0226137,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(b*x + c*x^2)^3),x]","\frac{\frac{5 b^2 (A c-b B)}{(b+c x)^2}+(5 b B-9 A c) \, _2F_1\left(-\frac{5}{2},2;-\frac{3}{2};-\frac{c x}{b}\right)}{10 b^3 c x^{5/2}}","\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 c (5 b B-9 A c)}{4 b^5 \sqrt{x}}-\frac{7 (5 b B-9 A c)}{12 b^4 x^{3/2}}+\frac{7 (5 b B-9 A c)}{20 b^3 c x^{5/2}}-\frac{5 b B-9 A c}{4 b^2 c x^{5/2} (b+c x)}-\frac{b B-A c}{2 b c x^{5/2} (b+c x)^2}",1,"((5*b^2*(-(b*B) + A*c))/(b + c*x)^2 + (5*b*B - 9*A*c)*Hypergeometric2F1[-5/2, 2, -3/2, -((c*x)/b)])/(10*b^3*c*x^(5/2))","C",1
193,1,61,193,0.0232414,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/(x^(3/2)*(b*x + c*x^2)^3),x]","\frac{\frac{7 b^2 (A c-b B)}{(b+c x)^2}+(7 b B-11 A c) \, _2F_1\left(-\frac{7}{2},2;-\frac{5}{2};-\frac{c x}{b}\right)}{14 b^3 c x^{7/2}}","-\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{9 c^2 (7 b B-11 A c)}{4 b^6 \sqrt{x}}+\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{9 (7 b B-11 A c)}{28 b^3 c x^{7/2}}-\frac{7 b B-11 A c}{4 b^2 c x^{7/2} (b+c x)}-\frac{b B-A c}{2 b c x^{7/2} (b+c x)^2}",1,"((7*b^2*(-(b*B) + A*c))/(b + c*x)^2 + (7*b*B - 11*A*c)*Hypergeometric2F1[-7/2, 2, -5/2, -((c*x)/b)])/(14*b^3*c*x^(7/2))","C",1
194,1,113,207,0.0879956,"\int x^{7/2} (A+B x) \sqrt{b x+c x^2} \, dx","Integrate[x^(7/2)*(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{2 (x (b+c x))^{3/2} \left(128 b^4 c (13 A+15 B x)-96 b^3 c^2 x (26 A+25 B x)+80 b^2 c^3 x^2 (39 A+35 B x)-70 b c^4 x^3 (52 A+45 B x)+315 c^5 x^4 (13 A+11 B x)-1280 b^5 B\right)}{45045 c^6 x^{3/2}}","-\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,"(2*(x*(b + c*x))^(3/2)*(-1280*b^5*B + 315*c^5*x^4*(13*A + 11*B*x) + 128*b^4*c*(13*A + 15*B*x) - 96*b^3*c^2*x*(26*A + 25*B*x) + 80*b^2*c^3*x^2*(39*A + 35*B*x) - 70*b*c^4*x^3*(52*A + 45*B*x)))/(45045*c^6*x^(3/2))","A",1
195,1,94,170,0.0708358,"\int x^{5/2} (A+B x) \sqrt{b x+c x^2} \, dx","Integrate[x^(5/2)*(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{2 (x (b+c x))^{3/2} \left(-16 b^3 c (11 A+12 B x)+24 b^2 c^2 x (11 A+10 B x)-10 b c^3 x^2 (33 A+28 B x)+35 c^4 x^3 (11 A+9 B x)+128 b^4 B\right)}{3465 c^5 x^{3/2}}","\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,"(2*(x*(b + c*x))^(3/2)*(128*b^4*B + 35*c^4*x^3*(11*A + 9*B*x) + 24*b^2*c^2*x*(11*A + 10*B*x) - 16*b^3*c*(11*A + 12*B*x) - 10*b*c^3*x^2*(33*A + 28*B*x)))/(3465*c^5*x^(3/2))","A",1
196,1,72,133,0.0531809,"\int x^{3/2} (A+B x) \sqrt{b x+c x^2} \, dx","Integrate[x^(3/2)*(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{2 (x (b+c x))^{3/2} \left(24 b^2 c (A+B x)-6 b c^2 x (6 A+5 B x)+5 c^3 x^2 (9 A+7 B x)-16 b^3 B\right)}{315 c^4 x^{3/2}}","-\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,"(2*(x*(b + c*x))^(3/2)*(-16*b^3*B + 24*b^2*c*(A + B*x) - 6*b*c^2*x*(6*A + 5*B*x) + 5*c^3*x^2*(9*A + 7*B*x)))/(315*c^4*x^(3/2))","A",1
197,1,56,96,0.0413296,"\int \sqrt{x} (A+B x) \sqrt{b x+c x^2} \, dx","Integrate[Sqrt[x]*(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{2 (x (b+c x))^{3/2} \left(-2 b c (7 A+6 B x)+3 c^2 x (7 A+5 B x)+8 b^2 B\right)}{105 c^3 x^{3/2}}","\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 \left(b x+c x^2\right)^{3/2} (4 b B-7 A c)}{35 c^2 \sqrt{x}}+\frac{2 B \sqrt{x} \left(b x+c x^2\right)^{3/2}}{7 c}",1,"(2*(x*(b + c*x))^(3/2)*(8*b^2*B + 3*c^2*x*(7*A + 5*B*x) - 2*b*c*(7*A + 6*B*x)))/(105*c^3*x^(3/2))","A",1
198,1,37,61,0.0257653,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{\sqrt{x}} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/Sqrt[x],x]","\frac{2 (x (b+c x))^{3/2} (5 A c-2 b B+3 B c x)}{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*(x*(b + c*x))^(3/2)*(-2*b*B + 5*A*c + 3*B*c*x))/(15*c^2*x^(3/2))","A",1
199,1,80,81,0.0560399,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^(3/2),x]","\frac{2 \sqrt{x} \sqrt{b+c x} \left(\sqrt{b+c x} (3 A c+b B+B c x)-3 A \sqrt{b} c \tanh ^{-1}\left(\frac{\sqrt{b+c x}}{\sqrt{b}}\right)\right)}{3 c \sqrt{x (b+c 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}}",1,"(2*Sqrt[x]*Sqrt[b + c*x]*(Sqrt[b + c*x]*(b*B + 3*A*c + B*c*x) - 3*A*Sqrt[b]*c*ArcTanh[Sqrt[b + c*x]/Sqrt[b]]))/(3*c*Sqrt[x*(b + c*x)])","A",1
200,1,80,95,0.0478464,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^(5/2),x]","-\frac{\sqrt{x (b+c x)} \left(\sqrt{b} (A-2 B x) \sqrt{b+c x}+x (A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b+c x}}{\sqrt{b}}\right)\right)}{\sqrt{b} x^{3/2} \sqrt{b+c 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}}",1,"-((Sqrt[x*(b + c*x)]*(Sqrt[b]*(A - 2*B*x)*Sqrt[b + c*x] + (2*b*B + A*c)*x*ArcTanh[Sqrt[b + c*x]/Sqrt[b]]))/(Sqrt[b]*x^(3/2)*Sqrt[b + c*x]))","A",1
201,1,83,105,0.0999589,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^{7/2}} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^(7/2),x]","-\frac{c x^2 \sqrt{\frac{c x}{b}+1} (4 b B-A c) \tanh ^{-1}\left(\sqrt{\frac{c x}{b}+1}\right)+(b+c x) (2 A b+A c x+4 b B x)}{4 b x^{3/2} \sqrt{x (b+c 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}}",1,"-1/4*((b + c*x)*(2*A*b + 4*b*B*x + A*c*x) + c*(4*b*B - A*c)*x^2*Sqrt[1 + (c*x)/b]*ArcTanh[Sqrt[1 + (c*x)/b]])/(b*x^(3/2)*Sqrt[x*(b + c*x)])","A",1
202,1,61,142,0.0261827,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^{9/2}} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/x^(9/2),x]","-\frac{(x (b+c x))^{3/2} \left(A b^3+c^2 x^3 (2 b B-A c) \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{c x}{b}+1\right)\right)}{3 b^4 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,"-1/3*((x*(b + c*x))^(3/2)*(A*b^3 + c^2*(2*b*B - A*c)*x^3*Hypergeometric2F1[3/2, 3, 5/2, 1 + (c*x)/b]))/(b^4*x^(9/2))","C",1
203,1,110,207,0.0883317,"\int x^{5/2} (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Integrate[x^(5/2)*(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{2 (x (b+c x))^{5/2} \left(128 b^4 c (3 A+5 B x)-160 b^3 c^2 x (6 A+7 B x)+1680 b^2 c^3 x^2 (A+B x)-210 b c^4 x^3 (12 A+11 B x)+231 c^5 x^4 (15 A+13 B x)-256 b^5 B\right)}{45045 c^6 x^{5/2}}","-\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,"(2*(x*(b + c*x))^(5/2)*(-256*b^5*B + 1680*b^2*c^3*x^2*(A + B*x) + 128*b^4*c*(3*A + 5*B*x) - 160*b^3*c^2*x*(6*A + 7*B*x) - 210*b*c^4*x^3*(12*A + 11*B*x) + 231*c^5*x^4*(15*A + 13*B*x)))/(45045*c^6*x^(5/2))","A",1
204,1,94,170,0.0750855,"\int x^{3/2} (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Integrate[x^(3/2)*(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{2 (x (b+c x))^{5/2} \left(-16 b^3 c (13 A+20 B x)+40 b^2 c^2 x (13 A+14 B x)-70 b c^3 x^2 (13 A+12 B x)+105 c^4 x^3 (13 A+11 B x)+128 b^4 B\right)}{15015 c^5 x^{5/2}}","\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,"(2*(x*(b + c*x))^(5/2)*(128*b^4*B + 105*c^4*x^3*(13*A + 11*B*x) - 70*b*c^3*x^2*(13*A + 12*B*x) + 40*b^2*c^2*x*(13*A + 14*B*x) - 16*b^3*c*(13*A + 20*B*x)))/(15015*c^5*x^(5/2))","A",1
205,1,75,133,0.0579761,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Integrate[Sqrt[x]*(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{2 (x (b+c x))^{5/2} \left(8 b^2 c (11 A+15 B x)-10 b c^2 x (22 A+21 B x)+35 c^3 x^2 (11 A+9 B x)-48 b^3 B\right)}{3465 c^4 x^{5/2}}","-\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{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 \left(b x+c x^2\right)^{5/2} (6 b B-11 A c)}{99 c^2 \sqrt{x}}+\frac{2 B \sqrt{x} \left(b x+c x^2\right)^{5/2}}{11 c}",1,"(2*(x*(b + c*x))^(5/2)*(-48*b^3*B + 35*c^3*x^2*(11*A + 9*B*x) + 8*b^2*c*(11*A + 15*B*x) - 10*b*c^2*x*(22*A + 21*B*x)))/(3465*c^4*x^(5/2))","A",1
206,1,56,96,0.0437555,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/Sqrt[x],x]","\frac{2 (x (b+c x))^{5/2} \left(-2 b c (9 A+10 B x)+5 c^2 x (9 A+7 B x)+8 b^2 B\right)}{315 c^3 x^{5/2}}","\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 \left(b x+c x^2\right)^{5/2} (4 b B-9 A c)}{63 c^2 x^{3/2}}+\frac{2 B \left(b x+c x^2\right)^{5/2}}{9 c \sqrt{x}}",1,"(2*(x*(b + c*x))^(5/2)*(8*b^2*B + 5*c^2*x*(9*A + 7*B*x) - 2*b*c*(9*A + 10*B*x)))/(315*c^3*x^(5/2))","A",1
207,1,37,61,0.0294986,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{3/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(3/2),x]","\frac{2 (x (b+c x))^{5/2} (7 A c-2 b B+5 B c x)}{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*(x*(b + c*x))^(5/2)*(-2*b*B + 7*A*c + 5*B*c*x))/(35*c^2*x^(5/2))","A",1
208,1,100,105,0.0808911,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{5/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(5/2),x]","\frac{2 \sqrt{x} \sqrt{b+c x} \left(\sqrt{b+c x} \left(b (20 A c+6 B c x)+c^2 x (5 A+3 B x)+3 b^2 B\right)-15 A b^{3/2} c \tanh ^{-1}\left(\frac{\sqrt{b+c x}}{\sqrt{b}}\right)\right)}{15 c \sqrt{x (b+c x)}}","-2 A b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 A b \sqrt{b x+c x^2}}{\sqrt{x}}+\frac{2 A \left(b x+c x^2\right)^{3/2}}{3 x^{3/2}}+\frac{2 B \left(b x+c x^2\right)^{5/2}}{5 c x^{5/2}}",1,"(2*Sqrt[x]*Sqrt[b + c*x]*(Sqrt[b + c*x]*(3*b^2*B + c^2*x*(5*A + 3*B*x) + b*(20*A*c + 6*B*c*x)) - 15*A*b^(3/2)*c*ArcTanh[Sqrt[b + c*x]/Sqrt[b]]))/(15*c*Sqrt[x*(b + c*x)])","A",1
209,1,94,128,0.0587236,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{7/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(7/2),x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{b+c x} (2 B x (4 b+c x)-3 A (b-2 c x))-3 \sqrt{b} x (3 A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b+c x}}{\sqrt{b}}\right)\right)}{3 x^{3/2} \sqrt{b+c x}}","\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{\left(b x+c x^2\right)^{3/2} (3 A c+2 b B)}{3 b x^{3/2}}-\frac{A \left(b x+c x^2\right)^{5/2}}{b x^{7/2}}",1,"(Sqrt[x*(b + c*x)]*(Sqrt[b + c*x]*(-3*A*(b - 2*c*x) + 2*B*x*(4*b + c*x)) - 3*Sqrt[b]*(2*b*B + 3*A*c)*x*ArcTanh[Sqrt[b + c*x]/Sqrt[b]]))/(3*x^(3/2)*Sqrt[b + c*x])","A",1
210,1,59,137,0.0318809,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{9/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(9/2),x]","\frac{(x (b+c x))^{5/2} \left(c x^2 (A c+4 b B) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{c x}{b}+1\right)-5 A b^2\right)}{10 b^3 x^{9/2}}","\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{\left(b x+c x^2\right)^{3/2} (A c+4 b B)}{4 b x^{5/2}}-\frac{A \left(b x+c x^2\right)^{5/2}}{2 b x^{9/2}}",1,"((x*(b + c*x))^(5/2)*(-5*A*b^2 + c*(4*b*B + A*c)*x^2*Hypergeometric2F1[2, 5/2, 7/2, 1 + (c*x)/b]))/(10*b^3*x^(9/2))","C",1
211,1,107,142,0.1240149,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{11/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(11/2),x]","-\frac{(b+c x) \left(A \left(8 b^2+14 b c x+3 c^2 x^2\right)+6 b B x (2 b+5 c x)\right)+3 c^2 x^3 \sqrt{\frac{c x}{b}+1} (6 b B-A c) \tanh ^{-1}\left(\sqrt{\frac{c x}{b}+1}\right)}{24 b x^{5/2} \sqrt{x (b+c 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}}",1,"-1/24*((b + c*x)*(6*b*B*x*(2*b + 5*c*x) + A*(8*b^2 + 14*b*c*x + 3*c^2*x^2)) + 3*c^2*(6*b*B - A*c)*x^3*Sqrt[1 + (c*x)/b]*ArcTanh[Sqrt[1 + (c*x)/b]])/(b*x^(5/2)*Sqrt[x*(b + c*x)])","A",1
212,1,62,179,0.0338599,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{13/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(13/2),x]","\frac{(x (b+c x))^{5/2} \left(c^3 x^4 (8 b B-3 A c) \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{c x}{b}+1\right)-5 A b^4\right)}{20 b^5 x^{13/2}}","\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^2 \sqrt{b x+c x^2} (8 b B-3 A c)}{64 b^2 x^{3/2}}-\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,"((x*(b + c*x))^(5/2)*(-5*A*b^4 + c^3*(8*b*B - 3*A*c)*x^4*Hypergeometric2F1[5/2, 4, 7/2, 1 + (c*x)/b]))/(20*b^5*x^(13/2))","C",1
213,1,61,216,0.0339453,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{15/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(15/2),x]","-\frac{(x (b+c x))^{5/2} \left(A b^5+c^4 x^5 (2 b B-A c) \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};\frac{c x}{b}+1\right)\right)}{5 b^6 x^{15/2}}","-\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{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{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,"-1/5*((x*(b + c*x))^(5/2)*(A*b^5 + c^4*(2*b*B - A*c)*x^5*Hypergeometric2F1[5/2, 5, 7/2, 1 + (c*x)/b]))/(b^6*x^(15/2))","C",1
214,1,120,207,0.0933841,"\int x^{3/2} (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Integrate[x^(3/2)*(A + B*x)*(b*x + c*x^2)^(5/2),x]","\frac{2 (b+c x)^3 \sqrt{x (b+c x)} \left(128 b^4 c (17 A+35 B x)-224 b^3 c^2 x (34 A+45 B x)+336 b^2 c^3 x^2 (51 A+55 B x)-462 b c^4 x^3 (68 A+65 B x)+3003 c^5 x^4 (17 A+15 B x)-1280 b^5 B\right)}{765765 c^6 \sqrt{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}",1,"(2*(b + c*x)^3*Sqrt[x*(b + c*x)]*(-1280*b^5*B + 3003*c^5*x^4*(17*A + 15*B*x) + 128*b^4*c*(17*A + 35*B*x) - 224*b^3*c^2*x*(34*A + 45*B*x) + 336*b^2*c^3*x^2*(51*A + 55*B*x) - 462*b*c^4*x^3*(68*A + 65*B*x)))/(765765*c^6*Sqrt[x])","A",1
215,1,101,170,0.073616,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Integrate[Sqrt[x]*(A + B*x)*(b*x + c*x^2)^(5/2),x]","\frac{2 (b+c x)^3 \sqrt{x (b+c x)} \left(-16 b^3 c (15 A+28 B x)+168 b^2 c^2 x (5 A+6 B x)-42 b c^3 x^2 (45 A+44 B x)+231 c^4 x^3 (15 A+13 B x)+128 b^4 B\right)}{45045 c^5 \sqrt{x}}","\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{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{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 \left(b x+c x^2\right)^{7/2} (8 b B-15 A c)}{195 c^2 \sqrt{x}}+\frac{2 B \sqrt{x} \left(b x+c x^2\right)^{7/2}}{15 c}",1,"(2*(b + c*x)^3*Sqrt[x*(b + c*x)]*(128*b^4*B + 168*b^2*c^2*x*(5*A + 6*B*x) + 231*c^4*x^3*(15*A + 13*B*x) - 16*b^3*c*(15*A + 28*B*x) - 42*b*c^3*x^2*(45*A + 44*B*x)))/(45045*c^5*Sqrt[x])","A",1
216,1,82,133,0.0584012,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/Sqrt[x],x]","\frac{2 (b+c x)^3 \sqrt{x (b+c x)} \left(8 b^2 c (13 A+21 B x)-14 b c^2 x (26 A+27 B x)+63 c^3 x^2 (13 A+11 B x)-48 b^3 B\right)}{9009 c^4 \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{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 \left(b x+c x^2\right)^{7/2} (6 b B-13 A c)}{143 c^2 x^{3/2}}+\frac{2 B \left(b x+c x^2\right)^{7/2}}{13 c \sqrt{x}}",1,"(2*(b + c*x)^3*Sqrt[x*(b + c*x)]*(-48*b^3*B + 63*c^3*x^2*(13*A + 11*B*x) + 8*b^2*c*(13*A + 21*B*x) - 14*b*c^2*x*(26*A + 27*B*x)))/(9009*c^4*Sqrt[x])","A",1
217,1,63,96,0.0455286,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{3/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(3/2),x]","\frac{2 (b+c x)^3 \sqrt{x (b+c x)} \left(-2 b c (11 A+14 B x)+7 c^2 x (11 A+9 B x)+8 b^2 B\right)}{693 c^3 \sqrt{x}}","\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 \left(b x+c x^2\right)^{7/2} (4 b B-11 A c)}{99 c^2 x^{5/2}}+\frac{2 B \left(b x+c x^2\right)^{7/2}}{11 c x^{3/2}}",1,"(2*(b + c*x)^3*Sqrt[x*(b + c*x)]*(8*b^2*B + 7*c^2*x*(11*A + 9*B*x) - 2*b*c*(11*A + 14*B*x)))/(693*c^3*Sqrt[x])","A",1
218,1,44,61,0.0307778,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{5/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(5/2),x]","\frac{2 (b+c x)^3 \sqrt{x (b+c x)} (9 A c-2 b B+7 B c x)}{63 c^2 \sqrt{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}}",1,"(2*(b + c*x)^3*Sqrt[x*(b + c*x)]*(-2*b*B + 9*A*c + 7*B*c*x))/(63*c^2*Sqrt[x])","A",1
219,1,95,131,0.2106412,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{7/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(7/2),x]","\frac{(x (b+c x))^{5/2} \left(-\frac{14 A b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b+c x}}{\sqrt{b}}\right)}{(b+c x)^{5/2}}+A \left(\frac{14 b^2}{(b+c x)^2}+\frac{14 b}{3 (b+c x)}+\frac{14}{5}\right)+\frac{2 B (b+c x)}{c}\right)}{7 x^{5/2}}","-2 A b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 A b^2 \sqrt{b x+c x^2}}{\sqrt{x}}+\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,"((x*(b + c*x))^(5/2)*((2*B*(b + c*x))/c + A*(14/5 + (14*b^2)/(b + c*x)^2 + (14*b)/(3*(b + c*x))) - (14*A*b^(5/2)*ArcTanh[Sqrt[b + c*x]/Sqrt[b]])/(b + c*x)^(5/2)))/(7*x^(5/2))","A",1
220,1,118,160,0.0765519,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{9/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(9/2),x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{b+c x} \left(A \left(-15 b^2+70 b c x+10 c^2 x^2\right)+2 B x \left(23 b^2+11 b c x+3 c^2 x^2\right)\right)-15 b^{3/2} x (5 A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b+c x}}{\sqrt{b}}\right)\right)}{15 x^{3/2} \sqrt{b+c 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{b \sqrt{b x+c x^2} (5 A c+2 b B)}{\sqrt{x}}+\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{A \left(b x+c x^2\right)^{7/2}}{b x^{9/2}}",1,"(Sqrt[x*(b + c*x)]*(Sqrt[b + c*x]*(2*B*x*(23*b^2 + 11*b*c*x + 3*c^2*x^2) + A*(-15*b^2 + 70*b*c*x + 10*c^2*x^2)) - 15*b^(3/2)*(2*b*B + 5*A*c)*x*ArcTanh[Sqrt[b + c*x]/Sqrt[b]]))/(15*x^(3/2)*Sqrt[b + c*x])","A",1
221,1,67,172,0.0317716,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{11/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(11/2),x]","\frac{(b+c x)^3 \sqrt{x (b+c x)} \left(c x^2 (3 A c+4 b B) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{c x}{b}+1\right)-7 A b^2\right)}{14 b^3 x^{5/2}}","\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{\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{A \left(b x+c x^2\right)^{7/2}}{2 b x^{11/2}}",1,"((b + c*x)^3*Sqrt[x*(b + c*x)]*(-7*A*b^2 + c*(4*b*B + 3*A*c)*x^2*Hypergeometric2F1[2, 7/2, 9/2, 1 + (c*x)/b]))/(14*b^3*x^(5/2))","C",1
222,1,68,175,0.0331307,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{13/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(13/2),x]","-\frac{(b+c x)^3 \sqrt{x (b+c x)} \left(7 A b^3+c^2 x^3 (A c+6 b B) \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{c x}{b}+1\right)\right)}{21 b^4 x^{7/2}}","\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,"-1/21*((b + c*x)^3*Sqrt[x*(b + c*x)]*(7*A*b^3 + c^2*(6*b*B + A*c)*x^3*Hypergeometric2F1[3, 7/2, 9/2, 1 + (c*x)/b]))/(b^4*x^(7/2))","C",1
223,1,129,179,0.138798,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{15/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(15/2),x]","-\frac{(b+c x) \left(A \left(48 b^3+136 b^2 c x+118 b c^2 x^2+15 c^3 x^3\right)+8 b B x \left(8 b^2+26 b c x+33 c^2 x^2\right)\right)+15 c^3 x^4 \sqrt{\frac{c x}{b}+1} (8 b B-A c) \tanh ^{-1}\left(\sqrt{\frac{c x}{b}+1}\right)}{192 b x^{7/2} \sqrt{x (b+c 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}}",1,"-1/192*((b + c*x)*(8*b*B*x*(8*b^2 + 26*b*c*x + 33*c^2*x^2) + A*(48*b^3 + 136*b^2*c*x + 118*b*c^2*x^2 + 15*c^3*x^3)) + 15*c^3*(8*b*B - A*c)*x^4*Sqrt[1 + (c*x)/b]*ArcTanh[Sqrt[1 + (c*x)/b]])/(b*x^(7/2)*Sqrt[x*(b + c*x)])","A",1
224,1,69,216,0.0358176,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{17/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(17/2),x]","-\frac{(b+c x)^3 \sqrt{x (b+c x)} \left(7 A b^5+c^4 x^5 (10 b B-3 A c) \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{c x}{b}+1\right)\right)}{35 b^6 x^{11/2}}","\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^3 \sqrt{b x+c x^2} (10 b B-3 A c)}{128 b^2 x^{3/2}}-\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,"-1/35*((b + c*x)^3*Sqrt[x*(b + c*x)]*(7*A*b^5 + c^4*(10*b*B - 3*A*c)*x^5*Hypergeometric2F1[7/2, 5, 9/2, 1 + (c*x)/b]))/(b^6*x^(11/2))","C",1
225,1,94,170,0.0704635,"\int \frac{x^{7/2} (A+B x)}{\sqrt{b x+c x^2}} \, dx","Integrate[(x^(7/2)*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{x (b+c x)} \left(-16 b^3 c (9 A+4 B x)+24 b^2 c^2 x (3 A+2 B x)-2 b c^3 x^2 (27 A+20 B x)+5 c^4 x^3 (9 A+7 B x)+128 b^4 B\right)}{315 c^5 \sqrt{x}}","\frac{32 b^3 \sqrt{b x+c x^2} (8 b B-9 A c)}{315 c^5 \sqrt{x}}-\frac{16 b^2 \sqrt{x} \sqrt{b x+c x^2} (8 b B-9 A c)}{315 c^4}+\frac{4 b x^{3/2} \sqrt{b x+c x^2} (8 b B-9 A c)}{105 c^3}-\frac{2 x^{5/2} \sqrt{b x+c x^2} (8 b B-9 A c)}{63 c^2}+\frac{2 B x^{7/2} \sqrt{b x+c x^2}}{9 c}",1,"(2*Sqrt[x*(b + c*x)]*(128*b^4*B + 24*b^2*c^2*x*(3*A + 2*B*x) - 16*b^3*c*(9*A + 4*B*x) + 5*c^4*x^3*(9*A + 7*B*x) - 2*b*c^3*x^2*(27*A + 20*B*x)))/(315*c^5*Sqrt[x])","A",1
226,1,75,133,0.0560412,"\int \frac{x^{5/2} (A+B x)}{\sqrt{b x+c x^2}} \, dx","Integrate[(x^(5/2)*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{x (b+c x)} \left(8 b^2 c (7 A+3 B x)-2 b c^2 x (14 A+9 B x)+3 c^3 x^2 (7 A+5 B x)-48 b^3 B\right)}{105 c^4 \sqrt{x}}","-\frac{16 b^2 \sqrt{b x+c x^2} (6 b B-7 A c)}{105 c^4 \sqrt{x}}+\frac{8 b \sqrt{x} \sqrt{b x+c x^2} (6 b B-7 A c)}{105 c^3}-\frac{2 x^{3/2} \sqrt{b x+c x^2} (6 b B-7 A c)}{35 c^2}+\frac{2 B x^{5/2} \sqrt{b x+c x^2}}{7 c}",1,"(2*Sqrt[x*(b + c*x)]*(-48*b^3*B + 8*b^2*c*(7*A + 3*B*x) + 3*c^3*x^2*(7*A + 5*B*x) - 2*b*c^2*x*(14*A + 9*B*x)))/(105*c^4*Sqrt[x])","A",1
227,1,55,96,0.0392026,"\int \frac{x^{3/2} (A+B x)}{\sqrt{b x+c x^2}} \, dx","Integrate[(x^(3/2)*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{x (b+c x)} \left(-2 b c (5 A+2 B x)+c^2 x (5 A+3 B x)+8 b^2 B\right)}{15 c^3 \sqrt{x}}","\frac{4 b \sqrt{b x+c x^2} (4 b B-5 A c)}{15 c^3 \sqrt{x}}-\frac{2 \sqrt{x} \sqrt{b x+c x^2} (4 b B-5 A c)}{15 c^2}+\frac{2 B x^{3/2} \sqrt{b x+c x^2}}{5 c}",1,"(2*Sqrt[x*(b + c*x)]*(8*b^2*B - 2*b*c*(5*A + 2*B*x) + c^2*x*(5*A + 3*B*x)))/(15*c^3*Sqrt[x])","A",1
228,1,36,61,0.0260922,"\int \frac{\sqrt{x} (A+B x)}{\sqrt{b x+c x^2}} \, dx","Integrate[(Sqrt[x]*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{x (b+c x)} (3 A c-2 b B+B c x)}{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*Sqrt[x*(b + c*x)]*(-2*b*B + 3*A*c + B*c*x))/(3*c^2*Sqrt[x])","A",1
229,1,71,72,0.0360511,"\int \frac{A+B x}{\sqrt{e x} \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(Sqrt[e*x]*Sqrt[b*x + c*x^2]),x]","\frac{2 x \left(\sqrt{b} B (b+c x)-A c \sqrt{b+c x} \tanh ^{-1}\left(\frac{\sqrt{b+c x}}{\sqrt{b}}\right)\right)}{\sqrt{b} c \sqrt{e x} \sqrt{x (b+c 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}}",1,"(2*x*(Sqrt[b]*B*(b + c*x) - A*c*Sqrt[b + c*x]*ArcTanh[Sqrt[b + c*x]/Sqrt[b]]))/(Sqrt[b]*c*Sqrt[e*x]*Sqrt[x*(b + c*x)])","A",1
230,1,73,66,0.034891,"\int \frac{A+B x}{x^{3/2} \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^(3/2)*Sqrt[b*x + c*x^2]),x]","\frac{-x \sqrt{b+c x} (2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b+c x}}{\sqrt{b}}\right)-A \sqrt{b} (b+c x)}{b^{3/2} \sqrt{x} \sqrt{x (b+c 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}}",1,"(-(A*Sqrt[b]*(b + c*x)) - (2*b*B - A*c)*x*Sqrt[b + c*x]*ArcTanh[Sqrt[b + c*x]/Sqrt[b]])/(b^(3/2)*Sqrt[x]*Sqrt[x*(b + c*x)])","A",1
231,1,92,105,0.0908256,"\int \frac{A+B x}{x^{5/2} \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^(5/2)*Sqrt[b*x + c*x^2]),x]","\frac{\sqrt{x (b+c x)} \left(c x^2 (4 b B-3 A c) \tanh ^{-1}\left(\sqrt{\frac{c x}{b}+1}\right)+b \sqrt{\frac{c x}{b}+1} (-2 A b+3 A c x-4 b B x)\right)}{4 b^3 x^{5/2} \sqrt{\frac{c x}{b}+1}}","\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{\sqrt{b x+c x^2} (4 b B-3 A c)}{4 b^2 x^{3/2}}-\frac{A \sqrt{b x+c x^2}}{2 b x^{5/2}}",1,"(Sqrt[x*(b + c*x)]*(b*(-2*A*b - 4*b*B*x + 3*A*c*x)*Sqrt[1 + (c*x)/b] + c*(4*b*B - 3*A*c)*x^2*ArcTanh[Sqrt[1 + (c*x)/b]]))/(4*b^3*x^(5/2)*Sqrt[1 + (c*x)/b])","A",1
232,1,61,142,0.0266494,"\int \frac{A+B x}{x^{7/2} \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^(7/2)*Sqrt[b*x + c*x^2]),x]","-\frac{\sqrt{x (b+c x)} \left(A b^3+c^2 x^3 (6 b B-5 A c) \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{c x}{b}+1\right)\right)}{3 b^4 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,"-1/3*(Sqrt[x*(b + c*x)]*(A*b^3 + c^2*(6*b*B - 5*A*c)*x^3*Hypergeometric2F1[1/2, 3, 3/2, 1 + (c*x)/b]))/(b^4*x^(7/2))","C",1
233,1,93,178,0.063682,"\int \frac{x^{9/2} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^(9/2)*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{x} \left(16 b^3 c (7 A-4 B x)+8 b^2 c^2 x (7 A+2 B x)-2 b c^3 x^2 (7 A+4 B x)+c^4 x^3 (7 A+5 B x)-128 b^4 B\right)}{35 c^5 \sqrt{x (b+c x)}}","-\frac{32 b^2 \sqrt{b x+c x^2} (8 b B-7 A c)}{35 c^5 \sqrt{x}}+\frac{16 b \sqrt{x} \sqrt{b x+c x^2} (8 b B-7 A c)}{35 c^4}-\frac{12 x^{3/2} \sqrt{b x+c x^2} (8 b B-7 A c)}{35 c^3}+\frac{2 x^{5/2} \sqrt{b x+c x^2} (8 b B-7 A c)}{7 b c^2}-\frac{2 x^{9/2} (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(2*Sqrt[x]*(-128*b^4*B + 16*b^3*c*(7*A - 4*B*x) + 8*b^2*c^2*x*(7*A + 2*B*x) - 2*b*c^3*x^2*(7*A + 4*B*x) + c^4*x^3*(7*A + 5*B*x)))/(35*c^5*Sqrt[x*(b + c*x)])","A",1
234,1,74,141,0.0478998,"\int \frac{x^{7/2} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^(7/2)*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{x} \left(-8 b^2 c (5 A-3 B x)-2 b c^2 x (10 A+3 B x)+c^3 x^2 (5 A+3 B x)+48 b^3 B\right)}{15 c^4 \sqrt{x (b+c x)}}","\frac{16 b \sqrt{b x+c x^2} (6 b B-5 A c)}{15 c^4 \sqrt{x}}-\frac{8 \sqrt{x} \sqrt{b x+c x^2} (6 b B-5 A c)}{15 c^3}+\frac{2 x^{3/2} \sqrt{b x+c x^2} (6 b B-5 A c)}{5 b c^2}-\frac{2 x^{7/2} (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(2*Sqrt[x]*(48*b^3*B - 8*b^2*c*(5*A - 3*B*x) + c^3*x^2*(5*A + 3*B*x) - 2*b*c^2*x*(10*A + 3*B*x)))/(15*c^4*Sqrt[x*(b + c*x)])","A",1
235,1,54,106,0.033477,"\int \frac{x^{5/2} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^(5/2)*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{x} \left(b (6 A c-4 B c x)+c^2 x (3 A+B x)-8 b^2 B\right)}{3 c^3 \sqrt{x (b+c x)}}","-\frac{4 \sqrt{b x+c x^2} (4 b B-3 A c)}{3 c^3 \sqrt{x}}+\frac{2 \sqrt{x} \sqrt{b x+c x^2} (4 b B-3 A c)}{3 b c^2}-\frac{2 x^{5/2} (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(2*Sqrt[x]*(-8*b^2*B + c^2*x*(3*A + B*x) + b*(6*A*c - 4*B*c*x)))/(3*c^3*Sqrt[x*(b + c*x)])","A",1
236,1,34,70,0.0203779,"\int \frac{x^{3/2} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^(3/2)*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{x} (-A c+2 b B+B c x)}{c^2 \sqrt{x (b+c 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}}",1,"(2*Sqrt[x]*(2*b*B - A*c + B*c*x))/(c^2*Sqrt[x*(b + c*x)])","A",1
237,1,69,68,0.0340493,"\int \frac{\sqrt{x} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(b*x + c*x^2)^(3/2),x]","-\frac{2 \sqrt{x} \left(\sqrt{b} (b B-A c)+A c \sqrt{b+c x} \tanh ^{-1}\left(\frac{\sqrt{b+c x}}{\sqrt{b}}\right)\right)}{b^{3/2} c \sqrt{x (b+c 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}}",1,"(-2*Sqrt[x]*(Sqrt[b]*(b*B - A*c) + A*c*Sqrt[b + c*x]*ArcTanh[Sqrt[b + c*x]/Sqrt[b]]))/(b^(3/2)*c*Sqrt[x*(b + c*x)])","A",1
238,1,52,97,0.0228292,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(b*x + c*x^2)^(3/2)),x]","\frac{x (2 b B-3 A c) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{c x}{b}+1\right)-A b}{b^2 \sqrt{x} \sqrt{x (b+c x)}}","-\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{\sqrt{x} (2 b B-3 A c)}{b^2 \sqrt{b x+c x^2}}-\frac{A}{b \sqrt{x} \sqrt{b x+c x^2}}",1,"(-(A*b) + (2*b*B - 3*A*c)*x*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (c*x)/b])/(b^2*Sqrt[x]*Sqrt[x*(b + c*x)])","C",1
239,1,60,140,0.0237394,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(3/2)*(b*x + c*x^2)^(3/2)),x]","\frac{c x^2 (5 A c-4 b B) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{c x}{b}+1\right)-A b^2}{2 b^3 x^{3/2} \sqrt{x (b+c x)}}","\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{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{A}{2 b x^{3/2} \sqrt{b x+c x^2}}",1,"(-(A*b^2) + c*(-4*b*B + 5*A*c)*x^2*Hypergeometric2F1[-1/2, 2, 1/2, 1 + (c*x)/b])/(2*b^3*x^(3/2)*Sqrt[x*(b + c*x)])","C",1
240,1,62,179,0.0226593,"\int \frac{A+B x}{x^{5/2} \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(5/2)*(b*x + c*x^2)^(3/2)),x]","\frac{c^2 x^3 (6 b B-7 A c) \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{c x}{b}+1\right)-A b^3}{3 b^4 x^{5/2} \sqrt{x (b+c x)}}","-\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^2 \sqrt{x} (6 b B-7 A c)}{8 b^4 \sqrt{b x+c x^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*b^3) + c^2*(6*b*B - 7*A*c)*x^3*Hypergeometric2F1[-1/2, 3, 1/2, 1 + (c*x)/b])/(3*b^4*x^(5/2)*Sqrt[x*(b + c*x)])","C",1
241,1,62,216,0.023539,"\int \frac{A+B x}{x^{7/2} \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(7/2)*(b*x + c*x^2)^(3/2)),x]","\frac{c^3 x^4 (9 A c-8 b B) \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};\frac{c x}{b}+1\right)-A b^4}{4 b^5 x^{7/2} \sqrt{x (b+c x)}}","\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{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{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*b^4) + c^3*(-8*b*B + 9*A*c)*x^4*Hypergeometric2F1[-1/2, 4, 1/2, 1 + (c*x)/b])/(4*b^5*x^(7/2)*Sqrt[x*(b + c*x)])","C",1
242,1,93,180,0.0675143,"\int \frac{x^{11/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^(11/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x^{3/2} \left(b^3 (192 B c x-80 A c)+24 b^2 c^2 x (2 B x-5 A)-2 b c^3 x^2 (15 A+4 B x)+c^4 x^3 (5 A+3 B x)+128 b^4 B\right)}{15 c^5 (x (b+c x))^{3/2}}","\frac{32 b^2 \sqrt{x} (8 b B-5 A c)}{15 c^5 \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{4 x^{5/2} (8 b B-5 A c)}{15 c^3 \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{2 x^{11/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(2*x^(3/2)*(128*b^4*B + 24*b^2*c^2*x*(-5*A + 2*B*x) + c^4*x^3*(5*A + 3*B*x) - 2*b*c^3*x^2*(15*A + 4*B*x) + b^3*(-80*A*c + 192*B*c*x)))/(15*c^5*(x*(b + c*x))^(3/2))","A",1
243,1,70,143,0.0469652,"\int \frac{x^{9/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^(9/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x^{3/2} \left(8 b^2 c (A-3 B x)-6 b c^2 x (B x-2 A)+c^3 x^2 (3 A+B x)-16 b^3 B\right)}{3 c^4 (x (b+c x))^{3/2}}","-\frac{16 b \sqrt{x} (2 b B-A c)}{3 c^4 \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{2 x^{5/2} (2 b B-A c)}{3 b c^2 \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*x^(3/2)*(-16*b^3*B + 8*b^2*c*(A - 3*B*x) - 6*b*c^2*x*(-2*A + B*x) + c^3*x^2*(3*A + B*x)))/(3*c^4*(x*(b + c*x))^(3/2))","A",1
244,1,53,108,0.0349174,"\int \frac{x^{7/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^(7/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x^{3/2} \left(-2 b c (A-6 B x)+3 c^2 x (B x-A)+8 b^2 B\right)}{3 c^3 (x (b+c x))^{3/2}}","\frac{4 \sqrt{x} (4 b B-A c)}{3 c^3 \sqrt{b x+c x^2}}+\frac{2 x^{3/2} (4 b B-A c)}{3 b c^2 \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*x^(3/2)*(8*b^2*B - 2*b*c*(A - 6*B*x) + 3*c^2*x*(-A + B*x)))/(3*c^3*(x*(b + c*x))^(3/2))","A",1
245,1,36,73,0.0249934,"\int \frac{x^{5/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^(5/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","-\frac{2 x^{3/2} (c (A+3 B x)+2 b B)}{3 c^2 (x (b+c x))^{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*x^(3/2)*(2*b*B + c*(A + 3*B*x)))/(3*c^2*(x*(b + c*x))^(3/2))","A",1
246,1,62,94,0.0265323,"\int \frac{x^{3/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^(3/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x^{3/2} \left(b (A c-b B)+3 A c (b+c x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{c x}{b}+1\right)\right)}{3 b^2 c (x (b+c x))^{3/2}}","-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{5/2}}+\frac{2 A \sqrt{x}}{b^2 \sqrt{b x+c x^2}}-\frac{2 x^{3/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(2*x^(3/2)*(b*(-(b*B) + A*c) + 3*A*c*(b + c*x)*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (c*x)/b]))/(3*b^2*c*(x*(b + c*x))^(3/2))","C",1
247,1,55,146,0.0263469,"\int \frac{\sqrt{x} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{\sqrt{x} \left(x (2 b B-5 A c) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{c x}{b}+1\right)-3 A b\right)}{3 b^2 (x (b+c x))^{3/2}}","-\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{\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 \sqrt{x} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(Sqrt[x]*(-3*A*b + (2*b*B - 5*A*c)*x*Hypergeometric2F1[-3/2, 1, -1/2, 1 + (c*x)/b]))/(3*b^2*(x*(b + c*x))^(3/2))","C",1
248,1,60,174,0.026502,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(b*x + c*x^2)^(5/2)),x]","\frac{c x^2 (7 A c-4 b B) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{c x}{b}+1\right)-3 A b^2}{6 b^3 \sqrt{x} (x (b+c x))^{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{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{A}{2 b \sqrt{x} \left(b x+c x^2\right)^{3/2}}",1,"(-3*A*b^2 + c*(-4*b*B + 7*A*c)*x^2*Hypergeometric2F1[-3/2, 2, -1/2, 1 + (c*x)/b])/(6*b^3*Sqrt[x]*(x*(b + c*x))^(3/2))","C",1
249,1,62,214,0.0272809,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^(3/2)*(b*x + c*x^2)^(5/2)),x]","\frac{c^2 x^3 (2 b B-3 A c) \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};\frac{c x}{b}+1\right)-A b^3}{3 b^4 x^{3/2} (x (b+c x))^{3/2}}","-\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 \sqrt{x} (2 b B-3 A c)}{8 b^5 \sqrt{b x+c x^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*b^3) + c^2*(2*b*B - 3*A*c)*x^3*Hypergeometric2F1[-3/2, 3, -1/2, 1 + (c*x)/b])/(3*b^4*x^(3/2)*(x*(b + c*x))^(3/2))","C",1
250,1,22,24,0.0140082,"\int x^{1+p} (2 b+3 c x) \left(b x+c x^2\right)^p \, dx","Integrate[x^(1 + p)*(2*b + 3*c*x)*(b*x + c*x^2)^p,x]","\frac{x^{p+1} (x (b+c x))^{p+1}}{p+1}","\frac{x^{p+1} \left(b x+c x^2\right)^{p+1}}{p+1}",1,"(x^(1 + p)*(x*(b + c*x))^(1 + p))/(1 + p)","A",1
251,1,37,37,0.0019029,"\int x^3 (A+B x) \left(a+c x^2\right) \, dx","Integrate[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",1
252,1,37,37,0.0018975,"\int x^2 (A+B x) \left(a+c x^2\right) \, dx","Integrate[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",1
253,1,37,37,0.001816,"\int x (A+B x) \left(a+c x^2\right) \, dx","Integrate[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",1
254,1,32,31,0.0014411,"\int (A+B x) \left(a+c x^2\right) \, dx","Integrate[(A + B*x)*(a + c*x^2),x]","a A x+\frac{1}{2} a B x^2+\frac{1}{3} A c x^3+\frac{1}{4} B c x^4","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*B*x^2)/2 + (A*c*x^3)/3 + (B*c*x^4)/4","A",1
255,1,28,28,0.0032115,"\int \frac{(A+B x) \left(a+c x^2\right)}{x} \, dx","Integrate[((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",1
256,1,26,26,0.0034789,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^2} \, dx","Integrate[((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",1
257,1,26,26,0.0043681,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^3} \, dx","Integrate[((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,"-1/2*(a*A)/x^2 - (a*B)/x + B*c*x + A*c*Log[x]","A",1
258,1,65,65,0.0028521,"\int x^3 (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[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",1
259,1,65,65,0.0028239,"\int x^2 (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[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",1
260,1,65,65,0.0024374,"\int x (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[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",1
261,1,60,45,0.0022165,"\int (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(a + c*x^2)^2,x]","a^2 A x+\frac{1}{2} a^2 B x^2+\frac{2}{3} a A c x^3+\frac{1}{2} a B c x^4+\frac{1}{5} A c^2 x^5+\frac{1}{6} B c^2 x^6","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 + (a^2*B*x^2)/2 + (2*a*A*c*x^3)/3 + (a*B*c*x^4)/2 + (A*c^2*x^5)/5 + (B*c^2*x^6)/6","A",1
262,1,53,53,0.006316,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x} \, dx","Integrate[((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",1
263,1,52,52,0.0066338,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^2} \, dx","Integrate[((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",1
264,1,56,56,0.0066655,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^3} \, dx","Integrate[((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,"-1/2*(a^2*A)/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",1
265,1,93,93,0.0034809,"\int x^3 (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[x^3*(A + B*x)*(a + c*x^2)^3,x]","\frac{1}{4} a^3 A x^4+\frac{1}{5} a^3 B x^5+\frac{1}{2} a^2 A c x^6+\frac{3}{7} a^2 B c x^7+\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}{4} a^3 A x^4+\frac{1}{5} a^3 B x^5+\frac{1}{2} a^2 A c x^6+\frac{3}{7} a^2 B c x^7+\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",1
266,1,93,93,0.0033216,"\int x^2 (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[x^2*(A + B*x)*(a + c*x^2)^3,x]","\frac{1}{3} a^3 A x^3+\frac{1}{4} a^3 B x^4+\frac{3}{5} a^2 A c x^5+\frac{1}{2} a^2 B c x^6+\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{1}{3} a^3 A x^3+\frac{1}{4} a^3 B x^4+\frac{3}{5} a^2 A c x^5+\frac{1}{2} a^2 B c x^6+\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",1
267,1,93,93,0.0029588,"\int x (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[x*(A + B*x)*(a + c*x^2)^3,x]","\frac{1}{2} a^3 A x^2+\frac{1}{3} a^3 B x^3+\frac{3}{4} a^2 A c x^4+\frac{3}{5} a^2 B c x^5+\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{1}{2} a^3 A x^2+\frac{1}{3} a^3 B x^3+\frac{3}{4} a^2 A c x^4+\frac{3}{5} a^2 B c x^5+\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",1
268,1,85,56,0.0025469,"\int (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(a + c*x^2)^3,x]","a^3 A x+\frac{1}{2} a^3 B x^2+a^2 A c x^3+\frac{3}{4} a^2 B c x^4+\frac{3}{5} a A c^2 x^5+\frac{1}{2} a B c^2 x^6+\frac{1}{7} A c^3 x^7+\frac{1}{8} B c^3 x^8","a^3 A x+a^2 A c x^3+\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^3*B*x^2)/2 + a^2*A*c*x^3 + (3*a^2*B*c*x^4)/4 + (3*a*A*c^2*x^5)/5 + (a*B*c^2*x^6)/2 + (A*c^3*x^7)/7 + (B*c^3*x^8)/8","A",1
269,1,81,81,0.0067783,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/x,x]","a^3 A \log (x)+a^3 B x+\frac{3}{2} a^2 A c x^2+a^2 B c x^3+\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","a^3 A \log (x)+a^3 B x+\frac{3}{2} a^2 A c x^2+a^2 B c x^3+\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",1
270,1,80,80,0.0068837,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^2} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/x^2,x]","-\frac{a^3 A}{x}+a^3 B \log (x)+3 a^2 A c x+\frac{3}{2} a^2 B c x^2+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","-\frac{a^3 A}{x}+a^3 B \log (x)+3 a^2 A c x+\frac{3}{2} a^2 B c x^2+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",1
271,1,81,81,0.0074523,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^3} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/x^3,x]","-\frac{a^3 A}{2 x^2}-\frac{a^3 B}{x}+3 a^2 A c \log (x)+3 a^2 B c 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","-\frac{a^3 A}{2 x^2}-\frac{a^3 B}{x}+3 a^2 A c \log (x)+3 a^2 B c 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,"-1/2*(a^3*A)/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",1
272,1,121,121,0.0039996,"\int x^3 (A+B x) \left(a+c x^2\right)^4 \, dx","Integrate[x^3*(A + B*x)*(a + c*x^2)^4,x]","\frac{1}{4} a^4 A x^4+\frac{1}{5} a^4 B x^5+\frac{2}{3} a^3 A c x^6+\frac{4}{7} a^3 B c x^7+\frac{3}{4} a^2 A c^2 x^8+\frac{2}{3} a^2 B c^2 x^9+\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{1}{4} a^4 A x^4+\frac{1}{5} a^4 B x^5+\frac{2}{3} a^3 A c x^6+\frac{4}{7} a^3 B c x^7+\frac{3}{4} a^2 A c^2 x^8+\frac{2}{3} a^2 B c^2 x^9+\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",1
273,1,121,121,0.0034692,"\int x^2 (A+B x) \left(a+c x^2\right)^4 \, dx","Integrate[x^2*(A + B*x)*(a + c*x^2)^4,x]","\frac{1}{3} a^4 A x^3+\frac{1}{4} a^4 B x^4+\frac{4}{5} a^3 A c x^5+\frac{2}{3} a^3 B c x^6+\frac{6}{7} a^2 A c^2 x^7+\frac{3}{4} a^2 B c^2 x^8+\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{1}{3} a^4 A x^3+\frac{1}{4} a^4 B x^4+\frac{4}{5} a^3 A c x^5+\frac{2}{3} a^3 B c x^6+\frac{6}{7} a^2 A c^2 x^7+\frac{3}{4} a^2 B c^2 x^8+\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",1
274,1,115,115,0.0033774,"\int x (A+B x) \left(a+c x^2\right)^4 \, dx","Integrate[x*(A + B*x)*(a + c*x^2)^4,x]","\frac{1}{2} a^4 A x^2+\frac{1}{3} a^4 B x^3+a^3 A c x^4+\frac{4}{5} a^3 B c x^5+a^2 A c^2 x^6+\frac{6}{7} a^2 B c^2 x^7+\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}","\frac{1}{2} a^4 A x^2+\frac{1}{3} a^4 B x^3+a^3 A c x^4+\frac{4}{5} a^3 B c x^5+a^2 A c^2 x^6+\frac{6}{7} a^2 B c^2 x^7+\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",1
275,1,110,73,0.003023,"\int (A+B x) \left(a+c x^2\right)^4 \, dx","Integrate[(A + B*x)*(a + c*x^2)^4,x]","a^4 A x+\frac{1}{2} a^4 B x^2+\frac{4}{3} a^3 A c x^3+a^3 B c x^4+\frac{6}{5} a^2 A c^2 x^5+a^2 B c^2 x^6+\frac{4}{7} a A c^3 x^7+\frac{1}{2} a B c^3 x^8+\frac{1}{9} A c^4 x^9+\frac{1}{10} B c^4 x^{10}","a^4 A x+\frac{4}{3} a^3 A c x^3+\frac{6}{5} a^2 A c^2 x^5+\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 + (a^4*B*x^2)/2 + (4*a^3*A*c*x^3)/3 + a^3*B*c*x^4 + (6*a^2*A*c^2*x^5)/5 + a^2*B*c^2*x^6 + (4*a*A*c^3*x^7)/7 + (a*B*c^3*x^8)/2 + (A*c^4*x^9)/9 + (B*c^4*x^10)/10","A",1
276,1,110,110,0.0072608,"\int \frac{(A+B x) \left(a+c x^2\right)^4}{x} \, dx","Integrate[((A + B*x)*(a + c*x^2)^4)/x,x]","a^4 A \log (x)+a^4 B x+2 a^3 A c x^2+\frac{4}{3} a^3 B c x^3+\frac{3}{2} a^2 A c^2 x^4+\frac{6}{5} a^2 B c^2 x^5+\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","a^4 A \log (x)+a^4 B x+2 a^3 A c x^2+\frac{4}{3} a^3 B c x^3+\frac{3}{2} a^2 A c^2 x^4+\frac{6}{5} a^2 B c^2 x^5+\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",1
277,1,107,107,0.0072732,"\int \frac{(A+B x) \left(a+c x^2\right)^4}{x^2} \, dx","Integrate[((A + B*x)*(a + c*x^2)^4)/x^2,x]","-\frac{a^4 A}{x}+a^4 B \log (x)+4 a^3 A c x+2 a^3 B c x^2+2 a^2 A c^2 x^3+\frac{3}{2} a^2 B c^2 x^4+\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","-\frac{a^4 A}{x}+a^4 B \log (x)+4 a^3 A c x+2 a^3 B c x^2+2 a^2 A c^2 x^3+\frac{3}{2} a^2 B c^2 x^4+\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",1
278,1,105,105,0.0074229,"\int \frac{(A+B x) \left(a+c x^2\right)^4}{x^3} \, dx","Integrate[((A + B*x)*(a + c*x^2)^4)/x^3,x]","-\frac{a^4 A}{2 x^2}-\frac{a^4 B}{x}+4 a^3 A c \log (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+\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","-\frac{a^4 A}{2 x^2}-\frac{a^4 B}{x}+4 a^3 A c \log (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+\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,"-1/2*(a^4*A)/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",1
279,1,75,87,0.0343529,"\int \frac{x^4 (d+e x)}{a+c x^2} \, dx","Integrate[(x^4*(d + e*x))/(a + c*x^2),x]","\frac{12 a^{3/2} \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)+6 a^2 e \log \left(a+c x^2\right)+c x \left(c x^2 (4 d+3 e x)-6 a (2 d+e x)\right)}{12 c^3}","\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,"(c*x*(-6*a*(2*d + e*x) + c*x^2*(4*d + 3*e*x)) + 12*a^(3/2)*Sqrt[c]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]] + 6*a^2*e*Log[a + c*x^2])/(12*c^3)","A",1
280,1,64,73,0.0385006,"\int \frac{x^3 (d+e x)}{a+c x^2} \, dx","Integrate[(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{x (c x (3 d+2 e x)-6 a e)-3 a d \log \left(a+c x^2\right)}{6 c^2}","\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^(3/2)*e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/c^(5/2) + (x*(-6*a*e + c*x*(3*d + 2*e*x)) - 3*a*d*Log[a + c*x^2])/(6*c^2)","A",1
281,1,56,61,0.0206041,"\int \frac{x^2 (d+e x)}{a+c x^2} \, dx","Integrate[(x^2*(d + e*x))/(a + c*x^2),x]","\frac{-2 \sqrt{a} \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)-a e \log \left(a+c x^2\right)+c x (2 d+e x)}{2 c^2}","-\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,"(c*x*(2*d + e*x) - 2*Sqrt[a]*Sqrt[c]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]] - a*e*Log[a + c*x^2])/(2*c^2)","A",1
282,1,49,49,0.0206212,"\int \frac{x (d+e x)}{a+c x^2} \, dx","Integrate[(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",1
283,1,42,42,0.0136233,"\int \frac{d+e x}{a+c x^2} \, dx","Integrate[(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",1
284,1,49,49,0.0203068,"\int \frac{d+e x}{x \left(a+c x^2\right)} \, dx","Integrate[(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",1
285,1,59,59,0.0326201,"\int \frac{d+e x}{x^2 \left(a+c x^2\right)} \, dx","Integrate[(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",1
286,1,73,73,0.0281111,"\int \frac{d+e x}{x^3 \left(a+c x^2\right)} \, dx","Integrate[(d + e*x)/(x^3*(a + c*x^2)),x]","-\frac{\sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a^{3/2}}+\frac{c d \log \left(a+c x^2\right)}{2 a^2}-\frac{c d \log (x)}{a^2}-\frac{d}{2 a x^2}-\frac{e}{a x}","-\frac{\sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a^{3/2}}+\frac{c d \log \left(a+c x^2\right)}{2 a^2}-\frac{c d \log (x)}{a^2}-\frac{d}{2 a x^2}-\frac{e}{a x}",1,"-1/2*d/(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",1
287,1,77,83,0.0411093,"\int \frac{d+e x}{x^4 \left(a+c x^2\right)} \, dx","Integrate[(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{-3 c e x^3 \log \left(a+c x^2\right)+2 a d+3 a e x-6 c d x^2+6 c e x^3 \log (x)}{6 a^2 x^3}","\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,"(c^(3/2)*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/a^(5/2) - (2*a*d + 3*a*e*x - 6*c*d*x^2 + 6*c*e*x^3*Log[x] - 3*c*e*x^3*Log[a + c*x^2])/(6*a^2*x^3)","A",1
288,1,43,43,0.0148903,"\int \frac{d+e x}{a-c x^2} \, dx","Integrate[(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",1
289,1,77,85,0.0580282,"\int \frac{x^4 (d+e x)}{\left(a+c x^2\right)^2} \, dx","Integrate[(x^4*(d + e*x))/(a + c*x^2)^2,x]","\frac{\frac{a (c d x-a e)}{a+c x^2}-3 \sqrt{a} \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)-2 a e \log \left(a+c x^2\right)+2 c d x+c e x^2}{2 c^3}","-\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,"(2*c*d*x + c*e*x^2 + (a*(-(a*e) + c*d*x))/(a + c*x^2) - 3*Sqrt[a]*Sqrt[c]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]] - 2*a*e*Log[a + c*x^2])/(2*c^3)","A",1
290,1,75,78,0.0501481,"\int \frac{x^3 (d+e x)}{\left(a+c x^2\right)^2} \, dx","Integrate[(x^3*(d + e*x))/(a + c*x^2)^2,x]","-\frac{3 \sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 c^{5/2}}+\frac{a d+a e x}{2 c^2 \left(a+c x^2\right)}+\frac{d \log \left(a+c x^2\right)}{2 c^2}+\frac{e x}{c^2}","-\frac{3 \sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 c^{5/2}}+\frac{d \log \left(a+c x^2\right)}{2 c^2}-\frac{x^2 (d+e x)}{2 c \left(a+c x^2\right)}+\frac{3 e x}{2 c^2}",1,"(e*x)/c^2 + (a*d + a*e*x)/(2*c^2*(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",1
291,1,62,67,0.0368719,"\int \frac{x^2 (d+e x)}{\left(a+c x^2\right)^2} \, dx","Integrate[(x^2*(d + e*x))/(a + c*x^2)^2,x]","\frac{\frac{a e-c d x}{a+c x^2}+\frac{\sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a}}+e \log \left(a+c x^2\right)}{2 c^2}","\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,"((a*e - c*d*x)/(a + c*x^2) + (Sqrt[c]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[a] + e*Log[a + c*x^2])/(2*c^2)","A",1
292,1,53,50,0.0329723,"\int \frac{x (d+e x)}{\left(a+c x^2\right)^2} \, dx","Integrate[(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",1
293,1,57,57,0.0217322,"\int \frac{d+e x}{\left(a+c x^2\right)^2} \, dx","Integrate[(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{c d x-a e}{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",1
294,1,65,73,0.0596015,"\int \frac{d+e x}{x \left(a+c x^2\right)^2} \, dx","Integrate[(d + e*x)/(x*(a + c*x^2)^2),x]","\frac{\frac{a (d+e x)}{a+c x^2}-d \log \left(a+c x^2\right)+\frac{\sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{c}}+2 d \log (x)}{2 a^2}","\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}-\frac{d \log \left(a+c x^2\right)}{2 a^2}+\frac{d \log (x)}{a^2}+\frac{d+e x}{2 a \left(a+c x^2\right)}",1,"((a*(d + e*x))/(a + c*x^2) + (Sqrt[a]*e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[c] + 2*d*Log[x] - d*Log[a + c*x^2])/(2*a^2)","A",1
295,1,81,87,0.1168805,"\int \frac{d+e x}{x^2 \left(a+c x^2\right)^2} \, dx","Integrate[(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{\frac{2 a d-a e x+3 c d x^2}{a x+c x^3}+e \log \left(a+c x^2\right)-2 e \log (x)}{2 a^2}","-\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*Sqrt[c]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(5/2)) - ((2*a*d - a*e*x + 3*c*d*x^2)/(a*x + c*x^3) - 2*e*Log[x] + e*Log[a + c*x^2])/(2*a^2)","A",1
296,1,82,96,0.1033737,"\int \frac{d+e x}{x^3 \left(a+c x^2\right)^2} \, dx","Integrate[(d + e*x)/(x^3*(a + c*x^2)^2),x]","-\frac{\frac{a c (d+e x)}{a+c x^2}-2 c d \log \left(a+c x^2\right)+3 \sqrt{a} \sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)+\frac{a d}{x^2}+\frac{2 a e}{x}+4 c d \log (x)}{2 a^3}","-\frac{3 \sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{c d \log \left(a+c x^2\right)}{a^3}-\frac{2 c d \log (x)}{a^3}-\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,"-1/2*((a*d)/x^2 + (2*a*e)/x + (a*c*(d + e*x))/(a + c*x^2) + 3*Sqrt[a]*Sqrt[c]*e*ArcTan[(Sqrt[c]*x)/Sqrt[a]] + 4*c*d*Log[x] - 2*c*d*Log[a + c*x^2])/a^3","A",1
297,1,86,95,0.0158556,"\int \frac{x^4 (d+e x)}{a^2-c^2 x^2} \, dx","Integrate[(x^4*(d + e*x))/(a^2 - c^2*x^2),x]","\frac{a^3 d \tanh ^{-1}\left(\frac{c x}{a}\right)}{c^5}-\frac{a^2 d x}{c^4}-\frac{a^2 e x^2}{2 c^4}-\frac{a^4 e \log \left(a^2-c^2 x^2\right)}{2 c^6}-\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*d*ArcTanh[(c*x)/a])/c^5 - (a^4*e*Log[a^2 - c^2*x^2])/(2*c^6)","A",1
298,1,72,81,0.0138164,"\int \frac{x^3 (d+e x)}{a^2-c^2 x^2} \, dx","Integrate[(x^3*(d + e*x))/(a^2 - c^2*x^2),x]","\frac{a^3 e \tanh ^{-1}\left(\frac{c x}{a}\right)}{c^5}-\frac{a^2 e x}{c^4}-\frac{a^2 d \log \left(a^2-c^2 x^2\right)}{2 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^3*e*ArcTanh[(c*x)/a])/c^5 - (a^2*d*Log[a^2 - c^2*x^2])/(2*c^4)","A",1
299,1,56,63,0.0113683,"\int \frac{x^2 (d+e x)}{a^2-c^2 x^2} \, dx","Integrate[(x^2*(d + e*x))/(a^2 - c^2*x^2),x]","-\frac{a^2 e \log \left(a^2-c^2 x^2\right)}{2 c^4}+\frac{a d \tanh ^{-1}\left(\frac{c x}{a}\right)}{c^3}-\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*d*ArcTanh[(c*x)/a])/c^3 - (a^2*e*Log[a^2 - c^2*x^2])/(2*c^4)","A",1
300,1,42,50,0.0091799,"\int \frac{x (d+e x)}{a^2-c^2 x^2} \, dx","Integrate[(x*(d + e*x))/(a^2 - c^2*x^2),x]","-\frac{d \log \left(a^2-c^2 x^2\right)}{2 c^2}+\frac{a e \tanh ^{-1}\left(\frac{c x}{a}\right)}{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) + (a*e*ArcTanh[(c*x)/a])/c^3 - (d*Log[a^2 - c^2*x^2])/(2*c^2)","A",1
301,1,37,46,0.0066348,"\int \frac{d+e x}{a^2-c^2 x^2} \, dx","Integrate[(d + e*x)/(a^2 - c^2*x^2),x]","\frac{d \tanh ^{-1}\left(\frac{c x}{a}\right)}{a c}-\frac{e \log \left(a^2-c^2 x^2\right)}{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,"(d*ArcTanh[(c*x)/a])/(a*c) - (e*Log[a^2 - c^2*x^2])/(2*c^2)","A",1
302,1,44,56,0.0130413,"\int \frac{d+e x}{x \left(a^2-c^2 x^2\right)} \, dx","Integrate[(d + e*x)/(x*(a^2 - c^2*x^2)),x]","-\frac{d \log \left(a^2-c^2 x^2\right)}{2 a^2}+\frac{d \log (x)}{a^2}+\frac{e \tanh ^{-1}\left(\frac{c x}{a}\right)}{a c}","-\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,"(e*ArcTanh[(c*x)/a])/(a*c) + (d*Log[x])/a^2 - (d*Log[a^2 - c^2*x^2])/(2*a^2)","A",1
303,1,51,59,0.013096,"\int \frac{d+e x}{x^2 \left(a^2-c^2 x^2\right)} \, dx","Integrate[(d + e*x)/(x^2*(a^2 - c^2*x^2)),x]","\frac{c d \tanh ^{-1}\left(\frac{c x}{a}\right)}{a^3}-\frac{e \log \left(a^2-c^2 x^2\right)}{2 a^2}-\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)) + (c*d*ArcTanh[(c*x)/a])/a^3 + (e*Log[x])/a^2 - (e*Log[a^2 - c^2*x^2])/(2*a^2)","A",1
304,1,68,75,0.0164245,"\int \frac{d+e x}{x^3 \left(a^2-c^2 x^2\right)} \, dx","Integrate[(d + e*x)/(x^3*(a^2 - c^2*x^2)),x]","\frac{c^2 d \log (x)}{a^4}+\frac{c e \tanh ^{-1}\left(\frac{c x}{a}\right)}{a^3}-\frac{d}{2 a^2 x^2}-\frac{e}{a^2 x}-\frac{c^2 d \log \left(a^2-c^2 x^2\right)}{2 a^4}","\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,"-1/2*d/(a^2*x^2) - e/(a^2*x) + (c*e*ArcTanh[(c*x)/a])/a^3 + (c^2*d*Log[x])/a^4 - (c^2*d*Log[a^2 - c^2*x^2])/(2*a^4)","A",1
305,1,84,93,0.0156335,"\int \frac{d+e x}{x^4 \left(a^2-c^2 x^2\right)} \, dx","Integrate[(d + e*x)/(x^4*(a^2 - c^2*x^2)),x]","\frac{c^3 d \tanh ^{-1}\left(\frac{c x}{a}\right)}{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 e \log \left(a^2-c^2 x^2\right)}{2 a^4}","-\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,"-1/3*d/(a^2*x^3) - e/(2*a^2*x^2) - (c^2*d)/(a^4*x) + (c^3*d*ArcTanh[(c*x)/a])/a^5 + (c^2*e*Log[x])/a^4 - (c^2*e*Log[a^2 - c^2*x^2])/(2*a^4)","A",1
306,1,84,94,0.0464054,"\int \frac{x^4 (d+e x)}{\left(a^2-c^2 x^2\right)^2} \, dx","Integrate[(x^4*(d + e*x))/(a^2 - c^2*x^2)^2,x]","\frac{2 a^2 e \log \left(a^2-c^2 x^2\right)+\frac{a^4 e+a^2 c^2 d x}{a^2-c^2 x^2}-3 a c d \tanh ^{-1}\left(\frac{c x}{a}\right)+2 c^2 d x+c^2 e x^2}{2 c^6}","\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,"(2*c^2*d*x + c^2*e*x^2 + (a^4*e + a^2*c^2*d*x)/(a^2 - c^2*x^2) - 3*a*c*d*ArcTanh[(c*x)/a] + 2*a^2*e*Log[a^2 - c^2*x^2])/(2*c^6)","A",1
307,1,64,84,0.0538472,"\int \frac{x^3 (d+e x)}{\left(a^2-c^2 x^2\right)^2} \, dx","Integrate[(x^3*(d + e*x))/(a^2 - c^2*x^2)^2,x]","\frac{\frac{a^2 c (d+e x)}{a^2-c^2 x^2}+c d \log \left(a^2-c^2 x^2\right)-3 a e \tanh ^{-1}\left(\frac{c x}{a}\right)+2 c e x}{2 c^5}","\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,"(2*c*e*x + (a^2*c*(d + e*x))/(a^2 - c^2*x^2) - 3*a*e*ArcTanh[(c*x)/a] + c*d*Log[a^2 - c^2*x^2])/(2*c^5)","A",1
308,1,64,77,0.0356852,"\int \frac{x^2 (d+e x)}{\left(a^2-c^2 x^2\right)^2} \, dx","Integrate[(x^2*(d + e*x))/(a^2 - c^2*x^2)^2,x]","\frac{\frac{a^2 e+c^2 d x}{a^2-c^2 x^2}+e \log \left(a^2-c^2 x^2\right)-\frac{c d \tanh ^{-1}\left(\frac{c x}{a}\right)}{a}}{2 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,"((a^2*e + c^2*d*x)/(a^2 - c^2*x^2) - (c*d*ArcTanh[(c*x)/a])/a + e*Log[a^2 - c^2*x^2])/(2*c^4)","A",1
309,1,42,45,0.0219161,"\int \frac{x (d+e x)}{\left(a^2-c^2 x^2\right)^2} \, dx","Integrate[(x*(d + e*x))/(a^2 - c^2*x^2)^2,x]","\frac{\frac{c (d+e x)}{a^2-c^2 x^2}-\frac{e \tanh ^{-1}\left(\frac{c x}{a}\right)}{a}}{2 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,"((c*(d + e*x))/(a^2 - c^2*x^2) - (e*ArcTanh[(c*x)/a])/a)/(2*c^3)","A",1
310,1,58,55,0.0131043,"\int \frac{d+e x}{\left(a^2-c^2 x^2\right)^2} \, dx","Integrate[(d + e*x)/(a^2 - c^2*x^2)^2,x]","\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(c^2 x^2-a^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)}",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",1
311,1,65,84,0.064145,"\int \frac{d+e x}{x \left(a^2-c^2 x^2\right)^2} \, dx","Integrate[(d + e*x)/(x*(a^2 - c^2*x^2)^2),x]","\frac{\frac{a^2 (d+e x)}{a^2-c^2 x^2}-d \log \left(a^2-c^2 x^2\right)+\frac{a e \tanh ^{-1}\left(\frac{c x}{a}\right)}{c}+2 d \log (x)}{2 a^4}","-\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)}",1,"((a^2*(d + e*x))/(a^2 - c^2*x^2) + (a*e*ArcTanh[(c*x)/a])/c + 2*d*Log[x] - d*Log[a^2 - c^2*x^2])/(2*a^4)","A",1
312,1,77,93,0.0805542,"\int \frac{d+e x}{x^2 \left(a^2-c^2 x^2\right)^2} \, dx","Integrate[(d + e*x)/(x^2*(a^2 - c^2*x^2)^2),x]","\frac{-a e \log \left(a^2-c^2 x^2\right)+\frac{a^3 e+a c^2 d x}{a^2-c^2 x^2}+3 c d \tanh ^{-1}\left(\frac{c x}{a}\right)-\frac{2 a d}{x}+2 a e \log (x)}{2 a^5}","-\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)}",1,"((-2*a*d)/x + (a^3*e + a*c^2*d*x)/(a^2 - c^2*x^2) + 3*c*d*ArcTanh[(c*x)/a] + 2*a*e*Log[x] - a*e*Log[a^2 - c^2*x^2])/(2*a^5)","A",1
313,1,91,108,0.0700344,"\int \frac{d+e x}{x^3 \left(a^2-c^2 x^2\right)^2} \, dx","Integrate[(d + e*x)/(x^3*(a^2 - c^2*x^2)^2),x]","\frac{\frac{a^2 c^2 (d+e x)}{a^2-c^2 x^2}-2 c^2 d \log \left(a^2-c^2 x^2\right)-\frac{a^2 d}{x^2}-\frac{2 a^2 e}{x}+3 a c e \tanh ^{-1}\left(\frac{c x}{a}\right)+4 c^2 d \log (x)}{2 a^6}","\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)}",1,"(-((a^2*d)/x^2) - (2*a^2*e)/x + (a^2*c^2*(d + e*x))/(a^2 - c^2*x^2) + 3*a*c*e*ArcTanh[(c*x)/a] + 4*c^2*d*Log[x] - 2*c^2*d*Log[a^2 - c^2*x^2])/(2*a^6)","A",1
314,1,113,152,0.2113609,"\int x^4 (A+B x) \sqrt{a+c x^2} \, dx","Integrate[x^4*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} \left(\frac{105 a^{5/2} A \sqrt{c} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}+128 a^3 B-a^2 c x (105 A+64 B x)+2 a c^2 x^3 (35 A+24 B x)+40 c^3 x^5 (7 A+6 B x)\right)}{1680 c^3}","\frac{a^3 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{5/2}}+\frac{a^2 A x \sqrt{a+c x^2}}{16 c^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,"(Sqrt[a + c*x^2]*(128*a^3*B + 40*c^3*x^5*(7*A + 6*B*x) + 2*a*c^2*x^3*(35*A + 24*B*x) - a^2*c*x*(105*A + 64*B*x) + (105*a^(5/2)*A*Sqrt[c]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(1680*c^3)","A",1
315,1,107,127,0.1828076,"\int x^3 (A+B x) \sqrt{a+c x^2} \, dx","Integrate[x^3*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} \left(\frac{15 a^{5/2} B \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}+\sqrt{c} \left(-a^2 (32 A+15 B x)+2 a c x^2 (8 A+5 B x)+8 c^2 x^4 (6 A+5 B x)\right)\right)}{240 c^{5/2}}","\frac{a^3 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{5/2}}+\frac{a^2 B x \sqrt{a+c x^2}}{16 c^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,"(Sqrt[a + c*x^2]*(Sqrt[c]*(8*c^2*x^4*(6*A + 5*B*x) + 2*a*c*x^2*(8*A + 5*B*x) - a^2*(32*A + 15*B*x)) + (15*a^(5/2)*B*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(240*c^(5/2))","A",1
316,1,93,104,0.1682806,"\int x^2 (A+B x) \sqrt{a+c x^2} \, dx","Integrate[x^2*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} \left(-\frac{15 a^{3/2} A \sqrt{c} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}-16 a^2 B+a c x (15 A+8 B x)+6 c^2 x^3 (5 A+4 B x)\right)}{120 c^2}","-\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,"(Sqrt[a + c*x^2]*(-16*a^2*B + 6*c^2*x^3*(5*A + 4*B*x) + a*c*x*(15*A + 8*B*x) - (15*a^(3/2)*A*Sqrt[c]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(120*c^2)","A",1
317,1,86,80,0.1401111,"\int x (A+B x) \sqrt{a+c x^2} \, dx","Integrate[x*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} \left(\sqrt{c} \left(8 a A+3 a B x+8 A c x^2+6 B c x^3\right)-\frac{3 a^{3/2} B \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}\right)}{24 c^{3/2}}","-\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,"(Sqrt[a + c*x^2]*(Sqrt[c]*(8*a*A + 3*a*B*x + 8*A*c*x^2 + 6*B*c*x^3) - (3*a^(3/2)*B*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(24*c^(3/2))","A",1
318,1,67,67,0.0439388,"\int (A+B x) \sqrt{a+c x^2} \, dx","Integrate[(A + B*x)*Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} (2 a B+c x (3 A+2 B x))+3 a A \sqrt{c} \log \left(\sqrt{c} \sqrt{a+c x^2}+c x\right)}{6 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,"(Sqrt[a + c*x^2]*(2*a*B + c*x*(3*A + 2*B*x)) + 3*a*A*Sqrt[c]*Log[c*x + Sqrt[c]*Sqrt[a + c*x^2]])/(6*c)","A",1
319,1,100,79,0.2153346,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/x,x]","\frac{1}{2} \left(\frac{a^{3/2} B \sqrt{\frac{c x^2}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{c} \sqrt{a+c x^2}}+\sqrt{a+c x^2} (2 A+B x)-2 \sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)\right)","\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] + (a^(3/2)*B*Sqrt[1 + (c*x^2)/a]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[c]*Sqrt[a + c*x^2]) - 2*Sqrt[a]*A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/2","A",1
320,1,99,75,0.1543084,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^2} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/x^2,x]","\frac{\sqrt{a+c x^2} (B x-A)}{x}+\frac{\sqrt{a} A \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a+c x^2}}-\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 + (Sqrt[a]*A*Sqrt[c]*Sqrt[1 + (c*x^2)/a]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[a + c*x^2] - Sqrt[a]*B*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]","A",1
321,1,108,80,0.085007,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^3} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/x^3,x]","-\frac{\sqrt{a+c x^2} \left(a \sqrt{\frac{c x^2}{a}+1} (A+2 B x)+A c x^2 \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)-2 \sqrt{a} B \sqrt{c} x^2 \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)\right)}{2 a x^2 \sqrt{\frac{c x^2}{a}+1}}","-\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,"-1/2*(Sqrt[a + c*x^2]*(a*(A + 2*B*x)*Sqrt[1 + (c*x^2)/a] - 2*Sqrt[a]*B*Sqrt[c]*x^2*ArcSinh[(Sqrt[c]*x)/Sqrt[a]] + A*c*x^2*ArcTanh[Sqrt[1 + (c*x^2)/a]]))/(a*x^2*Sqrt[1 + (c*x^2)/a])","A",1
322,1,85,71,0.0348337,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^4} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/x^4,x]","\frac{-\left(a+c x^2\right) \left(2 a A+3 a B x+2 A c x^2\right)-3 a B c x^3 \sqrt{\frac{c x^2}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)}{6 a x^3 \sqrt{a+c x^2}}","-\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,"(-((a + c*x^2)*(2*a*A + 3*a*B*x + 2*A*c*x^2)) - 3*a*B*c*x^3*Sqrt[1 + (c*x^2)/a]*ArcTanh[Sqrt[1 + (c*x^2)/a]])/(6*a*x^3*Sqrt[a + c*x^2])","A",1
323,1,53,99,0.0152275,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^5} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/x^5,x]","-\frac{\left(a+c x^2\right)^{3/2} \left(a^2 B+A c^2 x^3 \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{c x^2}{a}+1\right)\right)}{3 a^3 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,"-1/3*((a + c*x^2)^(3/2)*(a^2*B + A*c^2*x^3*Hypergeometric2F1[3/2, 3, 5/2, 1 + (c*x^2)/a]))/(a^3*x^3)","C",1
324,1,62,122,0.0218289,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^6} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/x^6,x]","-\frac{\left(a+c x^2\right)^{3/2} \left(a A \left(3 a-2 c x^2\right)+5 B c^2 x^5 \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{c x^2}{a}+1\right)\right)}{15 a^3 x^5}","\frac{B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{2 A c \left(a+c x^2\right)^{3/2}}{15 a^2 x^3}-\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,"-1/15*((a + c*x^2)^(3/2)*(a*A*(3*a - 2*c*x^2) + 5*B*c^2*x^5*Hypergeometric2F1[3/2, 3, 5/2, 1 + (c*x^2)/a]))/(a^3*x^5)","C",1
325,1,64,147,0.0311058,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^7} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/x^7,x]","\frac{\left(a+c x^2\right)^{3/2} \left(a^2 B \left(2 c x^2-3 a\right)+5 A c^3 x^5 \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{c x^2}{a}+1\right)\right)}{15 a^4 x^5}","-\frac{A c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 a^{5/2}}-\frac{A c^2 \sqrt{a+c x^2}}{16 a^2 x^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*x^2)^(3/2)*(a^2*B*(-3*a + 2*c*x^2) + 5*A*c^3*x^5*Hypergeometric2F1[3/2, 4, 5/2, 1 + (c*x^2)/a]))/(15*a^4*x^5)","C",1
326,1,132,175,0.2463402,"\int x^4 (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Integrate[x^4*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{\sqrt{a+c x^2} \left(\frac{945 a^{7/2} A \sqrt{c} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}+1024 a^4 B-a^3 c x (945 A+512 B x)+6 a^2 c^2 x^3 (105 A+64 B x)+40 a c^3 x^5 (189 A+160 B x)+560 c^4 x^7 (9 A+8 B x)\right)}{40320 c^3}","\frac{3 a^4 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{5/2}}+\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{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,"(Sqrt[a + c*x^2]*(1024*a^4*B + 560*c^4*x^7*(9*A + 8*B*x) + 6*a^2*c^2*x^3*(105*A + 64*B*x) + 40*a*c^3*x^5*(189*A + 160*B*x) - a^3*c*x*(945*A + 512*B*x) + (945*a^(7/2)*A*Sqrt[c]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(40320*c^3)","A",1
327,1,126,150,0.2246645,"\int x^3 (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Integrate[x^3*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{\sqrt{a+c x^2} \left(\frac{105 a^{7/2} B \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}+\sqrt{c} \left(-a^3 (256 A+105 B x)+2 a^2 c x^2 (64 A+35 B x)+8 a c^2 x^4 (128 A+105 B x)+80 c^3 x^6 (8 A+7 B x)\right)\right)}{4480 c^{5/2}}","\frac{3 a^4 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{5/2}}+\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{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,"(Sqrt[a + c*x^2]*(Sqrt[c]*(80*c^3*x^6*(8*A + 7*B*x) + 2*a^2*c*x^2*(64*A + 35*B*x) + 8*a*c^2*x^4*(128*A + 105*B*x) - a^3*(256*A + 105*B*x)) + (105*a^(7/2)*B*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(4480*c^(5/2))","A",1
328,1,113,127,0.2099161,"\int x^2 (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Integrate[x^2*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{\sqrt{a+c x^2} \left(-\frac{105 a^{5/2} A \sqrt{c} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}-96 a^3 B+3 a^2 c x (35 A+16 B x)+2 a c^2 x^3 (245 A+192 B x)+40 c^3 x^5 (7 A+6 B x)\right)}{1680 c^2}","-\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,"(Sqrt[a + c*x^2]*(-96*a^3*B + 40*c^3*x^5*(7*A + 6*B*x) + 3*a^2*c*x*(35*A + 16*B*x) + 2*a*c^2*x^3*(245*A + 192*B*x) - (105*a^(5/2)*A*Sqrt[c]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(1680*c^2)","A",1
329,1,107,103,0.1762235,"\int x (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Integrate[x*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{\sqrt{a+c x^2} \left(\sqrt{c} \left(3 a^2 (16 A+5 B x)+2 a c x^2 (48 A+35 B x)+8 c^2 x^4 (6 A+5 B x)\right)-\frac{15 a^{5/2} B \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}\right)}{240 c^{3/2}}","-\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,"(Sqrt[a + c*x^2]*(Sqrt[c]*(8*c^2*x^4*(6*A + 5*B*x) + 3*a^2*(16*A + 5*B*x) + 2*a*c*x^2*(48*A + 35*B*x)) - (15*a^(5/2)*B*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(240*c^(3/2))","A",1
330,1,88,87,0.0595168,"\int (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{\sqrt{a+c x^2} \left(8 a^2 B+a c x (25 A+16 B x)+2 c^2 x^3 (5 A+4 B x)\right)+15 a^2 A \sqrt{c} \log \left(\sqrt{c} \sqrt{a+c x^2}+c x\right)}{40 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,"(Sqrt[a + c*x^2]*(8*a^2*B + 2*c^2*x^3*(5*A + 4*B*x) + a*c*x*(25*A + 16*B*x)) + 15*a^2*A*Sqrt[c]*Log[c*x + Sqrt[c]*Sqrt[a + c*x^2]])/(40*c)","A",1
331,1,118,106,0.2494255,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/x,x]","\frac{1}{24} \left(-24 a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{9 a^{5/2} B \sqrt{\frac{c x^2}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{c} \sqrt{a+c x^2}}+\sqrt{a+c x^2} \left(32 a A+15 a B x+8 A c x^2+6 B c x^3\right)\right)","-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,"(Sqrt[a + c*x^2]*(32*a*A + 15*a*B*x + 8*A*c*x^2 + 6*B*c*x^3) + (9*a^(5/2)*B*Sqrt[1 + (c*x^2)/a]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[c]*Sqrt[a + c*x^2]) - 24*a^(3/2)*A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/24","A",1
332,1,105,108,0.1637739,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^2} \, dx","Integrate[((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{a^2 A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{c x^2}{a}\right)}{x \sqrt{a+c x^2}}+\frac{1}{3} B \sqrt{a+c x^2} \left(4 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,"(B*Sqrt[a + c*x^2]*(4*a + c*x^2))/3 - a^(3/2)*B*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]] - (a^2*A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-3/2, -1/2, 1/2, -((c*x^2)/a)])/(x*Sqrt[a + c*x^2])","C",1
333,1,90,111,0.0355307,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^3} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/x^3,x]","\frac{A c \left(a+c x^2\right)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{c x^2}{a}+1\right)}{5 a^2}-\frac{a B \sqrt{a+c x^2} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{c x^2}{a}\right)}{x \sqrt{\frac{c x^2}{a}+1}}","-\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,"-((a*B*Sqrt[a + c*x^2]*Hypergeometric2F1[-3/2, -1/2, 1/2, -((c*x^2)/a)])/(x*Sqrt[1 + (c*x^2)/a])) + (A*c*(a + c*x^2)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, 1 + (c*x^2)/a])/(5*a^2)","C",1
334,1,92,109,0.0365804,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^4} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/x^4,x]","\frac{B c \left(a+c x^2\right)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{c x^2}{a}+1\right)}{5 a^2}-\frac{a A \sqrt{a+c x^2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{c x^2}{a}\right)}{3 x^3 \sqrt{\frac{c x^2}{a}+1}}","-\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,"-1/3*(a*A*Sqrt[a + c*x^2]*Hypergeometric2F1[-3/2, -3/2, -1/2, -((c*x^2)/a)])/(x^3*Sqrt[1 + (c*x^2)/a]) + (B*c*(a + c*x^2)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, 1 + (c*x^2)/a])/(5*a^2)","C",1
335,1,114,111,0.0814483,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^5} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/x^5,x]","-\frac{\sqrt{a+c x^2} \left(8 a^2 B x \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{c x^2}{a}\right)+9 A c^2 x^4 \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)+3 a A \left(2 a+5 c x^2\right) \sqrt{\frac{c x^2}{a}+1}\right)}{24 a x^4 \sqrt{\frac{c x^2}{a}+1}}","-\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,"-1/24*(Sqrt[a + c*x^2]*(3*a*A*(2*a + 5*c*x^2)*Sqrt[1 + (c*x^2)/a] + 9*A*c^2*x^4*ArcTanh[Sqrt[1 + (c*x^2)/a]] + 8*a^2*B*x*Hypergeometric2F1[-3/2, -3/2, -1/2, -((c*x^2)/a)]))/(a*x^4*Sqrt[1 + (c*x^2)/a])","C",1
336,1,103,93,0.0811457,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^6} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/x^6,x]","\frac{-\frac{\left(a+c x^2\right) \left(2 a^2 (4 A+5 B x)+a c x^2 (16 A+25 B x)+8 A c^2 x^4\right)}{a x^5}-15 B c^2 \sqrt{\frac{c x^2}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)}{40 \sqrt{a+c 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{3 B c \sqrt{a+c x^2}}{8 x^2}-\frac{B \left(a+c x^2\right)^{3/2}}{4 x^4}",1,"(-(((a + c*x^2)*(8*A*c^2*x^4 + 2*a^2*(4*A + 5*B*x) + a*c*x^2*(16*A + 25*B*x)))/(a*x^5)) - 15*B*c^2*Sqrt[1 + (c*x^2)/a]*ArcTanh[Sqrt[1 + (c*x^2)/a]])/(40*Sqrt[a + c*x^2])","A",1
337,1,54,124,0.0198899,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^7} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/x^7,x]","\frac{\left(a+c x^2\right)^{5/2} \left(A c^3 x^5 \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{c x^2}{a}+1\right)-a^3 B\right)}{5 a^4 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 \left(a+c x^2\right)^{5/2}}{6 a x^6}+\frac{A c \left(a+c x^2\right)^{3/2}}{24 a x^4}-\frac{B \left(a+c x^2\right)^{5/2}}{5 a x^5}",1,"((a + c*x^2)^(5/2)*(-(a^3*B) + A*c^3*x^5*Hypergeometric2F1[5/2, 4, 7/2, 1 + (c*x^2)/a]))/(5*a^4*x^5)","C",1
338,1,64,147,0.0283849,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^8} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/x^8,x]","\frac{\left(a+c x^2\right)^{5/2} \left(a^2 A \left(2 c x^2-5 a\right)+7 B c^3 x^7 \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{c x^2}{a}+1\right)\right)}{35 a^4 x^7}","\frac{B c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 a^{3/2}}+\frac{2 A c \left(a+c x^2\right)^{5/2}}{35 a^2 x^5}-\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 \left(a+c x^2\right)^{5/2}}{6 a x^6}+\frac{B c \left(a+c x^2\right)^{3/2}}{24 a x^4}",1,"((a + c*x^2)^(5/2)*(a^2*A*(-5*a + 2*c*x^2) + 7*B*c^3*x^7*Hypergeometric2F1[5/2, 4, 7/2, 1 + (c*x^2)/a]))/(35*a^4*x^7)","C",1
339,1,151,198,0.2863275,"\int x^4 (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Integrate[x^4*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{\sqrt{a+c x^2} \left(\frac{10395 a^{9/2} A \sqrt{c} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}+10240 a^5 B-5 a^4 c x (2079 A+1024 B x)+30 a^3 c^2 x^3 (231 A+128 B x)+8 a^2 c^3 x^5 (21483 A+18080 B x)+112 a c^4 x^7 (2079 A+1840 B x)+8064 c^5 x^9 (11 A+10 B x)\right)}{887040 c^3}","\frac{3 a^5 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{256 c^{5/2}}+\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{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,"(Sqrt[a + c*x^2]*(10240*a^5*B + 8064*c^5*x^9*(11*A + 10*B*x) + 30*a^3*c^2*x^3*(231*A + 128*B*x) - 5*a^4*c*x*(2079*A + 1024*B*x) + 112*a*c^4*x^7*(2079*A + 1840*B*x) + 8*a^2*c^3*x^5*(21483*A + 18080*B*x) + (10395*a^(9/2)*A*Sqrt[c]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(887040*c^3)","A",1
340,1,145,173,0.2677092,"\int x^3 (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Integrate[x^3*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{\sqrt{a+c x^2} \left(\frac{945 a^{9/2} B \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}+\sqrt{c} \left(-5 a^4 (512 A+189 B x)+10 a^3 c x^2 (128 A+63 B x)+24 a^2 c^2 x^4 (800 A+651 B x)+16 a c^3 x^6 (1520 A+1323 B x)+896 c^4 x^8 (10 A+9 B x)\right)\right)}{80640 c^{5/2}}","\frac{3 a^5 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{256 c^{5/2}}+\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{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,"(Sqrt[a + c*x^2]*(Sqrt[c]*(896*c^4*x^8*(10*A + 9*B*x) + 10*a^3*c*x^2*(128*A + 63*B*x) - 5*a^4*(512*A + 189*B*x) + 24*a^2*c^2*x^4*(800*A + 651*B*x) + 16*a*c^3*x^6*(1520*A + 1323*B*x)) + (945*a^(9/2)*B*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(80640*c^(5/2))","A",1
341,1,131,150,0.2558577,"\int x^2 (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Integrate[x^2*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{\sqrt{a+c x^2} \left(-\frac{315 a^{7/2} A \sqrt{c} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{\frac{c x^2}{a}+1}}-256 a^4 B+a^3 c x (315 A+128 B x)+6 a^2 c^2 x^3 (413 A+320 B x)+8 a c^3 x^5 (357 A+304 B x)+112 c^4 x^7 (9 A+8 B x)\right)}{8064 c^2}","-\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,"(Sqrt[a + c*x^2]*(-256*a^4*B + 112*c^4*x^7*(9*A + 8*B*x) + a^3*c*x*(315*A + 128*B*x) + 8*a*c^3*x^5*(357*A + 304*B*x) + 6*a^2*c^2*x^3*(413*A + 320*B*x) - (315*a^(7/2)*A*Sqrt[c]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[1 + (c*x^2)/a]))/(8064*c^2)","A",1
342,1,112,126,0.4877577,"\int x (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Integrate[x*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{\left(a+c x^2\right)^{7/2} \left(-\frac{7 a B x \left(\frac{15 a^{7/2} \sqrt{\frac{c x^2}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{c} x}+\left(a+c x^2\right) \left(33 a^2+26 a c x^2+8 c^2 x^4\right)\right)}{\left(a+c x^2\right)^4}+384 A+336 B x\right)}{2688 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,"((a + c*x^2)^(7/2)*(384*A + 336*B*x - (7*a*B*x*((a + c*x^2)*(33*a^2 + 26*a*c*x^2 + 8*c^2*x^4) + (15*a^(7/2)*Sqrt[1 + (c*x^2)/a]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[c]*x)))/(a + c*x^2)^4))/(2688*c)","A",1
343,1,108,107,0.0797854,"\int (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{105 a^3 A \sqrt{c} \log \left(\sqrt{c} \sqrt{a+c x^2}+c x\right)+\sqrt{a+c x^2} \left(48 a^3 B+3 a^2 c x (77 A+48 B x)+2 a c^2 x^3 (91 A+72 B x)+8 c^3 x^5 (7 A+6 B x)\right)}{336 c}","\frac{5 a^3 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{5}{16} a^2 A x \sqrt{a+c x^2}+\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,"(Sqrt[a + c*x^2]*(48*a^3*B + 8*c^3*x^5*(7*A + 6*B*x) + 3*a^2*c*x*(77*A + 48*B*x) + 2*a*c^2*x^3*(91*A + 72*B*x)) + 105*a^3*A*Sqrt[c]*Log[c*x + Sqrt[c]*Sqrt[a + c*x^2]])/(336*c)","A",1
344,1,139,132,0.3266135,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x,x]","-a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{5 a^{7/2} B \sqrt{\frac{c x^2}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 \sqrt{c} \sqrt{a+c x^2}}+\frac{1}{240} \sqrt{a+c x^2} \left(a^2 (368 A+165 B x)+2 a c x^2 (88 A+65 B x)+8 c^2 x^4 (6 A+5 B x)\right)","-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}{16} a^2 \sqrt{a+c x^2} (16 A+5 B x)+\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,"(Sqrt[a + c*x^2]*(8*c^2*x^4*(6*A + 5*B*x) + 2*a*c*x^2*(88*A + 65*B*x) + a^2*(368*A + 165*B*x)))/240 + (5*a^(7/2)*B*Sqrt[1 + (c*x^2)/a]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/(16*Sqrt[c]*Sqrt[a + c*x^2]) - a^(5/2)*A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]","A",1
345,1,117,136,0.2134156,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^2} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x^2,x]","-a^{5/2} B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)-\frac{a^3 A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{c x^2}{a}\right)}{x \sqrt{a+c x^2}}+\frac{1}{15} B \sqrt{a+c x^2} \left(23 a^2+11 a c x^2+3 c^2 x^4\right)","a^{5/2} (-B) \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{15}{8} a^2 A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\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,"(B*Sqrt[a + c*x^2]*(23*a^2 + 11*a*c*x^2 + 3*c^2*x^4))/15 - a^(5/2)*B*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]] - (a^3*A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-5/2, -1/2, 1/2, -((c*x^2)/a)])/(x*Sqrt[a + c*x^2])","C",1
346,1,92,141,0.0275634,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^3} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x^3,x]","\frac{A c \left(a+c x^2\right)^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{c x^2}{a}+1\right)}{7 a^2}-\frac{a^2 B \sqrt{a+c x^2} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{c x^2}{a}\right)}{x \sqrt{\frac{c x^2}{a}+1}}","-\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,"-((a^2*B*Sqrt[a + c*x^2]*Hypergeometric2F1[-5/2, -1/2, 1/2, -((c*x^2)/a)])/(x*Sqrt[1 + (c*x^2)/a])) + (A*c*(a + c*x^2)^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, 1 + (c*x^2)/a])/(7*a^2)","C",1
347,1,94,137,0.0267051,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^4} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x^4,x]","\frac{B c \left(a+c x^2\right)^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{c x^2}{a}+1\right)}{7 a^2}-\frac{a^2 A \sqrt{a+c x^2} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{c x^2}{a}\right)}{3 x^3 \sqrt{\frac{c x^2}{a}+1}}","-\frac{5}{2} a^{3/2} B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)-\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{\left(a+c x^2\right)^{5/2} (A-B x)}{3 x^3}+\frac{5}{2} a A c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)",1,"-1/3*(a^2*A*Sqrt[a + c*x^2]*Hypergeometric2F1[-5/2, -3/2, -1/2, -((c*x^2)/a)])/(x^3*Sqrt[1 + (c*x^2)/a]) + (B*c*(a + c*x^2)^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, 1 + (c*x^2)/a])/(7*a^2)","C",1
348,1,96,143,0.0293514,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^5} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x^5,x]","-\frac{A c^2 \left(a+c x^2\right)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{c x^2}{a}+1\right)}{7 a^3}-\frac{a^2 B \sqrt{a+c x^2} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{c x^2}{a}\right)}{3 x^3 \sqrt{\frac{c x^2}{a}+1}}","-\frac{5 c \sqrt{a+c x^2} (4 a B-3 A c x)}{8 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{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,"-1/3*(a^2*B*Sqrt[a + c*x^2]*Hypergeometric2F1[-5/2, -3/2, -1/2, -((c*x^2)/a)])/(x^3*Sqrt[1 + (c*x^2)/a]) - (A*c^2*(a + c*x^2)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, 1 + (c*x^2)/a])/(7*a^3)","C",1
349,1,96,140,0.0266827,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^6} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x^6,x]","-\frac{B c^2 \left(a+c x^2\right)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{c x^2}{a}+1\right)}{7 a^3}-\frac{a^2 A \sqrt{a+c x^2} \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};-\frac{c x^2}{a}\right)}{5 x^5 \sqrt{\frac{c x^2}{a}+1}}","-\frac{c^2 \sqrt{a+c x^2} (8 A-15 B x)}{8 x}-\frac{\left(a+c x^2\right)^{5/2} (4 A+5 B x)}{20 x^5}-\frac{c \left(a+c x^2\right)^{3/2} (8 A+15 B x)}{24 x^3}+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,"-1/5*(a^2*A*Sqrt[a + c*x^2]*Hypergeometric2F1[-5/2, -5/2, -3/2, -((c*x^2)/a)])/(x^5*Sqrt[1 + (c*x^2)/a]) - (B*c^2*(a + c*x^2)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, 1 + (c*x^2)/a])/(7*a^3)","C",1
350,1,125,140,0.1176693,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^7} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x^7,x]","-\frac{\sqrt{a+c x^2} \left(48 a^3 B x \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};-\frac{c x^2}{a}\right)+5 a A \sqrt{\frac{c x^2}{a}+1} \left(8 a^2+26 a c x^2+33 c^2 x^4\right)+75 A c^3 x^6 \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)\right)}{240 a x^6 \sqrt{\frac{c x^2}{a}+1}}","-\frac{c^2 \sqrt{a+c x^2} (5 A+16 B x)}{16 x^2}-\frac{\left(a+c x^2\right)^{5/2} (5 A+6 B x)}{30 x^6}-\frac{c \left(a+c x^2\right)^{3/2} (5 A+8 B x)}{24 x^4}-\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,"-1/240*(Sqrt[a + c*x^2]*(5*a*A*Sqrt[1 + (c*x^2)/a]*(8*a^2 + 26*a*c*x^2 + 33*c^2*x^4) + 75*A*c^3*x^6*ArcTanh[Sqrt[1 + (c*x^2)/a]] + 48*a^3*B*x*Hypergeometric2F1[-5/2, -5/2, -3/2, -((c*x^2)/a)]))/(a*x^6*Sqrt[1 + (c*x^2)/a])","C",1
351,1,123,115,0.0918041,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^8} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x^8,x]","\frac{-\frac{\left(a+c x^2\right) \left(8 a^3 (6 A+7 B x)+2 a^2 c x^2 (72 A+91 B x)+3 a c^2 x^4 (48 A+77 B x)+48 A c^3 x^6\right)}{a x^7}-105 B c^3 \sqrt{\frac{c x^2}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)}{336 \sqrt{a+c x^2}}","-\frac{A \left(a+c x^2\right)^{7/2}}{7 a x^7}-\frac{5 B c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{5 B c^2 \sqrt{a+c x^2}}{16 x^2}-\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,"(-(((a + c*x^2)*(48*A*c^3*x^6 + 8*a^3*(6*A + 7*B*x) + 3*a*c^2*x^4*(48*A + 77*B*x) + 2*a^2*c*x^2*(72*A + 91*B*x)))/(a*x^7)) - 105*B*c^3*Sqrt[1 + (c*x^2)/a]*ArcTanh[Sqrt[1 + (c*x^2)/a]])/(336*Sqrt[a + c*x^2])","A",1
352,1,53,149,0.0177516,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^9} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x^9,x]","-\frac{\left(a+c x^2\right)^{7/2} \left(a^4 B+A c^4 x^7 \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{c x^2}{a}+1\right)\right)}{7 a^5 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 \left(a+c x^2\right)^{7/2}}{8 a x^8}+\frac{A c \left(a+c x^2\right)^{5/2}}{48 a x^6}-\frac{B \left(a+c x^2\right)^{7/2}}{7 a x^7}",1,"-1/7*((a + c*x^2)^(7/2)*(a^4*B + A*c^4*x^7*Hypergeometric2F1[7/2, 5, 9/2, 1 + (c*x^2)/a]))/(a^5*x^7)","C",1
353,1,64,172,0.023948,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^{10}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/x^10,x]","-\frac{\left(a+c x^2\right)^{7/2} \left(a^3 A \left(7 a-2 c x^2\right)+9 B c^4 x^9 \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{c x^2}{a}+1\right)\right)}{63 a^5 x^9}","\frac{5 B c^4 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{128 a^{3/2}}+\frac{2 A c \left(a+c x^2\right)^{7/2}}{63 a^2 x^7}-\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 \left(a+c x^2\right)^{7/2}}{8 a x^8}+\frac{B c \left(a+c x^2\right)^{5/2}}{48 a x^6}",1,"-1/63*((a + c*x^2)^(7/2)*(a^3*A*(7*a - 2*c*x^2) + 9*B*c^4*x^9*Hypergeometric2F1[7/2, 5, 9/2, 1 + (c*x^2)/a]))/(a^5*x^9)","C",1
354,1,86,129,0.0583984,"\int \frac{x^4 (A+B x)}{\sqrt{a+c x^2}} \, dx","Integrate[(x^4*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} \left(64 a^2 B-a c x (45 A+32 B x)+6 c^2 x^3 (5 A+4 B x)\right)+45 a^2 A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{120 c^3}","\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,"(Sqrt[a + c*x^2]*(64*a^2*B + 6*c^2*x^3*(5*A + 4*B*x) - a*c*x*(45*A + 32*B*x)) + 45*a^2*A*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(120*c^3)","A",1
355,1,76,104,0.0411228,"\int \frac{x^3 (A+B x)}{\sqrt{a+c x^2}} \, dx","Integrate[(x^3*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{9 a^2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)+\sqrt{c} \sqrt{a+c x^2} \left(-16 a A-9 a B x+8 A c x^2+6 B c x^3\right)}{24 c^{5/2}}","\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,"(Sqrt[c]*Sqrt[a + c*x^2]*(-16*a*A - 9*a*B*x + 8*A*c*x^2 + 6*B*c*x^3) + 9*a^2*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(24*c^(5/2))","A",1
356,1,64,81,0.035749,"\int \frac{x^2 (A+B x)}{\sqrt{a+c x^2}} \, dx","Integrate[(x^2*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} (c x (3 A+2 B x)-4 a B)-3 a A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{6 c^2}","-\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,"(Sqrt[a + c*x^2]*(-4*a*B + c*x*(3*A + 2*B*x)) - 3*a*A*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(6*c^2)","A",1
357,1,57,56,0.0315317,"\int \frac{x (A+B x)}{\sqrt{a+c x^2}} \, dx","Integrate[(x*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{\sqrt{c} \sqrt{a+c x^2} (2 A+B x)-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,"(Sqrt[c]*(2*A + B*x)*Sqrt[a + c*x^2] - a*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2))","A",1
358,1,46,43,0.0311322,"\int \frac{A+B x}{\sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/Sqrt[a + c*x^2],x]","\frac{A \log \left(\sqrt{c} \sqrt{a+c x^2}+c x\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*Log[c*x + Sqrt[c]*Sqrt[a + c*x^2]])/Sqrt[c]","A",1
359,1,53,53,0.0148035,"\int \frac{A+B x}{x \sqrt{a+c x^2}} \, dx","Integrate[(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",1
360,1,47,47,0.0150198,"\int \frac{A+B x}{x^2 \sqrt{a+c x^2}} \, dx","Integrate[(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",1
361,1,63,72,0.1014143,"\int \frac{A+B x}{x^3 \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/(x^3*Sqrt[a + c*x^2]),x]","\frac{\sqrt{a+c x^2} \left(\frac{A c \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)}{\sqrt{\frac{c x^2}{a}+1}}-\frac{a (A+2 B x)}{x^2}\right)}{2 a^2}","\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,"(Sqrt[a + c*x^2]*(-((a*(A + 2*B*x))/x^2) + (A*c*ArcTanh[Sqrt[1 + (c*x^2)/a]])/Sqrt[1 + (c*x^2)/a]))/(2*a^2)","A",1
362,1,73,97,0.1508142,"\int \frac{A+B x}{x^4 \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/(x^4*Sqrt[a + c*x^2]),x]","\frac{\sqrt{a+c x^2} \left(\frac{-2 a A-3 a B x+4 A c x^2}{x^3}+\frac{3 B c \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)}{\sqrt{\frac{c x^2}{a}+1}}\right)}{6 a^2}","\frac{B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}+\frac{2 A c \sqrt{a+c x^2}}{3 a^2 x}-\frac{A \sqrt{a+c x^2}}{3 a x^3}-\frac{B \sqrt{a+c x^2}}{2 a x^2}",1,"(Sqrt[a + c*x^2]*((-2*a*A - 3*a*B*x + 4*A*c*x^2)/x^3 + (3*B*c*ArcTanh[Sqrt[1 + (c*x^2)/a]])/Sqrt[1 + (c*x^2)/a]))/(6*a^2)","A",1
363,1,60,122,0.0211917,"\int \frac{A+B x}{x^5 \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/(x^5*Sqrt[a + c*x^2]),x]","-\frac{\sqrt{a+c x^2} \left(3 A c^2 x^3 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{c x^2}{a}+1\right)+a B \left(a-2 c x^2\right)\right)}{3 a^3 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,"-1/3*(Sqrt[a + c*x^2]*(a*B*(a - 2*c*x^2) + 3*A*c^2*x^3*Hypergeometric2F1[1/2, 3, 3/2, 1 + (c*x^2)/a]))/(a^3*x^3)","C",1
364,1,72,147,0.0200784,"\int \frac{A+B x}{x^6 \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/(x^6*Sqrt[a + c*x^2]),x]","-\frac{\sqrt{a+c x^2} \left(A \left(3 a^2-4 a c x^2+8 c^2 x^4\right)+15 B c^2 x^5 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{c x^2}{a}+1\right)\right)}{15 a^3 x^5}","-\frac{3 B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{5/2}}-\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 \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,"-1/15*(Sqrt[a + c*x^2]*(A*(3*a^2 - 4*a*c*x^2 + 8*c^2*x^4) + 15*B*c^2*x^5*Hypergeometric2F1[1/2, 3, 3/2, 1 + (c*x^2)/a]))/(a^3*x^5)","C",1
365,1,91,105,0.0472575,"\int \frac{x^4 (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[(x^4*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{-16 a^2 B+a c x (9 A-8 B x)-9 a A \sqrt{c} \sqrt{a+c x^2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)+c^2 x^3 (3 A+2 B x)}{6 c^3 \sqrt{a+c x^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,"(-16*a^2*B + a*c*x*(9*A - 8*B*x) + c^2*x^3*(3*A + 2*B*x) - 9*a*A*Sqrt[c]*Sqrt[a + c*x^2]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(6*c^3*Sqrt[a + c*x^2])","A",1
366,1,72,81,0.0479042,"\int \frac{x^3 (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[(x^3*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{a (4 A+3 B x)+c x^2 (2 A+B x)}{2 c^2 \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,"(c*x^2*(2*A + B*x) + a*(4*A + 3*B*x))/(2*c^2*Sqrt[a + c*x^2]) - (3*a*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(5/2))","A",1
367,1,67,66,0.0341543,"\int \frac{x^2 (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[(x^2*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{A \sqrt{c} \sqrt{a+c x^2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)+2 a B+c x (B x-A)}{c^2 \sqrt{a+c x^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,"(2*a*B + c*x*(-A + B*x) + A*Sqrt[c]*Sqrt[a + c*x^2]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(c^2*Sqrt[a + c*x^2])","A",1
368,1,64,48,0.0523913,"\int \frac{x (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[(x*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{\sqrt{a} B \sqrt{\frac{c x^2}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)-\sqrt{c} (A+B x)}{c^{3/2} \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,"(-(Sqrt[c]*(A + B*x)) + Sqrt[a]*B*Sqrt[1 + (c*x^2)/a]*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/(c^(3/2)*Sqrt[a + c*x^2])","A",1
369,1,27,28,0.0141014,"\int \frac{A+B x}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(a + c*x^2)^(3/2),x]","\frac{A c x-a B}{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
370,1,47,47,0.0281354,"\int \frac{A+B x}{x \left(a+c x^2\right)^{3/2}} \, dx","Integrate[(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",1
371,1,72,70,0.0374659,"\int \frac{A+B x}{x^2 \left(a+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^2*(a + c*x^2)^(3/2)),x]","-\frac{a (A-B x)+\sqrt{a} B x \sqrt{a+c x^2} \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+2 A c x^2}{a^2 x \sqrt{a+c x^2}}","-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2 A \sqrt{a+c x^2}}{a^2 x}+\frac{A+B x}{a x \sqrt{a+c x^2}}",1,"-((2*A*c*x^2 + a*(A - B*x) + Sqrt[a]*B*x*Sqrt[a + c*x^2]*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(a^2*x*Sqrt[a + c*x^2]))","A",1
372,1,75,95,0.1547395,"\int \frac{A+B x}{x^3 \left(a+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^3*(a + c*x^2)^(3/2)),x]","\frac{-\frac{a (A+2 B x)}{x^2}+3 A c \sqrt{\frac{c x^2}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)-c (3 A+4 B x)}{2 a^2 \sqrt{a+c x^2}}","\frac{3 A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3 A \sqrt{a+c x^2}}{2 a^2 x^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*(A + 2*B*x))/x^2) - c*(3*A + 4*B*x) + 3*A*c*Sqrt[1 + (c*x^2)/a]*ArcTanh[Sqrt[1 + (c*x^2)/a]])/(2*a^2*Sqrt[a + c*x^2])","A",1
373,1,90,120,0.1350373,"\int \frac{A+B x}{x^4 \left(a+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^4*(a + c*x^2)^(3/2)),x]","\frac{-\frac{a^2 (2 A+3 B x)}{x^3}+a \left(\frac{8 A c}{x}-9 B c\right)+9 a B c \sqrt{\frac{c x^2}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)+16 A c^2 x}{6 a^3 \sqrt{a+c x^2}}","\frac{3 B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}+\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{A+B x}{a x^3 \sqrt{a+c x^2}}",1,"(a*(-9*B*c + (8*A*c)/x) + 16*A*c^2*x - (a^2*(2*A + 3*B*x))/x^3 + 9*a*B*c*Sqrt[1 + (c*x^2)/a]*ArcTanh[Sqrt[1 + (c*x^2)/a]])/(6*a^3*Sqrt[a + c*x^2])","A",1
374,1,89,99,0.0643432,"\int \frac{x^4 (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[(x^4*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{8 a^2 B-3 a c x (A-4 B x)+3 A \sqrt{c} \left(a+c x^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)+c^2 x^3 (3 B x-4 A)}{3 c^3 \left(a+c x^2\right)^{3/2}}","-\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,"(8*a^2*B - 3*a*c*x*(A - 4*B*x) + c^2*x^3*(-4*A + 3*B*x) + 3*A*Sqrt[c]*(a + c*x^2)^(3/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(3*c^3*(a + c*x^2)^(3/2))","A",1
375,1,69,79,0.0692857,"\int \frac{x^3 (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[(x^3*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{5/2}}-\frac{a (2 A+3 B x)+c x^2 (3 A+4 B x)}{3 c^2 \left(a+c x^2\right)^{3/2}}","-\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,"-1/3*(a*(2*A + 3*B*x) + c*x^2*(3*A + 4*B*x))/(c^2*(a + c*x^2)^(3/2)) + (B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(5/2)","A",1
376,1,44,53,0.0169097,"\int \frac{x^2 (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[(x^2*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{-2 a^2 B-3 a B c x^2+A c^2 x^3}{3 a c^2 \left(a+c x^2\right)^{3/2}}","-\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,"(-2*a^2*B - 3*a*B*c*x^2 + A*c^2*x^3)/(3*a*c^2*(a + c*x^2)^(3/2))","A",1
377,1,32,50,0.0172959,"\int \frac{x (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[(x*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{B c x^3-a A}{3 a c \left(a+c x^2\right)^{3/2}}","\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}}",1,"(-(a*A) + B*c*x^3)/(3*a*c*(a + c*x^2)^(3/2))","A",1
378,1,43,51,0.0191291,"\int \frac{A+B x}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(a + c*x^2)^(5/2),x]","\frac{-a^2 B+3 a A c x+2 A c^2 x^3}{3 a^2 c \left(a+c x^2\right)^{3/2}}","\frac{2 A x}{3 a^2 \sqrt{a+c x^2}}+\frac{A c x-a B}{3 a c \left(a+c x^2\right)^{3/2}}",1,"(-(a^2*B) + 3*a*A*c*x + 2*A*c^2*x^3)/(3*a^2*c*(a + c*x^2)^(3/2))","A",1
379,1,69,76,0.0548199,"\int \frac{A+B x}{x \left(a+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x*(a + c*x^2)^(5/2)),x]","\frac{a (4 A+3 B x)+c x^2 (3 A+2 B x)}{3 a^2 \left(a+c x^2\right)^{3/2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{5/2}}","-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{3 A+2 B x}{3 a^2 \sqrt{a+c x^2}}+\frac{A+B x}{3 a \left(a+c x^2\right)^{3/2}}",1,"(c*x^2*(3*A + 2*B*x) + a*(4*A + 3*B*x))/(3*a^2*(a + c*x^2)^(3/2)) - (A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/a^(5/2)","A",1
380,1,95,104,0.0537296,"\int \frac{A+B x}{x^2 \left(a+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^2*(a + c*x^2)^(5/2)),x]","\frac{a^2 (4 B x-3 A)+3 a c x^2 (B x-4 A)-3 \sqrt{a} B x \left(a+c x^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)-8 A c^2 x^4}{3 a^3 x \left(a+c x^2\right)^{3/2}}","-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{8 A \sqrt{a+c x^2}}{3 a^3 x}+\frac{4 A+3 B x}{3 a^2 x \sqrt{a+c x^2}}+\frac{A+B x}{3 a x \left(a+c x^2\right)^{3/2}}",1,"(-8*A*c^2*x^4 + 3*a*c*x^2*(-4*A + B*x) + a^2*(-3*A + 4*B*x) - 3*Sqrt[a]*B*x*(a + c*x^2)^(3/2)*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(3*a^3*x*(a + c*x^2)^(3/2))","A",1
381,1,106,129,0.1443675,"\int \frac{A+B x}{x^3 \left(a+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^3*(a + c*x^2)^(5/2)),x]","\frac{-\frac{3 a^3 (A+2 B x)}{x^2}-4 a^2 c (5 A+6 B x)-a c^2 x^2 (15 A+16 B x)+\frac{15 A c \left(a+c x^2\right)^2 \tanh ^{-1}\left(\sqrt{\frac{c x^2}{a}+1}\right)}{\sqrt{\frac{c x^2}{a}+1}}}{6 a^4 \left(a+c x^2\right)^{3/2}}","\frac{5 A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{5 A \sqrt{a+c x^2}}{2 a^3 x^2}-\frac{8 B \sqrt{a+c x^2}}{3 a^3 x}+\frac{5 A+4 B x}{3 a^2 x^2 \sqrt{a+c x^2}}+\frac{A+B x}{3 a x^2 \left(a+c x^2\right)^{3/2}}",1,"((-3*a^3*(A + 2*B*x))/x^2 - 4*a^2*c*(5*A + 6*B*x) - a*c^2*x^2*(15*A + 16*B*x) + (15*A*c*(a + c*x^2)^2*ArcTanh[Sqrt[1 + (c*x^2)/a]])/Sqrt[1 + (c*x^2)/a])/(6*a^4*(a + c*x^2)^(3/2))","A",1
382,1,55,71,0.026716,"\int \frac{d+e x}{\left(a+c x^2\right)^{7/2}} \, dx","Integrate[(d + e*x)/(a + c*x^2)^(7/2),x]","\frac{-3 a^3 e+15 a^2 c d x+20 a c^2 d x^3+8 c^3 d x^5}{15 a^3 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{c d x-a e}{5 a c \left(a+c x^2\right)^{5/2}}",1,"(-3*a^3*e + 15*a^2*c*d*x + 20*a*c^2*d*x^3 + 8*c^3*d*x^5)/(15*a^3*c*(a + c*x^2)^(5/2))","A",1
383,1,67,91,0.0321027,"\int \frac{d+e x}{\left(a+c x^2\right)^{9/2}} \, dx","Integrate[(d + e*x)/(a + c*x^2)^(9/2),x]","\frac{-5 a^4 e+35 a^3 c d x+70 a^2 c^2 d x^3+56 a c^3 d x^5+16 c^4 d x^7}{35 a^4 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{c d x-a e}{7 a c \left(a+c x^2\right)^{7/2}}",1,"(-5*a^4*e + 35*a^3*c*d*x + 70*a^2*c^2*d*x^3 + 56*a*c^3*d*x^5 + 16*c^4*d*x^7)/(35*a^4*c*(a + c*x^2)^(7/2))","A",1
384,1,35,45,0.0128444,"\int x^{7/2} (A+B x) \left(a+c x^2\right) \, dx","Integrate[x^(7/2)*(A + B*x)*(a + c*x^2),x]","\frac{2 x^{9/2} \left(65 a (11 A+9 B x)+33 c x^2 (15 A+13 B x)\right)}{6435}","\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*x^(9/2)*(65*a*(11*A + 9*B*x) + 33*c*x^2*(15*A + 13*B*x)))/6435","A",1
385,1,35,45,0.0128098,"\int x^{5/2} (A+B x) \left(a+c x^2\right) \, dx","Integrate[x^(5/2)*(A + B*x)*(a + c*x^2),x]","\frac{2 x^{7/2} \left(143 a (9 A+7 B x)+63 c x^2 (13 A+11 B x)\right)}{9009}","\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*x^(7/2)*(143*a*(9*A + 7*B*x) + 63*c*x^2*(13*A + 11*B*x)))/9009","A",1
386,1,37,45,0.0162973,"\int x^{3/2} (A+B x) \left(a+c x^2\right) \, dx","Integrate[x^(3/2)*(A + B*x)*(a + c*x^2),x]","\frac{2}{35} a x^{5/2} (7 A+5 B x)+\frac{2}{99} c x^{9/2} (11 A+9 B 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}",1,"(2*a*x^(5/2)*(7*A + 5*B*x))/35 + (2*c*x^(9/2)*(11*A + 9*B*x))/99","A",1
387,1,35,45,0.011904,"\int \sqrt{x} (A+B x) \left(a+c x^2\right) \, dx","Integrate[Sqrt[x]*(A + B*x)*(a + c*x^2),x]","\frac{2}{315} x^{3/2} \left(21 a (5 A+3 B x)+5 c x^2 (9 A+7 B x)\right)","\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*x^(3/2)*(21*a*(5*A + 3*B*x) + 5*c*x^2*(9*A + 7*B*x)))/315","A",1
388,1,34,43,0.0123952,"\int \frac{(A+B x) \left(a+c x^2\right)}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a + c*x^2))/Sqrt[x],x]","\frac{2}{105} \sqrt{x} \left(35 a (3 A+B x)+3 c x^2 (7 A+5 B x)\right)","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*Sqrt[x]*(35*a*(3*A + B*x) + 3*c*x^2*(7*A + 5*B*x)))/105","A",1
389,1,32,41,0.013537,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2))/x^(3/2),x]","\frac{2 \left(c x^2 (5 A+3 B x)-15 a (A-B x)\right)}{15 \sqrt{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}",1,"(2*(-15*a*(A - B*x) + c*x^2*(5*A + 3*B*x)))/(15*Sqrt[x])","A",1
390,1,32,41,0.0114429,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2))/x^(5/2),x]","\frac{2 c x^2 (3 A+B x)-2 a (A+3 B x)}{3 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*c*x^2*(3*A + B*x) - 2*a*(A + 3*B*x))/(3*x^(3/2))","A",1
391,1,32,41,0.0137564,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2))/x^(7/2),x]","-\frac{2 \left(a (3 A+5 B x)+15 c x^2 (A-B x)\right)}{15 x^{5/2}}","-\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*(15*c*x^2*(A - B*x) + a*(3*A + 5*B*x)))/(15*x^(5/2))","A",1
392,1,33,43,0.0141665,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2))/x^(9/2),x]","\frac{-6 a (5 A+7 B x)-70 c x^2 (A+3 B x)}{105 x^{7/2}}","-\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,"(-70*c*x^2*(A + 3*B*x) - 6*a*(5*A + 7*B*x))/(105*x^(7/2))","A",1
393,1,60,77,0.0237767,"\int x^{7/2} (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[x^(7/2)*(A + B*x)*(a + c*x^2)^2,x]","\frac{2}{99} a^2 x^{9/2} (11 A+9 B x)+\frac{4}{195} a c x^{13/2} (15 A+13 B x)+\frac{2}{323} c^2 x^{17/2} (19 A+17 B 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}",1,"(2*a^2*x^(9/2)*(11*A + 9*B*x))/99 + (4*a*c*x^(13/2)*(15*A + 13*B*x))/195 + (2*c^2*x^(17/2)*(19*A + 17*B*x))/323","A",1
394,1,60,77,0.0233987,"\int x^{5/2} (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[x^(5/2)*(A + B*x)*(a + c*x^2)^2,x]","\frac{2}{63} a^2 x^{7/2} (9 A+7 B x)+\frac{4}{143} a c x^{11/2} (13 A+11 B x)+\frac{2}{255} c^2 x^{15/2} (17 A+15 B 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}",1,"(2*a^2*x^(7/2)*(9*A + 7*B*x))/63 + (4*a*c*x^(11/2)*(13*A + 11*B*x))/143 + (2*c^2*x^(15/2)*(17*A + 15*B*x))/255","A",1
395,1,54,77,0.0198347,"\int x^{3/2} (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[x^(3/2)*(A + B*x)*(a + c*x^2)^2,x]","\frac{2 x^{5/2} \left(1287 a^2 (7 A+5 B x)+910 a c x^2 (11 A+9 B x)+231 c^2 x^4 (15 A+13 B x)\right)}{45045}","\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*x^(5/2)*(1287*a^2*(7*A + 5*B*x) + 910*a*c*x^2*(11*A + 9*B*x) + 231*c^2*x^4*(15*A + 13*B*x)))/45045","A",1
396,1,60,77,0.0203119,"\int \sqrt{x} (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[Sqrt[x]*(A + B*x)*(a + c*x^2)^2,x]","\frac{2}{15} a^2 x^{3/2} (5 A+3 B x)+\frac{4}{63} a c x^{7/2} (9 A+7 B x)+\frac{2}{143} c^2 x^{11/2} (13 A+11 B 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}",1,"(2*a^2*x^(3/2)*(5*A + 3*B*x))/15 + (4*a*c*x^(7/2)*(9*A + 7*B*x))/63 + (2*c^2*x^(11/2)*(13*A + 11*B*x))/143","A",1
397,1,59,75,0.0270349,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/Sqrt[x],x]","\frac{2}{3} a^2 \sqrt{x} (3 A+B x)+\frac{4}{35} a c x^{5/2} (7 A+5 B x)+\frac{2}{99} c^2 x^{9/2} (11 A+9 B 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}",1,"(2*a^2*Sqrt[x]*(3*A + B*x))/3 + (4*a*c*x^(5/2)*(7*A + 5*B*x))/35 + (2*c^2*x^(9/2)*(11*A + 9*B*x))/99","A",1
398,1,52,73,0.0177982,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/x^(3/2),x]","\frac{-630 a^2 (A-B x)+84 a c x^2 (5 A+3 B x)+10 c^2 x^4 (9 A+7 B x)}{315 \sqrt{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}",1,"(-630*a^2*(A - B*x) + 84*a*c*x^2*(5*A + 3*B*x) + 10*c^2*x^4*(9*A + 7*B*x))/(315*Sqrt[x])","A",1
399,1,51,73,0.0179409,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/x^(5/2),x]","\frac{-70 a^2 (A+3 B x)+140 a c x^2 (3 A+B x)+6 c^2 x^4 (7 A+5 B x)}{105 x^{3/2}}","-\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,"(140*a*c*x^2*(3*A + B*x) - 70*a^2*(A + 3*B*x) + 6*c^2*x^4*(7*A + 5*B*x))/(105*x^(3/2))","A",1
400,1,53,73,0.0215308,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/x^(7/2),x]","\frac{-2 a^2 (3 A+5 B x)+60 a c x^2 (B x-A)+2 c^2 x^4 (5 A+3 B x)}{15 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,"(60*a*c*x^2*(-A + B*x) + 2*c^2*x^4*(5*A + 3*B*x) - 2*a^2*(3*A + 5*B*x))/(15*x^(5/2))","A",1
401,1,51,73,0.0218344,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/x^(9/2),x]","\frac{-6 a^2 (5 A+7 B x)-140 a c x^2 (A+3 B x)+70 c^2 x^4 (3 A+B x)}{105 x^{7/2}}","-\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,"(70*c^2*x^4*(3*A + B*x) - 140*a*c*x^2*(A + 3*B*x) - 6*a^2*(5*A + 7*B*x))/(105*x^(7/2))","A",1
402,1,83,109,0.0433933,"\int x^{7/2} (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[x^(7/2)*(A + B*x)*(a + c*x^2)^3,x]","\frac{2}{99} a^3 x^{9/2} (11 A+9 B x)+\frac{2}{65} a^2 c x^{13/2} (15 A+13 B x)+\frac{6}{323} a c^2 x^{17/2} (19 A+17 B x)+\frac{2}{483} c^3 x^{21/2} (23 A+21 B x)","\frac{2}{9} a^3 A x^{9/2}+\frac{2}{11} a^3 B x^{11/2}+\frac{6}{13} a^2 A c x^{13/2}+\frac{2}{5} a^2 B c x^{15/2}+\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*x^(9/2)*(11*A + 9*B*x))/99 + (2*a^2*c*x^(13/2)*(15*A + 13*B*x))/65 + (6*a*c^2*x^(17/2)*(19*A + 17*B*x))/323 + (2*c^3*x^(21/2)*(23*A + 21*B*x))/483","A",1
403,1,83,109,0.0387374,"\int x^{5/2} (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[x^(5/2)*(A + B*x)*(a + c*x^2)^3,x]","\frac{2}{63} a^3 x^{7/2} (9 A+7 B x)+\frac{6}{143} a^2 c x^{11/2} (13 A+11 B x)+\frac{2}{85} a c^2 x^{15/2} (17 A+15 B x)+\frac{2}{399} c^3 x^{19/2} (21 A+19 B x)","\frac{2}{7} a^3 A x^{7/2}+\frac{2}{9} a^3 B x^{9/2}+\frac{6}{11} a^2 A c x^{11/2}+\frac{6}{13} a^2 B c x^{13/2}+\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*x^(7/2)*(9*A + 7*B*x))/63 + (6*a^2*c*x^(11/2)*(13*A + 11*B*x))/143 + (2*a*c^2*x^(15/2)*(17*A + 15*B*x))/85 + (2*c^3*x^(19/2)*(21*A + 19*B*x))/399","A",1
404,1,83,109,0.0385414,"\int x^{3/2} (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[x^(3/2)*(A + B*x)*(a + c*x^2)^3,x]","\frac{2}{35} a^3 x^{5/2} (7 A+5 B x)+\frac{2}{33} a^2 c x^{9/2} (11 A+9 B x)+\frac{2}{65} a c^2 x^{13/2} (15 A+13 B x)+\frac{2}{323} c^3 x^{17/2} (19 A+17 B x)","\frac{2}{5} a^3 A x^{5/2}+\frac{2}{7} a^3 B x^{7/2}+\frac{2}{3} a^2 A c x^{9/2}+\frac{6}{11} a^2 B c x^{11/2}+\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*x^(5/2)*(7*A + 5*B*x))/35 + (2*a^2*c*x^(9/2)*(11*A + 9*B*x))/33 + (2*a*c^2*x^(13/2)*(15*A + 13*B*x))/65 + (2*c^3*x^(17/2)*(19*A + 17*B*x))/323","A",1
405,1,83,109,0.0444787,"\int \sqrt{x} (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[Sqrt[x]*(A + B*x)*(a + c*x^2)^3,x]","\frac{2}{15} a^3 x^{3/2} (5 A+3 B x)+\frac{2}{21} a^2 c x^{7/2} (9 A+7 B x)+\frac{6}{143} a c^2 x^{11/2} (13 A+11 B x)+\frac{2}{255} c^3 x^{15/2} (17 A+15 B x)","\frac{2}{3} a^3 A x^{3/2}+\frac{2}{5} a^3 B x^{5/2}+\frac{6}{7} a^2 A c x^{7/2}+\frac{2}{3} a^2 B c x^{9/2}+\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*x^(3/2)*(5*A + 3*B*x))/15 + (2*a^2*c*x^(7/2)*(9*A + 7*B*x))/21 + (6*a*c^2*x^(11/2)*(13*A + 11*B*x))/143 + (2*c^3*x^(15/2)*(17*A + 15*B*x))/255","A",1
406,1,72,107,0.0272043,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/Sqrt[x],x]","\frac{2 \sqrt{x} \left(5005 a^3 (3 A+B x)+1287 a^2 c x^2 (7 A+5 B x)+455 a c^2 x^4 (11 A+9 B x)+77 c^3 x^6 (15 A+13 B x)\right)}{15015}","2 a^3 A \sqrt{x}+\frac{2}{3} a^3 B x^{3/2}+\frac{6}{5} a^2 A c x^{5/2}+\frac{6}{7} a^2 B c x^{7/2}+\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*Sqrt[x]*(5005*a^3*(3*A + B*x) + 1287*a^2*c*x^2*(7*A + 5*B*x) + 455*a*c^2*x^4*(11*A + 9*B*x) + 77*c^3*x^6*(15*A + 13*B*x)))/15015","A",1
407,1,80,103,0.0389029,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/x^(3/2),x]","\frac{2 a^3 (B x-A)}{\sqrt{x}}+\frac{2}{5} a^2 c x^{3/2} (5 A+3 B x)+\frac{2}{21} a c^2 x^{7/2} (9 A+7 B x)+\frac{2}{143} c^3 x^{11/2} (13 A+11 B x)","-\frac{2 a^3 A}{\sqrt{x}}+2 a^3 B \sqrt{x}+2 a^2 A c x^{3/2}+\frac{6}{5} a^2 B c x^{5/2}+\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 + B*x))/Sqrt[x] + (2*a^2*c*x^(3/2)*(5*A + 3*B*x))/5 + (2*a*c^2*x^(7/2)*(9*A + 7*B*x))/21 + (2*c^3*x^(11/2)*(13*A + 11*B*x))/143","A",1
408,1,78,103,0.0343736,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/x^(5/2),x]","-\frac{2 a^3 (A+3 B x)}{3 x^{3/2}}+2 a^2 c \sqrt{x} (3 A+B x)+\frac{6}{35} a c^2 x^{5/2} (7 A+5 B x)+\frac{2}{99} c^3 x^{9/2} (11 A+9 B x)","-\frac{2 a^3 A}{3 x^{3/2}}-\frac{2 a^3 B}{\sqrt{x}}+6 a^2 A c \sqrt{x}+2 a^2 B c x^{3/2}+\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^2*c*Sqrt[x]*(3*A + B*x) - (2*a^3*(A + 3*B*x))/(3*x^(3/2)) + (6*a*c^2*x^(5/2)*(7*A + 5*B*x))/35 + (2*c^3*x^(9/2)*(11*A + 9*B*x))/99","A",1
409,1,72,103,0.0266196,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/x^(7/2),x]","\frac{2 \left(-21 a^3 (3 A+5 B x)+945 a^2 c x^2 (B x-A)+63 a c^2 x^4 (5 A+3 B x)+5 c^3 x^6 (9 A+7 B x)\right)}{315 x^{5/2}}","-\frac{2 a^3 A}{5 x^{5/2}}-\frac{2 a^3 B}{3 x^{3/2}}-\frac{6 a^2 A c}{\sqrt{x}}+6 a^2 B c \sqrt{x}+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*(945*a^2*c*x^2*(-A + B*x) + 63*a*c^2*x^4*(5*A + 3*B*x) - 21*a^3*(3*A + 5*B*x) + 5*c^3*x^6*(9*A + 7*B*x)))/(315*x^(5/2))","A",1
410,1,70,101,0.0286416,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/x^(9/2),x]","\frac{-2 a^3 (5 A+7 B x)-70 a^2 c x^2 (A+3 B x)+70 a c^2 x^4 (3 A+B x)+2 c^3 x^6 (7 A+5 B x)}{35 x^{7/2}}","-\frac{2 a^3 A}{7 x^{7/2}}-\frac{2 a^3 B}{5 x^{5/2}}-\frac{2 a^2 A c}{x^{3/2}}-\frac{6 a^2 B c}{\sqrt{x}}+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,"(70*a*c^2*x^4*(3*A + B*x) - 70*a^2*c*x^2*(A + 3*B*x) + 2*c^3*x^6*(7*A + 5*B*x) - 2*a^3*(5*A + 7*B*x))/(35*x^(7/2))","A",1
411,1,71,103,0.0271222,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{11/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/x^(11/2),x]","-\frac{2 \left(5 a^3 (7 A+9 B x)+63 a^2 c x^2 (3 A+5 B x)+945 a c^2 x^4 (A-B x)-21 c^3 x^6 (5 A+3 B x)\right)}{315 x^{9/2}}","-\frac{2 a^3 A}{9 x^{9/2}}-\frac{2 a^3 B}{7 x^{7/2}}-\frac{6 a^2 A c}{5 x^{5/2}}-\frac{2 a^2 B c}{x^{3/2}}-\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*(945*a*c^2*x^4*(A - B*x) - 21*c^3*x^6*(5*A + 3*B*x) + 63*a^2*c*x^2*(3*A + 5*B*x) + 5*a^3*(7*A + 9*B*x)))/(315*x^(9/2))","A",1
412,1,290,292,0.0994126,"\int \frac{x^{5/2} (A+B x)}{a+c x^2} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + c*x^2),x]","\frac{-15 \sqrt{2} a^{5/4} B \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)+15 \sqrt{2} a^{5/4} B \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)-30 \sqrt{2} a^{5/4} B \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)+30 \sqrt{2} a^{5/4} B \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)+60 (-a)^{3/4} A \sqrt{c} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)-60 (-a)^{3/4} A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)-120 a B \sqrt[4]{c} \sqrt{x}+40 A c^{5/4} x^{3/2}+24 B c^{5/4} x^{5/2}}{60 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) \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,"(-120*a*B*c^(1/4)*Sqrt[x] + 40*A*c^(5/4)*x^(3/2) + 24*B*c^(5/4)*x^(5/2) - 30*Sqrt[2]*a^(5/4)*B*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)] + 30*Sqrt[2]*a^(5/4)*B*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)] + 60*(-a)^(3/4)*A*Sqrt[c]*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)] - 60*(-a)^(3/4)*A*Sqrt[c]*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)] - 15*Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x] + 15*Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(60*c^(9/4))","A",1
413,1,287,278,0.0649248,"\int \frac{x^{3/2} (A+B x)}{a+c x^2} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + c*x^2),x]","\frac{\sqrt[4]{a} A \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{5/4}}-\frac{\sqrt[4]{a} A \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{5/4}}+\frac{\sqrt[4]{a} A \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} c^{5/4}}-\frac{\sqrt[4]{a} A \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} c^{5/4}}+\frac{(-a)^{3/4} B \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{7/4}}-\frac{(-a)^{3/4} B \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{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)*A*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*c^(5/4)) - (a^(1/4)*A*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*c^(5/4)) + ((-a)^(3/4)*B*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(7/4) - ((-a)^(3/4)*B*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(7/4) + (a^(1/4)*A*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(5/4)) - (a^(1/4)*A*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(5/4))","A",1
414,1,266,265,0.0605496,"\int \frac{\sqrt{x} (A+B x)}{a+c x^2} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + c*x^2),x]","\frac{\sqrt{2} a^{5/4} B \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)-\sqrt{2} a^{5/4} B \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)+2 \sqrt{2} a^{5/4} B \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)-2 \sqrt{2} a^{5/4} B \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)-4 (-a)^{3/4} A \sqrt{c} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)+4 (-a)^{3/4} A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)+8 a B \sqrt[4]{c} \sqrt{x}}{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) \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,"(8*a*B*c^(1/4)*Sqrt[x] + 2*Sqrt[2]*a^(5/4)*B*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)] - 2*Sqrt[2]*a^(5/4)*B*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)] - 4*(-a)^(3/4)*A*Sqrt[c]*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)] + 4*(-a)^(3/4)*A*Sqrt[c]*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)] + Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x] - Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(4*a*c^(5/4))","A",1
415,1,262,254,0.0574305,"\int \frac{A+B x}{\sqrt{x} \left(a+c x^2\right)} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + c*x^2)),x]","\frac{-\sqrt{2} \sqrt[4]{a} A \sqrt{c} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)+\sqrt{2} \sqrt[4]{a} A \sqrt{c} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)-2 \sqrt{2} \sqrt[4]{a} A \sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)+2 \sqrt{2} \sqrt[4]{a} A \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)-4 (-a)^{3/4} B \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)+4 (-a)^{3/4} B \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{4 a 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,"(-2*Sqrt[2]*a^(1/4)*A*Sqrt[c]*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)] + 2*Sqrt[2]*a^(1/4)*A*Sqrt[c]*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)] - 4*(-a)^(3/4)*B*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)] + 4*(-a)^(3/4)*B*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)] - Sqrt[2]*a^(1/4)*A*Sqrt[c]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x] + Sqrt[2]*a^(1/4)*A*Sqrt[c]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(4*a*c^(3/4))","A",1
416,1,177,265,0.0784083,"\int \frac{A+B x}{x^{3/2} \left(a+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + c*x^2)),x]","\frac{\frac{\sqrt{2} \sqrt[4]{a} B \left(-\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)+\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)\right)}{\sqrt[4]{c}}-\frac{8 A \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{c x^2}{a}\right)}{\sqrt{x}}}{4 a}","-\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,"((-8*A*Hypergeometric2F1[-1/4, 1, 3/4, -((c*x^2)/a)])/Sqrt[x] + (Sqrt[2]*a^(1/4)*B*(-2*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)] - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x] + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x]))/c^(1/4))/(4*a)","C",1
417,1,53,278,0.014245,"\int \frac{A+B x}{x^{5/2} \left(a+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a + c*x^2)),x]","-\frac{2 \left(A \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};-\frac{c x^2}{a}\right)+3 B x \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{3 a x^{3/2}}","-\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*Hypergeometric2F1[-3/4, 1, 1/4, -((c*x^2)/a)] + 3*B*x*Hypergeometric2F1[-1/4, 1, 3/4, -((c*x^2)/a)]))/(3*a*x^(3/2))","C",1
418,1,54,292,0.0134672,"\int \frac{A+B x}{x^{7/2} \left(a+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a + c*x^2)),x]","-\frac{2 \left(3 A \, _2F_1\left(-\frac{5}{4},1;-\frac{1}{4};-\frac{c x^2}{a}\right)+5 B x \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{15 a x^{5/2}}","\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*(3*A*Hypergeometric2F1[-5/4, 1, -1/4, -((c*x^2)/a)] + 5*B*x*Hypergeometric2F1[-3/4, 1, 1/4, -((c*x^2)/a)]))/(15*a*x^(5/2))","C",1
419,1,54,306,0.0139199,"\int \frac{A+B x}{x^{9/2} \left(a+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(9/2)*(a + c*x^2)),x]","-\frac{2 \left(5 A \, _2F_1\left(-\frac{7}{4},1;-\frac{3}{4};-\frac{c x^2}{a}\right)+7 B x \, _2F_1\left(-\frac{5}{4},1;-\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{35 a x^{7/2}}","\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*(5*A*Hypergeometric2F1[-7/4, 1, -3/4, -((c*x^2)/a)] + 7*B*x*Hypergeometric2F1[-5/4, 1, -1/4, -((c*x^2)/a)]))/(35*a*x^(7/2))","C",1
420,1,344,304,0.5206889,"\int \frac{x^{5/2} (A+B x)}{\left(a+c x^2\right)^2} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + c*x^2)^2,x]","\frac{1}{16} \left(\frac{8 A x^{7/2}}{a^2+a c x^2}+\frac{8 B x^{9/2}}{a^2+a c x^2}+\frac{12 A \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{\sqrt[4]{-a} c^{7/4}}-\frac{12 A \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{\sqrt[4]{-a} c^{7/4}}-\frac{8 A x^{3/2}}{a c}+\frac{5 \sqrt{2} \sqrt[4]{a} B \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{9/4}}-\frac{5 \sqrt{2} \sqrt[4]{a} B \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{9/4}}+\frac{10 \sqrt{2} \sqrt[4]{a} B \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{c^{9/4}}-\frac{10 \sqrt{2} \sqrt[4]{a} B \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{c^{9/4}}-\frac{8 B x^{5/2}}{a c}+\frac{40 B \sqrt{x}}{c^2}\right)","\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,"((40*B*Sqrt[x])/c^2 - (8*A*x^(3/2))/(a*c) - (8*B*x^(5/2))/(a*c) + (8*A*x^(7/2))/(a^2 + a*c*x^2) + (8*B*x^(9/2))/(a^2 + a*c*x^2) + (10*Sqrt[2]*a^(1/4)*B*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(9/4) - (10*Sqrt[2]*a^(1/4)*B*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(9/4) + (12*A*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/((-a)^(1/4)*c^(7/4)) - (12*A*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/((-a)^(1/4)*c^(7/4)) + (5*Sqrt[2]*a^(1/4)*B*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(9/4) - (5*Sqrt[2]*a^(1/4)*B*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(9/4))/16","A",1
421,1,323,289,0.2344682,"\int \frac{x^{3/2} (A+B x)}{\left(a+c x^2\right)^2} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + c*x^2)^2,x]","\frac{-\frac{\sqrt{2} \sqrt[4]{a} A \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{5/4}}+\frac{\sqrt{2} \sqrt[4]{a} A \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{5/4}}-\frac{2 \sqrt{2} \sqrt[4]{a} A \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{c^{5/4}}+\frac{2 \sqrt{2} \sqrt[4]{a} A \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{c^{5/4}}+\frac{8 A x^{5/2}}{a+c x^2}-\frac{12 (-a)^{3/4} B \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{7/4}}+\frac{12 (-a)^{3/4} B \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{7/4}}+\frac{8 B x^{7/2}}{a+c x^2}-\frac{8 A \sqrt{x}}{c}-\frac{8 B x^{3/2}}{c}}{16 a}","\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,"((-8*A*Sqrt[x])/c - (8*B*x^(3/2))/c + (8*A*x^(5/2))/(a + c*x^2) + (8*B*x^(7/2))/(a + c*x^2) - (2*Sqrt[2]*a^(1/4)*A*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(5/4) + (2*Sqrt[2]*a^(1/4)*A*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(5/4) - (12*(-a)^(3/4)*B*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(7/4) + (12*(-a)^(3/4)*B*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(7/4) - (Sqrt[2]*a^(1/4)*A*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(5/4) + (Sqrt[2]*a^(1/4)*A*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(5/4))/(16*a)","A",1
422,1,315,292,0.229453,"\int \frac{\sqrt{x} (A+B x)}{\left(a+c x^2\right)^2} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + c*x^2)^2,x]","\frac{-\frac{\sqrt{2} a^{5/4} B \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{5/4}}+\frac{\sqrt{2} a^{5/4} B \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{5/4}}-\frac{2 \sqrt{2} a^{5/4} B \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{c^{5/4}}+\frac{2 \sqrt{2} a^{5/4} B \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{c^{5/4}}-\frac{4 (-a)^{3/4} A \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{3/4}}+\frac{4 (-a)^{3/4} A \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{3/4}}+\frac{8 a A x^{3/2}}{a+c x^2}+\frac{8 a B x^{5/2}}{a+c x^2}-\frac{8 a B \sqrt{x}}{c}}{16 a^2}","-\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,"((-8*a*B*Sqrt[x])/c + (8*a*A*x^(3/2))/(a + c*x^2) + (8*a*B*x^(5/2))/(a + c*x^2) - (2*Sqrt[2]*a^(5/4)*B*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(5/4) + (2*Sqrt[2]*a^(5/4)*B*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(5/4) - (4*(-a)^(3/4)*A*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(3/4) + (4*(-a)^(3/4)*A*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(3/4) - (Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(5/4) + (Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(5/4))/(16*a^2)","A",1
423,1,304,287,0.2224931,"\int \frac{A+B x}{\sqrt{x} \left(a+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + c*x^2)^2),x]","\frac{\frac{8 a A \sqrt{x}}{a+c x^2}-\frac{3 \sqrt{2} \sqrt[4]{a} A \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{\sqrt[4]{c}}+\frac{3 \sqrt{2} \sqrt[4]{a} A \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{\sqrt[4]{c}}-\frac{6 \sqrt{2} \sqrt[4]{a} A \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{6 \sqrt{2} \sqrt[4]{a} A \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{c}}-\frac{4 (-a)^{3/4} B \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{3/4}}+\frac{4 (-a)^{3/4} B \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{3/4}}+\frac{8 a B x^{3/2}}{a+c x^2}}{16 a^2}","\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,"((8*a*A*Sqrt[x])/(a + c*x^2) + (8*a*B*x^(3/2))/(a + c*x^2) - (6*Sqrt[2]*a^(1/4)*A*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(1/4) + (6*Sqrt[2]*a^(1/4)*A*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(1/4) - (4*(-a)^(3/4)*B*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(3/4) + (4*(-a)^(3/4)*B*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(3/4) - (3*Sqrt[2]*a^(1/4)*A*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(1/4) + (3*Sqrt[2]*a^(1/4)*A*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(1/4))/(16*a^2)","A",1
424,1,256,304,0.4614452,"\int \frac{A+B x}{x^{3/2} \left(a+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + c*x^2)^2),x]","\frac{\sqrt[4]{a} \left(\frac{8 a^{3/4} A}{\sqrt{x} \left(a+c x^2\right)}+\frac{8 a^{3/4} B \sqrt{x}}{a+c x^2}-\frac{3 \sqrt{2} B \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{\sqrt[4]{c}}+\frac{3 \sqrt{2} B \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{\sqrt[4]{c}}-\frac{6 \sqrt{2} B \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{6 \sqrt{2} B \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{c}}\right)-\frac{40 A \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{c x^2}{a}\right)}{\sqrt{x}}}{16 a^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)}{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,"((-40*A*Hypergeometric2F1[-1/4, 1, 3/4, -((c*x^2)/a)])/Sqrt[x] + a^(1/4)*((8*a^(3/4)*A)/(Sqrt[x]*(a + c*x^2)) + (8*a^(3/4)*B*Sqrt[x])/(a + c*x^2) - (6*Sqrt[2]*B*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(1/4) + (6*Sqrt[2]*B*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(1/4) - (3*Sqrt[2]*B*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(1/4) + (3*Sqrt[2]*B*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(1/4)))/(16*a^2)","C",1
425,1,85,317,0.032025,"\int \frac{A+B x}{x^{5/2} \left(a+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a + c*x^2)^2),x]","\frac{3 a (A+B x)-7 A \left(a+c x^2\right) \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};-\frac{c x^2}{a}\right)-15 B x \left(a+c x^2\right) \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{c x^2}{a}\right)}{6 a^2 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,"(3*a*(A + B*x) - 7*A*(a + c*x^2)*Hypergeometric2F1[-3/4, 1, 1/4, -((c*x^2)/a)] - 15*B*x*(a + c*x^2)*Hypergeometric2F1[-1/4, 1, 3/4, -((c*x^2)/a)])/(6*a^2*x^(3/2)*(a + c*x^2))","C",1
426,1,385,320,0.4754606,"\int \frac{x^{7/2} (A+B x)}{\left(a+c x^2\right)^3} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a + c*x^2)^3,x]","\frac{-\frac{5 \sqrt{2} a^{5/4} A \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{9/4}}+\frac{5 \sqrt{2} a^{5/4} A \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{9/4}}-\frac{10 \sqrt{2} a^{5/4} A \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{c^{9/4}}+\frac{10 \sqrt{2} a^{5/4} A \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{c^{9/4}}-\frac{40 a A \sqrt{x}}{c^2}-\frac{8 A x^{9/2}}{a+c x^2}+\frac{32 a A x^{9/2}}{\left(a+c x^2\right)^2}+\frac{84 (-a)^{7/4} B \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{11/4}}+\frac{84 (-a)^{3/4} a B \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{11/4}}-\frac{56 a B x^{3/2}}{c^2}-\frac{24 B x^{11/2}}{a+c x^2}+\frac{32 a B x^{11/2}}{\left(a+c x^2\right)^2}+\frac{8 A x^{5/2}}{c}+\frac{24 B x^{7/2}}{c}}{128 a^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,"((-40*a*A*Sqrt[x])/c^2 - (56*a*B*x^(3/2))/c^2 + (8*A*x^(5/2))/c + (24*B*x^(7/2))/c + (32*a*A*x^(9/2))/(a + c*x^2)^2 + (32*a*B*x^(11/2))/(a + c*x^2)^2 - (8*A*x^(9/2))/(a + c*x^2) - (24*B*x^(11/2))/(a + c*x^2) - (10*Sqrt[2]*a^(5/4)*A*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(9/4) + (10*Sqrt[2]*a^(5/4)*A*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(9/4) + (84*(-a)^(7/4)*B*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(11/4) + (84*(-a)^(3/4)*a*B*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(11/4) - (5*Sqrt[2]*a^(5/4)*A*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(9/4) + (5*Sqrt[2]*a^(5/4)*A*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(9/4))/(128*a^2)","A",1
427,1,372,325,0.3418433,"\int \frac{x^{5/2} (A+B x)}{\left(a+c x^2\right)^3} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + c*x^2)^3,x]","\frac{-\frac{5 \sqrt{2} a^{5/4} B \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{9/4}}+\frac{5 \sqrt{2} a^{5/4} B \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{9/4}}-\frac{10 \sqrt{2} a^{5/4} B \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{c^{9/4}}+\frac{10 \sqrt{2} a^{5/4} B \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{c^{9/4}}-\frac{12 (-a)^{3/4} A \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{7/4}}+\frac{12 (-a)^{3/4} A \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{7/4}}+\frac{8 A x^{7/2}}{a+c x^2}+\frac{32 a A x^{7/2}}{\left(a+c x^2\right)^2}-\frac{40 a B \sqrt{x}}{c^2}-\frac{8 B x^{9/2}}{a+c x^2}+\frac{32 a B x^{9/2}}{\left(a+c x^2\right)^2}-\frac{8 A x^{3/2}}{c}+\frac{8 B x^{5/2}}{c}}{128 a^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,"((-40*a*B*Sqrt[x])/c^2 - (8*A*x^(3/2))/c + (8*B*x^(5/2))/c + (32*a*A*x^(7/2))/(a + c*x^2)^2 + (32*a*B*x^(9/2))/(a + c*x^2)^2 + (8*A*x^(7/2))/(a + c*x^2) - (8*B*x^(9/2))/(a + c*x^2) - (10*Sqrt[2]*a^(5/4)*B*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(9/4) + (10*Sqrt[2]*a^(5/4)*B*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(9/4) - (12*(-a)^(3/4)*A*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(7/4) + (12*(-a)^(3/4)*A*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(7/4) - (5*Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(9/4) + (5*Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(9/4))/(128*a^2)","A",1
428,1,360,315,0.174985,"\int \frac{x^{3/2} (A+B x)}{\left(a+c x^2\right)^3} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + c*x^2)^3,x]","\frac{-\frac{3 \sqrt{2} \sqrt[4]{a} A \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{5/4}}+\frac{3 \sqrt{2} \sqrt[4]{a} A \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{5/4}}-\frac{6 \sqrt{2} \sqrt[4]{a} A \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{c^{5/4}}+\frac{6 \sqrt{2} \sqrt[4]{a} A \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{c^{5/4}}+\frac{24 A x^{5/2}}{a+c x^2}+\frac{32 a A x^{5/2}}{\left(a+c x^2\right)^2}-\frac{12 (-a)^{3/4} B \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{7/4}}+\frac{12 (-a)^{3/4} B \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{7/4}}+\frac{8 B x^{7/2}}{a+c x^2}+\frac{32 a B x^{7/2}}{\left(a+c x^2\right)^2}-\frac{24 A \sqrt{x}}{c}-\frac{8 B x^{3/2}}{c}}{128 a^2}","\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,"((-24*A*Sqrt[x])/c - (8*B*x^(3/2))/c + (32*a*A*x^(5/2))/(a + c*x^2)^2 + (32*a*B*x^(7/2))/(a + c*x^2)^2 + (24*A*x^(5/2))/(a + c*x^2) + (8*B*x^(7/2))/(a + c*x^2) - (6*Sqrt[2]*a^(1/4)*A*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(5/4) + (6*Sqrt[2]*a^(1/4)*A*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(5/4) - (12*(-a)^(3/4)*B*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(7/4) + (12*(-a)^(3/4)*B*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(7/4) - (3*Sqrt[2]*a^(1/4)*A*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(5/4) + (3*Sqrt[2]*a^(1/4)*A*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(5/4))/(128*a^2)","A",1
429,1,356,331,0.1769921,"\int \frac{\sqrt{x} (A+B x)}{\left(a+c x^2\right)^3} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + c*x^2)^3,x]","\frac{-\frac{3 \sqrt{2} a^{5/4} B \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{5/4}}+\frac{3 \sqrt{2} a^{5/4} B \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{c^{5/4}}-\frac{6 \sqrt{2} a^{5/4} B \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{c^{5/4}}+\frac{6 \sqrt{2} a^{5/4} B \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{c^{5/4}}+\frac{32 a^2 A x^{3/2}}{\left(a+c x^2\right)^2}+\frac{32 a^2 B x^{5/2}}{\left(a+c x^2\right)^2}-\frac{20 (-a)^{3/4} A \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{3/4}}+\frac{20 (-a)^{3/4} A \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{3/4}}+\frac{40 a A x^{3/2}}{a+c x^2}+\frac{24 a B x^{5/2}}{a+c x^2}-\frac{24 a B \sqrt{x}}{c}}{128 a^3}","-\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,"((-24*a*B*Sqrt[x])/c + (32*a^2*A*x^(3/2))/(a + c*x^2)^2 + (32*a^2*B*x^(5/2))/(a + c*x^2)^2 + (40*a*A*x^(3/2))/(a + c*x^2) + (24*a*B*x^(5/2))/(a + c*x^2) - (6*Sqrt[2]*a^(5/4)*B*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(5/4) + (6*Sqrt[2]*a^(5/4)*B*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(5/4) - (20*(-a)^(3/4)*A*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(3/4) + (20*(-a)^(3/4)*A*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(3/4) - (3*Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(5/4) + (3*Sqrt[2]*a^(5/4)*B*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(5/4))/(128*a^3)","A",1
430,1,344,320,0.1717181,"\int \frac{A+B x}{\sqrt{x} \left(a+c x^2\right)^3} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + c*x^2)^3),x]","\frac{\frac{32 a^2 A \sqrt{x}}{\left(a+c x^2\right)^2}+\frac{32 a^2 B x^{3/2}}{\left(a+c x^2\right)^2}+\frac{56 a A \sqrt{x}}{a+c x^2}-\frac{21 \sqrt{2} \sqrt[4]{a} A \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{\sqrt[4]{c}}+\frac{21 \sqrt{2} \sqrt[4]{a} A \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{\sqrt[4]{c}}-\frac{42 \sqrt{2} \sqrt[4]{a} A \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{42 \sqrt{2} \sqrt[4]{a} A \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{c}}-\frac{20 (-a)^{3/4} B \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{3/4}}+\frac{20 (-a)^{3/4} B \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-a}}\right)}{c^{3/4}}+\frac{40 a B x^{3/2}}{a+c x^2}}{128 a^3}","\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,"((32*a^2*A*Sqrt[x])/(a + c*x^2)^2 + (32*a^2*B*x^(3/2))/(a + c*x^2)^2 + (56*a*A*Sqrt[x])/(a + c*x^2) + (40*a*B*x^(3/2))/(a + c*x^2) - (42*Sqrt[2]*a^(1/4)*A*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(1/4) + (42*Sqrt[2]*a^(1/4)*A*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(1/4) - (20*(-a)^(3/4)*B*ArcTan[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(3/4) + (20*(-a)^(3/4)*B*ArcTanh[(c^(1/4)*Sqrt[x])/(-a)^(1/4)])/c^(3/4) - (21*Sqrt[2]*a^(1/4)*A*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(1/4) + (21*Sqrt[2]*a^(1/4)*A*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(1/4))/(128*a^3)","A",1
431,1,300,333,0.2862295,"\int \frac{A+B x}{x^{3/2} \left(a+c x^2\right)^3} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + c*x^2)^3),x]","\frac{\sqrt[4]{a} \left(\frac{32 a^{7/4} A}{\sqrt{x} \left(a+c x^2\right)^2}+\frac{72 a^{3/4} A}{\sqrt{x} \left(a+c x^2\right)}+\frac{32 a^{7/4} B \sqrt{x}}{\left(a+c x^2\right)^2}+\frac{56 a^{3/4} B \sqrt{x}}{a+c x^2}-\frac{21 \sqrt{2} B \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{\sqrt[4]{c}}+\frac{21 \sqrt{2} B \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{\sqrt[4]{c}}-\frac{42 \sqrt{2} B \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{42 \sqrt{2} B \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{c}}\right)-\frac{360 A \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{c x^2}{a}\right)}{\sqrt{x}}}{128 a^3}","-\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{9 A+7 B x}{16 a^2 \sqrt{x} \left(a+c x^2\right)}+\frac{A+B x}{4 a \sqrt{x} \left(a+c x^2\right)^2}",1,"((-360*A*Hypergeometric2F1[-1/4, 1, 3/4, -((c*x^2)/a)])/Sqrt[x] + a^(1/4)*((32*a^(7/4)*A)/(Sqrt[x]*(a + c*x^2)^2) + (32*a^(7/4)*B*Sqrt[x])/(a + c*x^2)^2 + (72*a^(3/4)*A)/(Sqrt[x]*(a + c*x^2)) + (56*a^(3/4)*B*Sqrt[x])/(a + c*x^2) - (42*Sqrt[2]*B*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(1/4) + (42*Sqrt[2]*B*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/c^(1/4) - (21*Sqrt[2]*B*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(1/4) + (21*Sqrt[2]*B*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/c^(1/4)))/(128*a^3)","C",1
432,1,99,45,0.0358245,"\int \frac{1-x}{\sqrt{x} \left(1+x^2\right)} \, dx","Integrate[(1 - x)/(Sqrt[x]*(1 + x^2)),x]","\frac{1}{12} \left(3 \sqrt{2} \left(-\log \left(x-\sqrt{2} \sqrt{x}+1\right)+\log \left(x+\sqrt{2} \sqrt{x}+1\right)-2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)+2 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)\right)-8 x^{3/2} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-x^2\right)\right)","\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,"(-8*x^(3/2)*Hypergeometric2F1[3/4, 1, 7/4, -x^2] + 3*Sqrt[2]*(-2*ArcTan[1 - Sqrt[2]*Sqrt[x]] + 2*ArcTan[1 + Sqrt[2]*Sqrt[x]] - Log[1 - Sqrt[2]*Sqrt[x] + x] + Log[1 + Sqrt[2]*Sqrt[x] + x]))/12","C",1
433,1,142,427,0.1344348,"\int (e x)^{7/2} (A+B x) \sqrt{a+c x^2} \, dx","Integrate[(e*x)^(7/2)*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{2 e^3 \sqrt{e x} \sqrt{a+c x^2} \left(585 a^2 A \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)+539 a^2 B x \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-\left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \left(a (585 A+539 B x)-63 c x^2 (13 A+11 B x)\right)\right)}{9009 c^2 \sqrt{\frac{c x^2}{a}+1}}","\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^{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{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{2 a^2 e^3 \sqrt{e x} \sqrt{a+c x^2} (325 A+539 B x)}{15015 c^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*e^3*Sqrt[e*x]*Sqrt[a + c*x^2]*(-((a + c*x^2)*Sqrt[1 + (c*x^2)/a]*(-63*c*x^2*(13*A + 11*B*x) + a*(585*A + 539*B*x))) + 585*a^2*A*Hypergeometric2F1[-1/2, 1/4, 5/4, -((c*x^2)/a)] + 539*a^2*B*x*Hypergeometric2F1[-1/2, 3/4, 7/4, -((c*x^2)/a)]))/(9009*c^2*Sqrt[1 + (c*x^2)/a])","C",1
434,1,133,397,0.1136501,"\int (e x)^{5/2} (A+B x) \sqrt{a+c x^2} \, dx","Integrate[(e*x)^(5/2)*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{2 e^2 \sqrt{e x} \sqrt{a+c x^2} \left(45 a^2 B \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)-\left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} (45 a B-7 c x (11 A+9 B x))-77 a A c x \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)\right)}{693 c^2 \sqrt{\frac{c x^2}{a}+1}}","\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^{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{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{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,"(2*e^2*Sqrt[e*x]*Sqrt[a + c*x^2]*(-((a + c*x^2)*Sqrt[1 + (c*x^2)/a]*(45*a*B - 7*c*x*(11*A + 9*B*x))) + 45*a^2*B*Hypergeometric2F1[-1/2, 1/4, 5/4, -((c*x^2)/a)] - 77*a*A*c*x*Hypergeometric2F1[-1/2, 3/4, 7/4, -((c*x^2)/a)]))/(693*c^2*Sqrt[1 + (c*x^2)/a])","C",1
435,1,118,363,0.0864357,"\int (e x)^{3/2} (A+B x) \sqrt{a+c x^2} \, dx","Integrate[(e*x)^(3/2)*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{2 e \sqrt{e x} \sqrt{a+c x^2} \left(\sqrt{\frac{c x^2}{a}+1} \left(a+c x^2\right) (9 A+7 B x)-9 a A \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)-7 a B x \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)\right)}{63 c \sqrt{\frac{c x^2}{a}+1}}","-\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^{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{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{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*e*Sqrt[e*x]*Sqrt[a + c*x^2]*((9*A + 7*B*x)*(a + c*x^2)*Sqrt[1 + (c*x^2)/a] - 9*a*A*Hypergeometric2F1[-1/2, 1/4, 5/4, -((c*x^2)/a)] - 7*a*B*x*Hypergeometric2F1[-1/2, 3/4, 7/4, -((c*x^2)/a)]))/(63*c*Sqrt[1 + (c*x^2)/a])","C",1
436,1,111,328,0.0605457,"\int \sqrt{e x} (A+B x) \sqrt{a+c x^2} \, dx","Integrate[Sqrt[e*x]*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{2 \sqrt{e x} \sqrt{a+c x^2} \left(7 A c x \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-3 a B \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)+3 B \sqrt{\frac{c x^2}{a}+1} \left(a+c x^2\right)\right)}{21 c \sqrt{\frac{c x^2}{a}+1}}","-\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,"(2*Sqrt[e*x]*Sqrt[a + c*x^2]*(3*B*(a + c*x^2)*Sqrt[1 + (c*x^2)/a] - 3*a*B*Hypergeometric2F1[-1/2, 1/4, 5/4, -((c*x^2)/a)] + 7*A*c*x*Hypergeometric2F1[-1/2, 3/4, 7/4, -((c*x^2)/a)]))/(21*c*Sqrt[1 + (c*x^2)/a])","C",1
437,1,82,297,0.0243718,"\int \frac{(A+B x) \sqrt{a+c x^2}}{\sqrt{e x}} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/Sqrt[e*x],x]","\frac{2 x \sqrt{a+c x^2} \left(3 A \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)+B x \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)\right)}{3 \sqrt{e x} \sqrt{\frac{c x^2}{a}+1}}","\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*x*Sqrt[a + c*x^2]*(3*A*Hypergeometric2F1[-1/2, 1/4, 5/4, -((c*x^2)/a)] + B*x*Hypergeometric2F1[-1/2, 3/4, 7/4, -((c*x^2)/a)]))/(3*Sqrt[e*x]*Sqrt[1 + (c*x^2)/a])","C",1
438,1,80,300,0.0291585,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(e x)^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/(e*x)^(3/2),x]","\frac{2 x \sqrt{a+c x^2} \left(B x \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)-A \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{(e x)^{3/2} \sqrt{\frac{c x^2}{a}+1}}","-\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*x*Sqrt[a + c*x^2]*(-(A*Hypergeometric2F1[-1/2, -1/4, 3/4, -((c*x^2)/a)]) + B*x*Hypergeometric2F1[-1/2, 1/4, 5/4, -((c*x^2)/a)]))/((e*x)^(3/2)*Sqrt[1 + (c*x^2)/a])","C",1
439,1,82,298,0.0297921,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(e x)^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/(e*x)^(5/2),x]","-\frac{2 x \sqrt{a+c x^2} \left(A \, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{4};-\frac{c x^2}{a}\right)+3 B x \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{3 (e x)^{5/2} \sqrt{\frac{c x^2}{a}+1}}","\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*x*Sqrt[a + c*x^2]*(A*Hypergeometric2F1[-3/4, -1/2, 1/4, -((c*x^2)/a)] + 3*B*x*Hypergeometric2F1[-1/2, -1/4, 3/4, -((c*x^2)/a)]))/(3*(e*x)^(5/2)*Sqrt[1 + (c*x^2)/a])","C",1
440,1,83,338,0.0284945,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(e x)^{7/2}} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/(e*x)^(7/2),x]","-\frac{2 x \sqrt{a+c x^2} \left(3 A \, _2F_1\left(-\frac{5}{4},-\frac{1}{2};-\frac{1}{4};-\frac{c x^2}{a}\right)+5 B x \, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{15 (e x)^{7/2} \sqrt{\frac{c x^2}{a}+1}}","\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,"(-2*x*Sqrt[a + c*x^2]*(3*A*Hypergeometric2F1[-5/4, -1/2, -1/4, -((c*x^2)/a)] + 5*B*x*Hypergeometric2F1[-3/4, -1/2, 1/4, -((c*x^2)/a)]))/(15*(e*x)^(7/2)*Sqrt[1 + (c*x^2)/a])","C",1
441,1,88,368,0.0330746,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(e x)^{9/2}} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/(e*x)^(9/2),x]","-\frac{2 \sqrt{e x} \sqrt{a+c x^2} \left(5 A \, _2F_1\left(-\frac{7}{4},-\frac{1}{2};-\frac{3}{4};-\frac{c x^2}{a}\right)+7 B x \, _2F_1\left(-\frac{5}{4},-\frac{1}{2};-\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{35 e^5 x^4 \sqrt{\frac{c x^2}{a}+1}}","\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,"(-2*Sqrt[e*x]*Sqrt[a + c*x^2]*(5*A*Hypergeometric2F1[-7/4, -1/2, -3/4, -((c*x^2)/a)] + 7*B*x*Hypergeometric2F1[-5/4, -1/2, -1/4, -((c*x^2)/a)]))/(35*e^5*x^4*Sqrt[1 + (c*x^2)/a])","C",1
442,1,137,438,0.1450698,"\int (e x)^{5/2} (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Integrate[(e*x)^(5/2)*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{2 e^2 \sqrt{e x} \sqrt{a+c x^2} \left(65 a^3 B \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)-165 a^2 A c x \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-\left(a+c x^2\right)^2 \sqrt{\frac{c x^2}{a}+1} (65 a B-11 c x (15 A+13 B x))\right)}{2145 c^2 \sqrt{\frac{c x^2}{a}+1}}","\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^{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{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{4 a^2 e^2 \sqrt{e x} \sqrt{a+c x^2} (65 a B-231 A c x)}{15015 c^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,"(2*e^2*Sqrt[e*x]*Sqrt[a + c*x^2]*(-((a + c*x^2)^2*Sqrt[1 + (c*x^2)/a]*(65*a*B - 11*c*x*(15*A + 13*B*x))) + 65*a^3*B*Hypergeometric2F1[-3/2, 1/4, 5/4, -((c*x^2)/a)] - 165*a^2*A*c*x*Hypergeometric2F1[-3/2, 3/4, 7/4, -((c*x^2)/a)]))/(2145*c^2*Sqrt[1 + (c*x^2)/a])","C",1
443,1,124,400,0.1150398,"\int (e x)^{3/2} (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Integrate[(e*x)^(3/2)*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{2 e \sqrt{e x} \sqrt{a+c x^2} \left(-13 a^2 A \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)-11 a^2 B x \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+\left(a+c x^2\right)^2 \sqrt{\frac{c x^2}{a}+1} (13 A+11 B x)\right)}{143 c \sqrt{\frac{c x^2}{a}+1}}","-\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{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{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{4 a^2 e \sqrt{e x} \sqrt{a+c x^2} (65 A+77 B x)}{5005 c}-\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,"(2*e*Sqrt[e*x]*Sqrt[a + c*x^2]*((13*A + 11*B*x)*(a + c*x^2)^2*Sqrt[1 + (c*x^2)/a] - 13*a^2*A*Hypergeometric2F1[-3/2, 1/4, 5/4, -((c*x^2)/a)] - 11*a^2*B*x*Hypergeometric2F1[-3/2, 3/4, 7/4, -((c*x^2)/a)]))/(143*c*Sqrt[1 + (c*x^2)/a])","C",1
444,1,116,366,0.0755335,"\int \sqrt{e x} (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Integrate[Sqrt[e*x]*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{2 \sqrt{e x} \sqrt{a+c x^2} \left(-3 a^2 B \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)+11 a A c x \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+3 B \left(a+c x^2\right)^2 \sqrt{\frac{c x^2}{a}+1}\right)}{33 c \sqrt{\frac{c x^2}{a}+1}}","-\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,"(2*Sqrt[e*x]*Sqrt[a + c*x^2]*(3*B*(a + c*x^2)^2*Sqrt[1 + (c*x^2)/a] - 3*a^2*B*Hypergeometric2F1[-3/2, 1/4, 5/4, -((c*x^2)/a)] + 11*a*A*c*x*Hypergeometric2F1[-3/2, 3/4, 7/4, -((c*x^2)/a)]))/(33*c*Sqrt[1 + (c*x^2)/a])","C",1
445,1,83,333,0.0266824,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{\sqrt{e x}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/Sqrt[e*x],x]","\frac{2 a x \sqrt{a+c x^2} \left(3 A \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)+B x \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)\right)}{3 \sqrt{e x} \sqrt{\frac{c x^2}{a}+1}}","\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,"(2*a*x*Sqrt[a + c*x^2]*(3*A*Hypergeometric2F1[-3/2, 1/4, 5/4, -((c*x^2)/a)] + B*x*Hypergeometric2F1[-3/2, 3/4, 7/4, -((c*x^2)/a)]))/(3*Sqrt[e*x]*Sqrt[1 + (c*x^2)/a])","C",1
446,1,81,341,0.0252677,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(e x)^{3/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/(e*x)^(3/2),x]","\frac{2 a x \sqrt{a+c x^2} \left(B x \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)-A \, _2F_1\left(-\frac{3}{2},-\frac{1}{4};\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{(e x)^{3/2} \sqrt{\frac{c x^2}{a}+1}}","\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,"(2*a*x*Sqrt[a + c*x^2]*(-(A*Hypergeometric2F1[-3/2, -1/4, 3/4, -((c*x^2)/a)]) + B*x*Hypergeometric2F1[-3/2, 1/4, 5/4, -((c*x^2)/a)]))/((e*x)^(3/2)*Sqrt[1 + (c*x^2)/a])","C",1
447,1,83,341,0.0316973,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(e x)^{5/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/(e*x)^(5/2),x]","-\frac{2 a x \sqrt{a+c x^2} \left(A \, _2F_1\left(-\frac{3}{2},-\frac{3}{4};\frac{1}{4};-\frac{c x^2}{a}\right)+3 B x \, _2F_1\left(-\frac{3}{2},-\frac{1}{4};\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{3 (e x)^{5/2} \sqrt{\frac{c x^2}{a}+1}}","\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,"(-2*a*x*Sqrt[a + c*x^2]*(A*Hypergeometric2F1[-3/2, -3/4, 1/4, -((c*x^2)/a)] + 3*B*x*Hypergeometric2F1[-3/2, -1/4, 3/4, -((c*x^2)/a)]))/(3*(e*x)^(5/2)*Sqrt[1 + (c*x^2)/a])","C",1
448,1,84,339,0.0310692,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(e x)^{7/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/(e*x)^(7/2),x]","-\frac{2 a x \sqrt{a+c x^2} \left(3 A \, _2F_1\left(-\frac{3}{2},-\frac{5}{4};-\frac{1}{4};-\frac{c x^2}{a}\right)+5 B x \, _2F_1\left(-\frac{3}{2},-\frac{3}{4};\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{15 (e x)^{7/2} \sqrt{\frac{c x^2}{a}+1}}","\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,"(-2*a*x*Sqrt[a + c*x^2]*(3*A*Hypergeometric2F1[-3/2, -5/4, -1/4, -((c*x^2)/a)] + 5*B*x*Hypergeometric2F1[-3/2, -3/4, 1/4, -((c*x^2)/a)]))/(15*(e*x)^(7/2)*Sqrt[1 + (c*x^2)/a])","C",1
449,1,89,339,0.0325302,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(e x)^{9/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/(e*x)^(9/2),x]","-\frac{2 a \sqrt{e x} \sqrt{a+c x^2} \left(5 A \, _2F_1\left(-\frac{7}{4},-\frac{3}{2};-\frac{3}{4};-\frac{c x^2}{a}\right)+7 B x \, _2F_1\left(-\frac{3}{2},-\frac{5}{4};-\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{35 e^5 x^4 \sqrt{\frac{c x^2}{a}+1}}","\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,"(-2*a*Sqrt[e*x]*Sqrt[a + c*x^2]*(5*A*Hypergeometric2F1[-7/4, -3/2, -3/4, -((c*x^2)/a)] + 7*B*x*Hypergeometric2F1[-3/2, -5/4, -1/4, -((c*x^2)/a)]))/(35*e^5*x^4*Sqrt[1 + (c*x^2)/a])","C",1
450,1,124,437,0.1365768,"\int (e x)^{3/2} (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Integrate[(e*x)^(3/2)*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{2 e \sqrt{e x} \sqrt{a+c x^2} \left(-17 a^3 A \, _2F_1\left(-\frac{5}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)-15 a^3 B x \, _2F_1\left(-\frac{5}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+\left(a+c x^2\right)^3 \sqrt{\frac{c x^2}{a}+1} (17 A+15 B x)\right)}{255 c \sqrt{\frac{c x^2}{a}+1}}","-\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{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{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{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{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,"(2*e*Sqrt[e*x]*Sqrt[a + c*x^2]*((17*A + 15*B*x)*(a + c*x^2)^3*Sqrt[1 + (c*x^2)/a] - 17*a^3*A*Hypergeometric2F1[-5/2, 1/4, 5/4, -((c*x^2)/a)] - 15*a^3*B*x*Hypergeometric2F1[-5/2, 3/4, 7/4, -((c*x^2)/a)]))/(255*c*Sqrt[1 + (c*x^2)/a])","C",1
451,1,117,404,0.0916404,"\int \sqrt{e x} (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Integrate[Sqrt[e*x]*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{2 \sqrt{e x} \sqrt{a+c x^2} \left(a^3 (-B) \, _2F_1\left(-\frac{5}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)+5 a^2 A c x \, _2F_1\left(-\frac{5}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+B \left(a+c x^2\right)^3 \sqrt{\frac{c x^2}{a}+1}\right)}{15 c \sqrt{\frac{c x^2}{a}+1}}","-\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{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{8 a^2 \sqrt{e x} \sqrt{a+c x^2} (13 a B-77 A c x)}{3003 c}-\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,"(2*Sqrt[e*x]*Sqrt[a + c*x^2]*(B*(a + c*x^2)^3*Sqrt[1 + (c*x^2)/a] - a^3*B*Hypergeometric2F1[-5/2, 1/4, 5/4, -((c*x^2)/a)] + 5*a^2*A*c*x*Hypergeometric2F1[-5/2, 3/4, 7/4, -((c*x^2)/a)]))/(15*c*Sqrt[1 + (c*x^2)/a])","C",1
452,1,85,369,0.0277634,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{\sqrt{e x}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/Sqrt[e*x],x]","\frac{2 a^2 x \sqrt{a+c x^2} \left(3 A \, _2F_1\left(-\frac{5}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)+B x \, _2F_1\left(-\frac{5}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)\right)}{3 \sqrt{e x} \sqrt{\frac{c x^2}{a}+1}}","\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{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{8 a^2 \sqrt{e x} \sqrt{a+c x^2} (195 A+77 B x)}{3003 e}+\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,"(2*a^2*x*Sqrt[a + c*x^2]*(3*A*Hypergeometric2F1[-5/2, 1/4, 5/4, -((c*x^2)/a)] + B*x*Hypergeometric2F1[-5/2, 3/4, 7/4, -((c*x^2)/a)]))/(3*Sqrt[e*x]*Sqrt[1 + (c*x^2)/a])","C",1
453,1,83,379,0.02739,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{3/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(3/2),x]","\frac{2 a^2 x \sqrt{a+c x^2} \left(B x \, _2F_1\left(-\frac{5}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^2}{a}\right)-A \, _2F_1\left(-\frac{5}{2},-\frac{1}{4};\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{(e x)^{3/2} \sqrt{\frac{c x^2}{a}+1}}","\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^{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{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{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,"(2*a^2*x*Sqrt[a + c*x^2]*(-(A*Hypergeometric2F1[-5/2, -1/4, 3/4, -((c*x^2)/a)]) + B*x*Hypergeometric2F1[-5/2, 1/4, 5/4, -((c*x^2)/a)]))/((e*x)^(3/2)*Sqrt[1 + (c*x^2)/a])","C",1
454,1,85,378,0.0345819,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{5/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(5/2),x]","-\frac{2 a^2 x \sqrt{a+c x^2} \left(A \, _2F_1\left(-\frac{5}{2},-\frac{3}{4};\frac{1}{4};-\frac{c x^2}{a}\right)+3 B x \, _2F_1\left(-\frac{5}{2},-\frac{1}{4};\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{3 (e x)^{5/2} \sqrt{\frac{c x^2}{a}+1}}","\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^{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{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{8 a c \sqrt{e x} \sqrt{a+c x^2} (5 A+7 B x)}{21 e^3}-\frac{20 \left(a+c x^2\right)^{3/2} (7 a B-3 A c x)}{63 e^2 \sqrt{e x}}-\frac{2 \left(a+c x^2\right)^{5/2} (3 A-B x)}{9 e (e x)^{3/2}}",1,"(-2*a^2*x*Sqrt[a + c*x^2]*(A*Hypergeometric2F1[-5/2, -3/4, 1/4, -((c*x^2)/a)] + 3*B*x*Hypergeometric2F1[-5/2, -1/4, 3/4, -((c*x^2)/a)]))/(3*(e*x)^(5/2)*Sqrt[1 + (c*x^2)/a])","C",1
455,1,86,376,0.0273702,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{7/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(7/2),x]","-\frac{2 a^2 x \sqrt{a+c x^2} \left(3 A \, _2F_1\left(-\frac{5}{2},-\frac{5}{4};-\frac{1}{4};-\frac{c x^2}{a}\right)+5 B x \, _2F_1\left(-\frac{5}{2},-\frac{3}{4};\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{15 (e x)^{7/2} \sqrt{\frac{c x^2}{a}+1}}","\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{8 a c \sqrt{a+c x^2} (63 A-25 B x)}{105 e^3 \sqrt{e x}}-\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{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,"(-2*a^2*x*Sqrt[a + c*x^2]*(3*A*Hypergeometric2F1[-5/2, -5/4, -1/4, -((c*x^2)/a)] + 5*B*x*Hypergeometric2F1[-5/2, -3/4, 1/4, -((c*x^2)/a)]))/(15*(e*x)^(7/2)*Sqrt[1 + (c*x^2)/a])","C",1
456,1,91,377,0.0330177,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{9/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(9/2),x]","-\frac{2 a^2 \sqrt{e x} \sqrt{a+c x^2} \left(5 A \, _2F_1\left(-\frac{5}{2},-\frac{7}{4};-\frac{3}{4};-\frac{c x^2}{a}\right)+7 B x \, _2F_1\left(-\frac{5}{2},-\frac{5}{4};-\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{35 e^5 x^4 \sqrt{\frac{c x^2}{a}+1}}","\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{8 c \sqrt{a+c x^2} (63 a B-25 A c x)}{105 e^4 \sqrt{e x}}-\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{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,"(-2*a^2*Sqrt[e*x]*Sqrt[a + c*x^2]*(5*A*Hypergeometric2F1[-5/2, -7/4, -3/4, -((c*x^2)/a)] + 7*B*x*Hypergeometric2F1[-5/2, -5/4, -1/4, -((c*x^2)/a)]))/(35*e^5*x^4*Sqrt[1 + (c*x^2)/a])","C",1
457,1,91,375,0.0358855,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{11/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(11/2),x]","-\frac{2 a^2 \sqrt{e x} \sqrt{a+c x^2} \left(7 A \, _2F_1\left(-\frac{5}{2},-\frac{9}{4};-\frac{5}{4};-\frac{c x^2}{a}\right)+9 B x \, _2F_1\left(-\frac{5}{2},-\frac{7}{4};-\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{63 e^6 x^5 \sqrt{\frac{c x^2}{a}+1}}","\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{8 c^2 \sqrt{a+c x^2} (7 A-5 B x)}{21 e^5 \sqrt{e x}}-\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,"(-2*a^2*Sqrt[e*x]*Sqrt[a + c*x^2]*(7*A*Hypergeometric2F1[-5/2, -9/4, -5/4, -((c*x^2)/a)] + 9*B*x*Hypergeometric2F1[-5/2, -7/4, -3/4, -((c*x^2)/a)]))/(63*e^6*x^5*Sqrt[1 + (c*x^2)/a])","C",1
458,1,142,388,0.0731538,"\int \frac{(e x)^{7/2} (A+B x)}{\sqrt{a+c x^2}} \, dx","Integrate[((e*x)^(7/2)*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{2 e^3 \sqrt{e x} \left(75 a^2 A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+49 a^2 B x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-\left(a+c x^2\right) \left(a (75 A+49 B x)-5 c x^2 (9 A+7 B x)\right)\right)}{315 c^2 \sqrt{a+c x^2}}","\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^{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{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{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,"(2*e^3*Sqrt[e*x]*(-((a + c*x^2)*(-5*c*x^2*(9*A + 7*B*x) + a*(75*A + 49*B*x))) + 75*a^2*A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] + 49*a^2*B*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(315*c^2*Sqrt[a + c*x^2])","C",1
459,1,133,356,0.0627715,"\int \frac{(e x)^{5/2} (A+B x)}{\sqrt{a+c x^2}} \, dx","Integrate[((e*x)^(5/2)*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{2 e^2 \sqrt{e x} \left(25 a^2 B \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)-\left(a+c x^2\right) (25 a B-3 c x (7 A+5 B x))-21 a A c x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)\right)}{105 c^2 \sqrt{a+c x^2}}","\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,"(2*e^2*Sqrt[e*x]*(-((a + c*x^2)*(25*a*B - 3*c*x*(7*A + 5*B*x))) + 25*a^2*B*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - 21*a*A*c*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(105*c^2*Sqrt[a + c*x^2])","C",1
460,1,118,326,0.0513451,"\int \frac{(e x)^{3/2} (A+B x)}{\sqrt{a+c x^2}} \, dx","Integrate[((e*x)^(3/2)*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{2 e \sqrt{e x} \left(\left(a+c x^2\right) (5 A+3 B x)-5 a A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)-3 a B x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)\right)}{15 c \sqrt{a+c x^2}}","-\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*e*Sqrt[e*x]*((5*A + 3*B*x)*(a + c*x^2) - 5*a*A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - 3*a*B*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(15*c*Sqrt[a + c*x^2])","C",1
461,1,109,287,0.0410245,"\int \frac{\sqrt{e x} (A+B x)}{\sqrt{a+c x^2}} \, dx","Integrate[(Sqrt[e*x]*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{2 \sqrt{e x} \left(A c x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-a B \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+B \left(a+c x^2\right)\right)}{3 c \sqrt{a+c x^2}}","-\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*Sqrt[e*x]*(B*(a + c*x^2) - a*B*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] + A*c*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(3*c*Sqrt[a + c*x^2])","C",1
462,1,82,253,0.0259391,"\int \frac{A+B x}{\sqrt{e x} \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/(Sqrt[e*x]*Sqrt[a + c*x^2]),x]","\frac{2 x \sqrt{\frac{c x^2}{a}+1} \left(3 A \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+B x \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)\right)}{3 \sqrt{e x} \sqrt{a+c x^2}}","\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*x*Sqrt[1 + (c*x^2)/a]*(3*A*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] + B*x*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(3*Sqrt[e*x]*Sqrt[a + c*x^2])","C",1
463,1,80,293,0.0317869,"\int \frac{A+B x}{(e x)^{3/2} \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/((e*x)^(3/2)*Sqrt[a + c*x^2]),x]","\frac{2 x \sqrt{\frac{c x^2}{a}+1} \left(B x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)-A \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{(e x)^{3/2} \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+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*x*Sqrt[1 + (c*x^2)/a]*(-(A*Hypergeometric2F1[-1/4, 1/2, 3/4, -((c*x^2)/a)]) + B*x*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)]))/((e*x)^(3/2)*Sqrt[a + c*x^2])","C",1
464,1,82,327,0.0317015,"\int \frac{A+B x}{(e x)^{5/2} \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/((e*x)^(5/2)*Sqrt[a + c*x^2]),x]","-\frac{2 x \sqrt{\frac{c x^2}{a}+1} \left(A \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-\frac{c x^2}{a}\right)+3 B x \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{c x^2}{a}\right)\right)}{3 (e x)^{5/2} \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(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*x*Sqrt[1 + (c*x^2)/a]*(A*Hypergeometric2F1[-3/4, 1/2, 1/4, -((c*x^2)/a)] + 3*B*x*Hypergeometric2F1[-1/4, 1/2, 3/4, -((c*x^2)/a)]))/(3*(e*x)^(5/2)*Sqrt[a + c*x^2])","C",1
465,1,83,363,0.0298232,"\int \frac{A+B x}{(e x)^{7/2} \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/((e*x)^(7/2)*Sqrt[a + c*x^2]),x]","-\frac{2 x \sqrt{\frac{c x^2}{a}+1} \left(3 A \, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};-\frac{c x^2}{a}\right)+5 B x \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{15 (e x)^{7/2} \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(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^{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^{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 \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*x*Sqrt[1 + (c*x^2)/a]*(3*A*Hypergeometric2F1[-5/4, 1/2, -1/4, -((c*x^2)/a)] + 5*B*x*Hypergeometric2F1[-3/4, 1/2, 1/4, -((c*x^2)/a)]))/(15*(e*x)^(7/2)*Sqrt[a + c*x^2])","C",1
466,1,127,360,0.0667052,"\int \frac{(e x)^{7/2} (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[((e*x)^(7/2)*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{e^3 \sqrt{e x} \left(-25 a A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+25 a A-21 a B x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+21 a B x+10 A c x^2+6 B c x^3\right)}{15 c^2 \sqrt{a+c x^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^3*Sqrt[e*x]*(25*a*A + 21*a*B*x + 10*A*c*x^2 + 6*B*c*x^3 - 25*a*A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - 21*a*B*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(15*c^2*Sqrt[a + c*x^2])","C",1
467,1,120,326,0.0597759,"\int \frac{(e x)^{5/2} (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[((e*x)^(5/2)*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{e^2 \sqrt{e x} \left(3 A c x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-5 a B \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+5 a B-3 A c x+2 B c x^2\right)}{3 c^2 \sqrt{a+c x^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^2*Sqrt[e*x]*(5*a*B - 3*A*c*x + 2*B*c*x^2 - 5*a*B*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] + 3*A*c*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(3*c^2*Sqrt[a + c*x^2])","C",1
468,1,102,296,0.0507325,"\int \frac{(e x)^{3/2} (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[((e*x)^(3/2)*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{e \sqrt{e x} \left(A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+B x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-A-B x\right)}{c \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 + A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] + B*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(c*Sqrt[a + c*x^2])","C",1
469,1,113,298,0.0609655,"\int \frac{\sqrt{e x} (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[(Sqrt[e*x]*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{\sqrt{e x} \left(-A c x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+3 a B \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)-3 a B+3 A c x\right)}{3 a c \sqrt{a+c x^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-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]*(-3*a*B + 3*A*c*x + 3*a*B*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - A*c*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(3*a*c*Sqrt[a + c*x^2])","C",1
470,1,107,290,0.054243,"\int \frac{A+B x}{\sqrt{e x} \left(a+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(Sqrt[e*x]*(a + c*x^2)^(3/2)),x]","\frac{x \left(3 A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)-B x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+3 (A+B x)\right)}{3 a \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-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,"(x*(3*(A + B*x) + 3*A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - B*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(3*a*Sqrt[e*x]*Sqrt[a + c*x^2])","C",1
471,1,100,327,0.0486635,"\int \frac{A+B x}{(e x)^{3/2} \left(a+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((e*x)^(3/2)*(a + c*x^2)^(3/2)),x]","\frac{x \left(-3 A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{c x^2}{a}\right)+B x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+A+B x\right)}{a (e x)^{3/2} \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[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{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{A+B x}{a e \sqrt{e x} \sqrt{a+c x^2}}",1,"(x*(A + B*x - 3*A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-1/4, 1/2, 3/4, -((c*x^2)/a)] + B*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)]))/(a*(e*x)^(3/2)*Sqrt[a + c*x^2])","C",1
472,1,107,357,0.05718,"\int \frac{A+B x}{(e x)^{5/2} \left(a+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((e*x)^(5/2)*(a + c*x^2)^(3/2)),x]","\frac{x \left(3 \left(-3 B x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{c x^2}{a}\right)+A+B x\right)-5 A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-\frac{c x^2}{a}\right)\right)}{3 a (e x)^{5/2} \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{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{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{A+B x}{a e (e x)^{3/2} \sqrt{a+c x^2}}",1,"(x*(-5*A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-3/4, 1/2, 1/4, -((c*x^2)/a)] + 3*(A + B*x - 3*B*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-1/4, 1/2, 3/4, -((c*x^2)/a)])))/(3*a*(e*x)^(5/2)*Sqrt[a + c*x^2])","C",1
473,1,107,393,0.0584917,"\int \frac{A+B x}{(e x)^{7/2} \left(a+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((e*x)^(7/2)*(a + c*x^2)^(3/2)),x]","\frac{x \left(-21 A \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};-\frac{c x^2}{a}\right)-25 B x \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-\frac{c x^2}{a}\right)+15 (A+B x)\right)}{15 a (e x)^{7/2} \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^{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^{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 \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,"(x*(15*(A + B*x) - 21*A*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-5/4, 1/2, -1/4, -((c*x^2)/a)] - 25*B*x*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-3/4, 1/2, 1/4, -((c*x^2)/a)]))/(15*a*(e*x)^(7/2)*Sqrt[a + c*x^2])","C",1
474,1,183,428,0.1397376,"\int \frac{(e x)^{13/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[((e*x)^(13/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{e^6 \sqrt{e x} \left(-975 a^3 B+539 a^2 A c x+975 a^2 B \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)-1365 a^2 B c x^2+693 a A c^2 x^3-539 a A c x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-260 a B c^2 x^4+84 A c^3 x^5+60 B c^3 x^6\right)}{210 c^4 \left(a+c x^2\right)^{3/2}}","\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^6*Sqrt[e*x]*(-975*a^3*B + 539*a^2*A*c*x - 1365*a^2*B*c*x^2 + 693*a*A*c^2*x^3 - 260*a*B*c^2*x^4 + 84*A*c^3*x^5 + 60*B*c^3*x^6 + 975*a^2*B*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - 539*a*A*c*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(210*c^4*(a + c*x^2)^(3/2))","C",1
475,1,165,398,0.1276918,"\int \frac{(e x)^{11/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[((e*x)^(11/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{e^5 \sqrt{e x} \left(75 a^2 A+77 a^2 B x-75 a A \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+105 a A c x^2-77 a B x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+99 a B c x^3+20 A c^2 x^4+12 B c^2 x^5\right)}{30 c^3 \left(a+c x^2\right)^{3/2}}","-\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^5*Sqrt[e*x]*(75*a^2*A + 77*a^2*B*x + 105*a*A*c*x^2 + 99*a*B*c*x^3 + 20*A*c^2*x^4 + 12*B*c^2*x^5 - 75*a*A*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - 77*a*B*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(30*c^3*(a + c*x^2)^(3/2))","C",1
476,1,156,368,0.1203834,"\int \frac{(e x)^{9/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[((e*x)^(9/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{e^4 \sqrt{e x} \left(15 a^2 B+7 A c x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-7 a A c x-15 a B \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+21 a B c x^2-9 A c^2 x^3+4 B c^2 x^4\right)}{6 c^3 \left(a+c x^2\right)^{3/2}}","-\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^3 (e x)^{3/2} (7 A+9 B x)}{6 c^2 \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^4*Sqrt[e*x]*(15*a^2*B - 7*a*A*c*x + 21*a*B*c*x^2 - 9*A*c^2*x^3 + 4*B*c^2*x^4 - 15*a*B*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] + 7*A*c*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(6*c^3*(a + c*x^2)^(3/2))","C",1
477,1,139,339,0.1118252,"\int \frac{(e x)^{7/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[((e*x)^(7/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{e^3 \sqrt{e x} \left(5 A \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)-5 a A+7 B x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)-7 a B x-7 A c x^2-9 B c x^3\right)}{6 c^2 \left(a+c x^2\right)^{3/2}}","\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^3 \sqrt{e x} (5 A+7 B x)}{6 c^2 \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^3*Sqrt[e*x]*(-5*a*A - 7*a*B*x - 7*A*c*x^2 - 9*B*c*x^3 + 5*A*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] + 7*B*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(6*c^2*(a + c*x^2)^(3/2))","C",1
478,1,149,347,0.1559495,"\int \frac{(e x)^{5/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[((e*x)^(5/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{e^2 \sqrt{e x} \left(-5 a^2 B-A c x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+a A c x+5 a B \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)-7 a B c x^2+3 A c^2 x^3\right)}{6 a c^2 \left(a+c x^2\right)^{3/2}}","\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^2*Sqrt[e*x]*(-5*a^2*B + a*A*c*x - 7*a*B*c*x^2 + 3*A*c^2*x^3 + 5*a*B*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - A*c*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(6*a*c^2*(a + c*x^2)^(3/2))","C",1
479,1,137,341,0.1459567,"\int \frac{(e x)^{3/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[((e*x)^(3/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{e \sqrt{e x} \left(A \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)-a A-B x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+a B x+A c x^2+3 B c x^3\right)}{6 a c \left(a+c x^2\right)^{3/2}}","-\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)}{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*A) + a*B*x + A*c*x^2 + 3*B*c*x^3 + A*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - B*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(6*a*c*(a + c*x^2)^(3/2))","C",1
480,1,145,342,0.1291445,"\int \frac{\sqrt{e x} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[(Sqrt[e*x]*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{\sqrt{e x} \left(-a^2 B-A c x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+5 a A c x+a B \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+a B c x^2+3 A c^2 x^3\right)}{6 a^2 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{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{\sqrt{e x} (a B+3 A c x)}{6 a^2 c \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^2*B) + 5*a*A*c*x + a*B*c*x^2 + 3*A*c^2*x^3 + a*B*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] - A*c*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(6*a^2*c*(a + c*x^2)^(3/2))","C",1
481,1,140,335,0.1077339,"\int \frac{A+B x}{\sqrt{e x} \left(a+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(Sqrt[e*x]*(a + c*x^2)^(5/2)),x]","\frac{x \left(7 a A-B x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^2}{a}\right)+5 a B x+5 A c x^2+3 B c x^3\right)+5 A x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)}{6 a^2 \sqrt{e x} \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{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{\sqrt{e x} (5 A+3 B x)}{6 a^2 e \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,"(5*A*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)] + x*(7*a*A + 5*a*B*x + 5*A*c*x^2 + 3*B*c*x^3 - B*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((c*x^2)/a)]))/(6*a^2*Sqrt[e*x]*(a + c*x^2)^(3/2))","C",1
482,1,137,373,0.0887676,"\int \frac{A+B x}{(e x)^{3/2} \left(a+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((e*x)^(3/2)*(a + c*x^2)^(5/2)),x]","\frac{x \left(-21 A \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{c x^2}{a}\right)+9 a A+5 B x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{c x^2}{a}\right)+7 a B x+7 A c x^2+5 B c x^3\right)}{6 a^2 (e x)^{3/2} \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(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[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{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+5 B x}{6 a^2 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,"(x*(9*a*A + 7*a*B*x + 7*A*c*x^2 + 5*B*c*x^3 - 21*A*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-1/4, 1/2, 3/4, -((c*x^2)/a)] + 5*B*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((c*x^2)/a)]))/(6*a^2*(e*x)^(3/2)*(a + c*x^2)^(3/2))","C",1
483,1,137,402,0.0926092,"\int \frac{A+B x}{(e x)^{5/2} \left(a+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((e*x)^(5/2)*(a + c*x^2)^(5/2)),x]","\frac{x \left(-15 A \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-\frac{c x^2}{a}\right)+11 a A-21 B x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{c x^2}{a}\right)+9 a B x+9 A c x^2+7 B c x^3\right)}{6 a^2 (e x)^{5/2} \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{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{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{9 A+7 B x}{6 a^2 e (e x)^{3/2} \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,"(x*(11*a*A + 9*a*B*x + 9*A*c*x^2 + 7*B*c*x^3 - 15*A*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-3/4, 1/2, 1/4, -((c*x^2)/a)] - 21*B*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-1/4, 1/2, 3/4, -((c*x^2)/a)]))/(6*a^2*(e*x)^(5/2)*(a + c*x^2)^(3/2))","C",1
484,1,137,432,0.0921554,"\int \frac{A+B x}{(e x)^{7/2} \left(a+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((e*x)^(7/2)*(a + c*x^2)^(5/2)),x]","\frac{x \left(-77 A \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};-\frac{c x^2}{a}\right)+65 a A-75 B x \left(a+c x^2\right) \sqrt{\frac{c x^2}{a}+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-\frac{c x^2}{a}\right)+55 a B x+55 A c x^2+45 B c x^3\right)}{30 a^2 (e x)^{7/2} \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{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^{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 \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{11 A+9 B x}{6 a^2 e (e x)^{5/2} \sqrt{a+c x^2}}+\frac{A+B x}{3 a e (e x)^{5/2} \left(a+c x^2\right)^{3/2}}",1,"(x*(65*a*A + 55*a*B*x + 55*A*c*x^2 + 45*B*c*x^3 - 77*A*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-5/4, 1/2, -1/4, -((c*x^2)/a)] - 75*B*x*(a + c*x^2)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[-3/4, 1/2, 1/4, -((c*x^2)/a)]))/(30*a^2*(e*x)^(7/2)*(a + c*x^2)^(3/2))","C",1
485,1,128,217,0.3028435,"\int (e x)^m (A+B x) \left(a+c x^2\right)^4 \, dx","Integrate[(e*x)^m*(A + B*x)*(a + c*x^2)^4,x]","x (e x)^m \left(a^4 \left(\frac{A}{m+1}+\frac{B x}{m+2}\right)+4 a^3 c x^2 \left(\frac{A}{m+3}+\frac{B x}{m+4}\right)+6 a^2 c^2 x^4 \left(\frac{A}{m+5}+\frac{B x}{m+6}\right)+4 a c^3 x^6 \left(\frac{A}{m+7}+\frac{B x}{m+8}\right)+c^4 x^8 \left(\frac{A}{m+9}+\frac{B x}{m+10}\right)\right)","\frac{a^4 A (e x)^{m+1}}{e (m+1)}+\frac{a^4 B (e x)^{m+2}}{e^2 (m+2)}+\frac{4 a^3 A c (e x)^{m+3}}{e^3 (m+3)}+\frac{4 a^3 B c (e x)^{m+4}}{e^4 (m+4)}+\frac{6 a^2 A c^2 (e x)^{m+5}}{e^5 (m+5)}+\frac{6 a^2 B c^2 (e x)^{m+6}}{e^6 (m+6)}+\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,"x*(e*x)^m*(a^4*(A/(1 + m) + (B*x)/(2 + m)) + 4*a^3*c*x^2*(A/(3 + m) + (B*x)/(4 + m)) + 6*a^2*c^2*x^4*(A/(5 + m) + (B*x)/(6 + m)) + 4*a*c^3*x^6*(A/(7 + m) + (B*x)/(8 + m)) + c^4*x^8*(A/(9 + m) + (B*x)/(10 + m)))","A",1
486,1,101,169,0.2168519,"\int (e x)^m (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[(e*x)^m*(A + B*x)*(a + c*x^2)^3,x]","x (e x)^m \left(a^3 \left(\frac{A}{m+1}+\frac{B x}{m+2}\right)+3 a^2 c x^2 \left(\frac{A}{m+3}+\frac{B x}{m+4}\right)+3 a c^2 x^4 \left(\frac{A}{m+5}+\frac{B x}{m+6}\right)+c^3 x^6 \left(\frac{A}{m+7}+\frac{B x}{m+8}\right)\right)","\frac{a^3 A (e x)^{m+1}}{e (m+1)}+\frac{a^3 B (e x)^{m+2}}{e^2 (m+2)}+\frac{3 a^2 A c (e x)^{m+3}}{e^3 (m+3)}+\frac{3 a^2 B c (e x)^{m+4}}{e^4 (m+4)}+\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,"x*(e*x)^m*(a^3*(A/(1 + m) + (B*x)/(2 + m)) + 3*a^2*c*x^2*(A/(3 + m) + (B*x)/(4 + m)) + 3*a*c^2*x^4*(A/(5 + m) + (B*x)/(6 + m)) + c^3*x^6*(A/(7 + m) + (B*x)/(8 + m)))","A",1
487,1,74,121,0.0732122,"\int (e x)^m (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[(e*x)^m*(A + B*x)*(a + c*x^2)^2,x]","x (e x)^m \left(a^2 \left(\frac{A}{m+1}+\frac{B x}{m+2}\right)+2 a c x^2 \left(\frac{A}{m+3}+\frac{B x}{m+4}\right)+c^2 x^4 \left(\frac{A}{m+5}+\frac{B x}{m+6}\right)\right)","\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,"x*(e*x)^m*(a^2*(A/(1 + m) + (B*x)/(2 + m)) + 2*a*c*x^2*(A/(3 + m) + (B*x)/(4 + m)) + c^2*x^4*(A/(5 + m) + (B*x)/(6 + m)))","A",1
488,1,47,73,0.0409419,"\int (e x)^m (A+B x) \left(a+c x^2\right) \, dx","Integrate[(e*x)^m*(A + B*x)*(a + c*x^2),x]","x (e x)^m \left(a \left(\frac{A}{m+1}+\frac{B x}{m+2}\right)+c x^2 \left(\frac{A}{m+3}+\frac{B x}{m+4}\right)\right)","\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,"x*(e*x)^m*(a*(A/(1 + m) + (B*x)/(2 + m)) + c*x^2*(A/(3 + m) + (B*x)/(4 + m)))","A",1
489,1,82,91,0.0302,"\int \frac{(e x)^m (A+B x)}{a+c x^2} \, dx","Integrate[((e*x)^m*(A + B*x))/(a + c*x^2),x]","\frac{x (e x)^m \left(A (m+2) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(1,\frac{m}{2}+1;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{a (m+1) (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,"(x*(e*x)^m*(B*(1 + m)*x*Hypergeometric2F1[1, 1 + m/2, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)]))/(a*(1 + m)*(2 + m))","A",1
490,1,82,91,0.0279489,"\int \frac{(e x)^m (A+B x)}{\left(a+c x^2\right)^2} \, dx","Integrate[((e*x)^m*(A + B*x))/(a + c*x^2)^2,x]","\frac{x (e x)^m \left(A (m+2) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(2,\frac{m}{2}+1;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{a^2 (m+1) (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,"(x*(e*x)^m*(B*(1 + m)*x*Hypergeometric2F1[2, 1 + m/2, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)]))/(a^2*(1 + m)*(2 + m))","A",1
491,1,82,91,0.0292763,"\int \frac{(e x)^m (A+B x)}{\left(a+c x^2\right)^3} \, dx","Integrate[((e*x)^m*(A + B*x))/(a + c*x^2)^3,x]","\frac{x (e x)^m \left(A (m+2) \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(3,\frac{m}{2}+1;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{a^3 (m+1) (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,"(x*(e*x)^m*(B*(1 + m)*x*Hypergeometric2F1[3, 1 + m/2, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)]))/(a^3*(1 + m)*(2 + m))","A",1
492,1,111,145,0.0542353,"\int (e x)^m (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Integrate[(e*x)^m*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{a^2 x \sqrt{a+c x^2} (e x)^m \left(A (m+2) \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(-\frac{5}{2},\frac{m}{2}+1;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{(m+1) (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*x*(e*x)^m*Sqrt[a + c*x^2]*(B*(1 + m)*x*Hypergeometric2F1[-5/2, 1 + m/2, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[-5/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)]))/((1 + m)*(2 + m)*Sqrt[1 + (c*x^2)/a])","A",1
493,1,109,141,0.0485406,"\int (e x)^m (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Integrate[(e*x)^m*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{a x \sqrt{a+c x^2} (e x)^m \left(A (m+2) \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(-\frac{3}{2},\frac{m}{2}+1;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{(m+1) (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*x*(e*x)^m*Sqrt[a + c*x^2]*(B*(1 + m)*x*Hypergeometric2F1[-3/2, 1 + m/2, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[-3/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)]))/((1 + m)*(2 + m)*Sqrt[1 + (c*x^2)/a])","A",1
494,1,108,139,0.0444632,"\int (e x)^m (A+B x) \sqrt{a+c x^2} \, dx","Integrate[(e*x)^m*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{x \sqrt{a+c x^2} (e x)^m \left(A (m+2) \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(-\frac{1}{2},\frac{m}{2}+1;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{(m+1) (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,"(x*(e*x)^m*Sqrt[a + c*x^2]*(B*(1 + m)*x*Hypergeometric2F1[-1/2, 1 + m/2, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)]))/((1 + m)*(2 + m)*Sqrt[1 + (c*x^2)/a])","A",1
495,1,108,139,0.0479644,"\int \frac{(e x)^m (A+B x)}{\sqrt{a+c x^2}} \, dx","Integrate[((e*x)^m*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{x \sqrt{\frac{c x^2}{a}+1} (e x)^m \left(A (m+2) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(\frac{1}{2},\frac{m}{2}+1;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{(m+1) (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,"(x*(e*x)^m*Sqrt[1 + (c*x^2)/a]*(B*(1 + m)*x*Hypergeometric2F1[1/2, 1 + m/2, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)]))/((1 + m)*(2 + m)*Sqrt[a + c*x^2])","A",1
496,1,111,145,0.0479615,"\int \frac{(e x)^m (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[((e*x)^m*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{x \sqrt{\frac{c x^2}{a}+1} (e x)^m \left(A (m+2) \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(\frac{3}{2},\frac{m}{2}+1;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{a (m+1) (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,"(x*(e*x)^m*Sqrt[1 + (c*x^2)/a]*(B*(1 + m)*x*Hypergeometric2F1[3/2, 1 + m/2, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)]))/(a*(1 + m)*(2 + m)*Sqrt[a + c*x^2])","A",1
497,1,111,145,0.0499287,"\int \frac{(e x)^m (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[((e*x)^m*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{x \sqrt{\frac{c x^2}{a}+1} (e x)^m \left(A (m+2) \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(\frac{5}{2},\frac{m}{2}+1;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{a^2 (m+1) (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,"(x*(e*x)^m*Sqrt[1 + (c*x^2)/a]*(B*(1 + m)*x*Hypergeometric2F1[5/2, 1 + m/2, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[5/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)]))/(a^2*(1 + m)*(2 + m)*Sqrt[a + c*x^2])","A",1
498,1,67,70,0.0336655,"\int \frac{x^m (1+a x)}{\left(1-a^2 x^2\right)^2} \, dx","Integrate[(x^m*(1 + a*x))/(1 - a^2*x^2)^2,x]","x^{m+1} \left(\frac{a x \, _2F_1\left(2,\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)}{m+2}+\frac{\, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}\right)","\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)*((a*x*Hypergeometric2F1[2, 1 + m/2, 2 + m/2, a^2*x^2])/(2 + m) + Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2]/(1 + m))","A",1
499,1,67,70,0.0063035,"\int \frac{x^m}{(1-a x)^2 (1+a x)} \, dx","Integrate[x^m/((1 - a*x)^2*(1 + a*x)),x]","x^{m+1} \left(\frac{a x \, _2F_1\left(2,\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)}{m+2}+\frac{\, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}\right)","\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)*((a*x*Hypergeometric2F1[2, 1 + m/2, 2 + m/2, a^2*x^2])/(2 + m) + Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2]/(1 + m))","A",1
500,1,67,70,0.0058192,"\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","Integrate[x^m/(1 - a^2*x^2)^2 + (a*x^(1 + m))/(1 - a^2*x^2)^2,x]","x^{m+1} \left(\frac{a x \, _2F_1\left(2,\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)}{m+2}+\frac{\, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}\right)","\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)*((a*x*Hypergeometric2F1[2, 1 + m/2, 2 + m/2, a^2*x^2])/(2 + m) + Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2]/(1 + m))","A",1
501,1,67,70,0.0059846,"\int \frac{x^m}{(1-a x) \left(1-a^2 x^2\right)} \, dx","Integrate[x^m/((1 - a*x)*(1 - a^2*x^2)),x]","x^{m+1} \left(\frac{a x \, _2F_1\left(2,\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)}{m+2}+\frac{\, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}\right)","\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)*((a*x*Hypergeometric2F1[2, 1 + m/2, 2 + m/2, a^2*x^2])/(2 + m) + Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2]/(1 + m))","A",1
502,1,106,135,0.0379201,"\int (e x)^m (A+B x) \left(a+c x^2\right)^p \, dx","Integrate[(e*x)^m*(A + B*x)*(a + c*x^2)^p,x]","\frac{x (e x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(A (m+2) \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)+B (m+1) x \, _2F_1\left(\frac{m}{2}+1,-p;\frac{m}{2}+2;-\frac{c x^2}{a}\right)\right)}{(m+1) (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,"(x*(e*x)^m*(a + c*x^2)^p*(B*(1 + m)*x*Hypergeometric2F1[1 + m/2, -p, 2 + m/2, -((c*x^2)/a)] + A*(2 + m)*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, -((c*x^2)/a)]))/((1 + m)*(2 + m)*(1 + (c*x^2)/a)^p)","A",1
503,1,87,100,0.0832377,"\int x^3 (d+e x) \left(a+c x^2\right)^p \, dx","Integrate[x^3*(d + e*x)*(a + c*x^2)^p,x]","\frac{1}{10} \left(a+c x^2\right)^p \left(2 e x^5 \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{5 d \left(a+c x^2\right) \left(a-c (p+1) x^2\right)}{c^2 (p+1) (p+2)}\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 + c*x^2)^p*((-5*d*(a + c*x^2)*(a - c*(1 + p)*x^2))/(c^2*(1 + p)*(2 + p)) + (2*e*x^5*Hypergeometric2F1[5/2, -p, 7/2, -((c*x^2)/a)])/(1 + (c*x^2)/a)^p))/10","A",1
504,1,87,100,0.0674116,"\int x^2 (d+e x) \left(a+c x^2\right)^p \, dx","Integrate[x^2*(d + e*x)*(a + c*x^2)^p,x]","\frac{1}{6} \left(a+c x^2\right)^p \left(2 d x^3 \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{3 e \left(a+c x^2\right) \left(a-c (p+1) x^2\right)}{c^2 (p+1) (p+2)}\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 + c*x^2)^p*((-3*e*(a + c*x^2)*(a - c*(1 + p)*x^2))/(c^2*(1 + p)*(2 + p)) + (2*d*x^3*Hypergeometric2F1[3/2, -p, 5/2, -((c*x^2)/a)])/(1 + (c*x^2)/a)^p))/6","A",1
505,1,71,75,0.0326196,"\int x (d+e x) \left(a+c x^2\right)^p \, dx","Integrate[x*(d + e*x)*(a + c*x^2)^p,x]","\frac{1}{6} \left(a+c x^2\right)^p \left(\frac{3 d \left(a+c x^2\right)}{c (p+1)}+2 e x^3 \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)\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,"((a + c*x^2)^p*((3*d*(a + c*x^2))/(c*(1 + p)) + (2*e*x^3*Hypergeometric2F1[3/2, -p, 5/2, -((c*x^2)/a)])/(1 + (c*x^2)/a)^p))/6","A",1
506,1,98,70,0.0548653,"\int (d+e x) \left(a+c x^2\right)^p \, dx","Integrate[(d + e*x)*(a + c*x^2)^p,x]","\frac{\left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(2 c d (p+1) x \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)+c e x^2 \left(\frac{c x^2}{a}+1\right)^p+a e \left(\left(\frac{c x^2}{a}+1\right)^p-1\right)\right)}{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,"((a + c*x^2)^p*(c*e*x^2*(1 + (c*x^2)/a)^p + a*e*(-1 + (1 + (c*x^2)/a)^p) + 2*c*d*(1 + p)*x*Hypergeometric2F1[1/2, -p, 3/2, -((c*x^2)/a)]))/(2*c*(1 + p)*(1 + (c*x^2)/a)^p)","A",1
507,1,88,88,0.0519284,"\int \frac{(d+e x) \left(a+c x^2\right)^p}{x} \, dx","Integrate[((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",1
508,1,91,91,0.0532248,"\int \frac{(d+e x) \left(a+c x^2\right)^p}{x^2} \, dx","Integrate[((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",1
509,1,89,92,0.0441358,"\int \frac{(d+e x) \left(a+c x^2\right)^p}{x^3} \, dx","Integrate[((d + e*x)*(a + c*x^2)^p)/x^3,x]","\frac{1}{2} \left(a+c x^2\right)^p \left(\frac{c d \left(a+c x^2\right) \, _2F_1\left(2,p+1;p+2;\frac{c x^2}{a}+1\right)}{a^2 (p+1)}-\frac{2 e \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}\right)","\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,"((a + c*x^2)^p*((-2*e*Hypergeometric2F1[-1/2, -p, 1/2, -((c*x^2)/a)])/(x*(1 + (c*x^2)/a)^p) + (c*d*(a + c*x^2)*Hypergeometric2F1[2, 1 + p, 2 + p, 1 + (c*x^2)/a])/(a^2*(1 + p))))/2","A",1
510,1,55,55,0.0087015,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[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",1
511,1,55,55,0.0073984,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[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",1
512,1,50,55,0.0123945,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{60} x^3 \left(5 a^2 (4 A+3 B x)+6 a b x (5 A+4 B x)+2 b^2 x^2 (6 A+5 B x)\right)","\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,"(x^3*(5*a^2*(4*A + 3*B*x) + 6*a*b*x*(5*A + 4*B*x) + 2*b^2*x^2*(6*A + 5*B*x)))/60","A",1
513,1,50,55,0.0104488,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{60} x^2 \left(10 a^2 (3 A+2 B x)+10 a b x (4 A+3 B x)+3 b^2 x^2 (5 A+4 B x)\right)","\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,"(x^2*(10*a^2*(3*A + 2*B*x) + 10*a*b*x*(4*A + 3*B*x) + 3*b^2*x^2*(5*A + 4*B*x)))/60","A",1
514,1,46,38,0.0089606,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{12} x \left(6 a^2 (2 A+B x)+4 a b x (3 A+2 B x)+b^2 x^2 (4 A+3 B x)\right)","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}",1,"(x*(6*a^2*(2*A + B*x) + 4*a*b*x*(3*A + 2*B*x) + b^2*x^2*(4*A + 3*B*x)))/12","A",1
515,1,43,40,0.0152112,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x,x]","a^2 A \log (x)+a^2 B x+a b x (2 A+B x)+\frac{1}{6} b^2 x^2 (3 A+2 B 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",1,"a^2*B*x + a*b*x*(2*A + B*x) + (b^2*x^2*(3*A + 2*B*x))/6 + a^2*A*Log[x]","A",1
516,1,43,44,0.0227108,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^2} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^2,x]","-\frac{a^2 A}{x}+a \log (x) (a B+2 A b)+2 a b B x+\frac{1}{2} b^2 x (2 A+B 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",1,"-((a^2*A)/x) + 2*a*b*B*x + (b^2*x*(2*A + B*x))/2 + a*(2*A*b + a*B)*Log[x]","A",1
517,1,43,44,0.0254216,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^3} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^3,x]","-\frac{a^2 (A+2 B x)}{2 x^2}+b \log (x) (2 a B+A b)-\frac{2 a A b}{x}+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,"(-2*a*A*b)/x + b^2*B*x - (a^2*(A + 2*B*x))/(2*x^2) + b*(A*b + 2*a*B)*Log[x]","A",1
518,1,48,49,0.0253701,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^4} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^4,x]","b^2 B \log (x)-\frac{a^2 (2 A+3 B x)+6 a b x (A+2 B x)+6 A b^2 x^2}{6 x^3}","-\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,"-1/6*(6*A*b^2*x^2 + 6*a*b*x*(A + 2*B*x) + a^2*(2*A + 3*B*x))/x^3 + b^2*B*Log[x]","A",1
519,1,47,44,0.0161812,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^5} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^5,x]","-\frac{a^2 (3 A+4 B x)+4 a b x (2 A+3 B x)+6 b^2 x^2 (A+2 B x)}{12 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,"-1/12*(6*b^2*x^2*(A + 2*B*x) + 4*a*b*x*(2*A + 3*B*x) + a^2*(3*A + 4*B*x))/x^4","A",1
520,1,50,55,0.0152215,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^6} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^6,x]","-\frac{3 a^2 (4 A+5 B x)+10 a b x (3 A+4 B x)+10 b^2 x^2 (2 A+3 B x)}{60 x^5}","-\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,"-1/60*(10*b^2*x^2*(2*A + 3*B*x) + 10*a*b*x*(3*A + 4*B*x) + 3*a^2*(4*A + 5*B*x))/x^5","A",1
521,1,50,55,0.0163141,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^7} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^7,x]","-\frac{2 a^2 (5 A+6 B x)+6 a b x (4 A+5 B x)+5 b^2 x^2 (3 A+4 B x)}{60 x^6}","-\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,"-1/60*(5*b^2*x^2*(3*A + 4*B*x) + 6*a*b*x*(4*A + 5*B*x) + 2*a^2*(5*A + 6*B*x))/x^6","A",1
522,1,50,55,0.0162935,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^8} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^8,x]","-\frac{10 a^2 (6 A+7 B x)+28 a b x (5 A+6 B x)+21 b^2 x^2 (4 A+5 B x)}{420 x^7}","-\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,"-1/420*(21*b^2*x^2*(4*A + 5*B*x) + 28*a*b*x*(5*A + 6*B*x) + 10*a^2*(6*A + 7*B*x))/x^7","A",1
523,1,99,99,0.0139727,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{1}{5} a^4 A x^5+\frac{1}{6} a^3 x^6 (a B+4 A b)+\frac{2}{7} a^2 b x^7 (2 a B+3 A b)+\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{1}{5} a^4 A x^5+\frac{1}{6} a^3 x^6 (a B+4 A b)+\frac{2}{7} a^2 b x^7 (2 a B+3 A b)+\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",1
524,1,99,99,0.0125194,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[x^3*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{1}{4} a^4 A x^4+\frac{1}{5} a^3 x^5 (a B+4 A b)+\frac{1}{3} a^2 b x^6 (2 a B+3 A b)+\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}{4} a^4 A x^4+\frac{1}{5} a^3 x^5 (a B+4 A b)+\frac{1}{3} a^2 b x^6 (2 a B+3 A b)+\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",1
525,1,88,87,0.0256224,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{1}{840} x^3 \left(70 a^4 (4 A+3 B x)+168 a^3 b x (5 A+4 B x)+168 a^2 b^2 x^2 (6 A+5 B x)+80 a b^3 x^3 (7 A+6 B x)+15 b^4 x^4 (8 A+7 B x)\right)","\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,"(x^3*(70*a^4*(4*A + 3*B*x) + 168*a^3*b*x*(5*A + 4*B*x) + 168*a^2*b^2*x^2*(6*A + 5*B*x) + 80*a*b^3*x^3*(7*A + 6*B*x) + 15*b^4*x^4*(8*A + 7*B*x)))/840","A",1
526,1,88,61,0.0231587,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{1}{210} x^2 \left(35 a^4 (3 A+2 B x)+70 a^3 b x (4 A+3 B x)+63 a^2 b^2 x^2 (5 A+4 B x)+28 a b^3 x^3 (6 A+5 B x)+5 b^4 x^4 (7 A+6 B x)\right)","\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,"(x^2*(35*a^4*(3*A + 2*B*x) + 70*a^3*b*x*(4*A + 3*B*x) + 63*a^2*b^2*x^2*(5*A + 4*B*x) + 28*a*b^3*x^3*(6*A + 5*B*x) + 5*b^4*x^4*(7*A + 6*B*x)))/210","A",1
527,1,84,38,0.0148801,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{1}{30} x \left(15 a^4 (2 A+B x)+20 a^3 b x (3 A+2 B x)+15 a^2 b^2 x^2 (4 A+3 B x)+6 a b^3 x^3 (5 A+4 B x)+b^4 x^4 (6 A+5 B x)\right)","\frac{(a+b x)^5 (A b-a B)}{5 b^2}+\frac{B (a+b x)^6}{6 b^2}",1,"(x*(15*a^4*(2*A + B*x) + 20*a^3*b*x*(3*A + 2*B*x) + 15*a^2*b^2*x^2*(4*A + 3*B*x) + 6*a*b^3*x^3*(5*A + 4*B*x) + b^4*x^4*(6*A + 5*B*x)))/30","B",1
528,1,83,66,0.0234091,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x,x]","a^4 A \log (x)+a^4 B x+2 a^3 b x (2 A+B x)+a^2 b^2 x^2 (3 A+2 B x)+\frac{1}{3} a b^3 x^3 (4 A+3 B x)+\frac{1}{20} b^4 x^4 (5 A+4 B x)","a^4 A \log (x)+4 a^3 A b x+3 a^2 A b^2 x^2+\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,"a^4*B*x + 2*a^3*b*x*(2*A + B*x) + a^2*b^2*x^2*(3*A + 2*B*x) + (a*b^3*x^3*(4*A + 3*B*x))/3 + (b^4*x^4*(5*A + 4*B*x))/20 + a^4*A*Log[x]","A",1
529,1,85,86,0.0353806,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^2} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^2,x]","-\frac{a^4 A}{x}+a^3 \log (x) (a B+4 A b)+4 a^3 b B x+3 a^2 b^2 x (2 A+B x)+\frac{2}{3} a b^3 x^2 (3 A+2 B x)+\frac{1}{12} b^4 x^3 (4 A+3 B x)","-\frac{a^4 A}{x}+a^3 \log (x) (a B+4 A b)+2 a^2 b x (2 a B+3 A b)+\frac{1}{3} b^3 x^3 (4 a B+A b)+a b^2 x^2 (3 a B+2 A b)+\frac{1}{4} b^4 B x^4",1,"-((a^4*A)/x) + 4*a^3*b*B*x + 3*a^2*b^2*x*(2*A + B*x) + (2*a*b^3*x^2*(3*A + 2*B*x))/3 + (b^4*x^3*(4*A + 3*B*x))/12 + a^3*(4*A*b + a*B)*Log[x]","A",1
530,1,86,90,0.0324262,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^3} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^3,x]","-\frac{a^4 (A+2 B x)}{2 x^2}-\frac{4 a^3 A b}{x}+2 a^2 b \log (x) (2 a B+3 A b)+6 a^2 b^2 B x+2 a b^3 x (2 A+B x)+\frac{1}{6} b^4 x^2 (3 A+2 B x)","-\frac{a^4 A}{2 x^2}-\frac{a^3 (a B+4 A b)}{x}+2 a^2 b \log (x) (2 a B+3 A b)+\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,"(-4*a^3*A*b)/x + 6*a^2*b^2*B*x + 2*a*b^3*x*(2*A + B*x) - (a^4*(A + 2*B*x))/(2*x^2) + (b^4*x^2*(3*A + 2*B*x))/6 + 2*a^2*b*(3*A*b + 2*a*B)*Log[x]","A",1
531,1,86,89,0.0343828,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^4} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^4,x]","-\frac{a^4 (2 A+3 B x)}{6 x^3}-\frac{2 a^3 b (A+2 B x)}{x^2}-\frac{6 a^2 A b^2}{x}+2 a b^2 \log (x) (3 a B+2 A b)+4 a b^3 B x+\frac{1}{2} b^4 x (2 A+B x)","-\frac{a^4 A}{3 x^3}-\frac{a^3 (a B+4 A b)}{2 x^2}-\frac{2 a^2 b (2 a B+3 A b)}{x}+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,"(-6*a^2*A*b^2)/x + 4*a*b^3*B*x + (b^4*x*(2*A + B*x))/2 - (2*a^3*b*(A + 2*B*x))/x^2 - (a^4*(2*A + 3*B*x))/(6*x^3) + 2*a*b^2*(2*A*b + 3*a*B)*Log[x]","A",1
532,1,85,86,0.040263,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^5} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^5,x]","-\frac{a^4 (3 A+4 B x)}{12 x^4}-\frac{2 a^3 b (2 A+3 B x)}{3 x^3}-\frac{3 a^2 b^2 (A+2 B x)}{x^2}+b^3 \log (x) (4 a B+A b)-\frac{4 a A b^3}{x}+b^4 B x","-\frac{a^4 A}{4 x^4}-\frac{a^3 (a B+4 A b)}{3 x^3}-\frac{a^2 b (2 a B+3 A b)}{x^2}+b^3 \log (x) (4 a B+A b)-\frac{2 a b^2 (3 a B+2 A b)}{x}+b^4 B x",1,"(-4*a*A*b^3)/x + b^4*B*x - (3*a^2*b^2*(A + 2*B*x))/x^2 - (2*a^3*b*(2*A + 3*B*x))/(3*x^3) - (a^4*(3*A + 4*B*x))/(12*x^4) + b^3*(A*b + 4*a*B)*Log[x]","A",1
533,1,87,71,0.0442582,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^6} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^6,x]","b^4 B \log (x)-\frac{3 a^4 (4 A+5 B x)+20 a^3 b x (3 A+4 B x)+60 a^2 b^2 x^2 (2 A+3 B x)+120 a b^3 x^3 (A+2 B x)+60 A b^4 x^4}{60 x^5}","-\frac{a^4 B}{4 x^4}-\frac{4 a^3 b B}{3 x^3}-\frac{3 a^2 b^2 B}{x^2}-\frac{A (a+b x)^5}{5 a x^5}-\frac{4 a b^3 B}{x}+b^4 B \log (x)",1,"-1/60*(60*A*b^4*x^4 + 120*a*b^3*x^3*(A + 2*B*x) + 60*a^2*b^2*x^2*(2*A + 3*B*x) + 20*a^3*b*x*(3*A + 4*B*x) + 3*a^4*(4*A + 5*B*x))/x^5 + b^4*B*Log[x]","A",1
534,1,85,44,0.0244276,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^7} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^7,x]","-\frac{a^4 (5 A+6 B x)+6 a^3 b x (4 A+5 B x)+15 a^2 b^2 x^2 (3 A+4 B x)+20 a b^3 x^3 (2 A+3 B x)+15 b^4 x^4 (A+2 B x)}{30 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,"-1/30*(15*b^4*x^4*(A + 2*B*x) + 20*a*b^3*x^3*(2*A + 3*B*x) + 15*a^2*b^2*x^2*(3*A + 4*B*x) + 6*a^3*b*x*(4*A + 5*B*x) + a^4*(5*A + 6*B*x))/x^6","A",1
535,1,88,99,0.0230131,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^8} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^8,x]","-\frac{5 a^4 (6 A+7 B x)+28 a^3 b x (5 A+6 B x)+63 a^2 b^2 x^2 (4 A+5 B x)+70 a b^3 x^3 (3 A+4 B x)+35 b^4 x^4 (2 A+3 B x)}{210 x^7}","-\frac{a^4 A}{7 x^7}-\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{b^3 (4 a B+A b)}{3 x^3}-\frac{a b^2 (3 a B+2 A b)}{2 x^4}-\frac{b^4 B}{2 x^2}",1,"-1/210*(35*b^4*x^4*(2*A + 3*B*x) + 70*a*b^3*x^3*(3*A + 4*B*x) + 63*a^2*b^2*x^2*(4*A + 5*B*x) + 28*a^3*b*x*(5*A + 6*B*x) + 5*a^4*(6*A + 7*B*x))/x^7","A",1
536,1,88,99,0.0255718,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^9} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^9,x]","-\frac{15 a^4 (7 A+8 B x)+80 a^3 b x (6 A+7 B x)+168 a^2 b^2 x^2 (5 A+6 B x)+168 a b^3 x^3 (4 A+5 B x)+70 b^4 x^4 (3 A+4 B x)}{840 x^8}","-\frac{a^4 A}{8 x^8}-\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{b^3 (4 a B+A b)}{4 x^4}-\frac{2 a b^2 (3 a B+2 A b)}{5 x^5}-\frac{b^4 B}{3 x^3}",1,"-1/840*(70*b^4*x^4*(3*A + 4*B*x) + 168*a*b^3*x^3*(4*A + 5*B*x) + 168*a^2*b^2*x^2*(5*A + 6*B*x) + 80*a^3*b*x*(6*A + 7*B*x) + 15*a^4*(7*A + 8*B*x))/x^8","A",1
537,1,88,99,0.0257262,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{10}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^10,x]","-\frac{35 a^4 (8 A+9 B x)+180 a^3 b x (7 A+8 B x)+360 a^2 b^2 x^2 (6 A+7 B x)+336 a b^3 x^3 (5 A+6 B x)+126 b^4 x^4 (4 A+5 B x)}{2520 x^9}","-\frac{a^4 A}{9 x^9}-\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{b^3 (4 a B+A b)}{5 x^5}-\frac{a b^2 (3 a B+2 A b)}{3 x^6}-\frac{b^4 B}{4 x^4}",1,"-1/2520*(126*b^4*x^4*(4*A + 5*B*x) + 336*a*b^3*x^3*(5*A + 6*B*x) + 360*a^2*b^2*x^2*(6*A + 7*B*x) + 180*a^3*b*x*(7*A + 8*B*x) + 35*a^4*(8*A + 9*B*x))/x^9","A",1
538,1,88,99,0.0253478,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{11}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^11,x]","-\frac{14 a^4 (9 A+10 B x)+70 a^3 b x (8 A+9 B x)+135 a^2 b^2 x^2 (7 A+8 B x)+120 a b^3 x^3 (6 A+7 B x)+42 b^4 x^4 (5 A+6 B x)}{1260 x^{10}}","-\frac{a^4 A}{10 x^{10}}-\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{b^3 (4 a B+A b)}{6 x^6}-\frac{2 a b^2 (3 a B+2 A b)}{7 x^7}-\frac{b^4 B}{5 x^5}",1,"-1/1260*(42*b^4*x^4*(5*A + 6*B*x) + 120*a*b^3*x^3*(6*A + 7*B*x) + 135*a^2*b^2*x^2*(7*A + 8*B*x) + 70*a^3*b*x*(8*A + 9*B*x) + 14*a^4*(9*A + 10*B*x))/x^10","A",1
539,1,143,143,0.0236898,"\int x^5 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[x^5*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{1}{6} a^6 A x^6+\frac{1}{7} a^5 x^7 (a B+6 A b)+\frac{3}{8} a^4 b x^8 (2 a B+5 A b)+\frac{5}{9} a^3 b^2 x^9 (3 a B+4 A b)+\frac{1}{2} a^2 b^3 x^{10} (4 a B+3 A b)+\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}{6} a^6 A x^6+\frac{1}{7} a^5 x^7 (a B+6 A b)+\frac{3}{8} a^4 b x^8 (2 a B+5 A b)+\frac{5}{9} a^3 b^2 x^9 (3 a B+4 A b)+\frac{1}{2} a^2 b^3 x^{10} (4 a B+3 A b)+\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",1
540,1,143,139,0.0190522,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{1}{5} a^6 A x^5+\frac{1}{6} a^5 x^6 (a B+6 A b)+\frac{3}{7} a^4 b x^7 (2 a B+5 A b)+\frac{5}{8} a^3 b^2 x^8 (3 a B+4 A b)+\frac{5}{9} a^2 b^3 x^9 (4 a B+3 A b)+\frac{1}{11} b^5 x^{11} (6 a B+A b)+\frac{3}{10} a b^4 x^{10} (5 a B+2 A b)+\frac{1}{12} b^6 B x^{12}","\frac{a^4 (a+b x)^7 (A b-a B)}{7 b^6}-\frac{a^3 (a+b x)^8 (4 A b-5 a B)}{8 b^6}+\frac{2 a^2 (a+b x)^9 (3 A b-5 a B)}{9 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^6*A*x^5)/5 + (a^5*(6*A*b + a*B)*x^6)/6 + (3*a^4*b*(5*A*b + 2*a*B)*x^7)/7 + (5*a^3*b^2*(4*A*b + 3*a*B)*x^8)/8 + (5*a^2*b^3*(3*A*b + 4*a*B)*x^9)/9 + (3*a*b^4*(2*A*b + 5*a*B)*x^10)/10 + (b^5*(A*b + 6*a*B)*x^11)/11 + (b^6*B*x^12)/12","A",1
541,1,143,112,0.0189399,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[x^3*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{1}{4} a^6 A x^4+\frac{1}{5} a^5 x^5 (a B+6 A b)+\frac{1}{2} a^4 b x^6 (2 a B+5 A b)+\frac{5}{7} a^3 b^2 x^7 (3 a B+4 A b)+\frac{5}{8} a^2 b^3 x^8 (4 a B+3 A b)+\frac{1}{10} b^5 x^{10} (6 a B+A b)+\frac{1}{3} a b^4 x^9 (5 a B+2 A b)+\frac{1}{11} b^6 B x^{11}","-\frac{a^3 (a+b x)^7 (A b-a B)}{7 b^5}+\frac{a^2 (a+b x)^8 (3 A b-4 a B)}{8 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^6*A*x^4)/4 + (a^5*(6*A*b + a*B)*x^5)/5 + (a^4*b*(5*A*b + 2*a*B)*x^6)/2 + (5*a^3*b^2*(4*A*b + 3*a*B)*x^7)/7 + (5*a^2*b^3*(3*A*b + 4*a*B)*x^8)/8 + (a*b^4*(2*A*b + 5*a*B)*x^9)/3 + (b^5*(A*b + 6*a*B)*x^10)/10 + (b^6*B*x^11)/11","A",1
542,1,143,87,0.0174186,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{1}{3} a^6 A x^3+\frac{1}{4} a^5 x^4 (a B+6 A b)+\frac{3}{5} a^4 b x^5 (2 a B+5 A b)+\frac{5}{6} a^3 b^2 x^6 (3 a B+4 A b)+\frac{5}{7} a^2 b^3 x^7 (4 a B+3 A b)+\frac{1}{9} b^5 x^9 (6 a B+A b)+\frac{3}{8} a b^4 x^8 (5 a B+2 A b)+\frac{1}{10} b^6 B x^{10}","\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^6*A*x^3)/3 + (a^5*(6*A*b + a*B)*x^4)/4 + (3*a^4*b*(5*A*b + 2*a*B)*x^5)/5 + (5*a^3*b^2*(4*A*b + 3*a*B)*x^6)/6 + (5*a^2*b^3*(3*A*b + 4*a*B)*x^7)/7 + (3*a*b^4*(2*A*b + 5*a*B)*x^8)/8 + (b^5*(A*b + 6*a*B)*x^9)/9 + (b^6*B*x^10)/10","A",1
543,1,140,61,0.0172732,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{1}{2} a^6 A x^2+\frac{1}{3} a^5 x^3 (a B+6 A b)+\frac{3}{4} a^4 b x^4 (2 a B+5 A b)+a^3 b^2 x^5 (3 a B+4 A b)+\frac{5}{6} a^2 b^3 x^6 (4 a B+3 A b)+\frac{1}{8} b^5 x^8 (6 a B+A b)+\frac{3}{7} a b^4 x^7 (5 a B+2 A b)+\frac{1}{9} b^6 B x^9","\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^6*A*x^2)/2 + (a^5*(6*A*b + a*B)*x^3)/3 + (3*a^4*b*(5*A*b + 2*a*B)*x^4)/4 + a^3*b^2*(4*A*b + 3*a*B)*x^5 + (5*a^2*b^3*(3*A*b + 4*a*B)*x^6)/6 + (3*a*b^4*(2*A*b + 5*a*B)*x^7)/7 + (b^5*(A*b + 6*a*B)*x^8)/8 + (b^6*B*x^9)/9","B",1
544,1,122,38,0.033501,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{1}{56} x \left(28 a^6 (2 A+B x)+56 a^5 b x (3 A+2 B x)+70 a^4 b^2 x^2 (4 A+3 B x)+56 a^3 b^3 x^3 (5 A+4 B x)+28 a^2 b^4 x^4 (6 A+5 B x)+8 a b^5 x^5 (7 A+6 B x)+b^6 x^6 (8 A+7 B x)\right)","\frac{(a+b x)^7 (A b-a B)}{7 b^2}+\frac{B (a+b x)^8}{8 b^2}",1,"(x*(28*a^6*(2*A + B*x) + 56*a^5*b*x*(3*A + 2*B*x) + 70*a^4*b^2*x^2*(4*A + 3*B*x) + 56*a^3*b^3*x^3*(5*A + 4*B*x) + 28*a^2*b^4*x^4*(6*A + 5*B*x) + 8*a*b^5*x^5*(7*A + 6*B*x) + b^6*x^6*(8*A + 7*B*x)))/56","B",1
545,1,128,96,0.0502106,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x,x]","a^6 A \log (x)+a^6 B x+3 a^5 b x (2 A+B x)+\frac{5}{2} a^4 b^2 x^2 (3 A+2 B x)+\frac{5}{3} a^3 b^3 x^3 (4 A+3 B x)+\frac{3}{4} a^2 b^4 x^4 (5 A+4 B x)+\frac{1}{5} a b^5 x^5 (6 A+5 B x)+\frac{1}{42} b^6 x^6 (7 A+6 B x)","a^6 A \log (x)+6 a^5 A b x+\frac{15}{2} a^4 A b^2 x^2+\frac{20}{3} a^3 A b^3 x^3+\frac{15}{4} a^2 A b^4 x^4+\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,"a^6*B*x + 3*a^5*b*x*(2*A + B*x) + (5*a^4*b^2*x^2*(3*A + 2*B*x))/2 + (5*a^3*b^3*x^3*(4*A + 3*B*x))/3 + (3*a^2*b^4*x^4*(5*A + 4*B*x))/4 + (a*b^5*x^5*(6*A + 5*B*x))/5 + (b^6*x^6*(7*A + 6*B*x))/42 + a^6*A*Log[x]","A",1
546,1,129,133,0.0506265,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^2} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^2,x]","-\frac{a^6 A}{x}+a^5 \log (x) (a B+6 A b)+6 a^5 b B x+\frac{15}{2} a^4 b^2 x (2 A+B x)+\frac{10}{3} a^3 b^3 x^2 (3 A+2 B x)+\frac{5}{4} a^2 b^4 x^3 (4 A+3 B x)+\frac{3}{10} a b^5 x^4 (5 A+4 B x)+\frac{1}{30} b^6 x^5 (6 A+5 B x)","-\frac{a^6 A}{x}+a^5 \log (x) (a B+6 A b)+3 a^4 b x (2 a B+5 A b)+\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)+\frac{1}{5} b^5 x^5 (6 a B+A b)+\frac{3}{4} a b^4 x^4 (5 a B+2 A b)+\frac{1}{6} b^6 B x^6",1,"-((a^6*A)/x) + 6*a^5*b*B*x + (15*a^4*b^2*x*(2*A + B*x))/2 + (10*a^3*b^3*x^2*(3*A + 2*B*x))/3 + (5*a^2*b^4*x^3*(4*A + 3*B*x))/4 + (3*a*b^5*x^4*(5*A + 4*B*x))/10 + (b^6*x^5*(6*A + 5*B*x))/30 + a^5*(6*A*b + a*B)*Log[x]","A",1
547,1,128,131,0.0570156,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^3} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^3,x]","-\frac{a^6 (A+2 B x)}{2 x^2}-\frac{6 a^5 A b}{x}+3 a^4 b \log (x) (2 a B+5 A b)+15 a^4 b^2 B x+10 a^3 b^3 x (2 A+B x)+\frac{5}{2} a^2 b^4 x^2 (3 A+2 B x)+\frac{1}{2} a b^5 x^3 (4 A+3 B x)+\frac{1}{20} b^6 x^4 (5 A+4 B x)","-\frac{a^6 A}{2 x^2}-\frac{a^5 (a B+6 A b)}{x}+3 a^4 b \log (x) (2 a B+5 A b)+5 a^3 b^2 x (3 a B+4 A b)+\frac{5}{2} a^2 b^3 x^2 (4 a B+3 A b)+\frac{1}{4} b^5 x^4 (6 a B+A b)+a b^4 x^3 (5 a B+2 A b)+\frac{1}{5} b^6 B x^5",1,"(-6*a^5*A*b)/x + 15*a^4*b^2*B*x + 10*a^3*b^3*x*(2*A + B*x) - (a^6*(A + 2*B*x))/(2*x^2) + (5*a^2*b^4*x^2*(3*A + 2*B*x))/2 + (a*b^5*x^3*(4*A + 3*B*x))/2 + (b^6*x^4*(5*A + 4*B*x))/20 + 3*a^4*b*(5*A*b + 2*a*B)*Log[x]","A",1
548,1,127,134,0.0467695,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^4} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^4,x]","-\frac{a^6 (2 A+3 B x)}{6 x^3}-\frac{3 a^5 b (A+2 B x)}{x^2}-\frac{15 a^4 A b^2}{x}+5 a^3 b^2 \log (x) (3 a B+4 A b)+20 a^3 b^3 B x+\frac{15}{2} a^2 b^4 x (2 A+B x)+a b^5 x^2 (3 A+2 B x)+\frac{1}{12} b^6 x^3 (4 A+3 B x)","-\frac{a^6 A}{3 x^3}-\frac{a^5 (a B+6 A b)}{2 x^2}-\frac{3 a^4 b (2 a B+5 A b)}{x}+5 a^3 b^2 \log (x) (3 a B+4 A b)+5 a^2 b^3 x (4 a B+3 A b)+\frac{1}{3} b^5 x^3 (6 a B+A b)+\frac{3}{2} a b^4 x^2 (5 a B+2 A b)+\frac{1}{4} b^6 B x^4",1,"(-15*a^4*A*b^2)/x + 20*a^3*b^3*B*x + (15*a^2*b^4*x*(2*A + B*x))/2 - (3*a^5*b*(A + 2*B*x))/x^2 + a*b^5*x^2*(3*A + 2*B*x) - (a^6*(2*A + 3*B*x))/(6*x^3) + (b^6*x^3*(4*A + 3*B*x))/12 + 5*a^3*b^2*(4*A*b + 3*a*B)*Log[x]","A",1
549,1,128,134,0.048181,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^5} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^5,x]","-\frac{a^6 (3 A+4 B x)}{12 x^4}-\frac{a^5 b (2 A+3 B x)}{x^3}-\frac{15 a^4 b^2 (A+2 B x)}{2 x^2}-\frac{20 a^3 A b^3}{x}+5 a^2 b^3 \log (x) (4 a B+3 A b)+15 a^2 b^4 B x+3 a b^5 x (2 A+B x)+\frac{1}{6} b^6 x^2 (3 A+2 B x)","-\frac{a^6 A}{4 x^4}-\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{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{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,"(-20*a^3*A*b^3)/x + 15*a^2*b^4*B*x + 3*a*b^5*x*(2*A + B*x) - (15*a^4*b^2*(A + 2*B*x))/(2*x^2) + (b^6*x^2*(3*A + 2*B*x))/6 - (a^5*b*(2*A + 3*B*x))/x^3 - (a^6*(3*A + 4*B*x))/(12*x^4) + 5*a^2*b^3*(3*A*b + 4*a*B)*Log[x]","A",1
550,1,128,131,0.0487821,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^6} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^6,x]","-\frac{a^6 (4 A+5 B x)}{20 x^5}-\frac{a^5 b (3 A+4 B x)}{2 x^4}-\frac{5 a^4 b^2 (2 A+3 B x)}{2 x^3}-\frac{10 a^3 b^3 (A+2 B x)}{x^2}-\frac{15 a^2 A b^4}{x}+3 a b^4 \log (x) (5 a B+2 A b)+6 a b^5 B x+\frac{1}{2} b^6 x (2 A+B x)","-\frac{a^6 A}{5 x^5}-\frac{a^5 (a B+6 A b)}{4 x^4}-\frac{a^4 b (2 a B+5 A b)}{x^3}-\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}+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,"(-15*a^2*A*b^4)/x + 6*a*b^5*B*x + (b^6*x*(2*A + B*x))/2 - (10*a^3*b^3*(A + 2*B*x))/x^2 - (5*a^4*b^2*(2*A + 3*B*x))/(2*x^3) - (a^5*b*(3*A + 4*B*x))/(2*x^4) - (a^6*(4*A + 5*B*x))/(20*x^5) + 3*a*b^4*(2*A*b + 5*a*B)*Log[x]","A",1
551,1,125,132,0.0693129,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^7} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^7,x]","b^5 \log (x) (6 a B+A b)-\frac{2 a^6 (5 A+6 B x)+18 a^5 b x (4 A+5 B x)+75 a^4 b^2 x^2 (3 A+4 B x)+200 a^3 b^3 x^3 (2 A+3 B x)+450 a^2 b^4 x^4 (A+2 B x)+360 a A b^5 x^5-60 b^6 B x^7}{60 x^6}","-\frac{a^6 A}{6 x^6}-\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{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}+b^5 \log (x) (6 a B+A b)-\frac{3 a b^4 (5 a B+2 A b)}{x}+b^6 B x",1,"-1/60*(360*a*A*b^5*x^5 - 60*b^6*B*x^7 + 450*a^2*b^4*x^4*(A + 2*B*x) + 200*a^3*b^3*x^3*(2*A + 3*B*x) + 75*a^4*b^2*x^2*(3*A + 4*B*x) + 18*a^5*b*x*(4*A + 5*B*x) + 2*a^6*(5*A + 6*B*x))/x^6 + b^5*(A*b + 6*a*B)*Log[x]","A",1
552,1,132,101,0.0547894,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^8} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^8,x]","-\frac{a^6 (6 A+7 B x)}{42 x^7}-\frac{a^5 b (5 A+6 B x)}{5 x^6}-\frac{3 a^4 b^2 (4 A+5 B x)}{4 x^5}-\frac{5 a^3 b^3 (3 A+4 B x)}{3 x^4}-\frac{5 a^2 b^4 (2 A+3 B x)}{2 x^3}-\frac{3 a b^5 (A+2 B x)}{x^2}-\frac{A b^6}{x}+b^6 B \log (x)","-\frac{a^6 B}{6 x^6}-\frac{6 a^5 b B}{5 x^5}-\frac{15 a^4 b^2 B}{4 x^4}-\frac{20 a^3 b^3 B}{3 x^3}-\frac{15 a^2 b^4 B}{2 x^2}-\frac{A (a+b x)^7}{7 a x^7}-\frac{6 a b^5 B}{x}+b^6 B \log (x)",1,"-((A*b^6)/x) - (3*a*b^5*(A + 2*B*x))/x^2 - (5*a^2*b^4*(2*A + 3*B*x))/(2*x^3) - (5*a^3*b^3*(3*A + 4*B*x))/(3*x^4) - (3*a^4*b^2*(4*A + 5*B*x))/(4*x^5) - (a^5*b*(5*A + 6*B*x))/(5*x^6) - (a^6*(6*A + 7*B*x))/(42*x^7) + b^6*B*Log[x]","A",1
553,1,123,44,0.0334527,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^9} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^9,x]","-\frac{a^6 (7 A+8 B x)+8 a^5 b x (6 A+7 B x)+28 a^4 b^2 x^2 (5 A+6 B x)+56 a^3 b^3 x^3 (4 A+5 B x)+70 a^2 b^4 x^4 (3 A+4 B x)+56 a b^5 x^5 (2 A+3 B x)+28 b^6 x^6 (A+2 B x)}{56 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,"-1/56*(28*b^6*x^6*(A + 2*B*x) + 56*a*b^5*x^5*(2*A + 3*B*x) + 70*a^2*b^4*x^4*(3*A + 4*B*x) + 56*a^3*b^3*x^3*(4*A + 5*B*x) + 28*a^4*b^2*x^2*(5*A + 6*B*x) + 8*a^5*b*x*(6*A + 7*B*x) + a^6*(7*A + 8*B*x))/x^8","B",1
554,1,126,72,0.032339,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{10}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^10,x]","-\frac{7 a^6 (8 A+9 B x)+54 a^5 b x (7 A+8 B x)+180 a^4 b^2 x^2 (6 A+7 B x)+336 a^3 b^3 x^3 (5 A+6 B x)+378 a^2 b^4 x^4 (4 A+5 B x)+252 a b^5 x^5 (3 A+4 B x)+84 b^6 x^6 (2 A+3 B x)}{504 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,"-1/504*(84*b^6*x^6*(2*A + 3*B*x) + 252*a*b^5*x^5*(3*A + 4*B*x) + 378*a^2*b^4*x^4*(4*A + 5*B*x) + 336*a^3*b^3*x^3*(5*A + 6*B*x) + 180*a^4*b^2*x^2*(6*A + 7*B*x) + 54*a^5*b*x*(7*A + 8*B*x) + 7*a^6*(8*A + 9*B*x))/x^9","A",1
555,1,126,143,0.0326285,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{11}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^11,x]","-\frac{28 a^6 (9 A+10 B x)+210 a^5 b x (8 A+9 B x)+675 a^4 b^2 x^2 (7 A+8 B x)+1200 a^3 b^3 x^3 (6 A+7 B x)+1260 a^2 b^4 x^4 (5 A+6 B x)+756 a b^5 x^5 (4 A+5 B x)+210 b^6 x^6 (3 A+4 B x)}{2520 x^{10}}","-\frac{a^6 A}{10 x^{10}}-\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{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{b^5 (6 a B+A b)}{4 x^4}-\frac{3 a b^4 (5 a B+2 A b)}{5 x^5}-\frac{b^6 B}{3 x^3}",1,"-1/2520*(210*b^6*x^6*(3*A + 4*B*x) + 756*a*b^5*x^5*(4*A + 5*B*x) + 1260*a^2*b^4*x^4*(5*A + 6*B*x) + 1200*a^3*b^3*x^3*(6*A + 7*B*x) + 675*a^4*b^2*x^2*(7*A + 8*B*x) + 210*a^5*b*x*(8*A + 9*B*x) + 28*a^6*(9*A + 10*B*x))/x^10","A",1
556,1,126,143,0.0332779,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{12}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^12,x]","-\frac{84 a^6 (10 A+11 B x)+616 a^5 b x (9 A+10 B x)+1925 a^4 b^2 x^2 (8 A+9 B x)+3300 a^3 b^3 x^3 (7 A+8 B x)+3300 a^2 b^4 x^4 (6 A+7 B x)+1848 a b^5 x^5 (5 A+6 B x)+462 b^6 x^6 (4 A+5 B x)}{9240 x^{11}}","-\frac{a^6 A}{11 x^{11}}-\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{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{b^5 (6 a B+A b)}{5 x^5}-\frac{a b^4 (5 a B+2 A b)}{2 x^6}-\frac{b^6 B}{4 x^4}",1,"-1/9240*(462*b^6*x^6*(4*A + 5*B*x) + 1848*a*b^5*x^5*(5*A + 6*B*x) + 3300*a^2*b^4*x^4*(6*A + 7*B*x) + 3300*a^3*b^3*x^3*(7*A + 8*B*x) + 1925*a^4*b^2*x^2*(8*A + 9*B*x) + 616*a^5*b*x*(9*A + 10*B*x) + 84*a^6*(10*A + 11*B*x))/x^11","A",1
557,1,126,143,0.0324813,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{13}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^13,x]","-\frac{210 a^6 (11 A+12 B x)+1512 a^5 b x (10 A+11 B x)+4620 a^4 b^2 x^2 (9 A+10 B x)+7700 a^3 b^3 x^3 (8 A+9 B x)+7425 a^2 b^4 x^4 (7 A+8 B x)+3960 a b^5 x^5 (6 A+7 B x)+924 b^6 x^6 (5 A+6 B x)}{27720 x^{12}}","-\frac{a^6 A}{12 x^{12}}-\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{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{b^5 (6 a B+A b)}{6 x^6}-\frac{3 a b^4 (5 a B+2 A b)}{7 x^7}-\frac{b^6 B}{5 x^5}",1,"-1/27720*(924*b^6*x^6*(5*A + 6*B*x) + 3960*a*b^5*x^5*(6*A + 7*B*x) + 7425*a^2*b^4*x^4*(7*A + 8*B*x) + 7700*a^3*b^3*x^3*(8*A + 9*B*x) + 4620*a^4*b^2*x^2*(9*A + 10*B*x) + 1512*a^5*b*x*(10*A + 11*B*x) + 210*a^6*(11*A + 12*B*x))/x^12","A",1
558,1,126,143,0.0331937,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{14}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^14,x]","-\frac{462 a^6 (12 A+13 B x)+3276 a^5 b x (11 A+12 B x)+9828 a^4 b^2 x^2 (10 A+11 B x)+16016 a^3 b^3 x^3 (9 A+10 B x)+15015 a^2 b^4 x^4 (8 A+9 B x)+7722 a b^5 x^5 (7 A+8 B x)+1716 b^6 x^6 (6 A+7 B x)}{72072 x^{13}}","-\frac{a^6 A}{13 x^{13}}-\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^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{b^5 (6 a B+A b)}{7 x^7}-\frac{3 a b^4 (5 a B+2 A b)}{8 x^8}-\frac{b^6 B}{6 x^6}",1,"-1/72072*(1716*b^6*x^6*(6*A + 7*B*x) + 7722*a*b^5*x^5*(7*A + 8*B*x) + 15015*a^2*b^4*x^4*(8*A + 9*B*x) + 16016*a^3*b^3*x^3*(9*A + 10*B*x) + 9828*a^4*b^2*x^2*(10*A + 11*B*x) + 3276*a^5*b*x*(11*A + 12*B*x) + 462*a^6*(12*A + 13*B*x))/x^13","A",1
559,1,149,131,0.0262212,"\int x^7 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^7*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{18} x^{18} (d+10 e)+\frac{5}{17} x^{17} (2 d+9 e)+\frac{15}{16} x^{16} (3 d+8 e)+2 x^{15} (4 d+7 e)+3 x^{14} (5 d+6 e)+\frac{42}{13} x^{13} (6 d+5 e)+\frac{5}{2} x^{12} (7 d+4 e)+\frac{15}{11} x^{11} (8 d+3 e)+\frac{1}{2} x^{10} (9 d+2 e)+\frac{1}{9} x^9 (10 d+e)+\frac{d x^8}{8}+\frac{e x^{19}}{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*x^8)/8 + ((10*d + e)*x^9)/9 + ((9*d + 2*e)*x^10)/2 + (15*(8*d + 3*e)*x^11)/11 + (5*(7*d + 4*e)*x^12)/2 + (42*(6*d + 5*e)*x^13)/13 + 3*(5*d + 6*e)*x^14 + 2*(4*d + 7*e)*x^15 + (15*(3*d + 8*e)*x^16)/16 + (5*(2*d + 9*e)*x^17)/17 + ((d + 10*e)*x^18)/18 + (e*x^19)/19","A",1
560,1,150,119,0.0189667,"\int x^6 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^6*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{17} x^{17} (d+10 e)+\frac{5}{16} x^{16} (2 d+9 e)+x^{15} (3 d+8 e)+\frac{15}{7} x^{14} (4 d+7 e)+\frac{42}{13} x^{13} (5 d+6 e)+\frac{7}{2} x^{12} (6 d+5 e)+\frac{30}{11} x^{11} (7 d+4 e)+\frac{3}{2} x^{10} (8 d+3 e)+\frac{5}{9} x^9 (9 d+2 e)+\frac{1}{8} x^8 (10 d+e)+\frac{d x^7}{7}+\frac{e x^{18}}{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*x^7)/7 + ((10*d + e)*x^8)/8 + (5*(9*d + 2*e)*x^9)/9 + (3*(8*d + 3*e)*x^10)/2 + (30*(7*d + 4*e)*x^11)/11 + (7*(6*d + 5*e)*x^12)/2 + (42*(5*d + 6*e)*x^13)/13 + (15*(4*d + 7*e)*x^14)/7 + (3*d + 8*e)*x^15 + (5*(2*d + 9*e)*x^16)/16 + ((d + 10*e)*x^17)/17 + (e*x^18)/18","A",1
561,1,151,99,0.0189936,"\int x^5 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^5*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{16} x^{16} (d+10 e)+\frac{1}{3} x^{15} (2 d+9 e)+\frac{15}{14} x^{14} (3 d+8 e)+\frac{30}{13} x^{13} (4 d+7 e)+\frac{7}{2} x^{12} (5 d+6 e)+\frac{42}{11} x^{11} (6 d+5 e)+3 x^{10} (7 d+4 e)+\frac{5}{3} x^9 (8 d+3 e)+\frac{5}{8} x^8 (9 d+2 e)+\frac{1}{7} x^7 (10 d+e)+\frac{d x^6}{6}+\frac{e x^{17}}{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*x^6)/6 + ((10*d + e)*x^7)/7 + (5*(9*d + 2*e)*x^8)/8 + (5*(8*d + 3*e)*x^9)/3 + 3*(7*d + 4*e)*x^10 + (42*(6*d + 5*e)*x^11)/11 + (7*(5*d + 6*e)*x^12)/2 + (30*(4*d + 7*e)*x^13)/13 + (15*(3*d + 8*e)*x^14)/14 + ((2*d + 9*e)*x^15)/3 + ((d + 10*e)*x^16)/16 + (e*x^17)/17","A",1
562,1,153,87,0.0182556,"\int x^4 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^4*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{15} x^{15} (d+10 e)+\frac{5}{14} x^{14} (2 d+9 e)+\frac{15}{13} x^{13} (3 d+8 e)+\frac{5}{2} x^{12} (4 d+7 e)+\frac{42}{11} x^{11} (5 d+6 e)+\frac{21}{5} x^{10} (6 d+5 e)+\frac{10}{3} x^9 (7 d+4 e)+\frac{15}{8} x^8 (8 d+3 e)+\frac{5}{7} x^7 (9 d+2 e)+\frac{1}{6} x^6 (10 d+e)+\frac{d x^5}{5}+\frac{e x^{16}}{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*x^5)/5 + ((10*d + e)*x^6)/6 + (5*(9*d + 2*e)*x^7)/7 + (15*(8*d + 3*e)*x^8)/8 + (10*(7*d + 4*e)*x^9)/3 + (21*(6*d + 5*e)*x^10)/5 + (42*(5*d + 6*e)*x^11)/11 + (5*(4*d + 7*e)*x^12)/2 + (15*(3*d + 8*e)*x^13)/13 + (5*(2*d + 9*e)*x^14)/14 + ((d + 10*e)*x^15)/15 + (e*x^16)/16","A",1
563,1,153,69,0.0186872,"\int x^3 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^3*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{14} x^{14} (d+10 e)+\frac{5}{13} x^{13} (2 d+9 e)+\frac{5}{4} x^{12} (3 d+8 e)+\frac{30}{11} x^{11} (4 d+7 e)+\frac{21}{5} x^{10} (5 d+6 e)+\frac{14}{3} x^9 (6 d+5 e)+\frac{15}{4} x^8 (7 d+4 e)+\frac{15}{7} x^7 (8 d+3 e)+\frac{5}{6} x^6 (9 d+2 e)+\frac{1}{5} x^5 (10 d+e)+\frac{d x^4}{4}+\frac{e x^{15}}{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*x^4)/4 + ((10*d + e)*x^5)/5 + (5*(9*d + 2*e)*x^6)/6 + (15*(8*d + 3*e)*x^7)/7 + (15*(7*d + 4*e)*x^8)/4 + (14*(6*d + 5*e)*x^9)/3 + (21*(5*d + 6*e)*x^10)/5 + (30*(4*d + 7*e)*x^11)/11 + (5*(3*d + 8*e)*x^12)/4 + (5*(2*d + 9*e)*x^13)/13 + ((d + 10*e)*x^14)/14 + (e*x^15)/15","B",1
564,1,148,55,0.0185704,"\int x^2 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^2*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{13} x^{13} (d+10 e)+\frac{5}{12} x^{12} (2 d+9 e)+\frac{15}{11} x^{11} (3 d+8 e)+3 x^{10} (4 d+7 e)+\frac{14}{3} x^9 (5 d+6 e)+\frac{21}{4} x^8 (6 d+5 e)+\frac{30}{7} x^7 (7 d+4 e)+\frac{5}{2} x^6 (8 d+3 e)+x^5 (9 d+2 e)+\frac{1}{4} x^4 (10 d+e)+\frac{d x^3}{3}+\frac{e x^{14}}{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*x^3)/3 + ((10*d + e)*x^4)/4 + (9*d + 2*e)*x^5 + (5*(8*d + 3*e)*x^6)/2 + (30*(7*d + 4*e)*x^7)/7 + (21*(6*d + 5*e)*x^8)/4 + (14*(5*d + 6*e)*x^9)/3 + 3*(4*d + 7*e)*x^10 + (15*(3*d + 8*e)*x^11)/11 + (5*(2*d + 9*e)*x^12)/12 + ((d + 10*e)*x^13)/13 + (e*x^14)/14","B",1
565,1,147,39,0.0155886,"\int x (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{12} x^{12} (d+10 e)+\frac{5}{11} x^{11} (2 d+9 e)+\frac{3}{2} x^{10} (3 d+8 e)+\frac{10}{3} x^9 (4 d+7 e)+\frac{21}{4} x^8 (5 d+6 e)+6 x^7 (6 d+5 e)+5 x^6 (7 d+4 e)+3 x^5 (8 d+3 e)+\frac{5}{4} x^4 (9 d+2 e)+\frac{1}{3} x^3 (10 d+e)+\frac{d x^2}{2}+\frac{e x^{13}}{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*x^2)/2 + ((10*d + e)*x^3)/3 + (5*(9*d + 2*e)*x^4)/4 + 3*(8*d + 3*e)*x^5 + 5*(7*d + 4*e)*x^6 + 6*(6*d + 5*e)*x^7 + (21*(5*d + 6*e)*x^8)/4 + (10*(4*d + 7*e)*x^9)/3 + (3*(3*d + 8*e)*x^10)/2 + (5*(2*d + 9*e)*x^11)/11 + ((d + 10*e)*x^12)/12 + (e*x^13)/13","B",1
566,1,113,25,0.0210412,"\int (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[(d + e*x)*(1 + 2*x + x^2)^5,x]","d \left(\frac{x^{11}}{11}+x^{10}+5 x^9+15 x^8+30 x^7+42 x^6+42 x^5+30 x^4+15 x^3+5 x^2+x\right)+\frac{1}{132} e \left(11 x^{10}+120 x^9+594 x^8+1760 x^7+3465 x^6+4752 x^5+4620 x^4+3168 x^3+1485 x^2+440 x+66\right) x^2","\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{12} e (x+1)^{12}",1,"(e*x^2*(66 + 440*x + 1485*x^2 + 3168*x^3 + 4620*x^4 + 4752*x^5 + 3465*x^6 + 1760*x^7 + 594*x^8 + 120*x^9 + 11*x^10))/132 + d*(x + 5*x^2 + 15*x^3 + 30*x^4 + 42*x^5 + 42*x^6 + 30*x^7 + 15*x^8 + 5*x^9 + x^10 + x^11/11)","B",1
567,1,85,87,0.032862,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x,x]","d \left(\frac{x^{10}}{10}+\frac{10 x^9}{9}+\frac{45 x^8}{8}+\frac{120 x^7}{7}+35 x^6+\frac{252 x^5}{5}+\frac{105 x^4}{2}+40 x^3+\frac{45 x^2}{2}+10 x+\frac{7381}{2520}\right)+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,"(e*(1 + x)^11)/11 + d*(7381/2520 + 10*x + (45*x^2)/2 + 40*x^3 + (105*x^4)/2 + (252*x^5)/5 + 35*x^6 + (120*x^7)/7 + (45*x^8)/8 + (10*x^9)/9 + x^10/10) + d*Log[-x]","A",1
568,1,139,139,0.0442763,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^2} \, dx","Integrate[((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",1
569,1,139,138,0.0406852,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^3} \, dx","Integrate[((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,"-1/2*d/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",1
570,1,140,138,0.0401609,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^4} \, dx","Integrate[((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,"-1/3*d/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",1
571,1,139,137,0.0359138,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^5} \, dx","Integrate[((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)+\frac{-10 d-e}{3 x^3}+21 x^2 (5 d+6 e)-\frac{5 (9 d+2 e)}{2 x^2}+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)-\frac{10 d+e}{3 x^3}+21 x^2 (5 d+6 e)-\frac{5 (9 d+2 e)}{2 x^2}+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,"-1/4*d/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",1
572,1,142,140,0.0353513,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^6} \, dx","Integrate[((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)+\frac{-10 d-e}{4 x^4}+5 x^3 (3 d+8 e)-\frac{5 (9 d+2 e)}{3 x^3}+15 x^2 (4 d+7 e)-\frac{15 (8 d+3 e)}{2 x^2}+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)-\frac{10 d+e}{4 x^4}+5 x^3 (3 d+8 e)-\frac{5 (9 d+2 e)}{3 x^3}+15 x^2 (4 d+7 e)-\frac{15 (8 d+3 e)}{2 x^2}+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,"-1/5*d/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",1
573,1,142,140,0.0376199,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^7} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^7,x]","\frac{-10 d-e}{5 x^5}+\frac{1}{4} x^4 (d+10 e)-\frac{5 (9 d+2 e)}{4 x^4}+\frac{5}{3} x^3 (2 d+9 e)-\frac{5 (8 d+3 e)}{x^3}+\frac{15}{2} x^2 (3 d+8 e)-\frac{15 (7 d+4 e)}{x^2}+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{10 d+e}{5 x^5}+\frac{1}{4} x^4 (d+10 e)-\frac{5 (9 d+2 e)}{4 x^4}+\frac{5}{3} x^3 (2 d+9 e)-\frac{5 (8 d+3 e)}{x^3}+\frac{15}{2} x^2 (3 d+8 e)-\frac{15 (7 d+4 e)}{x^2}+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,"-1/6*d/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",1
574,1,139,138,0.0380095,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^8} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^8,x]","\frac{-10 d-e}{6 x^6}+\frac{-9 d-2 e}{x^5}-\frac{15 (8 d+3 e)}{4 x^4}+\frac{1}{3} x^3 (d+10 e)-\frac{10 (7 d+4 e)}{x^3}+\frac{5}{2} x^2 (2 d+9 e)-\frac{21 (6 d+5 e)}{x^2}+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{10 d+e}{6 x^6}-\frac{9 d+2 e}{x^5}-\frac{15 (8 d+3 e)}{4 x^4}+\frac{1}{3} x^3 (d+10 e)-\frac{10 (7 d+4 e)}{x^3}+\frac{5}{2} x^2 (2 d+9 e)-\frac{21 (6 d+5 e)}{x^2}+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,"-1/7*d/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",1
575,1,140,138,0.04127,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^9} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^9,x]","\frac{-10 d-e}{7 x^7}-\frac{5 (9 d+2 e)}{6 x^6}-\frac{3 (8 d+3 e)}{x^5}-\frac{15 (7 d+4 e)}{2 x^4}-\frac{14 (6 d+5 e)}{x^3}+\frac{1}{2} x^2 (d+10 e)-\frac{21 (5 d+6 e)}{x^2}+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{10 d+e}{7 x^7}-\frac{5 (9 d+2 e)}{6 x^6}-\frac{3 (8 d+3 e)}{x^5}-\frac{15 (7 d+4 e)}{2 x^4}-\frac{14 (6 d+5 e)}{x^3}+\frac{1}{2} x^2 (d+10 e)-\frac{21 (5 d+6 e)}{x^2}+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,"-1/8*d/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",1
576,1,139,137,0.0407492,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{10}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^10,x]","\frac{-10 d-e}{8 x^8}-\frac{5 (9 d+2 e)}{7 x^7}-\frac{5 (8 d+3 e)}{2 x^6}-\frac{6 (7 d+4 e)}{x^5}-\frac{21 (6 d+5 e)}{2 x^4}-\frac{14 (5 d+6 e)}{x^3}-\frac{15 (4 d+7 e)}{x^2}+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{10 d+e}{8 x^8}-\frac{5 (9 d+2 e)}{7 x^7}-\frac{5 (8 d+3 e)}{2 x^6}-\frac{6 (7 d+4 e)}{x^5}-\frac{21 (6 d+5 e)}{2 x^4}-\frac{14 (5 d+6 e)}{x^3}-\frac{15 (4 d+7 e)}{x^2}+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,"-1/9*d/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",1
577,1,140,138,0.0400258,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{11}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^11,x]","\frac{-10 d-e}{9 x^9}-\frac{5 (9 d+2 e)}{8 x^8}-\frac{15 (8 d+3 e)}{7 x^7}-\frac{5 (7 d+4 e)}{x^6}-\frac{42 (6 d+5 e)}{5 x^5}-\frac{21 (5 d+6 e)}{2 x^4}-\frac{10 (4 d+7 e)}{x^3}-\frac{15 (3 d+8 e)}{2 x^2}-\frac{5 (2 d+9 e)}{x}+(d+10 e) \log (x)-\frac{d}{10 x^{10}}+e x","-\frac{10 d+e}{9 x^9}-\frac{5 (9 d+2 e)}{8 x^8}-\frac{15 (8 d+3 e)}{7 x^7}-\frac{5 (7 d+4 e)}{x^6}-\frac{42 (6 d+5 e)}{5 x^5}-\frac{21 (5 d+6 e)}{2 x^4}-\frac{10 (4 d+7 e)}{x^3}-\frac{15 (3 d+8 e)}{2 x^2}-\frac{5 (2 d+9 e)}{x}+(d+10 e) \log (x)-\frac{d}{10 x^{10}}+e x",1,"-1/10*d/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",1
578,1,143,92,0.0487876,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{12}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^12,x]","-\frac{10 d+e}{10 x^{10}}-\frac{5 (9 d+2 e)}{9 x^9}-\frac{15 (8 d+3 e)}{8 x^8}-\frac{30 (7 d+4 e)}{7 x^7}-\frac{7 (6 d+5 e)}{x^6}-\frac{42 (5 d+6 e)}{5 x^5}-\frac{15 (4 d+7 e)}{2 x^4}-\frac{5 (3 d+8 e)}{x^3}-\frac{5 (2 d+9 e)}{2 x^2}-\frac{d+10 e}{x}-\frac{d}{11 x^{11}}+e \log (x)","-\frac{d (x+1)^{11}}{11 x^{11}}-\frac{e}{10 x^{10}}-\frac{10 e}{9 x^9}-\frac{45 e}{8 x^8}-\frac{120 e}{7 x^7}-\frac{35 e}{x^6}-\frac{252 e}{5 x^5}-\frac{105 e}{2 x^4}-\frac{40 e}{x^3}-\frac{45 e}{2 x^2}-\frac{10 e}{x}+e \log (x)",1,"-1/11*d/x^11 - (10*d + e)/(10*x^10) - (5*(9*d + 2*e))/(9*x^9) - (15*(8*d + 3*e))/(8*x^8) - (30*(7*d + 4*e))/(7*x^7) - (7*(6*d + 5*e))/x^6 - (42*(5*d + 6*e))/(5*x^5) - (15*(4*d + 7*e))/(2*x^4) - (5*(3*d + 8*e))/x^3 - (5*(2*d + 9*e))/(2*x^2) - (d + 10*e)/x + e*Log[x]","A",1
579,1,114,31,0.0256375,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{13}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^13,x]","-\frac{d \left(66 x^{10}+440 x^9+1485 x^8+3168 x^7+4620 x^6+4752 x^5+3465 x^4+1760 x^3+594 x^2+120 x+11\right)+12 e x \left(11 x^{10}+55 x^9+165 x^8+330 x^7+462 x^6+462 x^5+330 x^4+165 x^3+55 x^2+11 x+1\right)}{132 x^{12}}","\frac{(x+1)^{11} (d-12 e)}{132 x^{11}}-\frac{d (x+1)^{11}}{12 x^{12}}",1,"-1/132*(12*e*x*(1 + 11*x + 55*x^2 + 165*x^3 + 330*x^4 + 462*x^5 + 462*x^6 + 330*x^7 + 165*x^8 + 55*x^9 + 11*x^10) + d*(11 + 120*x + 594*x^2 + 1760*x^3 + 3465*x^4 + 4752*x^5 + 4620*x^6 + 3168*x^7 + 1485*x^8 + 440*x^9 + 66*x^10))/x^12","B",1
580,1,115,52,0.0250652,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{14}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^14,x]","-\frac{2 d \left(286 x^{10}+2145 x^9+7722 x^8+17160 x^7+25740 x^6+27027 x^5+20020 x^4+10296 x^3+3510 x^2+715 x+66\right)+13 e x \left(66 x^{10}+440 x^9+1485 x^8+3168 x^7+4620 x^6+4752 x^5+3465 x^4+1760 x^3+594 x^2+120 x+11\right)}{1716 x^{13}}","\frac{(x+1)^{11} (2 d-13 e)}{156 x^{12}}-\frac{(x+1)^{11} (2 d-13 e)}{1716 x^{11}}-\frac{d (x+1)^{11}}{13 x^{13}}",1,"-1/1716*(13*e*x*(11 + 120*x + 594*x^2 + 1760*x^3 + 3465*x^4 + 4752*x^5 + 4620*x^6 + 3168*x^7 + 1485*x^8 + 440*x^9 + 66*x^10) + 2*d*(66 + 715*x + 3510*x^2 + 10296*x^3 + 20020*x^4 + 27027*x^5 + 25740*x^6 + 17160*x^7 + 7722*x^8 + 2145*x^9 + 286*x^10))/x^13","B",1
581,1,149,71,0.0370313,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{15}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^15,x]","-\frac{10 d+e}{13 x^{13}}-\frac{5 (9 d+2 e)}{12 x^{12}}-\frac{15 (8 d+3 e)}{11 x^{11}}-\frac{3 (7 d+4 e)}{x^{10}}-\frac{14 (6 d+5 e)}{3 x^9}-\frac{21 (5 d+6 e)}{4 x^8}-\frac{30 (4 d+7 e)}{7 x^7}-\frac{5 (3 d+8 e)}{2 x^6}-\frac{2 d+9 e}{x^5}-\frac{d+10 e}{4 x^4}-\frac{d}{14 x^{14}}-\frac{e}{3 x^3}","\frac{(x+1)^{11} (3 d-14 e)}{182 x^{13}}-\frac{(x+1)^{11} (3 d-14 e)}{1092 x^{12}}+\frac{(x+1)^{11} (3 d-14 e)}{12012 x^{11}}-\frac{d (x+1)^{11}}{14 x^{14}}",1,"-1/14*d/x^14 - (10*d + e)/(13*x^13) - (5*(9*d + 2*e))/(12*x^12) - (15*(8*d + 3*e))/(11*x^11) - (3*(7*d + 4*e))/x^10 - (14*(6*d + 5*e))/(3*x^9) - (21*(5*d + 6*e))/(4*x^8) - (30*(4*d + 7*e))/(7*x^7) - (5*(3*d + 8*e))/(2*x^6) - (2*d + 9*e)/x^5 - (d + 10*e)/(4*x^4) - e/(3*x^3)","B",1
582,1,153,90,0.0368836,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{16}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^16,x]","-\frac{10 d+e}{14 x^{14}}-\frac{5 (9 d+2 e)}{13 x^{13}}-\frac{5 (8 d+3 e)}{4 x^{12}}-\frac{30 (7 d+4 e)}{11 x^{11}}-\frac{21 (6 d+5 e)}{5 x^{10}}-\frac{14 (5 d+6 e)}{3 x^9}-\frac{15 (4 d+7 e)}{4 x^8}-\frac{15 (3 d+8 e)}{7 x^7}-\frac{5 (2 d+9 e)}{6 x^6}-\frac{d+10 e}{5 x^5}-\frac{d}{15 x^{15}}-\frac{e}{4 x^4}","\frac{(x+1)^{11} (4 d-15 e)}{210 x^{14}}-\frac{(x+1)^{11} (4 d-15 e)}{910 x^{13}}+\frac{(x+1)^{11} (4 d-15 e)}{5460 x^{12}}-\frac{(x+1)^{11} (4 d-15 e)}{60060 x^{11}}-\frac{d (x+1)^{11}}{15 x^{15}}",1,"-1/15*d/x^15 - (10*d + e)/(14*x^14) - (5*(9*d + 2*e))/(13*x^13) - (5*(8*d + 3*e))/(4*x^12) - (30*(7*d + 4*e))/(11*x^11) - (21*(6*d + 5*e))/(5*x^10) - (14*(5*d + 6*e))/(3*x^9) - (15*(4*d + 7*e))/(4*x^8) - (15*(3*d + 8*e))/(7*x^7) - (5*(2*d + 9*e))/(6*x^6) - (d + 10*e)/(5*x^5) - e/(4*x^4)","A",1
583,1,153,109,0.0352294,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{17}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^17,x]","-\frac{10 d+e}{15 x^{15}}-\frac{5 (9 d+2 e)}{14 x^{14}}-\frac{15 (8 d+3 e)}{13 x^{13}}-\frac{5 (7 d+4 e)}{2 x^{12}}-\frac{42 (6 d+5 e)}{11 x^{11}}-\frac{21 (5 d+6 e)}{5 x^{10}}-\frac{10 (4 d+7 e)}{3 x^9}-\frac{15 (3 d+8 e)}{8 x^8}-\frac{5 (2 d+9 e)}{7 x^7}-\frac{d+10 e}{6 x^6}-\frac{d}{16 x^{16}}-\frac{e}{5 x^5}","\frac{(x+1)^{11} (5 d-16 e)}{240 x^{15}}-\frac{(x+1)^{11} (5 d-16 e)}{840 x^{14}}+\frac{(x+1)^{11} (5 d-16 e)}{3640 x^{13}}-\frac{(x+1)^{11} (5 d-16 e)}{21840 x^{12}}+\frac{(x+1)^{11} (5 d-16 e)}{240240 x^{11}}-\frac{d (x+1)^{11}}{16 x^{16}}",1,"-1/16*d/x^16 - (10*d + e)/(15*x^15) - (5*(9*d + 2*e))/(14*x^14) - (15*(8*d + 3*e))/(13*x^13) - (5*(7*d + 4*e))/(2*x^12) - (42*(6*d + 5*e))/(11*x^11) - (21*(5*d + 6*e))/(5*x^10) - (10*(4*d + 7*e))/(3*x^9) - (15*(3*d + 8*e))/(8*x^8) - (5*(2*d + 9*e))/(7*x^7) - (d + 10*e)/(6*x^6) - e/(5*x^5)","A",1
584,1,151,128,0.0415258,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{18}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^18,x]","-\frac{10 d+e}{16 x^{16}}-\frac{9 d+2 e}{3 x^{15}}-\frac{15 (8 d+3 e)}{14 x^{14}}-\frac{30 (7 d+4 e)}{13 x^{13}}-\frac{7 (6 d+5 e)}{2 x^{12}}-\frac{42 (5 d+6 e)}{11 x^{11}}-\frac{3 (4 d+7 e)}{x^{10}}-\frac{5 (3 d+8 e)}{3 x^9}-\frac{5 (2 d+9 e)}{8 x^8}-\frac{d+10 e}{7 x^7}-\frac{d}{17 x^{17}}-\frac{e}{6 x^6}","\frac{(x+1)^{11} (6 d-17 e)}{272 x^{16}}-\frac{(x+1)^{11} (6 d-17 e)}{816 x^{15}}+\frac{(x+1)^{11} (6 d-17 e)}{2856 x^{14}}-\frac{(x+1)^{11} (6 d-17 e)}{12376 x^{13}}+\frac{(x+1)^{11} (6 d-17 e)}{74256 x^{12}}-\frac{(x+1)^{11} (6 d-17 e)}{816816 x^{11}}-\frac{d (x+1)^{11}}{17 x^{17}}",1,"-1/17*d/x^17 - (10*d + e)/(16*x^16) - (9*d + 2*e)/(3*x^15) - (15*(8*d + 3*e))/(14*x^14) - (30*(7*d + 4*e))/(13*x^13) - (7*(6*d + 5*e))/(2*x^12) - (42*(5*d + 6*e))/(11*x^11) - (3*(4*d + 7*e))/x^10 - (5*(3*d + 8*e))/(3*x^9) - (5*(2*d + 9*e))/(8*x^8) - (d + 10*e)/(7*x^7) - e/(6*x^6)","A",1
585,1,151,151,0.0459538,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{19}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^19,x]","-\frac{10 d+e}{17 x^{17}}-\frac{5 (9 d+2 e)}{16 x^{16}}-\frac{8 d+3 e}{x^{15}}-\frac{15 (7 d+4 e)}{7 x^{14}}-\frac{42 (6 d+5 e)}{13 x^{13}}-\frac{7 (5 d+6 e)}{2 x^{12}}-\frac{30 (4 d+7 e)}{11 x^{11}}-\frac{3 (3 d+8 e)}{2 x^{10}}-\frac{5 (2 d+9 e)}{9 x^9}-\frac{d+10 e}{8 x^8}-\frac{d}{18 x^{18}}-\frac{e}{7 x^7}","-\frac{10 d+e}{17 x^{17}}-\frac{5 (9 d+2 e)}{16 x^{16}}-\frac{8 d+3 e}{x^{15}}-\frac{15 (7 d+4 e)}{7 x^{14}}-\frac{42 (6 d+5 e)}{13 x^{13}}-\frac{7 (5 d+6 e)}{2 x^{12}}-\frac{30 (4 d+7 e)}{11 x^{11}}-\frac{3 (3 d+8 e)}{2 x^{10}}-\frac{5 (2 d+9 e)}{9 x^9}-\frac{d+10 e}{8 x^8}-\frac{d}{18 x^{18}}-\frac{e}{7 x^7}",1,"-1/18*d/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",1
586,1,149,149,0.0409912,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{20}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^20,x]","-\frac{10 d+e}{18 x^{18}}-\frac{5 (9 d+2 e)}{17 x^{17}}-\frac{15 (8 d+3 e)}{16 x^{16}}-\frac{2 (7 d+4 e)}{x^{15}}-\frac{3 (6 d+5 e)}{x^{14}}-\frac{42 (5 d+6 e)}{13 x^{13}}-\frac{5 (4 d+7 e)}{2 x^{12}}-\frac{15 (3 d+8 e)}{11 x^{11}}-\frac{2 d+9 e}{2 x^{10}}-\frac{d+10 e}{9 x^9}-\frac{d}{19 x^{19}}-\frac{e}{8 x^8}","-\frac{10 d+e}{18 x^{18}}-\frac{5 (9 d+2 e)}{17 x^{17}}-\frac{15 (8 d+3 e)}{16 x^{16}}-\frac{2 (7 d+4 e)}{x^{15}}-\frac{3 (6 d+5 e)}{x^{14}}-\frac{42 (5 d+6 e)}{13 x^{13}}-\frac{5 (4 d+7 e)}{2 x^{12}}-\frac{15 (3 d+8 e)}{11 x^{11}}-\frac{2 d+9 e}{2 x^{10}}-\frac{d+10 e}{9 x^9}-\frac{d}{19 x^{19}}-\frac{e}{8 x^8}",1,"-1/19*d/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",1
587,1,151,151,0.0467653,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{21}} \, dx","Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^21,x]","-\frac{10 d+e}{19 x^{19}}-\frac{5 (9 d+2 e)}{18 x^{18}}-\frac{15 (8 d+3 e)}{17 x^{17}}-\frac{15 (7 d+4 e)}{8 x^{16}}-\frac{14 (6 d+5 e)}{5 x^{15}}-\frac{3 (5 d+6 e)}{x^{14}}-\frac{30 (4 d+7 e)}{13 x^{13}}-\frac{5 (3 d+8 e)}{4 x^{12}}-\frac{5 (2 d+9 e)}{11 x^{11}}-\frac{d+10 e}{10 x^{10}}-\frac{d}{20 x^{20}}-\frac{e}{9 x^9}","-\frac{10 d+e}{19 x^{19}}-\frac{5 (9 d+2 e)}{18 x^{18}}-\frac{15 (8 d+3 e)}{17 x^{17}}-\frac{15 (7 d+4 e)}{8 x^{16}}-\frac{14 (6 d+5 e)}{5 x^{15}}-\frac{3 (5 d+6 e)}{x^{14}}-\frac{30 (4 d+7 e)}{13 x^{13}}-\frac{5 (3 d+8 e)}{4 x^{12}}-\frac{5 (2 d+9 e)}{11 x^{11}}-\frac{d+10 e}{10 x^{10}}-\frac{d}{20 x^{20}}-\frac{e}{9 x^9}",1,"-1/20*d/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",1
588,1,83,83,0.00189,"\int x^{11} (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[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",1
589,1,83,83,0.0017335,"\int x^{10} (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[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",1
590,1,81,91,0.0016413,"\int x^9 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^9*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{21}}{21}+\frac{11 x^{20}}{20}+\frac{55 x^{19}}{19}+\frac{55 x^{18}}{6}+\frac{330 x^{17}}{17}+\frac{231 x^{16}}{8}+\frac{154 x^{15}}{5}+\frac{165 x^{14}}{7}+\frac{165 x^{13}}{13}+\frac{55 x^{12}}{12}+x^{11}+\frac{x^{10}}{10}","\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,"x^10/10 + x^11 + (55*x^12)/12 + (165*x^13)/13 + (165*x^14)/7 + (154*x^15)/5 + (231*x^16)/8 + (330*x^17)/17 + (55*x^18)/6 + (55*x^19)/19 + (11*x^20)/20 + x^21/21","A",1
591,1,81,80,0.0018248,"\int x^8 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^8*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{20}}{20}+\frac{11 x^{19}}{19}+\frac{55 x^{18}}{18}+\frac{165 x^{17}}{17}+\frac{165 x^{16}}{8}+\frac{154 x^{15}}{5}+33 x^{14}+\frac{330 x^{13}}{13}+\frac{55 x^{12}}{4}+5 x^{11}+\frac{11 x^{10}}{10}+\frac{x^9}{9}","\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,"x^9/9 + (11*x^10)/10 + 5*x^11 + (55*x^12)/4 + (330*x^13)/13 + 33*x^14 + (154*x^15)/5 + (165*x^16)/8 + (165*x^17)/17 + (55*x^18)/18 + (11*x^19)/19 + x^20/20","A",1
592,1,79,73,0.0016713,"\int x^7 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^7*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{19}}{19}+\frac{11 x^{18}}{18}+\frac{55 x^{17}}{17}+\frac{165 x^{16}}{16}+22 x^{15}+33 x^{14}+\frac{462 x^{13}}{13}+\frac{55 x^{12}}{2}+15 x^{11}+\frac{11 x^{10}}{2}+\frac{11 x^9}{9}+\frac{x^8}{8}","\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,"x^8/8 + (11*x^9)/9 + (11*x^10)/2 + 15*x^11 + (55*x^12)/2 + (462*x^13)/13 + 33*x^14 + 22*x^15 + (165*x^16)/16 + (55*x^17)/17 + (11*x^18)/18 + x^19/19","A",1
593,1,81,64,0.0015866,"\int x^6 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^6*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{18}}{18}+\frac{11 x^{17}}{17}+\frac{55 x^{16}}{16}+11 x^{15}+\frac{165 x^{14}}{7}+\frac{462 x^{13}}{13}+\frac{77 x^{12}}{2}+30 x^{11}+\frac{33 x^{10}}{2}+\frac{55 x^9}{9}+\frac{11 x^8}{8}+\frac{x^7}{7}","\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,"x^7/7 + (11*x^8)/8 + (55*x^9)/9 + (33*x^10)/2 + 30*x^11 + (77*x^12)/2 + (462*x^13)/13 + (165*x^14)/7 + 11*x^15 + (55*x^16)/16 + (11*x^17)/17 + x^18/18","A",1
594,1,81,55,0.0019117,"\int x^5 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^5*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{17}}{17}+\frac{11 x^{16}}{16}+\frac{11 x^{15}}{3}+\frac{165 x^{14}}{14}+\frac{330 x^{13}}{13}+\frac{77 x^{12}}{2}+42 x^{11}+33 x^{10}+\frac{55 x^9}{3}+\frac{55 x^8}{8}+\frac{11 x^7}{7}+\frac{x^6}{6}","\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,"x^6/6 + (11*x^7)/7 + (55*x^8)/8 + (55*x^9)/3 + 33*x^10 + 42*x^11 + (77*x^12)/2 + (330*x^13)/13 + (165*x^14)/14 + (11*x^15)/3 + (11*x^16)/16 + x^17/17","A",1
595,1,83,46,0.0015521,"\int x^4 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^4*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{16}}{16}+\frac{11 x^{15}}{15}+\frac{55 x^{14}}{14}+\frac{165 x^{13}}{13}+\frac{55 x^{12}}{2}+42 x^{11}+\frac{231 x^{10}}{5}+\frac{110 x^9}{3}+\frac{165 x^8}{8}+\frac{55 x^7}{7}+\frac{11 x^6}{6}+\frac{x^5}{5}","\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,"x^5/5 + (11*x^6)/6 + (55*x^7)/7 + (165*x^8)/8 + (110*x^9)/3 + (231*x^10)/5 + 42*x^11 + (55*x^12)/2 + (165*x^13)/13 + (55*x^14)/14 + (11*x^15)/15 + x^16/16","A",1
596,1,83,37,0.0016121,"\int x^3 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^3*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{15}}{15}+\frac{11 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{55 x^{12}}{4}+30 x^{11}+\frac{231 x^{10}}{5}+\frac{154 x^9}{3}+\frac{165 x^8}{4}+\frac{165 x^7}{7}+\frac{55 x^6}{6}+\frac{11 x^5}{5}+\frac{x^4}{4}","\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,"x^4/4 + (11*x^5)/5 + (55*x^6)/6 + (165*x^7)/7 + (165*x^8)/4 + (154*x^9)/3 + (231*x^10)/5 + 30*x^11 + (55*x^12)/4 + (55*x^13)/13 + (11*x^14)/14 + x^15/15","B",1
597,1,79,28,0.0015683,"\int x^2 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^2*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{14}}{14}+\frac{11 x^{13}}{13}+\frac{55 x^{12}}{12}+15 x^{11}+33 x^{10}+\frac{154 x^9}{3}+\frac{231 x^8}{4}+\frac{330 x^7}{7}+\frac{55 x^6}{2}+11 x^5+\frac{11 x^4}{4}+\frac{x^3}{3}","\frac{1}{14} (x+1)^{14}-\frac{2}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12}",1,"x^3/3 + (11*x^4)/4 + 11*x^5 + (55*x^6)/2 + (330*x^7)/7 + (231*x^8)/4 + (154*x^9)/3 + 33*x^10 + 15*x^11 + (55*x^12)/12 + (11*x^13)/13 + x^14/14","B",1
598,1,77,19,0.0014106,"\int x (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{13}}{13}+\frac{11 x^{12}}{12}+5 x^{11}+\frac{33 x^{10}}{2}+\frac{110 x^9}{3}+\frac{231 x^8}{4}+66 x^7+55 x^6+33 x^5+\frac{55 x^4}{4}+\frac{11 x^3}{3}+\frac{x^2}{2}","\frac{1}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}",1,"x^2/2 + (11*x^3)/3 + (55*x^4)/4 + 33*x^5 + 55*x^6 + 66*x^7 + (231*x^8)/4 + (110*x^9)/3 + (33*x^10)/2 + 5*x^11 + (11*x^12)/12 + x^13/13","B",1
599,1,9,9,0.0012621,"\int (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[(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",1
600,1,96,72,0.0112219,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x,x]","\frac{1}{11} (x+1)^{11}+\frac{1}{10} (x+1)^{10}+\frac{1}{9} (x+1)^9+\frac{1}{8} (x+1)^8+\frac{1}{7} (x+1)^7+\frac{1}{6} (x+1)^6+\frac{1}{5} (x+1)^5+\frac{1}{4} (x+1)^4+\frac{1}{3} (x+1)^3+\frac{1}{2} (x+1)^2+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,"x + (1 + x)^2/2 + (1 + x)^3/3 + (1 + x)^4/4 + (1 + x)^5/5 + (1 + x)^6/6 + (1 + x)^7/7 + (1 + x)^8/8 + (1 + x)^9/9 + (1 + x)^10/10 + (1 + x)^11/11 + Log[-x]","A",1
601,1,72,72,0.0028471,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^2} \, dx","Integrate[((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",1
602,1,70,70,0.0026201,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^3} \, dx","Integrate[((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*1/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",1
603,1,70,70,0.0028775,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^4} \, dx","Integrate[((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-\frac{1}{3 x^3}+231 x^2-\frac{11}{2 x^2}+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-\frac{1}{3 x^3}+231 x^2-\frac{11}{2 x^2}+330 x-\frac{55}{x}+165 \log (x)",1,"-1/3*1/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",1
604,1,70,70,0.0027082,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^5} \, dx","Integrate[((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}-\frac{1}{4 x^4}+110 x^3-\frac{11}{3 x^3}+231 x^2-\frac{55}{2 x^2}+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}-\frac{1}{4 x^4}+110 x^3-\frac{11}{3 x^3}+231 x^2-\frac{55}{2 x^2}+462 x-\frac{165}{x}+330 \log (x)",1,"-1/4*1/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",1
605,1,72,72,0.0027711,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^6} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^6,x]","\frac{x^6}{6}+\frac{11 x^5}{5}-\frac{1}{5 x^5}+\frac{55 x^4}{4}-\frac{11}{4 x^4}+55 x^3-\frac{55}{3 x^3}+165 x^2-\frac{165}{2 x^2}+462 x-\frac{330}{x}+462 \log (x)","\frac{x^6}{6}+\frac{11 x^5}{5}-\frac{1}{5 x^5}+\frac{55 x^4}{4}-\frac{11}{4 x^4}+55 x^3-\frac{55}{3 x^3}+165 x^2-\frac{165}{2 x^2}+462 x-\frac{330}{x}+462 \log (x)",1,"-1/5*1/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",1
606,1,72,72,0.0025869,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^7} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^7,x]","-\frac{1}{6 x^6}+\frac{x^5}{5}-\frac{11}{5 x^5}+\frac{11 x^4}{4}-\frac{55}{4 x^4}+\frac{55 x^3}{3}-\frac{55}{x^3}+\frac{165 x^2}{2}-\frac{165}{x^2}+330 x-\frac{462}{x}+462 \log (x)","-\frac{1}{6 x^6}+\frac{x^5}{5}-\frac{11}{5 x^5}+\frac{11 x^4}{4}-\frac{55}{4 x^4}+\frac{55 x^3}{3}-\frac{55}{x^3}+\frac{165 x^2}{2}-\frac{165}{x^2}+330 x-\frac{462}{x}+462 \log (x)",1,"-1/6*1/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",1
607,1,70,70,0.0026695,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^8} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^8,x]","-\frac{1}{7 x^7}-\frac{11}{6 x^6}-\frac{11}{x^5}+\frac{x^4}{4}-\frac{165}{4 x^4}+\frac{11 x^3}{3}-\frac{110}{x^3}+\frac{55 x^2}{2}-\frac{231}{x^2}+165 x-\frac{462}{x}+330 \log (x)","-\frac{1}{7 x^7}-\frac{11}{6 x^6}-\frac{11}{x^5}+\frac{x^4}{4}-\frac{165}{4 x^4}+\frac{11 x^3}{3}-\frac{110}{x^3}+\frac{55 x^2}{2}-\frac{231}{x^2}+165 x-\frac{462}{x}+330 \log (x)",1,"-1/7*1/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",1
608,1,70,70,0.0026781,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^9} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^9,x]","-\frac{1}{8 x^8}-\frac{11}{7 x^7}-\frac{55}{6 x^6}-\frac{33}{x^5}-\frac{165}{2 x^4}+\frac{x^3}{3}-\frac{154}{x^3}+\frac{11 x^2}{2}-\frac{231}{x^2}+55 x-\frac{330}{x}+165 \log (x)","-\frac{1}{8 x^8}-\frac{11}{7 x^7}-\frac{55}{6 x^6}-\frac{33}{x^5}-\frac{165}{2 x^4}+\frac{x^3}{3}-\frac{154}{x^3}+\frac{11 x^2}{2}-\frac{231}{x^2}+55 x-\frac{330}{x}+165 \log (x)",1,"-1/8*1/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",1
609,1,70,70,0.0027816,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{10}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^10,x]","-\frac{1}{9 x^9}-\frac{11}{8 x^8}-\frac{55}{7 x^7}-\frac{55}{2 x^6}-\frac{66}{x^5}-\frac{231}{2 x^4}-\frac{154}{x^3}+\frac{x^2}{2}-\frac{165}{x^2}+11 x-\frac{165}{x}+55 \log (x)","-\frac{1}{9 x^9}-\frac{11}{8 x^8}-\frac{55}{7 x^7}-\frac{55}{2 x^6}-\frac{66}{x^5}-\frac{231}{2 x^4}-\frac{154}{x^3}+\frac{x^2}{2}-\frac{165}{x^2}+11 x-\frac{165}{x}+55 \log (x)",1,"-1/9*1/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",1
610,1,70,70,0.0034284,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{11}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^11,x]","-\frac{1}{10 x^{10}}-\frac{11}{9 x^9}-\frac{55}{8 x^8}-\frac{165}{7 x^7}-\frac{55}{x^6}-\frac{462}{5 x^5}-\frac{231}{2 x^4}-\frac{110}{x^3}-\frac{165}{2 x^2}+x-\frac{55}{x}+11 \log (x)","-\frac{1}{10 x^{10}}-\frac{11}{9 x^9}-\frac{55}{8 x^8}-\frac{165}{7 x^7}-\frac{55}{x^6}-\frac{462}{5 x^5}-\frac{231}{2 x^4}-\frac{110}{x^3}-\frac{165}{2 x^2}+x-\frac{55}{x}+11 \log (x)",1,"-1/10*1/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",1
611,1,74,74,0.0025523,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{12}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^12,x]","-\frac{1}{11 x^{11}}-\frac{11}{10 x^{10}}-\frac{55}{9 x^9}-\frac{165}{8 x^8}-\frac{330}{7 x^7}-\frac{77}{x^6}-\frac{462}{5 x^5}-\frac{165}{2 x^4}-\frac{55}{x^3}-\frac{55}{2 x^2}-\frac{11}{x}+\log (x)","-\frac{1}{11 x^{11}}-\frac{11}{10 x^{10}}-\frac{55}{9 x^9}-\frac{165}{8 x^8}-\frac{330}{7 x^7}-\frac{77}{x^6}-\frac{462}{5 x^5}-\frac{165}{2 x^4}-\frac{55}{x^3}-\frac{55}{2 x^2}-\frac{11}{x}+\log (x)",1,"-1/11*1/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",1
612,1,75,12,0.0024425,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{13}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^13,x]","-\frac{1}{12 x^{12}}-\frac{1}{x^{11}}-\frac{11}{2 x^{10}}-\frac{55}{3 x^9}-\frac{165}{4 x^8}-\frac{66}{x^7}-\frac{77}{x^6}-\frac{66}{x^5}-\frac{165}{4 x^4}-\frac{55}{3 x^3}-\frac{11}{2 x^2}-\frac{1}{x}","-\frac{(x+1)^{12}}{12 x^{12}}",1,"-1/12*1/x^12 - x^(-11) - 11/(2*x^10) - 55/(3*x^9) - 165/(4*x^8) - 66/x^7 - 77/x^6 - 66/x^5 - 165/(4*x^4) - 55/(3*x^3) - 11/(2*x^2) - x^(-1)","B",1
613,1,77,25,0.0025029,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{14}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^14,x]","-\frac{1}{13 x^{13}}-\frac{11}{12 x^{12}}-\frac{5}{x^{11}}-\frac{33}{2 x^{10}}-\frac{110}{3 x^9}-\frac{231}{4 x^8}-\frac{66}{x^7}-\frac{55}{x^6}-\frac{33}{x^5}-\frac{55}{4 x^4}-\frac{11}{3 x^3}-\frac{1}{2 x^2}","\frac{(x+1)^{12}}{156 x^{12}}-\frac{(x+1)^{12}}{13 x^{13}}",1,"-1/13*1/x^13 - 11/(12*x^12) - 5/x^11 - 33/(2*x^10) - 110/(3*x^9) - 231/(4*x^8) - 66/x^7 - 55/x^6 - 33/x^5 - 55/(4*x^4) - 11/(3*x^3) - 1/(2*x^2)","B",1
614,1,79,37,0.0024395,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{15}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^15,x]","-\frac{1}{14 x^{14}}-\frac{11}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{15}{x^{11}}-\frac{33}{x^{10}}-\frac{154}{3 x^9}-\frac{231}{4 x^8}-\frac{330}{7 x^7}-\frac{55}{2 x^6}-\frac{11}{x^5}-\frac{11}{4 x^4}-\frac{1}{3 x^3}","-\frac{(x+1)^{12}}{14 x^{14}}+\frac{(x+1)^{12}}{91 x^{13}}-\frac{(x+1)^{12}}{1092 x^{12}}",1,"-1/14*1/x^14 - 11/(13*x^13) - 55/(12*x^12) - 15/x^11 - 33/x^10 - 154/(3*x^9) - 231/(4*x^8) - 330/(7*x^7) - 55/(2*x^6) - 11/x^5 - 11/(4*x^4) - 1/(3*x^3)","B",1
615,1,83,49,0.0031544,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{16}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^16,x]","-\frac{1}{15 x^{15}}-\frac{11}{14 x^{14}}-\frac{55}{13 x^{13}}-\frac{55}{4 x^{12}}-\frac{30}{x^{11}}-\frac{231}{5 x^{10}}-\frac{154}{3 x^9}-\frac{165}{4 x^8}-\frac{165}{7 x^7}-\frac{55}{6 x^6}-\frac{11}{5 x^5}-\frac{1}{4 x^4}","-\frac{(x+1)^{12}}{15 x^{15}}+\frac{(x+1)^{12}}{70 x^{14}}-\frac{(x+1)^{12}}{455 x^{13}}+\frac{(x+1)^{12}}{5460 x^{12}}",1,"-1/15*1/x^15 - 11/(14*x^14) - 55/(13*x^13) - 55/(4*x^12) - 30/x^11 - 231/(5*x^10) - 154/(3*x^9) - 165/(4*x^8) - 165/(7*x^7) - 55/(6*x^6) - 11/(5*x^5) - 1/(4*x^4)","A",1
616,1,83,61,0.0024721,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{17}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^17,x]","-\frac{1}{16 x^{16}}-\frac{11}{15 x^{15}}-\frac{55}{14 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{2 x^{12}}-\frac{42}{x^{11}}-\frac{231}{5 x^{10}}-\frac{110}{3 x^9}-\frac{165}{8 x^8}-\frac{55}{7 x^7}-\frac{11}{6 x^6}-\frac{1}{5 x^5}","-\frac{(x+1)^{12}}{16 x^{16}}+\frac{(x+1)^{12}}{60 x^{15}}-\frac{(x+1)^{12}}{280 x^{14}}+\frac{(x+1)^{12}}{1820 x^{13}}-\frac{(x+1)^{12}}{21840 x^{12}}",1,"-1/16*1/x^16 - 11/(15*x^15) - 55/(14*x^14) - 165/(13*x^13) - 55/(2*x^12) - 42/x^11 - 231/(5*x^10) - 110/(3*x^9) - 165/(8*x^8) - 55/(7*x^7) - 11/(6*x^6) - 1/(5*x^5)","A",1
617,1,81,73,0.0024085,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{18}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^18,x]","-\frac{1}{17 x^{17}}-\frac{11}{16 x^{16}}-\frac{11}{3 x^{15}}-\frac{165}{14 x^{14}}-\frac{330}{13 x^{13}}-\frac{77}{2 x^{12}}-\frac{42}{x^{11}}-\frac{33}{x^{10}}-\frac{55}{3 x^9}-\frac{55}{8 x^8}-\frac{11}{7 x^7}-\frac{1}{6 x^6}","-\frac{(x+1)^{12}}{17 x^{17}}+\frac{5 (x+1)^{12}}{272 x^{16}}-\frac{(x+1)^{12}}{204 x^{15}}+\frac{(x+1)^{12}}{952 x^{14}}-\frac{(x+1)^{12}}{6188 x^{13}}+\frac{(x+1)^{12}}{74256 x^{12}}",1,"-1/17*1/x^17 - 11/(16*x^16) - 11/(3*x^15) - 165/(14*x^14) - 330/(13*x^13) - 77/(2*x^12) - 42/x^11 - 33/x^10 - 55/(3*x^9) - 55/(8*x^8) - 11/(7*x^7) - 1/(6*x^6)","A",1
618,1,81,85,0.0022211,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{19}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^19,x]","-\frac{1}{18 x^{18}}-\frac{11}{17 x^{17}}-\frac{55}{16 x^{16}}-\frac{11}{x^{15}}-\frac{165}{7 x^{14}}-\frac{462}{13 x^{13}}-\frac{77}{2 x^{12}}-\frac{30}{x^{11}}-\frac{33}{2 x^{10}}-\frac{55}{9 x^9}-\frac{11}{8 x^8}-\frac{1}{7 x^7}","-\frac{(x+1)^{12}}{18 x^{18}}+\frac{(x+1)^{12}}{51 x^{17}}-\frac{5 (x+1)^{12}}{816 x^{16}}+\frac{(x+1)^{12}}{612 x^{15}}-\frac{(x+1)^{12}}{2856 x^{14}}+\frac{(x+1)^{12}}{18564 x^{13}}-\frac{(x+1)^{12}}{222768 x^{12}}",1,"-1/18*1/x^18 - 11/(17*x^17) - 55/(16*x^16) - 11/x^15 - 165/(7*x^14) - 462/(13*x^13) - 77/(2*x^12) - 30/x^11 - 33/(2*x^10) - 55/(9*x^9) - 11/(8*x^8) - 1/(7*x^7)","A",1
619,1,79,97,0.0025074,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{20}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^20,x]","-\frac{1}{19 x^{19}}-\frac{11}{18 x^{18}}-\frac{55}{17 x^{17}}-\frac{165}{16 x^{16}}-\frac{22}{x^{15}}-\frac{33}{x^{14}}-\frac{462}{13 x^{13}}-\frac{55}{2 x^{12}}-\frac{15}{x^{11}}-\frac{11}{2 x^{10}}-\frac{11}{9 x^9}-\frac{1}{8 x^8}","-\frac{(x+1)^{12}}{19 x^{19}}+\frac{7 (x+1)^{12}}{342 x^{18}}-\frac{7 (x+1)^{12}}{969 x^{17}}+\frac{35 (x+1)^{12}}{15504 x^{16}}-\frac{7 (x+1)^{12}}{11628 x^{15}}+\frac{(x+1)^{12}}{7752 x^{14}}-\frac{(x+1)^{12}}{50388 x^{13}}+\frac{(x+1)^{12}}{604656 x^{12}}",1,"-1/19*1/x^19 - 11/(18*x^18) - 55/(17*x^17) - 165/(16*x^16) - 22/x^15 - 33/x^14 - 462/(13*x^13) - 55/(2*x^12) - 15/x^11 - 11/(2*x^10) - 11/(9*x^9) - 1/(8*x^8)","A",1
620,1,81,81,0.0022608,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{21}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^21,x]","-\frac{1}{20 x^{20}}-\frac{11}{19 x^{19}}-\frac{55}{18 x^{18}}-\frac{165}{17 x^{17}}-\frac{165}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{33}{x^{14}}-\frac{330}{13 x^{13}}-\frac{55}{4 x^{12}}-\frac{5}{x^{11}}-\frac{11}{10 x^{10}}-\frac{1}{9 x^9}","-\frac{1}{20 x^{20}}-\frac{11}{19 x^{19}}-\frac{55}{18 x^{18}}-\frac{165}{17 x^{17}}-\frac{165}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{33}{x^{14}}-\frac{330}{13 x^{13}}-\frac{55}{4 x^{12}}-\frac{5}{x^{11}}-\frac{11}{10 x^{10}}-\frac{1}{9 x^9}",1,"-1/20*1/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",1
621,1,83,83,0.0040824,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{22}} \, dx","Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^22,x]","-\frac{1}{21 x^{21}}-\frac{11}{20 x^{20}}-\frac{55}{19 x^{19}}-\frac{55}{6 x^{18}}-\frac{330}{17 x^{17}}-\frac{231}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{165}{7 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{1}{x^{11}}-\frac{1}{10 x^{10}}","-\frac{1}{21 x^{21}}-\frac{11}{20 x^{20}}-\frac{55}{19 x^{19}}-\frac{55}{6 x^{18}}-\frac{330}{17 x^{17}}-\frac{231}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{165}{7 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{1}{x^{11}}-\frac{1}{10 x^{10}}",1,"-1/21*1/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",1
622,1,127,134,0.0645528,"\int \frac{x^5 (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(x^5*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\frac{60 a^5 (A b-a B)}{a+b x}+60 a^4 (5 A b-6 a B) \log (a+b x)+60 a^3 b x (5 a B-4 A b)-30 a^2 b^2 x^2 (4 a B-3 A b)+15 b^4 x^4 (A b-2 a B)+20 a b^3 x^3 (3 a B-2 A b)+12 b^5 B x^5}{60 b^7}","\frac{a^5 (A b-a B)}{b^7 (a+b x)}+\frac{a^4 (5 A b-6 a B) \log (a+b x)}{b^7}-\frac{a^3 x (4 A b-5 a B)}{b^6}+\frac{a^2 x^2 (3 A b-4 a B)}{2 b^5}-\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,"(60*a^3*b*(-4*A*b + 5*a*B)*x - 30*a^2*b^2*(-3*A*b + 4*a*B)*x^2 + 20*a*b^3*(-2*A*b + 3*a*B)*x^3 + 15*b^4*(A*b - 2*a*B)*x^4 + 12*b^5*B*x^5 + (60*a^5*(A*b - a*B))/(a + b*x) + 60*a^4*(5*A*b - 6*a*B)*Log[a + b*x])/(60*b^7)","A",1
623,1,107,113,0.0542776,"\int \frac{x^4 (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\frac{12 a^4 (a B-A b)}{a+b x}+12 a^3 (5 a B-4 A b) \log (a+b x)-12 a^2 b x (4 a B-3 A b)+4 b^3 x^3 (A b-2 a B)+6 a b^2 x^2 (3 a B-2 A b)+3 b^4 B x^4}{12 b^6}","-\frac{a^4 (A b-a B)}{b^6 (a+b x)}-\frac{a^3 (4 A b-5 a B) \log (a+b x)}{b^6}+\frac{a^2 x (3 A b-4 a B)}{b^5}-\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,"(-12*a^2*b*(-3*A*b + 4*a*B)*x + 6*a*b^2*(-2*A*b + 3*a*B)*x^2 + 4*b^3*(A*b - 2*a*B)*x^3 + 3*b^4*B*x^4 + (12*a^4*(-(A*b) + a*B))/(a + b*x) + 12*a^3*(-4*A*b + 5*a*B)*Log[a + b*x])/(12*b^6)","A",1
624,1,87,90,0.0531747,"\int \frac{x^3 (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\frac{6 a^3 (A b-a B)}{a+b x}+6 a^2 (3 A b-4 a B) \log (a+b x)+3 b^2 x^2 (A b-2 a B)+6 a b x (3 a B-2 A b)+2 b^3 B x^3}{6 b^5}","\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{a x (2 A b-3 a B)}{b^4}+\frac{x^2 (A b-2 a B)}{2 b^3}+\frac{B x^3}{3 b^2}",1,"(6*a*b*(-2*A*b + 3*a*B)*x + 3*b^2*(A*b - 2*a*B)*x^2 + 2*b^3*B*x^3 + (6*a^3*(A*b - a*B))/(a + b*x) + 6*a^2*(3*A*b - 4*a*B)*Log[a + b*x])/(6*b^5)","A",1
625,1,66,69,0.0560361,"\int \frac{x^2 (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\frac{2 a^2 (a B-A b)}{a+b x}+2 b x (A b-2 a B)+2 a (3 a B-2 A b) \log (a+b x)+b^2 B x^2}{2 b^4}","-\frac{a^2 (A b-a B)}{b^4 (a+b x)}-\frac{a (2 A b-3 a B) \log (a+b x)}{b^4}+\frac{x (A b-2 a B)}{b^3}+\frac{B x^2}{2 b^2}",1,"(2*b*(A*b - 2*a*B)*x + b^2*B*x^2 + (2*a^2*(-(A*b) + a*B))/(a + b*x) + 2*a*(-2*A*b + 3*a*B)*Log[a + b*x])/(2*b^4)","A",1
626,1,41,45,0.0241829,"\int \frac{x (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\frac{a (A b-a B)}{a+b x}+(A b-2 a B) \log (a+b x)+b B x}{b^3}","\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*B*x + (a*(A*b - a*B))/(a + b*x) + (A*b - 2*a*B)*Log[a + b*x])/b^3","A",1
627,1,31,32,0.0104958,"\int \frac{A+B x}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{a B-A b}{b^2 (a+b x)}+\frac{B \log (a+b x)}{b^2}","\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",1
628,1,38,42,0.0253458,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{\frac{a (A b-a B)}{b (a+b x)}-A \log (a+b x)+A \log (x)}{a^2}","-\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*(A*b - a*B))/(b*(a + b*x)) + A*Log[x] - A*Log[a + b*x])/a^2","A",1
629,1,56,65,0.0386967,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{\frac{a (a B-A b)}{a+b x}+\log (x) (a B-2 A b)+(2 A b-a B) \log (a+b x)-\frac{a A}{x}}{a^3}","-\frac{\log (x) (2 A b-a B)}{a^3}+\frac{(2 A b-a B) \log (a+b x)}{a^3}-\frac{A b-a B}{a^2 (a+b x)}-\frac{A}{a^2 x}",1,"(-((a*A)/x) + (a*(-(A*b) + a*B))/(a + b*x) + (-2*A*b + a*B)*Log[x] + (2*A*b - a*B)*Log[a + b*x])/a^3","A",1
630,1,85,85,0.0667933,"\int \frac{A+B x}{x^3 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(x^3*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{-\frac{a \left(a^2 (A+2 B x)+a b x (4 B x-3 A)-6 A b^2 x^2\right)}{x^2 (a+b x)}+2 b \log (x) (3 A b-2 a B)+2 b (2 a B-3 A b) \log (a+b x)}{2 a^4}","\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{2 A b-a B}{a^3 x}+\frac{b (A b-a B)}{a^3 (a+b x)}-\frac{A}{2 a^2 x^2}",1,"(-((a*(-6*A*b^2*x^2 + a^2*(A + 2*B*x) + a*b*x*(-3*A + 4*B*x)))/(x^2*(a + b*x))) + 2*b*(3*A*b - 2*a*B)*Log[x] + 2*b*(-3*A*b + 2*a*B)*Log[a + b*x])/(2*a^4)","A",1
631,1,106,113,0.0836225,"\int \frac{A+B x}{x^4 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(x^4*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{-\frac{2 a^3 A}{x^3}-\frac{3 a^2 (a B-2 A b)}{x^2}+\frac{6 a b^2 (a B-A b)}{a+b x}+6 b^2 \log (x) (3 a B-4 A b)+6 b^2 (4 A b-3 a B) \log (a+b x)+\frac{6 a b (2 a B-3 A b)}{x}}{6 a^5}","-\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{b^2 (A b-a B)}{a^4 (a+b x)}-\frac{b (3 A b-2 a B)}{a^4 x}+\frac{2 A b-a B}{2 a^3 x^2}-\frac{A}{3 a^2 x^3}",1,"((-2*a^3*A)/x^3 - (3*a^2*(-2*A*b + a*B))/x^2 + (6*a*b*(-3*A*b + 2*a*B))/x + (6*a*b^2*(-(A*b) + a*B))/(a + b*x) + 6*b^2*(-4*A*b + 3*a*B)*Log[x] + 6*b^2*(4*A*b - 3*a*B)*Log[a + b*x])/(6*a^5)","A",1
632,1,129,133,0.0901479,"\int \frac{A+B x}{x^5 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(x^5*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{\frac{a \left(-\left(a^4 (3 A+4 B x)\right)+a^3 b x (5 A+8 B x)-2 a^2 b^2 x^2 (5 A+12 B x)+6 a b^3 x^3 (5 A-8 B x)+60 A b^4 x^4\right)}{x^4 (a+b x)}+12 b^3 \log (x) (5 A b-4 a B)+12 b^3 (4 a B-5 A b) \log (a+b x)}{12 a^6}","\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-a B)}{a^5 (a+b x)}+\frac{b^2 (4 A b-3 a B)}{a^5 x}-\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*(60*A*b^4*x^4 + 6*a*b^3*x^3*(5*A - 8*B*x) - a^4*(3*A + 4*B*x) + a^3*b*x*(5*A + 8*B*x) - 2*a^2*b^2*x^2*(5*A + 12*B*x)))/(x^4*(a + b*x)) + 12*b^3*(5*A*b - 4*a*B)*Log[x] + 12*b^3*(-5*A*b + 4*a*B)*Log[a + b*x])/(12*a^6)","A",1
633,1,147,143,0.0528813,"\int \frac{x^5 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(x^5*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{-74 a^6 B+a^5 b (47 A-102 B x)+3 a^4 b^2 x (27 A+26 B x)+a^3 b^3 x^2 (146 B x-9 A)+3 a^2 b^4 x^3 (10 B x-21 A)-60 a^2 (a+b x)^3 (2 a B-A b) \log (a+b x)-3 a b^5 x^4 (5 A+2 B x)+b^6 x^5 (3 A+2 B x)}{6 b^7 (a+b x)^3}","\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{2 a x (2 A b-5 a B)}{b^6}+\frac{x^2 (A b-4 a B)}{2 b^5}+\frac{B x^3}{3 b^4}",1,"(-74*a^6*B + a^5*b*(47*A - 102*B*x) + b^6*x^5*(3*A + 2*B*x) - 3*a*b^5*x^4*(5*A + 2*B*x) + 3*a^2*b^4*x^3*(-21*A + 10*B*x) + 3*a^4*b^2*x*(27*A + 26*B*x) + a^3*b^3*x^2*(-9*A + 146*B*x) - 60*a^2*(-(A*b) + 2*a*B)*(a + b*x)^3*Log[a + b*x])/(6*b^7*(a + b*x)^3)","A",1
634,1,129,121,0.044983,"\int \frac{x^4 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 \left(5 a^2 B-2 a A b\right) \log (a+b x)}{b^6}+\frac{a^5 B-a^4 A b}{3 b^6 (a+b x)^3}+\frac{4 a^3 A b-5 a^4 B}{2 b^6 (a+b x)^2}+\frac{2 \left(5 a^3 B-3 a^2 A b\right)}{b^6 (a+b x)}+\frac{x (A b-4 a B)}{b^5}+\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{2 a (2 A b-5 a B) \log (a+b x)}{b^6}+\frac{x (A b-4 a B)}{b^5}+\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^5*B)/(3*b^6*(a + b*x)^3) + (4*a^3*A*b - 5*a^4*B)/(2*b^6*(a + b*x)^2) + (2*(-3*a^2*A*b + 5*a^3*B))/(b^6*(a + b*x)) + (2*(-2*a*A*b + 5*a^2*B)*Log[a + b*x])/b^6","A",1
635,1,97,97,0.0355204,"\int \frac{x^3 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{-26 a^4 B+a^3 b (11 A-54 B x)+9 a^2 b^2 x (3 A-2 B x)+18 a b^3 x^2 (A+B x)+6 (a+b x)^3 (A b-4 a B) \log (a+b x)+6 b^4 B x^4}{6 b^5 (a+b x)^3}","\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,"(-26*a^4*B + 6*b^4*B*x^4 + a^3*b*(11*A - 54*B*x) + 9*a^2*b^2*x*(3*A - 2*B*x) + 18*a*b^3*x^2*(A + B*x) + 6*(A*b - 4*a*B)*(a + b*x)^3*Log[a + b*x])/(6*b^5*(a + b*x)^3)","A",1
636,1,73,72,0.026834,"\int \frac{x^2 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{11 a^3 B+a^2 (27 b B x-2 A b)-6 a b^2 x (A-3 B x)+6 B (a+b x)^3 \log (a+b x)-6 A b^3 x^2}{6 b^4 (a+b x)^3}","-\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,"(11*a^3*B - 6*A*b^3*x^2 - 6*a*b^2*x*(A - 3*B*x) + a^2*(-2*A*b + 27*b*B*x) + 6*B*(a + b*x)^3*Log[a + b*x])/(6*b^4*(a + b*x)^3)","A",1
637,1,42,59,0.0150298,"\int \frac{x (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{2 a^2 B+a b (A+6 B x)+3 b^2 x (A+2 B x)}{6 b^3 (a+b x)^3}","-\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,"-1/6*(2*a^2*B + 3*b^2*x*(A + 2*B*x) + a*b*(A + 6*B*x))/(b^3*(a + b*x)^3)","A",1
638,1,27,38,0.0100378,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{B (a+3 b x)+2 A b}{6 b^2 (a+b x)^3}","\frac{a B-A b}{3 b^2 (a+b x)^3}-\frac{B}{2 b^2 (a+b x)^2}",1,"-1/6*(2*A*b + B*(a + 3*b*x))/(b^2*(a + b*x)^3)","A",1
639,1,65,72,0.0478902,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{a \left(-2 a^3 B+11 a^2 A b+15 a A b^2 x+6 A b^3 x^2\right)}{b (a+b x)^3}-6 A \log (a+b x)+6 A \log (x)}{6 a^4}","-\frac{A \log (a+b x)}{a^4}+\frac{A \log (x)}{a^4}+\frac{A}{a^3 (a+b x)}+\frac{A}{2 a^2 (a+b x)^2}+\frac{A b-a B}{3 a b (a+b x)^3}",1,"((a*(11*a^2*A*b - 2*a^3*B + 15*a*A*b^2*x + 6*A*b^3*x^2))/(b*(a + b*x)^3) + 6*A*Log[x] - 6*A*Log[a + b*x])/(6*a^4)","A",1
640,1,102,111,0.063591,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{2 a^3 (a B-A b)}{(a+b x)^3}+\frac{3 a^2 (a B-2 A b)}{(a+b x)^2}+\frac{6 a (a B-3 A b)}{a+b x}+6 \log (x) (a B-4 A b)+6 (4 A b-a B) \log (a+b x)-\frac{6 a A}{x}}{6 a^5}","-\frac{\log (x) (4 A b-a B)}{a^5}+\frac{(4 A b-a B) \log (a+b x)}{a^5}-\frac{3 A b-a B}{a^4 (a+b x)}-\frac{A}{a^4 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}",1,"((-6*a*A)/x + (2*a^3*(-(A*b) + a*B))/(a + b*x)^3 + (3*a^2*(-2*A*b + a*B))/(a + b*x)^2 + (6*a*(-3*A*b + a*B))/(a + b*x) + 6*(-4*A*b + a*B)*Log[x] + 6*(4*A*b - a*B)*Log[a + b*x])/(6*a^5)","A",1
641,1,123,135,0.1174102,"\int \frac{A+B x}{x^3 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^3*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{a \left(-3 a^4 (A+2 B x)+a^3 b x (15 A-44 B x)+10 a^2 b^2 x^2 (11 A-6 B x)+6 a b^3 x^3 (25 A-4 B x)+60 A b^4 x^4\right)}{x^2 (a+b x)^3}+12 b \log (x) (5 A b-2 a B)+12 b (2 a B-5 A b) \log (a+b x)}{6 a^6}","\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{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{A}{2 a^4 x^2}+\frac{b (A b-a B)}{3 a^3 (a+b x)^3}",1,"((a*(60*A*b^4*x^4 + a^3*b*x*(15*A - 44*B*x) + 10*a^2*b^2*x^2*(11*A - 6*B*x) + 6*a*b^3*x^3*(25*A - 4*B*x) - 3*a^4*(A + 2*B*x)))/(x^2*(a + b*x)^3) + 12*b*(5*A*b - 2*a*B)*Log[x] + 12*b*(-5*A*b + 2*a*B)*Log[a + b*x])/(6*a^6)","A",1
642,1,148,166,0.1424898,"\int \frac{A+B x}{x^4 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^4*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{a \left(-\left(a^5 (2 A+3 B x)\right)+3 a^4 b x (2 A+5 B x)+10 a^3 b^2 x^2 (11 B x-3 A)+10 a^2 b^3 x^3 (15 B x-22 A)+60 a b^4 x^4 (B x-5 A)-120 A b^5 x^5\right)}{x^3 (a+b x)^3}-60 b^2 \log (x) (2 A b-a B)+60 b^2 (2 A b-a B) \log (a+b x)}{6 a^7}","-\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{2 b^2 (5 A b-3 a B)}{a^6 (a+b x)}-\frac{2 b (5 A b-2 a B)}{a^6 x}-\frac{b^2 (4 A b-3 a B)}{2 a^5 (a+b x)^2}+\frac{4 A b-a B}{2 a^5 x^2}-\frac{b^2 (A b-a B)}{3 a^4 (a+b x)^3}-\frac{A}{3 a^4 x^3}",1,"((a*(-120*A*b^5*x^5 + 60*a*b^4*x^4*(-5*A + B*x) - a^5*(2*A + 3*B*x) + 3*a^4*b*x*(2*A + 5*B*x) + 10*a^3*b^2*x^2*(-3*A + 11*B*x) + 10*a^2*b^3*x^3*(-22*A + 15*B*x)))/(x^3*(a + b*x)^3) - 60*b^2*(2*A*b - a*B)*Log[x] + 60*b^2*(2*A*b - a*B)*Log[a + b*x])/(6*a^7)","A",1
643,1,151,171,0.0953657,"\int \frac{x^6 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^6*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{\frac{4 a^6 (a B-A b)}{(a+b x)^5}+\frac{5 a^5 (6 A b-7 a B)}{(a+b x)^4}+\frac{20 a^4 (7 a B-5 A b)}{(a+b x)^3}-\frac{50 a^3 (7 a B-4 A b)}{(a+b x)^2}+\frac{100 a^2 (7 a B-3 A b)}{a+b x}+20 b x (A b-6 a B)+60 a (7 a B-2 A b) \log (a+b x)+10 b^2 B x^2}{20 b^8}","-\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{3 a (2 A b-7 a B) \log (a+b x)}{b^8}+\frac{x (A b-6 a B)}{b^7}+\frac{B x^2}{2 b^6}",1,"(20*b*(A*b - 6*a*B)*x + 10*b^2*B*x^2 + (4*a^6*(-(A*b) + a*B))/(a + b*x)^5 + (5*a^5*(6*A*b - 7*a*B))/(a + b*x)^4 + (20*a^4*(-5*A*b + 7*a*B))/(a + b*x)^3 - (50*a^3*(-4*A*b + 7*a*B))/(a + b*x)^2 + (100*a^2*(-3*A*b + 7*a*B))/(a + b*x) + 60*a*(-2*A*b + 7*a*B)*Log[a + b*x])/(20*b^8)","A",1
644,1,130,146,0.0774489,"\int \frac{x^5 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^5*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{\frac{12 a^5 (A b-a B)}{(a+b x)^5}+\frac{15 a^4 (6 a B-5 A b)}{(a+b x)^4}+\frac{100 a^3 (2 A b-3 a B)}{(a+b x)^3}+\frac{300 a^2 (2 a B-A b)}{(a+b x)^2}+\frac{300 a (A b-3 a B)}{a+b x}+60 (A b-6 a B) \log (a+b x)+60 b B x}{60 b^7}","\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,"(60*b*B*x + (12*a^5*(A*b - a*B))/(a + b*x)^5 + (15*a^4*(-5*A*b + 6*a*B))/(a + b*x)^4 + (100*a^3*(2*A*b - 3*a*B))/(a + b*x)^3 + (300*a^2*(-(A*b) + 2*a*B))/(a + b*x)^2 + (300*a*(A*b - 3*a*B))/(a + b*x) + 60*(A*b - 6*a*B)*Log[a + b*x])/(60*b^7)","A",1
645,1,113,106,0.0413996,"\int \frac{x^4 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{137 a^5 B+a^4 (625 b B x-12 A b)+20 a^3 b^2 x (55 B x-3 A)+60 a^2 b^3 x^2 (15 B x-2 A)+60 a b^4 x^3 (5 B x-2 A)+60 B (a+b x)^5 \log (a+b x)-60 A b^5 x^4}{60 b^6 (a+b x)^5}","-\frac{a^4 B}{4 b^6 (a+b x)^4}+\frac{4 a^3 B}{3 b^6 (a+b x)^3}-\frac{3 a^2 B}{b^6 (a+b x)^2}+\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,"(137*a^5*B - 60*A*b^5*x^4 + 60*a*b^4*x^3*(-2*A + 5*B*x) + 60*a^2*b^3*x^2*(-2*A + 15*B*x) + 20*a^3*b^2*x*(-3*A + 55*B*x) + a^4*(-12*A*b + 625*b*B*x) + 60*B*(a + b*x)^5*Log[a + b*x])/(60*b^6*(a + b*x)^5)","A",1
646,1,76,57,0.0310911,"\int \frac{x^3 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{4 a^4 B+a^3 b (A+20 B x)+5 a^2 b^2 x (A+8 B x)+10 a b^3 x^2 (A+4 B x)+10 b^4 x^3 (A+2 B x)}{20 b^5 (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,"-1/20*(4*a^4*B + 10*b^4*x^3*(A + 2*B*x) + 10*a*b^3*x^2*(A + 4*B*x) + 5*a^2*b^2*x*(A + 8*B*x) + a^3*b*(A + 20*B*x))/(b^5*(a + b*x)^5)","A",1
647,1,63,87,0.0230998,"\int \frac{x^2 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{3 a^3 B+a^2 b (2 A+15 B x)+10 a b^2 x (A+3 B x)+10 b^3 x^2 (2 A+3 B x)}{60 b^4 (a+b x)^5}","-\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,"-1/60*(3*a^3*B + 10*a*b^2*x*(A + 3*B*x) + 10*b^3*x^2*(2*A + 3*B*x) + a^2*b*(2*A + 15*B*x))/(b^4*(a + b*x)^5)","A",1
648,1,46,61,0.0162419,"\int \frac{x (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{2 a^2 B+a b (3 A+10 B x)+5 b^2 x (3 A+4 B x)}{60 b^3 (a+b x)^5}","-\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,"-1/60*(2*a^2*B + 5*b^2*x*(3*A + 4*B*x) + a*b*(3*A + 10*B*x))/(b^3*(a + b*x)^5)","A",1
649,1,27,38,0.0097132,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{B (a+5 b x)+4 A b}{20 b^2 (a+b x)^5}","\frac{a B-A b}{5 b^2 (a+b x)^5}-\frac{B}{4 b^2 (a+b x)^4}",1,"-1/20*(4*A*b + B*(a + 5*b*x))/(b^2*(a + b*x)^5)","A",1
650,1,89,102,0.0646807,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{a \left(-12 a^5 B+137 a^4 A b+385 a^3 A b^2 x+470 a^2 A b^3 x^2+270 a A b^4 x^3+60 A b^5 x^4\right)}{b (a+b x)^5}-60 A \log (a+b x)+60 A \log (x)}{60 a^6}","-\frac{A \log (a+b x)}{a^6}+\frac{A \log (x)}{a^6}+\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 b-a B}{5 a b (a+b x)^5}",1,"((a*(137*a^4*A*b - 12*a^5*B + 385*a^3*A*b^2*x + 470*a^2*A*b^3*x^2 + 270*a*A*b^4*x^3 + 60*A*b^5*x^4))/(b*(a + b*x)^5) + 60*A*Log[x] - 60*A*Log[a + b*x])/(60*a^6)","A",1
651,1,142,157,0.0915466,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{12 a^5 (a B-A b)}{(a+b x)^5}+\frac{15 a^4 (a B-2 A b)}{(a+b x)^4}+\frac{20 a^3 (a B-3 A b)}{(a+b x)^3}+\frac{30 a^2 (a B-4 A b)}{(a+b x)^2}+\frac{60 a (a B-5 A b)}{a+b x}+60 \log (x) (a B-6 A b)+60 (6 A b-a B) \log (a+b x)-\frac{60 a A}{x}}{60 a^7}","-\frac{\log (x) (6 A b-a B)}{a^7}+\frac{(6 A b-a B) \log (a+b x)}{a^7}-\frac{5 A b-a B}{a^6 (a+b x)}-\frac{A}{a^6 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}",1,"((-60*a*A)/x + (12*a^5*(-(A*b) + a*B))/(a + b*x)^5 + (15*a^4*(-2*A*b + a*B))/(a + b*x)^4 + (20*a^3*(-3*A*b + a*B))/(a + b*x)^3 + (30*a^2*(-4*A*b + a*B))/(a + b*x)^2 + (60*a*(-5*A*b + a*B))/(a + b*x) + 60*(-6*A*b + a*B)*Log[x] + 60*(6*A*b - a*B)*Log[a + b*x])/(60*a^7)","A",1
652,1,162,177,0.1773542,"\int \frac{A+B x}{x^3 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/(x^3*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{a \left(-10 a^6 (A+2 B x)+2 a^5 b x (35 A-137 B x)+7 a^4 b^2 x^2 (137 A-110 B x)+5 a^3 b^3 x^3 (539 A-188 B x)+10 a^2 b^4 x^4 (329 A-54 B x)+30 a b^5 x^5 (63 A-4 B x)+420 A b^6 x^6\right)}{x^2 (a+b x)^5}+60 b \log (x) (7 A b-2 a B)+60 b (2 a B-7 A b) \log (a+b x)}{20 a^8}","\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{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{A}{2 a^6 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}",1,"((a*(420*A*b^6*x^6 + 5*a^3*b^3*x^3*(539*A - 188*B*x) + 2*a^5*b*x*(35*A - 137*B*x) + 7*a^4*b^2*x^2*(137*A - 110*B*x) + 10*a^2*b^4*x^4*(329*A - 54*B*x) + 30*a*b^5*x^5*(63*A - 4*B*x) - 10*a^6*(A + 2*B*x)))/(x^2*(a + b*x)^5) + 60*b*(7*A*b - 2*a*B)*Log[x] + 60*b*(-7*A*b + 2*a*B)*Log[a + b*x])/(20*a^8)","A",1
653,1,49,114,0.0190281,"\int x^4 (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[x^4*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^5 \sqrt{(a+b x)^2} (7 a (6 A+5 B x)+5 b x (7 A+6 B x))}{210 (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,"(x^5*Sqrt[(a + b*x)^2]*(7*a*(6*A + 5*B*x) + 5*b*x*(7*A + 6*B*x)))/(210*(a + b*x))","A",1
654,1,49,114,0.016404,"\int x^3 (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[x^3*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^4 \sqrt{(a+b x)^2} (3 a (5 A+4 B x)+2 b x (6 A+5 B x))}{60 (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,"(x^4*Sqrt[(a + b*x)^2]*(3*a*(5*A + 4*B*x) + 2*b*x*(6*A + 5*B*x)))/(60*(a + b*x))","A",1
655,1,49,114,0.0161056,"\int x^2 (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[x^2*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^3 \sqrt{(a+b x)^2} (5 a (4 A+3 B x)+3 b x (5 A+4 B x))}{60 (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,"(x^3*Sqrt[(a + b*x)^2]*(5*a*(4*A + 3*B*x) + 3*b*x*(5*A + 4*B*x)))/(60*(a + b*x))","A",1
656,1,47,114,0.0162783,"\int x (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[x*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^2 \sqrt{(a+b x)^2} (a (6 A+4 B x)+b x (4 A+3 B x))}{12 (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,"(x^2*Sqrt[(a + b*x)^2]*(b*x*(4*A + 3*B*x) + a*(6*A + 4*B*x)))/(12*(a + b*x))","A",1
657,1,45,69,0.0148066,"\int (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} (3 a (2 A+B x)+b x (3 A+2 B x))}{6 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(3*a*(2*A + B*x) + b*x*(3*A + 2*B*x)))/(6*(a + b*x))","A",1
658,1,44,105,0.0203726,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x,x]","\frac{\sqrt{(a+b x)^2} (x (2 a B+2 A b+b B x)+2 a A \log (x))}{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,"(Sqrt[(a + b*x)^2]*(x*(2*A*b + 2*a*B + b*B*x) + 2*a*A*Log[x]))/(2*(a + b*x))","A",1
659,1,44,103,0.018442,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^2} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^2,x]","\frac{\sqrt{(a+b x)^2} \left(x \log (x) (a B+A b)-a A+b B x^2\right)}{x (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,"(Sqrt[(a + b*x)^2]*(-(a*A) + b*B*x^2 + (A*b + a*B)*x*Log[x]))/(x*(a + b*x))","A",1
660,1,48,108,0.0174329,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^3} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^3,x]","-\frac{\sqrt{(a+b x)^2} \left(a (A+2 B x)+2 A b x-2 b B x^2 \log (x)\right)}{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,"-1/2*(Sqrt[(a + b*x)^2]*(2*A*b*x + a*(A + 2*B*x) - 2*b*B*x^2*Log[x]))/(x^2*(a + b*x))","A",1
661,1,46,75,0.0143689,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^4} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^4,x]","-\frac{\sqrt{(a+b x)^2} (a (2 A+3 B x)+3 b x (A+2 B x))}{6 x^3 (a+b 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}",1,"-1/6*(Sqrt[(a + b*x)^2]*(3*b*x*(A + 2*B*x) + a*(2*A + 3*B*x)))/(x^3*(a + b*x))","A",1
662,1,47,114,0.0116829,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^5} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^5,x]","-\frac{\sqrt{(a+b x)^2} \left(3 a A+4 a B x+4 A b x+6 b B x^2\right)}{12 x^4 (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,"-1/12*(Sqrt[(a + b*x)^2]*(3*a*A + 4*A*b*x + 4*a*B*x + 6*b*B*x^2))/(x^4*(a + b*x))","A",1
663,1,49,114,0.0150476,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^6} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^6,x]","-\frac{\sqrt{(a+b x)^2} (3 a (4 A+5 B x)+5 b x (3 A+4 B x))}{60 x^5 (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,"-1/60*(Sqrt[(a + b*x)^2]*(5*b*x*(3*A + 4*B*x) + 3*a*(4*A + 5*B*x)))/(x^5*(a + b*x))","A",1
664,1,49,114,0.0140823,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^7} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^7,x]","-\frac{\sqrt{(a+b x)^2} (2 a (5 A+6 B x)+3 b x (4 A+5 B x))}{60 x^6 (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,"-1/60*(Sqrt[(a + b*x)^2]*(3*b*x*(4*A + 5*B*x) + 2*a*(5*A + 6*B*x)))/(x^6*(a + b*x))","A",1
665,1,87,210,0.0337703,"\int x^5 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[x^5*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^6 \sqrt{(a+b x)^2} \left(60 a^3 (7 A+6 B x)+135 a^2 b x (8 A+7 B x)+105 a b^2 x^2 (9 A+8 B x)+28 b^3 x^3 (10 A+9 B x)\right)}{2520 (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{b^3 B x^{10} \sqrt{a^2+2 a b x+b^2 x^2}}{10 (a+b x)}+\frac{a^3 A x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}",1,"(x^6*Sqrt[(a + b*x)^2]*(60*a^3*(7*A + 6*B*x) + 135*a^2*b*x*(8*A + 7*B*x) + 105*a*b^2*x^2*(9*A + 8*B*x) + 28*b^3*x^3*(10*A + 9*B*x)))/(2520*(a + b*x))","A",1
666,1,87,210,0.0310752,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^5 \sqrt{(a+b x)^2} \left(84 a^3 (6 A+5 B x)+180 a^2 b x (7 A+6 B x)+135 a b^2 x^2 (8 A+7 B x)+35 b^3 x^3 (9 A+8 B x)\right)}{2520 (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{b^3 B x^9 \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{a^3 A x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}",1,"(x^5*Sqrt[(a + b*x)^2]*(84*a^3*(6*A + 5*B*x) + 180*a^2*b*x*(7*A + 6*B*x) + 135*a*b^2*x^2*(8*A + 7*B*x) + 35*b^3*x^3*(9*A + 8*B*x)))/(2520*(a + b*x))","A",1
667,1,87,210,0.0294162,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[x^3*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^4 \sqrt{(a+b x)^2} \left(14 a^3 (5 A+4 B x)+28 a^2 b x (6 A+5 B x)+20 a b^2 x^2 (7 A+6 B x)+5 b^3 x^3 (8 A+7 B x)\right)}{280 (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{b^3 B x^8 \sqrt{a^2+2 a b x+b^2 x^2}}{8 (a+b x)}+\frac{a^3 A x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}",1,"(x^4*Sqrt[(a + b*x)^2]*(14*a^3*(5*A + 4*B*x) + 28*a^2*b*x*(6*A + 5*B*x) + 20*a*b^2*x^2*(7*A + 6*B*x) + 5*b^3*x^3*(8*A + 7*B*x)))/(280*(a + b*x))","A",1
668,1,87,210,0.0300361,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^3 \sqrt{(a+b x)^2} \left(35 a^3 (4 A+3 B x)+63 a^2 b x (5 A+4 B x)+42 a b^2 x^2 (6 A+5 B x)+10 b^3 x^3 (7 A+6 B x)\right)}{420 (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{b^3 B x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{a^3 A x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}",1,"(x^3*Sqrt[(a + b*x)^2]*(35*a^3*(4*A + 3*B*x) + 63*a^2*b*x*(5*A + 4*B*x) + 42*a*b^2*x^2*(6*A + 5*B*x) + 10*b^3*x^3*(7*A + 6*B*x)))/(420*(a + b*x))","A",1
669,1,87,121,0.028447,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^2 \sqrt{(a+b x)^2} \left(10 a^3 (3 A+2 B x)+15 a^2 b x (4 A+3 B x)+9 a b^2 x^2 (5 A+4 B x)+2 b^3 x^3 (6 A+5 B x)\right)}{60 (a+b 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}",1,"(x^2*Sqrt[(a + b*x)^2]*(10*a^3*(3*A + 2*B*x) + 15*a^2*b*x*(4*A + 3*B*x) + 9*a*b^2*x^2*(5*A + 4*B*x) + 2*b^3*x^3*(6*A + 5*B*x)))/(60*(a + b*x))","A",1
670,1,83,69,0.0288361,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(10 a^3 (2 A+B x)+10 a^2 b x (3 A+2 B x)+5 a b^2 x^2 (4 A+3 B x)+b^3 x^3 (5 A+4 B x)\right)}{20 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(10*a^3*(2*A + B*x) + 10*a^2*b*x*(3*A + 2*B*x) + 5*a*b^2*x^2*(4*A + 3*B*x) + b^3*x^3*(5*A + 4*B*x)))/(20*(a + b*x))","A",1
671,1,83,182,0.0366472,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x,x]","\frac{\sqrt{(a+b x)^2} \left(12 a^3 A \log (x)+x \left(12 a^3 B+18 a^2 b (2 A+B x)+6 a b^2 x (3 A+2 B x)+b^3 x^2 (4 A+3 B x)\right)\right)}{12 (a+b 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{B (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 b}+\frac{a^3 A \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"(Sqrt[(a + b*x)^2]*(x*(12*a^3*B + 18*a^2*b*(2*A + B*x) + 6*a*b^2*x*(3*A + 2*B*x) + b^3*x^2*(4*A + 3*B*x)) + 12*a^3*A*Log[x]))/(12*(a + b*x))","A",1
672,1,89,200,0.0325721,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^2} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^2,x]","\frac{\sqrt{(a+b x)^2} \left(-6 a^3 A+6 a^2 x \log (x) (a B+3 A b)+18 a^2 b B x^2+9 a b^2 x^2 (2 A+B x)+b^3 x^3 (3 A+2 B x)\right)}{6 x (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{b^3 B x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}",1,"(Sqrt[(a + b*x)^2]*(-6*a^3*A + 18*a^2*b*B*x^2 + 9*a*b^2*x^2*(2*A + B*x) + b^3*x^3*(3*A + 2*B*x) + 6*a^2*(3*A*b + a*B)*x*Log[x]))/(6*x*(a + b*x))","A",1
673,1,85,200,0.040609,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^3} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^3,x]","\frac{\sqrt{(a+b x)^2} \left(-\left(a^3 (A+2 B x)\right)-6 a^2 A b x+6 a b x^2 \log (x) (a B+A b)+6 a b^2 B x^3+b^3 x^3 (2 A+B x)\right)}{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)}{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{b^3 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}",1,"(Sqrt[(a + b*x)^2]*(-6*a^2*A*b*x + 6*a*b^2*B*x^3 + b^3*x^3*(2*A + B*x) - a^3*(A + 2*B*x) + 6*a*b*(A*b + a*B)*x^2*Log[x]))/(2*x^2*(a + b*x))","A",1
674,1,88,199,0.0332229,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^4} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^4,x]","-\frac{\sqrt{(a+b x)^2} \left(a^3 (2 A+3 B x)+9 a^2 b x (A+2 B x)-6 b^2 x^3 \log (x) (3 a B+A b)+18 a A b^2 x^2-6 b^3 B x^4\right)}{6 x^3 (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{b^3 B x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}",1,"-1/6*(Sqrt[(a + b*x)^2]*(18*a*A*b^2*x^2 - 6*b^3*B*x^4 + 9*a^2*b*x*(A + 2*B*x) + a^3*(2*A + 3*B*x) - 6*b^2*(A*b + 3*a*B)*x^3*Log[x]))/(x^3*(a + b*x))","A",1
675,1,88,187,0.0317744,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^5} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^5,x]","-\frac{\sqrt{(a+b x)^2} \left(a^3 (3 A+4 B x)+6 a^2 b x (2 A+3 B x)+18 a b^2 x^2 (A+2 B x)+12 A b^3 x^3-12 b^3 B x^4 \log (x)\right)}{12 x^4 (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{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^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}",1,"-1/12*(Sqrt[(a + b*x)^2]*(12*A*b^3*x^3 + 18*a*b^2*x^2*(A + 2*B*x) + 6*a^2*b*x*(2*A + 3*B*x) + a^3*(3*A + 4*B*x) - 12*b^3*B*x^4*Log[x]))/(x^4*(a + b*x))","A",1
676,1,84,77,0.0279877,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^6} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^6,x]","-\frac{\sqrt{(a+b x)^2} \left(a^3 (4 A+5 B x)+5 a^2 b x (3 A+4 B x)+10 a b^2 x^2 (2 A+3 B x)+10 b^3 x^3 (A+2 B x)\right)}{20 x^5 (a+b 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}",1,"-1/20*(Sqrt[(a + b*x)^2]*(10*b^3*x^3*(A + 2*B*x) + 10*a*b^2*x^2*(2*A + 3*B*x) + 5*a^2*b*x*(3*A + 4*B*x) + a^3*(4*A + 5*B*x)))/(x^5*(a + b*x))","A",1
677,1,87,210,0.0270409,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^7} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^7,x]","-\frac{\sqrt{(a+b x)^2} \left(2 a^3 (5 A+6 B x)+9 a^2 b x (4 A+5 B x)+15 a b^2 x^2 (3 A+4 B x)+10 b^3 x^3 (2 A+3 B x)\right)}{60 x^6 (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{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}",1,"-1/60*(Sqrt[(a + b*x)^2]*(10*b^3*x^3*(2*A + 3*B*x) + 15*a*b^2*x^2*(3*A + 4*B*x) + 9*a^2*b*x*(4*A + 5*B*x) + 2*a^3*(5*A + 6*B*x)))/(x^6*(a + b*x))","A",1
678,1,87,210,0.0275298,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^8} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^8,x]","-\frac{\sqrt{(a+b x)^2} \left(10 a^3 (6 A+7 B x)+42 a^2 b x (5 A+6 B x)+63 a b^2 x^2 (4 A+5 B x)+35 b^3 x^3 (3 A+4 B x)\right)}{420 x^7 (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{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}",1,"-1/420*(Sqrt[(a + b*x)^2]*(35*b^3*x^3*(3*A + 4*B*x) + 63*a*b^2*x^2*(4*A + 5*B*x) + 42*a^2*b*x*(5*A + 6*B*x) + 10*a^3*(6*A + 7*B*x)))/(x^7*(a + b*x))","A",1
679,1,87,210,0.0283836,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^9} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^9,x]","-\frac{\sqrt{(a+b x)^2} \left(5 a^3 (7 A+8 B x)+20 a^2 b x (6 A+7 B x)+28 a b^2 x^2 (5 A+6 B x)+14 b^3 x^3 (4 A+5 B x)\right)}{280 x^8 (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{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{8 x^8 (a+b x)}",1,"-1/280*(Sqrt[(a + b*x)^2]*(14*b^3*x^3*(4*A + 5*B*x) + 28*a*b^2*x^2*(5*A + 6*B*x) + 20*a^2*b*x*(6*A + 7*B*x) + 5*a^3*(7*A + 8*B*x)))/(x^8*(a + b*x))","A",1
680,1,87,210,0.028536,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{10}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^10,x]","-\frac{\sqrt{(a+b x)^2} \left(35 a^3 (8 A+9 B x)+135 a^2 b x (7 A+8 B x)+180 a b^2 x^2 (6 A+7 B x)+84 b^3 x^3 (5 A+6 B x)\right)}{2520 x^9 (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{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}",1,"-1/2520*(Sqrt[(a + b*x)^2]*(84*b^3*x^3*(5*A + 6*B*x) + 180*a*b^2*x^2*(6*A + 7*B*x) + 135*a^2*b*x*(7*A + 8*B*x) + 35*a^3*(8*A + 9*B*x)))/(x^9*(a + b*x))","A",1
681,1,87,210,0.0284558,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{11}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^11,x]","-\frac{\sqrt{(a+b x)^2} \left(28 a^3 (9 A+10 B x)+105 a^2 b x (8 A+9 B x)+135 a b^2 x^2 (7 A+8 B x)+60 b^3 x^3 (6 A+7 B x)\right)}{2520 x^{10} (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{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{10 x^{10} (a+b x)}",1,"-1/2520*(Sqrt[(a + b*x)^2]*(60*b^3*x^3*(6*A + 7*B*x) + 135*a*b^2*x^2*(7*A + 8*B*x) + 105*a^2*b*x*(8*A + 9*B*x) + 28*a^3*(9*A + 10*B*x)))/(x^10*(a + b*x))","A",1
682,1,87,210,0.0286996,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{12}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^12,x]","-\frac{\sqrt{(a+b x)^2} \left(84 a^3 (10 A+11 B x)+308 a^2 b x (9 A+10 B x)+385 a b^2 x^2 (8 A+9 B x)+165 b^3 x^3 (7 A+8 B x)\right)}{9240 x^{11} (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{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{11 x^{11} (a+b x)}",1,"-1/9240*(Sqrt[(a + b*x)^2]*(165*b^3*x^3*(7*A + 8*B*x) + 385*a*b^2*x^2*(8*A + 9*B*x) + 308*a^2*b*x*(9*A + 10*B*x) + 84*a^3*(10*A + 11*B*x)))/(x^11*(a + b*x))","A",1
683,1,125,303,0.0453483,"\int x^6 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[x^6*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^7 \sqrt{(a+b x)^2} \left(1287 a^5 (8 A+7 B x)+5005 a^4 b x (9 A+8 B x)+8008 a^3 b^2 x^2 (10 A+9 B x)+6552 a^2 b^3 x^3 (11 A+10 B x)+2730 a b^4 x^4 (12 A+11 B x)+462 b^5 x^5 (13 A+12 B x)\right)}{72072 (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{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{b^5 B x^{13} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (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{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{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)}",1,"(x^7*Sqrt[(a + b*x)^2]*(1287*a^5*(8*A + 7*B*x) + 5005*a^4*b*x*(9*A + 8*B*x) + 8008*a^3*b^2*x^2*(10*A + 9*B*x) + 6552*a^2*b^3*x^3*(11*A + 10*B*x) + 2730*a*b^4*x^4*(12*A + 11*B*x) + 462*b^5*x^5*(13*A + 12*B*x)))/(72072*(a + b*x))","A",1
684,1,125,306,0.0421425,"\int x^5 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[x^5*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^6 \sqrt{(a+b x)^2} \left(132 a^5 (7 A+6 B x)+495 a^4 b x (8 A+7 B x)+770 a^3 b^2 x^2 (9 A+8 B x)+616 a^2 b^3 x^3 (10 A+9 B x)+252 a b^4 x^4 (11 A+10 B x)+42 b^5 x^5 (12 A+11 B x)\right)}{5544 (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{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{b^5 B x^{12} \sqrt{a^2+2 a b x+b^2 x^2}}{12 (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{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{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)}",1,"(x^6*Sqrt[(a + b*x)^2]*(132*a^5*(7*A + 6*B*x) + 495*a^4*b*x*(8*A + 7*B*x) + 770*a^3*b^2*x^2*(9*A + 8*B*x) + 616*a^2*b^3*x^3*(10*A + 9*B*x) + 252*a*b^4*x^4*(11*A + 10*B*x) + 42*b^5*x^5*(12*A + 11*B*x)))/(5544*(a + b*x))","A",1
685,1,125,306,0.040773,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^5 \sqrt{(a+b x)^2} \left(462 a^5 (6 A+5 B x)+1650 a^4 b x (7 A+6 B x)+2475 a^3 b^2 x^2 (8 A+7 B x)+1925 a^2 b^3 x^3 (9 A+8 B x)+770 a b^4 x^4 (10 A+9 B x)+126 b^5 x^5 (11 A+10 B x)\right)}{13860 (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{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{b^5 B x^{11} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (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{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{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)}",1,"(x^5*Sqrt[(a + b*x)^2]*(462*a^5*(6*A + 5*B*x) + 1650*a^4*b*x*(7*A + 6*B*x) + 2475*a^3*b^2*x^2*(8*A + 7*B*x) + 1925*a^2*b^3*x^3*(9*A + 8*B*x) + 770*a*b^4*x^4*(10*A + 9*B*x) + 126*b^5*x^5*(11*A + 10*B*x)))/(13860*(a + b*x))","A",1
686,1,125,212,0.0395351,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[x^3*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^4 \sqrt{(a+b x)^2} \left(126 a^5 (5 A+4 B x)+420 a^4 b x (6 A+5 B x)+600 a^3 b^2 x^2 (7 A+6 B x)+450 a^2 b^3 x^3 (8 A+7 B x)+175 a b^4 x^4 (9 A+8 B x)+28 b^5 x^5 (10 A+9 B x)\right)}{2520 (a+b 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{B \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 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}",1,"(x^4*Sqrt[(a + b*x)^2]*(126*a^5*(5*A + 4*B*x) + 420*a^4*b*x*(6*A + 5*B*x) + 600*a^3*b^2*x^2*(7*A + 6*B*x) + 450*a^2*b^3*x^3*(8*A + 7*B*x) + 175*a*b^4*x^4*(9*A + 8*B*x) + 28*b^5*x^5*(10*A + 9*B*x)))/(2520*(a + b*x))","A",1
687,1,125,167,0.043459,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^3 \sqrt{(a+b x)^2} \left(42 a^5 (4 A+3 B x)+126 a^4 b x (5 A+4 B x)+168 a^3 b^2 x^2 (6 A+5 B x)+120 a^2 b^3 x^3 (7 A+6 B x)+45 a b^4 x^4 (8 A+7 B x)+7 b^5 x^5 (9 A+8 B x)\right)}{504 (a+b 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}",1,"(x^3*Sqrt[(a + b*x)^2]*(42*a^5*(4*A + 3*B*x) + 126*a^4*b*x*(5*A + 4*B*x) + 168*a^3*b^2*x^2*(6*A + 5*B*x) + 120*a^2*b^3*x^3*(7*A + 6*B*x) + 45*a*b^4*x^4*(8*A + 7*B*x) + 7*b^5*x^5*(9*A + 8*B*x)))/(504*(a + b*x))","A",1
688,1,125,121,0.0389555,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^2 \sqrt{(a+b x)^2} \left(28 a^5 (3 A+2 B x)+70 a^4 b x (4 A+3 B x)+84 a^3 b^2 x^2 (5 A+4 B x)+56 a^2 b^3 x^3 (6 A+5 B x)+20 a b^4 x^4 (7 A+6 B x)+3 b^5 x^5 (8 A+7 B x)\right)}{168 (a+b 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}",1,"(x^2*Sqrt[(a + b*x)^2]*(28*a^5*(3*A + 2*B*x) + 70*a^4*b*x*(4*A + 3*B*x) + 84*a^3*b^2*x^2*(5*A + 4*B*x) + 56*a^2*b^3*x^3*(6*A + 5*B*x) + 20*a*b^4*x^4*(7*A + 6*B*x) + 3*b^5*x^5*(8*A + 7*B*x)))/(168*(a + b*x))","A",1
689,1,121,69,0.0399419,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(21 a^5 (2 A+B x)+35 a^4 b x (3 A+2 B x)+35 a^3 b^2 x^2 (4 A+3 B x)+21 a^2 b^3 x^3 (5 A+4 B x)+7 a b^4 x^4 (6 A+5 B x)+b^5 x^5 (7 A+6 B x)\right)}{42 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(21*a^5*(2*A + B*x) + 35*a^4*b*x*(3*A + 2*B*x) + 35*a^3*b^2*x^2*(4*A + 3*B*x) + 21*a^2*b^3*x^3*(5*A + 4*B*x) + 7*a*b^4*x^4*(6*A + 5*B*x) + b^5*x^5*(7*A + 6*B*x)))/(42*(a + b*x))","A",1
690,1,122,262,0.0569626,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x,x]","\frac{\sqrt{(a+b x)^2} \left(60 a^5 A \log (x)+x \left(60 a^5 B+150 a^4 b (2 A+B x)+100 a^3 b^2 x (3 A+2 B x)+50 a^2 b^3 x^2 (4 A+3 B x)+15 a b^4 x^3 (5 A+4 B x)+2 b^5 x^4 (6 A+5 B x)\right)\right)}{60 (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{5 a A b^4 x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (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{B (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 b}+\frac{a^5 A \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b 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}",1,"(Sqrt[(a + b*x)^2]*(x*(60*a^5*B + 150*a^4*b*(2*A + B*x) + 100*a^3*b^2*x*(3*A + 2*B*x) + 50*a^2*b^3*x^2*(4*A + 3*B*x) + 15*a*b^4*x^3*(5*A + 4*B*x) + 2*b^5*x^4*(6*A + 5*B*x)) + 60*a^5*A*Log[x]))/(60*(a + b*x))","A",1
691,1,128,294,0.0473921,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^2} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^2,x]","\frac{\sqrt{(a+b x)^2} \left(-60 a^5 A+60 a^4 x \log (x) (a B+5 A b)+300 a^4 b B x^2+300 a^3 b^2 x^2 (2 A+B x)+100 a^2 b^3 x^3 (3 A+2 B x)+25 a b^4 x^4 (4 A+3 B x)+3 b^5 x^5 (5 A+4 B x)\right)}{60 x (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{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{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^5 B x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{x (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{5 a^3 b x \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}",1,"(Sqrt[(a + b*x)^2]*(-60*a^5*A + 300*a^4*b*B*x^2 + 300*a^3*b^2*x^2*(2*A + B*x) + 100*a^2*b^3*x^3*(3*A + 2*B*x) + 25*a*b^4*x^4*(4*A + 3*B*x) + 3*b^5*x^5*(5*A + 4*B*x) + 60*a^4*(5*A*b + a*B)*x*Log[x]))/(60*x*(a + b*x))","A",1
692,1,126,297,0.059032,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^3} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^3,x]","\frac{\sqrt{(a+b x)^2} \left(-6 a^5 (A+2 B x)-60 a^4 A b x+60 a^3 b x^2 \log (x) (a B+2 A b)+120 a^3 b^2 B x^3+60 a^2 b^3 x^3 (2 A+B x)+10 a b^4 x^4 (3 A+2 B x)+b^5 x^5 (4 A+3 B x)\right)}{12 x^2 (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{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 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^5 B x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (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{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{x (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}",1,"(Sqrt[(a + b*x)^2]*(-60*a^4*A*b*x + 120*a^3*b^2*B*x^3 + 60*a^2*b^3*x^3*(2*A + B*x) - 6*a^5*(A + 2*B*x) + 10*a*b^4*x^4*(3*A + 2*B*x) + b^5*x^5*(4*A + 3*B*x) + 60*a^3*b*(2*A*b + a*B)*x^2*Log[x]))/(12*x^2*(a + b*x))","A",1
693,1,127,297,0.0520185,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^4} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^4,x]","\frac{\sqrt{(a+b x)^2} \left(-\left(a^5 (2 A+3 B x)\right)-15 a^4 b x (A+2 B x)-60 a^3 A b^2 x^2+60 a^2 b^2 x^3 \log (x) (a B+A b)+60 a^2 b^3 B x^4+15 a b^4 x^4 (2 A+B x)+b^5 x^5 (3 A+2 B x)\right)}{6 x^3 (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{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{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^5 B x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (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{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)}",1,"(Sqrt[(a + b*x)^2]*(-60*a^3*A*b^2*x^2 + 60*a^2*b^3*B*x^4 + 15*a*b^4*x^4*(2*A + B*x) - 15*a^4*b*x*(A + 2*B*x) + b^5*x^5*(3*A + 2*B*x) - a^5*(2*A + 3*B*x) + 60*a^2*b^2*(A*b + a*B)*x^3*Log[x]))/(6*x^3*(a + b*x))","A",1
694,1,126,296,0.0422229,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^5} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^5,x]","-\frac{\sqrt{(a+b x)^2} \left(a^5 (3 A+4 B x)+10 a^4 b x (2 A+3 B x)+60 a^3 b^2 x^2 (A+2 B x)+120 a^2 A b^3 x^3-60 a b^3 x^4 \log (x) (2 a B+A b)-60 a b^4 B x^5-6 b^5 x^5 (2 A+B x)\right)}{12 x^4 (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{b^5 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (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{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)}",1,"-1/12*(Sqrt[(a + b*x)^2]*(120*a^2*A*b^3*x^3 - 60*a*b^4*B*x^5 - 6*b^5*x^5*(2*A + B*x) + 60*a^3*b^2*x^2*(A + 2*B*x) + 10*a^4*b*x*(2*A + 3*B*x) + a^5*(3*A + 4*B*x) - 60*a*b^3*(A*b + 2*a*B)*x^4*Log[x]))/(x^4*(a + b*x))","A",1
695,1,127,293,0.0572715,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^6} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^6,x]","-\frac{\sqrt{(a+b x)^2} \left(3 a^5 (4 A+5 B x)+25 a^4 b x (3 A+4 B x)+100 a^3 b^2 x^2 (2 A+3 B x)+300 a^2 b^3 x^3 (A+2 B x)-60 b^4 x^5 \log (x) (5 a B+A b)+300 a A b^4 x^4-60 b^5 B x^6\right)}{60 x^5 (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{b^4 \log (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 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{x (a+b x)}+\frac{b^5 B x \sqrt{a^2+2 a b x+b^2 x^2}}{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{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)}",1,"-1/60*(Sqrt[(a + b*x)^2]*(300*a*A*b^4*x^4 - 60*b^5*B*x^6 + 300*a^2*b^3*x^3*(A + 2*B*x) + 100*a^3*b^2*x^2*(2*A + 3*B*x) + 25*a^4*b*x*(3*A + 4*B*x) + 3*a^5*(4*A + 5*B*x) - 60*b^4*(A*b + 5*a*B)*x^5*Log[x]))/(x^5*(a + b*x))","A",1
696,1,127,267,0.0453293,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^7} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^7,x]","-\frac{\sqrt{(a+b x)^2} \left(2 a^5 (5 A+6 B x)+15 a^4 b x (4 A+5 B x)+50 a^3 b^2 x^2 (3 A+4 B x)+100 a^2 b^3 x^3 (2 A+3 B x)+150 a b^4 x^4 (A+2 B x)+60 A b^5 x^5-60 b^5 B x^6 \log (x)\right)}{60 x^6 (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{b^5 B \log (x) \sqrt{a^2+2 a b x+b^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{5 a^2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{x^2 (a+b x)}-\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)}",1,"-1/60*(Sqrt[(a + b*x)^2]*(60*A*b^5*x^5 + 150*a*b^4*x^4*(A + 2*B*x) + 100*a^2*b^3*x^3*(2*A + 3*B*x) + 50*a^3*b^2*x^2*(3*A + 4*B*x) + 15*a^4*b*x*(4*A + 5*B*x) + 2*a^5*(5*A + 6*B*x) - 60*b^5*B*x^6*Log[x]))/(x^6*(a + b*x))","A",1
697,1,122,77,0.0394498,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^8} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^8,x]","-\frac{\sqrt{(a+b x)^2} \left(a^5 (6 A+7 B x)+7 a^4 b x (5 A+6 B x)+21 a^3 b^2 x^2 (4 A+5 B x)+35 a^2 b^3 x^3 (3 A+4 B x)+35 a b^4 x^4 (2 A+3 B x)+21 b^5 x^5 (A+2 B x)\right)}{42 x^7 (a+b 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}",1,"-1/42*(Sqrt[(a + b*x)^2]*(21*b^5*x^5*(A + 2*B*x) + 35*a*b^4*x^4*(2*A + 3*B*x) + 35*a^2*b^3*x^3*(3*A + 4*B*x) + 21*a^3*b^2*x^2*(4*A + 5*B*x) + 7*a^4*b*x*(5*A + 6*B*x) + a^5*(6*A + 7*B*x)))/(x^7*(a + b*x))","A",1
698,1,125,130,0.0384068,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^9} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^9,x]","-\frac{\sqrt{(a+b x)^2} \left(3 a^5 (7 A+8 B x)+20 a^4 b x (6 A+7 B x)+56 a^3 b^2 x^2 (5 A+6 B x)+84 a^2 b^3 x^3 (4 A+5 B x)+70 a b^4 x^4 (3 A+4 B x)+28 b^5 x^5 (2 A+3 B x)\right)}{168 x^8 (a+b x)}","\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}",1,"-1/168*(Sqrt[(a + b*x)^2]*(28*b^5*x^5*(2*A + 3*B*x) + 70*a*b^4*x^4*(3*A + 4*B*x) + 84*a^2*b^3*x^3*(4*A + 5*B*x) + 56*a^3*b^2*x^2*(5*A + 6*B*x) + 20*a^4*b*x*(6*A + 7*B*x) + 3*a^5*(7*A + 8*B*x)))/(x^8*(a + b*x))","A",1
699,1,125,304,0.0380615,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{10}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^10,x]","-\frac{\sqrt{(a+b x)^2} \left(7 a^5 (8 A+9 B x)+45 a^4 b x (7 A+8 B x)+120 a^3 b^2 x^2 (6 A+7 B x)+168 a^2 b^3 x^3 (5 A+6 B x)+126 a b^4 x^4 (4 A+5 B x)+42 b^5 x^5 (3 A+4 B x)\right)}{504 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)}{3 x^6 (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 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^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (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{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)}",1,"-1/504*(Sqrt[(a + b*x)^2]*(42*b^5*x^5*(3*A + 4*B*x) + 126*a*b^4*x^4*(4*A + 5*B*x) + 168*a^2*b^3*x^3*(5*A + 6*B*x) + 120*a^3*b^2*x^2*(6*A + 7*B*x) + 45*a^4*b*x*(7*A + 8*B*x) + 7*a^5*(8*A + 9*B*x)))/(x^9*(a + b*x))","A",1
700,1,125,306,0.0378397,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{11}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^11,x]","-\frac{\sqrt{(a+b x)^2} \left(28 a^5 (9 A+10 B x)+175 a^4 b x (8 A+9 B x)+450 a^3 b^2 x^2 (7 A+8 B x)+600 a^2 b^3 x^3 (6 A+7 B x)+420 a b^4 x^4 (5 A+6 B x)+126 b^5 x^5 (4 A+5 B x)\right)}{2520 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)}{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)}{5 x^5 (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^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (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{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)}",1,"-1/2520*(Sqrt[(a + b*x)^2]*(126*b^5*x^5*(4*A + 5*B*x) + 420*a*b^4*x^4*(5*A + 6*B*x) + 600*a^2*b^3*x^3*(6*A + 7*B*x) + 450*a^3*b^2*x^2*(7*A + 8*B*x) + 175*a^4*b*x*(8*A + 9*B*x) + 28*a^5*(9*A + 10*B*x)))/(x^10*(a + b*x))","A",1
701,1,125,306,0.0366833,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{12}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^12,x]","-\frac{\sqrt{(a+b x)^2} \left(126 a^5 (10 A+11 B x)+770 a^4 b x (9 A+10 B x)+1925 a^3 b^2 x^2 (8 A+9 B x)+2475 a^2 b^3 x^3 (7 A+8 B x)+1650 a b^4 x^4 (6 A+7 B x)+462 b^5 x^5 (5 A+6 B x)\right)}{13860 x^{11} (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{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{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^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (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{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)}",1,"-1/13860*(Sqrt[(a + b*x)^2]*(462*b^5*x^5*(5*A + 6*B*x) + 1650*a*b^4*x^4*(6*A + 7*B*x) + 2475*a^2*b^3*x^3*(7*A + 8*B*x) + 1925*a^3*b^2*x^2*(8*A + 9*B*x) + 770*a^4*b*x*(9*A + 10*B*x) + 126*a^5*(10*A + 11*B*x)))/(x^11*(a + b*x))","A",1
702,1,125,306,0.0384672,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{13}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^13,x]","-\frac{\sqrt{(a+b x)^2} \left(42 a^5 (11 A+12 B x)+252 a^4 b x (10 A+11 B x)+616 a^3 b^2 x^2 (9 A+10 B x)+770 a^2 b^3 x^3 (8 A+9 B x)+495 a b^4 x^4 (7 A+8 B x)+132 b^5 x^5 (6 A+7 B x)\right)}{5544 x^{12} (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{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{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^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (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{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)}",1,"-1/5544*(Sqrt[(a + b*x)^2]*(132*b^5*x^5*(6*A + 7*B*x) + 495*a*b^4*x^4*(7*A + 8*B*x) + 770*a^2*b^3*x^3*(8*A + 9*B*x) + 616*a^3*b^2*x^2*(9*A + 10*B*x) + 252*a^4*b*x*(10*A + 11*B*x) + 42*a^5*(11*A + 12*B*x)))/(x^12*(a + b*x))","A",1
703,1,125,304,0.0410491,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{14}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^14,x]","-\frac{\sqrt{(a+b x)^2} \left(462 a^5 (12 A+13 B x)+2730 a^4 b x (11 A+12 B x)+6552 a^3 b^2 x^2 (10 A+11 B x)+8008 a^2 b^3 x^3 (9 A+10 B x)+5005 a b^4 x^4 (8 A+9 B x)+1287 b^5 x^5 (7 A+8 B x)\right)}{72072 x^{13} (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{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{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^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (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{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)}",1,"-1/72072*(Sqrt[(a + b*x)^2]*(1287*b^5*x^5*(7*A + 8*B*x) + 5005*a*b^4*x^4*(8*A + 9*B*x) + 8008*a^2*b^3*x^3*(9*A + 10*B*x) + 6552*a^3*b^2*x^2*(10*A + 11*B*x) + 2730*a^4*b*x*(11*A + 12*B*x) + 462*a^5*(12*A + 13*B*x)))/(x^13*(a + b*x))","A",1
704,1,116,258,0.0590628,"\int \frac{x^4 (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(x^4*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \left(b x \left(60 a^4 B-30 a^3 b (2 A+B x)+10 a^2 b^2 x (3 A+2 B x)-5 a b^3 x^2 (4 A+3 B x)+3 b^4 x^3 (5 A+4 B x)\right)-60 a^4 (a B-A b) \log (a+b x)\right)}{60 b^6 \sqrt{(a+b 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^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 x^3 (a+b x) (A b-a B)}{3 b^3 \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{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{a^3 x (a+b x) (A b-a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*(b*x*(60*a^4*B - 30*a^3*b*(2*A + B*x) + 10*a^2*b^2*x*(3*A + 2*B*x) - 5*a*b^3*x^2*(4*A + 3*B*x) + 3*b^4*x^3*(5*A + 4*B*x)) - 60*a^4*(-(A*b) + a*B)*Log[a + b*x]))/(60*b^6*Sqrt[(a + b*x)^2])","A",1
705,1,96,212,0.0440653,"\int \frac{x^3 (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(x^3*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \left(12 a^3 (a B-A b) \log (a+b x)+b x \left(-12 a^3 B+6 a^2 b (2 A+B x)-2 a b^2 x (3 A+2 B x)+b^3 x^2 (4 A+3 B x)\right)\right)}{12 b^5 \sqrt{(a+b 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^2 x (a+b x) (A b-a B)}{b^4 \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{B x^4 (a+b x)}{4 b \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}}",1,"((a + b*x)*(b*x*(-12*a^3*B + 6*a^2*b*(2*A + B*x) - 2*a*b^2*x*(3*A + 2*B*x) + b^3*x^2*(4*A + 3*B*x)) + 12*a^3*(-(A*b) + a*B)*Log[a + b*x]))/(12*b^5*Sqrt[(a + b*x)^2])","A",1
706,1,77,166,0.0364819,"\int \frac{x^2 (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(x^2*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \left(b x \left(6 a^2 B-3 a b (2 A+B x)+b^2 x (3 A+2 B x)\right)+6 a^2 (A b-a B) \log (a+b x)\right)}{6 b^4 \sqrt{(a+b 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^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{a x (a+b x) (A b-a B)}{b^3 \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 + b*x)*(b*x*(6*a^2*B - 3*a*b*(2*A + B*x) + b^2*x*(3*A + 2*B*x)) + 6*a^2*(A*b - a*B)*Log[a + b*x]))/(6*b^4*Sqrt[(a + b*x)^2])","A",1
707,1,57,120,0.0256239,"\int \frac{x (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(x*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (b x (-2 a B+2 A b+b B x)+2 a (a B-A b) \log (a+b x))}{2 b^3 \sqrt{(a+b 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*x)*(b*x*(2*A*b - 2*a*B + b*B*x) + 2*a*(-(A*b) + a*B)*Log[a + b*x]))/(2*b^3*Sqrt[(a + b*x)^2])","A",1
708,1,40,69,0.0166493,"\int \frac{A+B x}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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 B x)}{b^2 \sqrt{(a+b x)^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,"((a + b*x)*(b*B*x + (A*b - a*B)*Log[a + b*x]))/(b^2*Sqrt[(a + b*x)^2])","A",1
709,1,44,80,0.0192163,"\int \frac{A+B x}{x \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(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)+A b \log (x))}{a b \sqrt{(a+b 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 + b*x)*(A*b*Log[x] + (-(A*b) + a*B)*Log[a + b*x]))/(a*b*Sqrt[(a + b*x)^2])","A",1
710,1,57,113,0.0331336,"\int \frac{A+B x}{x^2 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) (\log (x) (a B x-A b x)+x (A b-a B) \log (a+b x)-a A)}{a^2 x \sqrt{(a+b x)^2}}","-\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 + b*x)*(-(a*A) + (-(A*b*x) + a*B*x)*Log[x] + (A*b - a*B)*x*Log[a + b*x]))/(a^2*x*Sqrt[(a + b*x)^2])","A",1
711,1,79,162,0.041253,"\int \frac{A+B x}{x^3 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{(a+b x) \left(2 b x^2 \log (x) (a B-A b)+2 b x^2 (A b-a B) \log (a+b x)+a (a A+2 a B x-2 A b x)\right)}{2 a^3 x^2 \sqrt{(a+b 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{A (a+b x)}{2 a x^2 \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}}",1,"-1/2*((a + b*x)*(a*(a*A - 2*A*b*x + 2*a*B*x) + 2*b*(-(A*b) + a*B)*x^2*Log[x] + 2*b*(A*b - a*B)*x^2*Log[a + b*x]))/(a^3*x^2*Sqrt[(a + b*x)^2])","A",1
712,1,102,211,0.0504723,"\int \frac{A+B x}{x^4 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{(a+b x) \left(a \left(a^2 (2 A+3 B x)-3 a b x (A+2 B x)+6 A b^2 x^2\right)+6 b^2 x^3 \log (x) (A b-a B)+6 b^2 x^3 (a B-A b) \log (a+b x)\right)}{6 a^4 x^3 \sqrt{(a+b 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{A (a+b x)}{3 a x^3 \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{b (a+b x) (A b-a B)}{a^3 x \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-1/6*((a + b*x)*(a*(6*A*b^2*x^2 - 3*a*b*x*(A + 2*B*x) + a^2*(2*A + 3*B*x)) + 6*b^2*(A*b - a*B)*x^3*Log[x] + 6*b^2*(-(A*b) + a*B)*x^3*Log[a + b*x]))/(a^4*x^3*Sqrt[(a + b*x)^2])","A",1
713,1,121,256,0.0597597,"\int \frac{A+B x}{x^5 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{(a+b x) \left(a \left(a^3 (3 A+4 B x)-2 a^2 b x (2 A+3 B x)+6 a b^2 x^2 (A+2 B x)-12 A b^3 x^3\right)-12 b^3 x^4 \log (x) (A b-a B)+12 b^3 x^4 (A b-a B) \log (a+b x)\right)}{12 a^5 x^4 \sqrt{(a+b 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{A (a+b x)}{4 a x^4 \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{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}}",1,"-1/12*((a + b*x)*(a*(-12*A*b^3*x^3 + 6*a*b^2*x^2*(A + 2*B*x) - 2*a^2*b*x*(2*A + 3*B*x) + a^3*(3*A + 4*B*x)) - 12*b^3*(A*b - a*B)*x^4*Log[x] + 12*b^3*(A*b - a*B)*x^4*Log[a + b*x]))/(a^5*x^4*Sqrt[(a + b*x)^2])","A",1
714,1,140,249,0.0617818,"\int \frac{x^4 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{-27 a^5 B+3 a^4 b (7 A+2 B x)+3 a^3 b^2 x (2 A+21 B x)+a^2 b^3 x^2 (20 B x-33 A)-12 a^2 (a+b x)^2 (5 a B-3 A b) \log (a+b x)-a b^4 x^3 (12 A+5 B x)+b^5 x^4 (3 A+2 B x)}{6 b^6 (a+b x) \sqrt{(a+b 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{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{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}}",1,"(-27*a^5*B + b^5*x^4*(3*A + 2*B*x) + 3*a^4*b*(7*A + 2*B*x) - a*b^4*x^3*(12*A + 5*B*x) + a^2*b^3*x^2*(-33*A + 20*B*x) + 3*a^3*b^2*x*(2*A + 21*B*x) - 12*a^2*(-3*A*b + 5*a*B)*(a + b*x)^2*Log[a + b*x])/(6*b^6*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
715,1,117,202,0.0515307,"\int \frac{x^3 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{7 a^4 B+a^3 (2 b B x-5 A b)-a^2 b^2 x (4 A+11 B x)+4 a b^3 x^2 (A-B x)+6 a (a+b x)^2 (2 a B-A b) \log (a+b x)+b^4 x^3 (2 A+B x)}{2 b^5 (a+b x) \sqrt{(a+b 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{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{x (a+b x) (A b-3 a B)}{b^4 \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}}",1,"(7*a^4*B + 4*a*b^3*x^2*(A - B*x) + b^4*x^3*(2*A + B*x) - a^2*b^2*x*(4*A + 11*B*x) + a^3*(-5*A*b + 2*b*B*x) + 6*a*(-(A*b) + 2*a*B)*(a + b*x)^2*Log[a + b*x])/(2*b^5*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
716,1,89,154,0.059373,"\int \frac{x^2 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{-5 a^3 B+a^2 b (3 A-4 B x)+4 a b^2 x (A+B x)+2 (a+b x)^2 (A b-3 a B) \log (a+b x)+2 b^3 B x^3}{2 b^4 (a+b x) \sqrt{(a+b 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,"(-5*a^3*B + 2*b^3*B*x^3 + a^2*b*(3*A - 4*B*x) + 4*a*b^2*x*(A + B*x) + 2*(A*b - 3*a*B)*(a + b*x)^2*Log[a + b*x])/(2*b^4*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
717,1,65,113,0.026808,"\int \frac{x (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{3 a^2 B-a b (A-4 B x)+2 B (a+b x)^2 \log (a+b x)-2 A b^2 x}{2 b^3 (a+b x) \sqrt{(a+b 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,"(3*a^2*B - 2*A*b^2*x - a*b*(A - 4*B*x) + 2*B*(a + b*x)^2*Log[a + b*x])/(2*b^3*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
718,1,39,69,0.014899,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{-B (a+2 b x)-A b}{2 b^2 (a+b x) \sqrt{(a+b 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,"(-(A*b) - B*(a + 2*b*x))/(2*b^2*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
719,1,80,140,0.0358432,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{a \left(a^2 (-B)+3 a A b+2 A b^2 x\right)+2 A b \log (x) (a+b x)^2-2 A b (a+b x)^2 \log (a+b x)}{2 a^3 b (a+b x) \sqrt{(a+b 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*(3*a*A*b - a^2*B + 2*A*b^2*x) + 2*A*b*(a + b*x)^2*Log[x] - 2*A*b*(a + b*x)^2*Log[a + b*x])/(2*a^3*b*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
720,1,110,196,0.0631836,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{a \left(a^2 (3 B x-2 A)+a b x (2 B x-9 A)-6 A b^2 x^2\right)+2 x \log (x) (a+b x)^2 (a B-3 A b)+2 x (a+b x)^2 (3 A b-a B) \log (a+b x)}{2 a^4 x (a+b x) \sqrt{(a+b 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{\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{2 A b-a B}{a^3 \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,"(a*(-6*A*b^2*x^2 + a*b*x*(-9*A + 2*B*x) + a^2*(-2*A + 3*B*x)) + 2*(-3*A*b + a*B)*x*(a + b*x)^2*Log[x] + 2*(3*A*b - a*B)*x*(a + b*x)^2*Log[a + b*x])/(2*a^4*x*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
721,1,133,243,0.073822,"\int \frac{A+B x}{x^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{-a \left(a^3 (A+2 B x)+a^2 b x (9 B x-4 A)+6 a b^2 x^2 (B x-3 A)-12 A b^3 x^3\right)+6 b x^2 \log (x) (a+b x)^2 (2 A b-a B)+6 b x^2 (a+b x)^2 (a B-2 A b) \log (a+b x)}{2 a^5 x^2 (a+b x) \sqrt{(a+b 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{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{A (a+b x)}{2 a^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-(a*(-12*A*b^3*x^3 + 6*a*b^2*x^2*(-3*A + B*x) + a^3*(A + 2*B*x) + a^2*b*x*(-4*A + 9*B*x))) + 6*b*(2*A*b - a*B)*x^2*(a + b*x)^2*Log[x] + 6*b*(-2*A*b + a*B)*x^2*(a + b*x)^2*Log[a + b*x])/(2*a^5*x^2*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
722,1,127,245,0.0661731,"\int \frac{x^4 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-77 a^5 B+a^4 b (25 A-248 B x)+4 a^3 b^2 x (22 A-63 B x)+12 a^2 b^3 x^2 (9 A-4 B x)+48 a b^4 x^3 (A+B x)+12 (a+b x)^4 (A b-5 a B) \log (a+b x)+12 b^5 B x^5}{12 b^6 (a+b x)^3 \sqrt{(a+b 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}}",1,"(-77*a^5*B + 12*b^5*B*x^5 + a^4*b*(25*A - 248*B*x) + 4*a^3*b^2*x*(22*A - 63*B*x) + 12*a^2*b^3*x^2*(9*A - 4*B*x) + 48*a*b^4*x^3*(A + B*x) + 12*(A*b - 5*a*B)*(a + b*x)^4*Log[a + b*x])/(12*b^6*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
723,1,103,188,0.0478345,"\int \frac{x^3 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{25 a^4 B+a^3 (88 b B x-3 A b)-12 a^2 b^2 x (A-9 B x)+6 a b^3 x^2 (8 B x-3 A)+12 B (a+b x)^4 \log (a+b x)-12 A b^4 x^3}{12 b^5 (a+b x)^3 \sqrt{(a+b 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{B (a+b x) \log (a+b x)}{b^5 \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}}",1,"(25*a^4*B - 12*A*b^4*x^3 - 12*a^2*b^2*x*(A - 9*B*x) + 6*a*b^3*x^2*(-3*A + 8*B*x) + a^3*(-3*A*b + 88*b*B*x) + 12*B*(a + b*x)^4*Log[a + b*x])/(12*b^5*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
724,1,73,77,0.0326236,"\int \frac{x^2 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-3 a^3 B-a^2 b (A+12 B x)-2 a b^2 x (2 A+9 B x)-6 b^3 x^2 (A+2 B x)}{12 b^4 (a+b x)^3 \sqrt{(a+b 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,"(-3*a^3*B - 6*b^3*x^2*(A + 2*B*x) - 2*a*b^2*x*(2*A + 9*B*x) - a^2*b*(A + 12*B*x))/(12*b^4*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
725,1,56,121,0.022507,"\int \frac{x (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{a^2 (-B)-a b (A+4 B x)-2 b^2 x (2 A+3 B x)}{12 b^3 (a+b x)^3 \sqrt{(a+b 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^2*B) - 2*b^2*x*(2*A + 3*B*x) - a*b*(A + 4*B*x))/(12*b^3*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
726,1,39,71,0.0201992,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-B (a+4 b x)-3 A b}{12 b^2 (a+b x)^3 \sqrt{(a+b x)^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,"(-3*A*b - B*(a + 4*b*x))/(12*b^2*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
727,1,104,210,0.0621512,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{a \left(-3 a^4 B+25 a^3 A b+52 a^2 A b^2 x+42 a A b^3 x^2+12 A b^4 x^3\right)+12 A b \log (x) (a+b x)^4-12 A b (a+b x)^4 \log (a+b x)}{12 a^5 b (a+b x)^3 \sqrt{(a+b 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}{3 a^2 (a+b x)^2 \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}{a^4 \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}}",1,"(a*(25*a^3*A*b - 3*a^4*B + 52*a^2*A*b^2*x + 42*a*A*b^3*x^2 + 12*A*b^4*x^3) + 12*A*b*(a + b*x)^4*Log[x] - 12*A*b*(a + b*x)^4*Log[a + b*x])/(12*a^5*b*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
728,1,148,282,0.1081771,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{a \left(a^4 (25 B x-12 A)+a^3 b x (52 B x-125 A)+2 a^2 b^2 x^2 (21 B x-130 A)+6 a b^3 x^3 (2 B x-35 A)-60 A b^4 x^4\right)+12 x \log (x) (a+b x)^4 (a B-5 A b)+12 x (a+b x)^4 (5 A b-a B) \log (a+b x)}{12 a^6 x (a+b x)^3 \sqrt{(a+b 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{\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{4 A b-a B}{a^5 \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{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}}",1,"(a*(-60*A*b^4*x^4 + 6*a*b^3*x^3*(-35*A + 2*B*x) + 2*a^2*b^2*x^2*(-130*A + 21*B*x) + a^4*(-12*A + 25*B*x) + a^3*b*x*(-125*A + 52*B*x)) + 12*(-5*A*b + a*B)*x*(a + b*x)^4*Log[x] + 12*(5*A*b - a*B)*x*(a + b*x)^4*Log[a + b*x])/(12*a^6*x*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
729,1,52,63,0.0224944,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 x^{9/2} \left(65 a^2 (11 A+9 B x)+90 a b x (13 A+11 B x)+33 b^2 x^2 (15 A+13 B x)\right)}{6435}","\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*x^(9/2)*(65*a^2*(11*A + 9*B*x) + 90*a*b*x*(13*A + 11*B*x) + 33*b^2*x^2*(15*A + 13*B*x)))/6435","A",1
730,1,52,63,0.0171139,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 x^{7/2} \left(143 a^2 (9 A+7 B x)+182 a b x (11 A+9 B x)+63 b^2 x^2 (13 A+11 B x)\right)}{9009}","\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*x^(7/2)*(143*a^2*(9*A + 7*B*x) + 182*a*b*x*(11*A + 9*B*x) + 63*b^2*x^2*(13*A + 11*B*x)))/9009","A",1
731,1,52,63,0.021324,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 x^{5/2} \left(99 a^2 (7 A+5 B x)+110 a b x (9 A+7 B x)+35 b^2 x^2 (11 A+9 B x)\right)}{3465}","\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*x^(5/2)*(99*a^2*(7*A + 5*B*x) + 110*a*b*x*(9*A + 7*B*x) + 35*b^2*x^2*(11*A + 9*B*x)))/3465","A",1
732,1,52,63,0.0174638,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2}{315} x^{3/2} \left(21 a^2 (5 A+3 B x)+18 a b x (7 A+5 B x)+5 b^2 x^2 (9 A+7 B x)\right)","\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*x^(3/2)*(21*a^2*(5*A + 3*B*x) + 18*a*b*x*(7*A + 5*B*x) + 5*b^2*x^2*(9*A + 7*B*x)))/315","A",1
733,1,51,61,0.0211324,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/Sqrt[x],x]","\frac{2}{105} \sqrt{x} \left(35 a^2 (3 A+B x)+14 a b x (5 A+3 B x)+3 b^2 x^2 (7 A+5 B x)\right)","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*Sqrt[x]*(35*a^2*(3*A + B*x) + 14*a*b*x*(5*A + 3*B*x) + 3*b^2*x^2*(7*A + 5*B*x)))/105","A",1
734,1,49,59,0.015083,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^(3/2),x]","\frac{-30 a^2 (A-B x)+20 a b x (3 A+B x)+2 b^2 x^2 (5 A+3 B x)}{15 \sqrt{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}",1,"(-30*a^2*(A - B*x) + 20*a*b*x*(3*A + B*x) + 2*b^2*x^2*(5*A + 3*B*x))/(15*Sqrt[x])","A",1
735,1,47,59,0.0160901,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^(5/2),x]","\frac{2 \left(-\left(a^2 (A+3 B x)\right)+6 a b x (B x-A)+b^2 x^2 (3 A+B x)\right)}{3 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*(6*a*b*x*(-A + B*x) + b^2*x^2*(3*A + B*x) - a^2*(A + 3*B*x)))/(3*x^(3/2))","A",1
736,1,47,59,0.0175517,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^(7/2),x]","-\frac{2 \left(a^2 (3 A+5 B x)+10 a b x (A+3 B x)+15 b^2 x^2 (A-B x)\right)}{15 x^{5/2}}","-\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*(15*b^2*x^2*(A - B*x) + 10*a*b*x*(A + 3*B*x) + a^2*(3*A + 5*B*x)))/(15*x^(5/2))","A",1
737,1,50,61,0.0173416,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^(9/2),x]","-\frac{2 \left(3 a^2 (5 A+7 B x)+14 a b x (3 A+5 B x)+35 b^2 x^2 (A+3 B x)\right)}{105 x^{7/2}}","-\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*(35*b^2*x^2*(A + 3*B*x) + 14*a*b*x*(3*A + 5*B*x) + 3*a^2*(5*A + 7*B*x)))/(105*x^(7/2))","A",1
738,1,81,111,0.0694269,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 \left(\frac{x^{9/2} \left(12155 a^4+39780 a^3 b x+50490 a^2 b^2 x^2+29172 a b^3 x^3+6435 b^4 x^4\right) (19 A b-9 a B)}{109395}+B x^{9/2} (a+b x)^5\right)}{19 b}","\frac{2}{9} a^4 A x^{9/2}+\frac{2}{11} a^3 x^{11/2} (a B+4 A b)+\frac{4}{13} a^2 b x^{13/2} (2 a B+3 A b)+\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*(B*x^(9/2)*(a + b*x)^5 + ((19*A*b - 9*a*B)*x^(9/2)*(12155*a^4 + 39780*a^3*b*x + 50490*a^2*b^2*x^2 + 29172*a*b^3*x^3 + 6435*b^4*x^4))/109395))/(19*b)","A",1
739,1,81,111,0.0756682,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 \left(\frac{x^{7/2} \left(6435 a^4+20020 a^3 b x+24570 a^2 b^2 x^2+13860 a b^3 x^3+3003 b^4 x^4\right) (17 A b-7 a B)}{45045}+B x^{7/2} (a+b x)^5\right)}{17 b}","\frac{2}{7} a^4 A x^{7/2}+\frac{2}{9} a^3 x^{9/2} (a B+4 A b)+\frac{4}{11} a^2 b x^{11/2} (2 a B+3 A b)+\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*(B*x^(7/2)*(a + b*x)^5 + ((17*A*b - 7*a*B)*x^(7/2)*(6435*a^4 + 20020*a^3*b*x + 24570*a^2*b^2*x^2 + 13860*a*b^3*x^3 + 3003*b^4*x^4))/45045))/(17*b)","A",1
740,1,81,111,0.063762,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 \left(\frac{x^{5/2} \left(3003 a^4+8580 a^3 b x+10010 a^2 b^2 x^2+5460 a b^3 x^3+1155 b^4 x^4\right) (3 A b-a B)}{3003}+B x^{5/2} (a+b x)^5\right)}{15 b}","\frac{2}{5} a^4 A x^{5/2}+\frac{2}{7} a^3 x^{7/2} (a B+4 A b)+\frac{4}{9} a^2 b x^{9/2} (2 a B+3 A b)+\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*(B*x^(5/2)*(a + b*x)^5 + ((3*A*b - a*B)*x^(5/2)*(3003*a^4 + 8580*a^3*b*x + 10010*a^2*b^2*x^2 + 5460*a*b^3*x^3 + 1155*b^4*x^4))/3003))/(15*b)","A",1
741,1,81,111,0.0585069,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 \left(\frac{x^{3/2} \left(1155 a^4+2772 a^3 b x+2970 a^2 b^2 x^2+1540 a b^3 x^3+315 b^4 x^4\right) (13 A b-3 a B)}{3465}+B x^{3/2} (a+b x)^5\right)}{13 b}","\frac{2}{3} a^4 A x^{3/2}+\frac{2}{5} a^3 x^{5/2} (a B+4 A b)+\frac{4}{7} a^2 b x^{7/2} (2 a B+3 A b)+\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*(B*x^(3/2)*(a + b*x)^5 + ((13*A*b - 3*a*B)*x^(3/2)*(1155*a^4 + 2772*a^3*b*x + 2970*a^2*b^2*x^2 + 1540*a*b^3*x^3 + 315*b^4*x^4))/3465))/(13*b)","A",1
742,1,89,109,0.0333302,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/Sqrt[x],x]","\frac{2 \sqrt{x} \left(1155 a^4 (3 A+B x)+924 a^3 b x (5 A+3 B x)+594 a^2 b^2 x^2 (7 A+5 B x)+220 a b^3 x^3 (9 A+7 B x)+35 b^4 x^4 (11 A+9 B x)\right)}{3465}","2 a^4 A \sqrt{x}+\frac{2}{3} a^3 x^{3/2} (a B+4 A b)+\frac{4}{5} a^2 b x^{5/2} (2 a B+3 A b)+\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*Sqrt[x]*(1155*a^4*(3*A + B*x) + 924*a^3*b*x*(5*A + 3*B*x) + 594*a^2*b^2*x^2*(7*A + 5*B*x) + 220*a*b^3*x^3*(9*A + 7*B*x) + 35*b^4*x^4*(11*A + 9*B*x)))/3465","A",1
743,1,87,107,0.0263554,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(3/2),x]","\frac{-630 a^4 (A-B x)+840 a^3 b x (3 A+B x)+252 a^2 b^2 x^2 (5 A+3 B x)+72 a b^3 x^3 (7 A+5 B x)+10 b^4 x^4 (9 A+7 B x)}{315 \sqrt{x}}","-\frac{2 a^4 A}{\sqrt{x}}+2 a^3 \sqrt{x} (a B+4 A b)+\frac{4}{3} a^2 b x^{3/2} (2 a B+3 A b)+\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,"(-630*a^4*(A - B*x) + 840*a^3*b*x*(3*A + B*x) + 252*a^2*b^2*x^2*(5*A + 3*B*x) + 72*a*b^3*x^3*(7*A + 5*B*x) + 10*b^4*x^4*(9*A + 7*B*x))/(315*Sqrt[x])","A",1
744,1,86,107,0.0336573,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(5/2),x]","\frac{-70 a^4 (A+3 B x)+840 a^3 b x (B x-A)+420 a^2 b^2 x^2 (3 A+B x)+56 a b^3 x^3 (5 A+3 B x)+6 b^4 x^4 (7 A+5 B x)}{105 x^{3/2}}","-\frac{2 a^4 A}{3 x^{3/2}}-\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}{5} b^3 x^{5/2} (4 a B+A b)+\frac{4}{3} a b^2 x^{3/2} (3 a B+2 A b)+\frac{2}{7} b^4 B x^{7/2}",1,"(840*a^3*b*x*(-A + B*x) + 420*a^2*b^2*x^2*(3*A + B*x) - 70*a^4*(A + 3*B*x) + 56*a*b^3*x^3*(5*A + 3*B*x) + 6*b^4*x^4*(7*A + 5*B*x))/(105*x^(3/2))","A",1
745,1,85,107,0.0285213,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(7/2),x]","\frac{2 \left(-\left(a^4 (3 A+5 B x)\right)-20 a^3 b x (A+3 B x)+90 a^2 b^2 x^2 (B x-A)+20 a b^3 x^3 (3 A+B x)+b^4 x^4 (5 A+3 B x)\right)}{15 x^{5/2}}","-\frac{2 a^4 A}{5 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}{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*(90*a^2*b^2*x^2*(-A + B*x) + 20*a*b^3*x^3*(3*A + B*x) - 20*a^3*b*x*(A + 3*B*x) + b^4*x^4*(5*A + 3*B*x) - a^4*(3*A + 5*B*x)))/(15*x^(5/2))","A",1
746,1,85,107,0.0278739,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(9/2),x]","-\frac{2 \left(3 a^4 (5 A+7 B x)+28 a^3 b x (3 A+5 B x)+210 a^2 b^2 x^2 (A+3 B x)+420 a b^3 x^3 (A-B x)-35 b^4 x^4 (3 A+B x)\right)}{105 x^{7/2}}","-\frac{2 a^4 A}{7 x^{7/2}}-\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}}+2 b^3 \sqrt{x} (4 a B+A b)-\frac{4 a b^2 (3 a B+2 A b)}{\sqrt{x}}+\frac{2}{3} b^4 B x^{3/2}",1,"(-2*(420*a*b^3*x^3*(A - B*x) - 35*b^4*x^4*(3*A + B*x) + 210*a^2*b^2*x^2*(A + 3*B*x) + 28*a^3*b*x*(3*A + 5*B*x) + 3*a^4*(5*A + 7*B*x)))/(105*x^(7/2))","A",1
747,1,131,159,0.0995791,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 \left(\frac{1}{2} \left(\frac{2}{9} a^6 x^{9/2}+\frac{12}{11} a^5 b x^{11/2}+\frac{30}{13} a^4 b^2 x^{13/2}+\frac{8}{3} a^3 b^3 x^{15/2}+\frac{30}{17} a^2 b^4 x^{17/2}+\frac{12}{19} a b^5 x^{19/2}+\frac{2}{21} b^6 x^{21/2}\right) (23 A b-9 a B)+B x^{9/2} (a+b x)^7\right)}{23 b}","\frac{2}{9} a^6 A x^{9/2}+\frac{2}{11} a^5 x^{11/2} (a B+6 A b)+\frac{6}{13} a^4 b x^{13/2} (2 a B+5 A b)+\frac{2}{3} a^3 b^2 x^{15/2} (3 a B+4 A b)+\frac{10}{17} a^2 b^3 x^{17/2} (4 a B+3 A b)+\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*(B*x^(9/2)*(a + b*x)^7 + ((23*A*b - 9*a*B)*((2*a^6*x^(9/2))/9 + (12*a^5*b*x^(11/2))/11 + (30*a^4*b^2*x^(13/2))/13 + (8*a^3*b^3*x^(15/2))/3 + (30*a^2*b^4*x^(17/2))/17 + (12*a*b^5*x^(19/2))/19 + (2*b^6*x^(21/2))/21))/2))/(23*b)","A",1
748,1,128,159,0.087796,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 \left(B x^{7/2} (a+b x)^7-\frac{7}{2} \left(\frac{2}{7} a^6 x^{7/2}+\frac{4}{3} a^5 b x^{9/2}+\frac{30}{11} a^4 b^2 x^{11/2}+\frac{40}{13} a^3 b^3 x^{13/2}+2 a^2 b^4 x^{15/2}+\frac{12}{17} a b^5 x^{17/2}+\frac{2}{19} b^6 x^{19/2}\right) (a B-3 A b)\right)}{21 b}","\frac{2}{7} a^6 A x^{7/2}+\frac{2}{9} a^5 x^{9/2} (a B+6 A b)+\frac{6}{11} a^4 b x^{11/2} (2 a B+5 A b)+\frac{10}{13} a^3 b^2 x^{13/2} (3 a B+4 A b)+\frac{2}{3} a^2 b^3 x^{15/2} (4 a B+3 A b)+\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*(B*x^(7/2)*(a + b*x)^7 - (7*(-3*A*b + a*B)*((2*a^6*x^(7/2))/7 + (4*a^5*b*x^(9/2))/3 + (30*a^4*b^2*x^(11/2))/11 + (40*a^3*b^3*x^(13/2))/13 + 2*a^2*b^4*x^(15/2) + (12*a*b^5*x^(17/2))/17 + (2*b^6*x^(19/2))/19))/2))/(21*b)","A",1
749,1,103,159,0.0862545,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 \left(\frac{x^{5/2} \left(51051 a^6+218790 a^5 b x+425425 a^4 b^2 x^2+464100 a^3 b^3 x^3+294525 a^2 b^4 x^4+102102 a b^5 x^5+15015 b^6 x^6\right) (19 A b-5 a B)}{255255}+B x^{5/2} (a+b x)^7\right)}{19 b}","\frac{2}{5} a^6 A x^{5/2}+\frac{2}{7} a^5 x^{7/2} (a B+6 A b)+\frac{2}{3} a^4 b x^{9/2} (2 a B+5 A b)+\frac{10}{11} a^3 b^2 x^{11/2} (3 a B+4 A b)+\frac{10}{13} a^2 b^3 x^{13/2} (4 a B+3 A b)+\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*(B*x^(5/2)*(a + b*x)^7 + ((19*A*b - 5*a*B)*x^(5/2)*(51051*a^6 + 218790*a^5*b*x + 425425*a^4*b^2*x^2 + 464100*a^3*b^3*x^3 + 294525*a^2*b^4*x^4 + 102102*a*b^5*x^5 + 15015*b^6*x^6))/255255))/(19*b)","A",1
750,1,103,159,0.0839546,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 \left(\frac{x^{3/2} \left(15015 a^6+54054 a^5 b x+96525 a^4 b^2 x^2+100100 a^3 b^3 x^3+61425 a^2 b^4 x^4+20790 a b^5 x^5+3003 b^6 x^6\right) (17 A b-3 a B)}{45045}+B x^{3/2} (a+b x)^7\right)}{17 b}","\frac{2}{3} a^6 A x^{3/2}+\frac{2}{5} a^5 x^{5/2} (a B+6 A b)+\frac{6}{7} a^4 b x^{7/2} (2 a B+5 A b)+\frac{10}{9} a^3 b^2 x^{9/2} (3 a B+4 A b)+\frac{10}{11} a^2 b^3 x^{11/2} (4 a B+3 A b)+\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*(B*x^(3/2)*(a + b*x)^7 + ((17*A*b - 3*a*B)*x^(3/2)*(15015*a^6 + 54054*a^5*b*x + 96525*a^4*b^2*x^2 + 100100*a^3*b^3*x^3 + 61425*a^2*b^4*x^4 + 20790*a*b^5*x^5 + 3003*b^6*x^6))/45045))/(17*b)","A",1
751,1,103,157,0.0882468,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/Sqrt[x],x]","\frac{2 \left(\frac{\sqrt{x} \left(3003 a^6+6006 a^5 b x+9009 a^4 b^2 x^2+8580 a^3 b^3 x^3+5005 a^2 b^4 x^4+1638 a b^5 x^5+231 b^6 x^6\right) (15 A b-a B)}{3003}+B \sqrt{x} (a+b x)^7\right)}{15 b}","2 a^6 A \sqrt{x}+\frac{2}{3} a^5 x^{3/2} (a B+6 A b)+\frac{6}{5} a^4 b x^{5/2} (2 a B+5 A b)+\frac{10}{7} a^3 b^2 x^{7/2} (3 a B+4 A b)+\frac{10}{9} a^2 b^3 x^{9/2} (4 a B+3 A b)+\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*(B*Sqrt[x]*(a + b*x)^7 + ((15*A*b - a*B)*Sqrt[x]*(3003*a^6 + 6006*a^5*b*x + 9009*a^4*b^2*x^2 + 8580*a^3*b^3*x^3 + 5005*a^2*b^4*x^4 + 1638*a*b^5*x^5 + 231*b^6*x^6))/3003))/(15*b)","A",1
752,1,101,151,0.0770439,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(3/2),x]","\frac{2 \left(\frac{\sqrt{x} \left(3003 a^6+6006 a^5 b x+9009 a^4 b^2 x^2+8580 a^3 b^3 x^3+5005 a^2 b^4 x^4+1638 a b^5 x^5+231 b^6 x^6\right) (a B+13 A b)}{3003}-\frac{A (a+b x)^7}{\sqrt{x}}\right)}{a}","-\frac{2 a^6 A}{\sqrt{x}}+2 a^5 \sqrt{x} (a B+6 A b)+2 a^4 b x^{3/2} (2 a B+5 A b)+2 a^3 b^2 x^{5/2} (3 a B+4 A b)+\frac{10}{7} a^2 b^3 x^{7/2} (4 a B+3 A b)+\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*(a + b*x)^7)/Sqrt[x]) + ((13*A*b + a*B)*Sqrt[x]*(3003*a^6 + 6006*a^5*b*x + 9009*a^4*b^2*x^2 + 8580*a^3*b^3*x^3 + 5005*a^2*b^4*x^4 + 1638*a*b^5*x^5 + 231*b^6*x^6))/3003))/a","A",1
753,1,97,153,0.0695685,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(5/2),x]","\frac{2 \left(x \left(-231 a^6+1386 a^5 b x+1155 a^4 b^2 x^2+924 a^3 b^3 x^3+495 a^2 b^4 x^4+154 a b^5 x^5+21 b^6 x^6\right) (3 a B+11 A b)-231 A (a+b x)^7\right)}{693 a x^{3/2}}","-\frac{2 a^6 A}{3 x^{3/2}}-\frac{2 a^5 (a B+6 A b)}{\sqrt{x}}+6 a^4 b \sqrt{x} (2 a B+5 A b)+\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}{9} b^5 x^{9/2} (6 a B+A b)+\frac{6}{7} a b^4 x^{7/2} (5 a B+2 A b)+\frac{2}{11} b^6 B x^{11/2}",1,"(2*(-231*A*(a + b*x)^7 + (11*A*b + 3*a*B)*x*(-231*a^6 + 1386*a^5*b*x + 1155*a^4*b^2*x^2 + 924*a^3*b^3*x^3 + 495*a^2*b^4*x^4 + 154*a*b^5*x^5 + 21*b^6*x^6)))/(693*a*x^(3/2))","A",1
754,1,124,155,0.0400539,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(7/2),x]","\frac{2 \left(-21 a^6 (3 A+5 B x)-630 a^5 b x (A+3 B x)+4725 a^4 b^2 x^2 (B x-A)+2100 a^3 b^3 x^3 (3 A+B x)+315 a^2 b^4 x^4 (5 A+3 B x)+54 a b^5 x^5 (7 A+5 B x)+5 b^6 x^6 (9 A+7 B x)\right)}{315 x^{5/2}}","-\frac{2 a^6 A}{5 x^{5/2}}-\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}}+10 a^3 b^2 \sqrt{x} (3 a B+4 A b)+\frac{10}{3} a^2 b^3 x^{3/2} (4 a B+3 A b)+\frac{2}{7} b^5 x^{7/2} (6 a B+A b)+\frac{6}{5} a b^4 x^{5/2} (5 a B+2 A b)+\frac{2}{9} b^6 B x^{9/2}",1,"(2*(4725*a^4*b^2*x^2*(-A + B*x) + 2100*a^3*b^3*x^3*(3*A + B*x) - 630*a^5*b*x*(A + 3*B*x) + 315*a^2*b^4*x^4*(5*A + 3*B*x) - 21*a^6*(3*A + 5*B*x) + 54*a*b^5*x^5*(7*A + 5*B*x) + 5*b^6*x^6*(9*A + 7*B*x)))/(315*x^(5/2))","A",1
755,1,123,151,0.038822,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(9/2),x]","\frac{2 \left(-\left(a^6 (5 A+7 B x)\right)-14 a^5 b x (3 A+5 B x)-175 a^4 b^2 x^2 (A+3 B x)+700 a^3 b^3 x^3 (B x-A)+175 a^2 b^4 x^4 (3 A+B x)+14 a b^5 x^5 (5 A+3 B x)+b^6 x^6 (7 A+5 B x)\right)}{35 x^{7/2}}","-\frac{2 a^6 A}{7 x^{7/2}}-\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{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}{5} b^5 x^{5/2} (6 a B+A b)+2 a b^4 x^{3/2} (5 a B+2 A b)+\frac{2}{7} b^6 B x^{7/2}",1,"(2*(700*a^3*b^3*x^3*(-A + B*x) + 175*a^2*b^4*x^4*(3*A + B*x) - 175*a^4*b^2*x^2*(A + 3*B*x) + 14*a*b^5*x^5*(5*A + 3*B*x) - 14*a^5*b*x*(3*A + 5*B*x) + b^6*x^6*(7*A + 5*B*x) - a^6*(5*A + 7*B*x)))/(35*x^(7/2))","A",1
756,1,123,155,0.0393168,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{11/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(11/2),x]","-\frac{2 \left(5 a^6 (7 A+9 B x)+54 a^5 b x (5 A+7 B x)+315 a^4 b^2 x^2 (3 A+5 B x)+2100 a^3 b^3 x^3 (A+3 B x)+4725 a^2 b^4 x^4 (A-B x)-630 a b^5 x^5 (3 A+B x)-21 b^6 x^6 (5 A+3 B x)\right)}{315 x^{9/2}}","-\frac{2 a^6 A}{9 x^{9/2}}-\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{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}{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*(4725*a^2*b^4*x^4*(A - B*x) - 630*a*b^5*x^5*(3*A + B*x) + 2100*a^3*b^3*x^3*(A + 3*B*x) - 21*b^6*x^6*(5*A + 3*B*x) + 315*a^4*b^2*x^2*(3*A + 5*B*x) + 54*a^5*b*x*(5*A + 7*B*x) + 5*a^6*(7*A + 9*B*x)))/(315*x^(9/2))","A",1
757,1,128,154,0.0887216,"\int \frac{x^{7/2} (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{a^{5/2} (9 a B-7 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{11/2}}+\frac{\sqrt{x} \left(-945 a^4 B+105 a^3 b (7 A-6 B x)+14 a^2 b^2 x (35 A+9 B x)-2 a b^3 x^2 (49 A+27 B x)+6 b^4 x^3 (7 A+5 B x)\right)}{105 b^5 (a+b x)}","-\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{a^2 \sqrt{x} (7 A b-9 a B)}{b^5}-\frac{a x^{3/2} (7 A b-9 a B)}{3 b^4}+\frac{x^{5/2} (7 A b-9 a B)}{5 b^3}-\frac{x^{7/2} (7 A b-9 a B)}{7 a b^2}+\frac{x^{9/2} (A b-a B)}{a b (a+b x)}",1,"(Sqrt[x]*(-945*a^4*B + 105*a^3*b*(7*A - 6*B*x) + 6*b^4*x^3*(7*A + 5*B*x) + 14*a^2*b^2*x*(35*A + 9*B*x) - 2*a*b^3*x^2*(49*A + 27*B*x)))/(105*b^5*(a + b*x)) + (a^(5/2)*(-7*A*b + 9*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(11/2)","A",1
758,1,110,130,0.0713457,"\int \frac{x^{5/2} (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\sqrt{x} \left(105 a^3 B+a^2 (70 b B x-75 A b)-2 a b^2 x (25 A+7 B x)+2 b^3 x^2 (5 A+3 B x)\right)}{15 b^4 (a+b x)}-\frac{a^{3/2} (7 a B-5 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{9/2}}","\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{a \sqrt{x} (5 A b-7 a B)}{b^4}+\frac{x^{3/2} (5 A b-7 a B)}{3 b^3}-\frac{x^{5/2} (5 A b-7 a B)}{5 a b^2}+\frac{x^{7/2} (A b-a B)}{a b (a+b x)}",1,"(Sqrt[x]*(105*a^3*B + 2*b^3*x^2*(5*A + 3*B*x) - 2*a*b^2*x*(25*A + 7*B*x) + a^2*(-75*A*b + 70*b*B*x)))/(15*b^4*(a + b*x)) - (a^(3/2)*(-5*A*b + 7*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(9/2)","A",1
759,1,88,108,0.0588283,"\int \frac{x^{3/2} (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\sqrt{x} \left(-15 a^2 B+a b (9 A-10 B x)+2 b^2 x (3 A+B x)\right)}{3 b^3 (a+b x)}+\frac{\sqrt{a} (5 a B-3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}","-\frac{\sqrt{a} (3 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{\sqrt{x} (3 A b-5 a B)}{b^3}-\frac{x^{3/2} (3 A b-5 a B)}{3 a b^2}+\frac{x^{5/2} (A b-a B)}{a b (a+b x)}",1,"(Sqrt[x]*(-15*a^2*B + a*b*(9*A - 10*B*x) + 2*b^2*x*(3*A + B*x)))/(3*b^3*(a + b*x)) + (Sqrt[a]*(-3*A*b + 5*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",1
760,1,67,85,0.041171,"\int \frac{\sqrt{x} (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}+\frac{\sqrt{x} (3 a B-A b+2 b B x)}{b^2 (a+b x)}","\frac{(A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}-\frac{\sqrt{x} (A b-3 a B)}{a b^2}+\frac{x^{3/2} (A b-a B)}{a b (a+b x)}",1,"(Sqrt[x]*(-(A*b) + 3*a*B + 2*b*B*x))/(b^2*(a + b*x)) + ((A*b - 3*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[a]*b^(5/2))","A",1
761,1,63,63,0.0370858,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(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",1
762,1,59,88,0.0170853,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{(a+b x) (a B-3 A b) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x}{a}\right)+a (A b-a B)}{a^2 b \sqrt{x} (a+b x)}","-\frac{(3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2} \sqrt{b}}-\frac{3 A b-a B}{a^2 b \sqrt{x}}+\frac{A b-a B}{a b \sqrt{x} (a+b x)}",1,"(a*(A*b - a*B) + (-3*A*b + a*B)*(a + b*x)*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x)/a)])/(a^2*b*Sqrt[x]*(a + b*x))","C",1
763,1,64,107,0.0184918,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{(a+b x) (3 a B-5 A b) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b x}{a}\right)+3 a (A b-a B)}{3 a^2 b x^{3/2} (a+b 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{5 A b-3 a B}{a^3 \sqrt{x}}-\frac{5 A b-3 a B}{3 a^2 b x^{3/2}}+\frac{A b-a B}{a b x^{3/2} (a+b x)}",1,"(3*a*(A*b - a*B) + (-5*A*b + 3*a*B)*(a + b*x)*Hypergeometric2F1[-3/2, 1, -1/2, -((b*x)/a)])/(3*a^2*b*x^(3/2)*(a + b*x))","C",1
764,1,64,131,0.0185139,"\int \frac{A+B x}{x^{7/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{(a+b x) (5 a B-7 A b) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{b x}{a}\right)+5 a (A b-a B)}{5 a^2 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{b (7 A b-5 a B)}{a^4 \sqrt{x}}+\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{A b-a B}{a b x^{5/2} (a+b x)}",1,"(5*a*(A*b - a*B) + (-7*A*b + 5*a*B)*(a + b*x)*Hypergeometric2F1[-5/2, 1, -3/2, -((b*x)/a)])/(5*a^2*b*x^(5/2)*(a + b*x))","C",1
765,1,64,153,0.0188952,"\int \frac{A+B x}{x^{9/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(x^(9/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{(a+b x) (7 a B-9 A b) \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};-\frac{b x}{a}\right)+7 a (A b-a B)}{7 a^2 b x^{7/2} (a+b 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^2 (9 A b-7 a B)}{a^5 \sqrt{x}}-\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,"(7*a*(A*b - a*B) + (-9*A*b + 7*a*B)*(a + b*x)*Hypergeometric2F1[-7/2, 1, -5/2, -((b*x)/a)])/(7*a^2*b*x^(7/2)*(a + b*x))","C",1
766,1,61,173,0.0309951,"\int \frac{x^{7/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{x^{9/2} \left(\frac{9 a^3 (A b-a B)}{(a+b x)^3}+(9 a B-3 A b) \, _2F_1\left(3,\frac{9}{2};\frac{11}{2};-\frac{b x}{a}\right)\right)}{27 a^4 b}","-\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{35 \sqrt{x} (A b-3 a B)}{8 b^5}-\frac{35 x^{3/2} (A b-3 a B)}{24 a b^4}+\frac{7 x^{5/2} (A b-3 a B)}{8 a b^3 (a+b x)}+\frac{x^{7/2} (A b-3 a B)}{4 a b^2 (a+b x)^2}+\frac{x^{9/2} (A b-a B)}{3 a b (a+b x)^3}",1,"(x^(9/2)*((9*a^3*(A*b - a*B))/(a + b*x)^3 + (-3*A*b + 9*a*B)*Hypergeometric2F1[3, 9/2, 11/2, -((b*x)/a)]))/(27*a^4*b)","C",1
767,1,61,153,0.0274097,"\int \frac{x^{5/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{x^{7/2} \left(\frac{7 a^3 (A b-a B)}{(a+b x)^3}+(7 a B-A b) \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};-\frac{b x}{a}\right)\right)}{21 a^4 b}","\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{5 \sqrt{x} (A b-7 a B)}{8 a b^4}+\frac{5 x^{3/2} (A b-7 a B)}{24 a b^3 (a+b x)}+\frac{x^{5/2} (A b-7 a B)}{12 a b^2 (a+b x)^2}+\frac{x^{7/2} (A b-a B)}{3 a b (a+b x)^3}",1,"(x^(7/2)*((7*a^3*(A*b - a*B))/(a + b*x)^3 + (-(A*b) + 7*a*B)*Hypergeometric2F1[3, 7/2, 9/2, -((b*x)/a)]))/(21*a^4*b)","C",1
768,1,105,130,0.0811876,"\int \frac{x^{3/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(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{\sqrt{x} \left(15 a^3 B+a^2 b (3 A+40 B x)+a b^2 x (8 A+33 B x)-3 A b^3 x^2\right)}{24 a b^3 (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{\sqrt{x} (5 a B+A b)}{8 a b^3 (a+b x)}-\frac{x^{3/2} (5 a B+A b)}{12 a b^2 (a+b x)^2}+\frac{x^{5/2} (A b-a B)}{3 a b (a+b x)^3}",1,"-1/24*(Sqrt[x]*(15*a^3*B - 3*A*b^3*x^2 + a*b^2*x*(8*A + 33*B*x) + a^2*b*(3*A + 40*B*x)))/(a*b^3*(a + b*x)^3) + ((A*b + 5*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(8*a^(3/2)*b^(7/2))","A",1
769,1,60,127,0.0238335,"\int \frac{\sqrt{x} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{x^{3/2} \left(\frac{3 a^3 (A b-a B)}{(a+b x)^3}+3 (a B+A b) \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};-\frac{b x}{a}\right)\right)}{9 a^4 b}","\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)}{8 a^2 b^2 (a+b x)}-\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,"(x^(3/2)*((3*a^3*(A*b - a*B))/(a + b*x)^3 + 3*(A*b + a*B)*Hypergeometric2F1[3/2, 3, 5/2, -((b*x)/a)]))/(9*a^4*b)","C",1
770,1,59,130,0.0249683,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\sqrt{x} \left(\frac{a^3 (A b-a B)}{(a+b x)^3}+(a B+5 A b) \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};-\frac{b x}{a}\right)\right)}{3 a^4 b}","\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,"(Sqrt[x]*((a^3*(A*b - a*B))/(a + b*x)^3 + (5*A*b + a*B)*Hypergeometric2F1[1/2, 3, 3/2, -((b*x)/a)]))/(3*a^4*b)","C",1
771,1,59,157,0.0350934,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{a^3 (A b-a B)}{(a+b x)^3}+(a B-7 A b) \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};-\frac{b x}{a}\right)}{3 a^4 b \sqrt{x}}","-\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{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{A b-a B}{3 a b \sqrt{x} (a+b x)^3}",1,"((a^3*(A*b - a*B))/(a + b*x)^3 + (-7*A*b + a*B)*Hypergeometric2F1[-1/2, 3, 1/2, -((b*x)/a)])/(3*a^4*b*Sqrt[x])","C",1
772,1,61,178,0.0277914,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{3 a^3 (A b-a B)}{(a+b x)^3}+(3 a B-9 A b) \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};-\frac{b x}{a}\right)}{9 a^4 b x^{3/2}}","\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{35 (3 A b-a B)}{8 a^5 \sqrt{x}}-\frac{35 (3 A b-a B)}{24 a^4 b x^{3/2}}+\frac{7 (3 A b-a B)}{8 a^3 b x^{3/2} (a+b x)}+\frac{3 A b-a B}{4 a^2 b x^{3/2} (a+b x)^2}+\frac{A b-a B}{3 a b x^{3/2} (a+b x)^3}",1,"((3*a^3*(A*b - a*B))/(a + b*x)^3 + (-9*A*b + 3*a*B)*Hypergeometric2F1[-3/2, 3, -1/2, -((b*x)/a)])/(9*a^4*b*x^(3/2))","C",1
773,1,61,240,0.0346306,"\int \frac{x^{11/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^(11/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x^{13/2} \left(\frac{13 a^5 (A b-a B)}{(a+b x)^5}+(13 a B-3 A b) \, _2F_1\left(5,\frac{13}{2};\frac{15}{2};-\frac{b x}{a}\right)\right)}{65 a^6 b}","-\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{231 \sqrt{x} (3 A b-13 a B)}{128 b^7}-\frac{77 x^{3/2} (3 A b-13 a B)}{128 a b^6}+\frac{231 x^{5/2} (3 A b-13 a B)}{640 a b^5 (a+b x)}+\frac{33 x^{7/2} (3 A b-13 a B)}{320 a b^4 (a+b x)^2}+\frac{11 x^{9/2} (3 A b-13 a B)}{240 a b^3 (a+b x)^3}+\frac{x^{11/2} (3 A b-13 a B)}{40 a b^2 (a+b x)^4}+\frac{x^{13/2} (A b-a B)}{5 a b (a+b x)^5}",1,"(x^(13/2)*((13*a^5*(A*b - a*B))/(a + b*x)^5 + (-3*A*b + 13*a*B)*Hypergeometric2F1[5, 13/2, 15/2, -((b*x)/a)]))/(65*a^6*b)","C",1
774,1,61,213,0.0318002,"\int \frac{x^{9/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^(9/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x^{11/2} \left(\frac{11 a^5 (A b-a B)}{(a+b x)^5}+(11 a B-A b) \, _2F_1\left(5,\frac{11}{2};\frac{13}{2};-\frac{b x}{a}\right)\right)}{55 a^6 b}","\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{63 \sqrt{x} (A b-11 a B)}{128 a b^6}+\frac{21 x^{3/2} (A b-11 a B)}{128 a b^5 (a+b x)}+\frac{21 x^{5/2} (A b-11 a B)}{320 a b^4 (a+b x)^2}+\frac{3 x^{7/2} (A b-11 a B)}{80 a b^3 (a+b x)^3}+\frac{x^{9/2} (A b-11 a B)}{40 a b^2 (a+b x)^4}+\frac{x^{11/2} (A b-a B)}{5 a b (a+b x)^5}",1,"(x^(11/2)*((11*a^5*(A*b - a*B))/(a + b*x)^5 + (-(A*b) + 11*a*B)*Hypergeometric2F1[5, 11/2, 13/2, -((b*x)/a)]))/(55*a^6*b)","C",1
775,1,134,190,0.1786137,"\int \frac{x^{7/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(9 a B+A b) \left(105 (a+b x)^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-\sqrt{a} \sqrt{b} \sqrt{x} \left(105 a^3+385 a^2 b x+511 a b^2 x^2+279 b^3 x^3\right)\right)}{1920 a^{3/2} b^{11/2} (a+b x)^4}+\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{7 \sqrt{x} (9 a B+A b)}{128 a b^5 (a+b x)}-\frac{7 x^{3/2} (9 a B+A b)}{192 a b^4 (a+b x)^2}-\frac{7 x^{5/2} (9 a B+A b)}{240 a b^3 (a+b x)^3}-\frac{x^{7/2} (9 a B+A b)}{40 a b^2 (a+b x)^4}+\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)*(-(Sqrt[a]*Sqrt[b]*Sqrt[x]*(105*a^3 + 385*a^2*b*x + 511*a*b^2*x^2 + 279*b^3*x^3)) + 105*(a + b*x)^4*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(1920*a^(3/2)*b^(11/2)*(a + b*x)^4)","A",1
776,1,61,195,0.0308876,"\int \frac{x^{5/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x^{7/2} \left(\frac{7 a^5 (A b-a B)}{(a+b x)^5}+(7 a B+3 A b) \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};-\frac{b x}{a}\right)\right)}{35 a^6 b}","\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{\sqrt{x} (7 a B+3 A b)}{128 a^2 b^4 (a+b x)}-\frac{\sqrt{x} (7 a B+3 A b)}{64 a b^4 (a+b x)^2}-\frac{x^{3/2} (7 a B+3 A b)}{48 a b^3 (a+b x)^3}-\frac{x^{5/2} (7 a B+3 A b)}{40 a b^2 (a+b x)^4}+\frac{x^{7/2} (A b-a B)}{5 a b (a+b x)^5}",1,"(x^(7/2)*((7*a^5*(A*b - a*B))/(a + b*x)^5 + (3*A*b + 7*a*B)*Hypergeometric2F1[7/2, 5, 9/2, -((b*x)/a)]))/(35*a^6*b)","C",1
777,1,60,185,0.0293719,"\int \frac{x^{3/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x^{5/2} \left(\frac{5 a^5 (A b-a B)}{(a+b x)^5}+5 (a B+A b) \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};-\frac{b x}{a}\right)\right)}{25 a^6 b}","\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{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{\sqrt{x} (a B+A b)}{16 a b^3 (a+b x)^3}-\frac{x^{3/2} (a B+A b)}{8 a b^2 (a+b x)^4}+\frac{x^{5/2} (A b-a B)}{5 a b (a+b x)^5}",1,"(x^(5/2)*((5*a^5*(A*b - a*B))/(a + b*x)^5 + 5*(A*b + a*B)*Hypergeometric2F1[5/2, 5, 7/2, -((b*x)/a)]))/(25*a^6*b)","C",1
778,1,61,195,0.0285583,"\int \frac{\sqrt{x} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x^{3/2} \left(\frac{3 a^5 (A b-a B)}{(a+b x)^5}+(3 a B+7 A b) \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};-\frac{b x}{a}\right)\right)}{15 a^6 b}","\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)}{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{\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,"(x^(3/2)*((3*a^5*(A*b - a*B))/(a + b*x)^5 + (7*A*b + 3*a*B)*Hypergeometric2F1[3/2, 5, 5/2, -((b*x)/a)]))/(15*a^6*b)","C",1
779,1,59,190,0.0296575,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\sqrt{x} \left(\frac{a^5 (A b-a B)}{(a+b x)^5}+(a B+9 A b) \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};-\frac{b x}{a}\right)\right)}{5 a^6 b}","\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,"(Sqrt[x]*((a^5*(A*b - a*B))/(a + b*x)^5 + (9*A*b + a*B)*Hypergeometric2F1[1/2, 5, 3/2, -((b*x)/a)]))/(5*a^6*b)","C",1
780,1,59,219,0.0295869,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{a^5 (A b-a B)}{(a+b x)^5}+(a B-11 A b) \, _2F_1\left(-\frac{1}{2},5;\frac{1}{2};-\frac{b x}{a}\right)}{5 a^6 b \sqrt{x}}","-\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{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{A b-a B}{5 a b \sqrt{x} (a+b x)^5}",1,"((a^5*(A*b - a*B))/(a + b*x)^5 + (-11*A*b + a*B)*Hypergeometric2F1[-1/2, 5, 1/2, -((b*x)/a)])/(5*a^6*b*Sqrt[x])","C",1
781,1,61,240,0.0306043,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{3 a^5 (A b-a B)}{(a+b x)^5}+(3 a B-13 A b) \, _2F_1\left(-\frac{3}{2},5;-\frac{1}{2};-\frac{b x}{a}\right)}{15 a^6 b x^{3/2}}","\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{231 (13 A b-3 a B)}{128 a^7 \sqrt{x}}-\frac{77 (13 A b-3 a B)}{128 a^6 b x^{3/2}}+\frac{231 (13 A b-3 a B)}{640 a^5 b x^{3/2} (a+b x)}+\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{A b-a B}{5 a b x^{3/2} (a+b x)^5}",1,"((3*a^5*(A*b - a*B))/(a + b*x)^5 + (-13*A*b + 3*a*B)*Hypergeometric2F1[-3/2, 5, -1/2, -((b*x)/a)])/(15*a^6*b*x^(3/2))","C",1
782,1,51,120,0.0318112,"\int x^{7/2} (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[x^(7/2)*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{9/2} \sqrt{(a+b x)^2} (13 a (11 A+9 B x)+9 b x (13 A+11 B x))}{1287 (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*x^(9/2)*Sqrt[(a + b*x)^2]*(13*a*(11*A + 9*B*x) + 9*b*x*(13*A + 11*B*x)))/(1287*(a + b*x))","A",1
783,1,51,120,0.0264843,"\int x^{5/2} (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[x^(5/2)*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{7/2} \sqrt{(a+b x)^2} (11 a (9 A+7 B x)+7 b x (11 A+9 B x))}{693 (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*x^(7/2)*Sqrt[(a + b*x)^2]*(11*a*(9*A + 7*B*x) + 7*b*x*(11*A + 9*B*x)))/(693*(a + b*x))","A",1
784,1,51,120,0.0265535,"\int x^{3/2} (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[x^(3/2)*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{5/2} \sqrt{(a+b x)^2} (9 a (7 A+5 B x)+5 b x (9 A+7 B x))}{315 (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*x^(5/2)*Sqrt[(a + b*x)^2]*(9*a*(7*A + 5*B*x) + 5*b*x*(9*A + 7*B*x)))/(315*(a + b*x))","A",1
785,1,51,120,0.0263955,"\int \sqrt{x} (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[Sqrt[x]*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{3/2} \sqrt{(a+b x)^2} (7 a (5 A+3 B x)+3 b x (7 A+5 B x))}{105 (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*x^(3/2)*Sqrt[(a + b*x)^2]*(7*a*(5*A + 3*B*x) + 3*b*x*(7*A + 5*B*x)))/(105*(a + b*x))","A",1
786,1,49,118,0.0292156,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x}} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/Sqrt[x],x]","\frac{2 \sqrt{x} \sqrt{(a+b x)^2} (5 a (3 A+B x)+b x (5 A+3 B x))}{15 (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*Sqrt[x]*Sqrt[(a + b*x)^2]*(5*a*(3*A + B*x) + b*x*(5*A + 3*B*x)))/(15*(a + b*x))","A",1
787,1,47,116,0.0255246,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} (b x (3 A+B x)-3 a (A-B x))}{3 \sqrt{x} (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*Sqrt[(a + b*x)^2]*(-3*a*(A - B*x) + b*x*(3*A + B*x)))/(3*Sqrt[x]*(a + b*x))","A",1
788,1,46,116,0.0258035,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^(5/2),x]","-\frac{2 \sqrt{(a+b x)^2} (a (A+3 B x)+3 b x (A-B x))}{3 x^{3/2} (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*Sqrt[(a + b*x)^2]*(3*b*x*(A - B*x) + a*(A + 3*B*x)))/(3*x^(3/2)*(a + b*x))","A",1
789,1,48,118,0.0251373,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^{7/2}} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^(7/2),x]","-\frac{2 \sqrt{(a+b x)^2} (a (3 A+5 B x)+5 b x (A+3 B x))}{15 x^{5/2} (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*Sqrt[(a + b*x)^2]*(5*b*x*(A + 3*B*x) + a*(3*A + 5*B*x)))/(15*x^(5/2)*(a + b*x))","A",1
790,1,51,120,0.0253649,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^{9/2}} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^(9/2),x]","-\frac{2 \sqrt{(a+b x)^2} (3 a (5 A+7 B x)+7 b x (3 A+5 B x))}{105 x^{7/2} (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*Sqrt[(a + b*x)^2]*(7*b*x*(3*A + 5*B*x) + 3*a*(5*A + 7*B*x)))/(105*x^(7/2)*(a + b*x))","A",1
791,1,89,220,0.0417393,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 x^{9/2} \sqrt{(a+b x)^2} \left(1105 a^3 (11 A+9 B x)+2295 a^2 b x (13 A+11 B x)+1683 a b^2 x^2 (15 A+13 B x)+429 b^3 x^3 (17 A+15 B x)\right)}{109395 (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 b^3 B x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2}}{17 (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)}",1,"(2*x^(9/2)*Sqrt[(a + b*x)^2]*(1105*a^3*(11*A + 9*B*x) + 2295*a^2*b*x*(13*A + 11*B*x) + 1683*a*b^2*x^2*(15*A + 13*B*x) + 429*b^3*x^3*(17*A + 15*B*x)))/(109395*(a + b*x))","A",1
792,1,89,220,0.035982,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 x^{7/2} \sqrt{(a+b x)^2} \left(715 a^3 (9 A+7 B x)+1365 a^2 b x (11 A+9 B x)+945 a b^2 x^2 (13 A+11 B x)+231 b^3 x^3 (15 A+13 B x)\right)}{45045 (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 b^3 B x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}{15 (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)}",1,"(2*x^(7/2)*Sqrt[(a + b*x)^2]*(715*a^3*(9*A + 7*B*x) + 1365*a^2*b*x*(11*A + 9*B*x) + 945*a*b^2*x^2*(13*A + 11*B*x) + 231*b^3*x^3*(15*A + 13*B*x)))/(45045*(a + b*x))","A",1
793,1,89,220,0.0362609,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 x^{5/2} \sqrt{(a+b x)^2} \left(429 a^3 (7 A+5 B x)+715 a^2 b x (9 A+7 B x)+455 a b^2 x^2 (11 A+9 B x)+105 b^3 x^3 (13 A+11 B x)\right)}{15015 (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 b^3 B x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (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)}",1,"(2*x^(5/2)*Sqrt[(a + b*x)^2]*(429*a^3*(7*A + 5*B*x) + 715*a^2*b*x*(9*A + 7*B*x) + 455*a*b^2*x^2*(11*A + 9*B*x) + 105*b^3*x^3*(13*A + 11*B*x)))/(15015*(a + b*x))","A",1
794,1,89,220,0.0352296,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 x^{3/2} \sqrt{(a+b x)^2} \left(231 a^3 (5 A+3 B x)+297 a^2 b x (7 A+5 B x)+165 a b^2 x^2 (9 A+7 B x)+35 b^3 x^3 (11 A+9 B x)\right)}{3465 (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 b^3 B x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (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)}",1,"(2*x^(3/2)*Sqrt[(a + b*x)^2]*(231*a^3*(5*A + 3*B*x) + 297*a^2*b*x*(7*A + 5*B*x) + 165*a*b^2*x^2*(9*A + 7*B*x) + 35*b^3*x^3*(11*A + 9*B*x)))/(3465*(a + b*x))","A",1
795,1,88,218,0.0381294,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/Sqrt[x],x]","\frac{2 \sqrt{x} \sqrt{(a+b x)^2} \left(105 a^3 (3 A+B x)+63 a^2 b x (5 A+3 B x)+27 a b^2 x^2 (7 A+5 B x)+5 b^3 x^3 (9 A+7 B x)\right)}{315 (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 b^3 B x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{2 a^3 A \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"(2*Sqrt[x]*Sqrt[(a + b*x)^2]*(105*a^3*(3*A + B*x) + 63*a^2*b*x*(5*A + 3*B*x) + 27*a*b^2*x^2*(7*A + 5*B*x) + 5*b^3*x^3*(9*A + 7*B*x)))/(315*(a + b*x))","A",1
796,1,85,214,0.0321751,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-35 a^3 (A-B x)+35 a^2 b x (3 A+B x)+7 a b^2 x^2 (5 A+3 B x)+b^3 x^3 (7 A+5 B x)\right)}{35 \sqrt{x} (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 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 b^3 B x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}-\frac{2 a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x} (a+b x)}",1,"(2*Sqrt[(a + b*x)^2]*(-35*a^3*(A - B*x) + 35*a^2*b*x*(3*A + B*x) + 7*a*b^2*x^2*(5*A + 3*B*x) + b^3*x^3*(7*A + 5*B*x)))/(35*Sqrt[x]*(a + b*x))","A",1
797,1,84,216,0.0327178,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^(5/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(5 a^3 (A+3 B x)+45 a^2 b x (A-B x)-15 a b^2 x^2 (3 A+B x)-b^3 x^3 (5 A+3 B x)\right)}{15 x^{3/2} (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 b^3 B x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (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)}",1,"(-2*Sqrt[(a + b*x)^2]*(45*a^2*b*x*(A - B*x) - 15*a*b^2*x^2*(3*A + B*x) + 5*a^3*(A + 3*B*x) - b^3*x^3*(5*A + 3*B*x)))/(15*x^(3/2)*(a + b*x))","A",1
798,1,83,216,0.0339837,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^(7/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(a^3 (3 A+5 B x)+15 a^2 b x (A+3 B x)+45 a b^2 x^2 (A-B x)-5 b^3 x^3 (3 A+B x)\right)}{15 x^{5/2} (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^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{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^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^{5/2} (a+b x)}",1,"(-2*Sqrt[(a + b*x)^2]*(45*a*b^2*x^2*(A - B*x) - 5*b^3*x^3*(3*A + B*x) + 15*a^2*b*x*(A + 3*B*x) + a^3*(3*A + 5*B*x)))/(15*x^(5/2)*(a + b*x))","A",1
799,1,84,214,0.0360441,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^(9/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(a^3 (5 A+7 B x)+7 a^2 b x (3 A+5 B x)+35 a b^2 x^2 (A+3 B x)+35 b^3 x^3 (A-B x)\right)}{35 x^{7/2} (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^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^3 B \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{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)}",1,"(-2*Sqrt[(a + b*x)^2]*(35*b^3*x^3*(A - B*x) + 35*a*b^2*x^2*(A + 3*B*x) + 7*a^2*b*x*(3*A + 5*B*x) + a^3*(5*A + 7*B*x)))/(35*x^(7/2)*(a + b*x))","A",1
800,1,110,320,0.0897302,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(\frac{x^{9/2} \left(46189 a^5+188955 a^4 b x+319770 a^3 b^2 x^2+277134 a^2 b^3 x^3+122265 a b^4 x^4+21879 b^5 x^5\right) (7 A b-3 a B)}{138567}+B x^{9/2} (a+b x)^6\right)}{21 b (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{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{2 b^5 B x^{21/2} \sqrt{a^2+2 a b x+b^2 x^2}}{21 (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 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{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)}",1,"(2*Sqrt[(a + b*x)^2]*(B*x^(9/2)*(a + b*x)^6 + ((7*A*b - 3*a*B)*x^(9/2)*(46189*a^5 + 188955*a^4*b*x + 319770*a^3*b^2*x^2 + 277134*a^2*b^3*x^3 + 122265*a*b^4*x^4 + 21879*b^5*x^5))/138567))/(21*b*(a + b*x))","A",1
801,1,110,320,0.0817498,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(\frac{x^{7/2} \left(21879 a^5+85085 a^4 b x+139230 a^3 b^2 x^2+117810 a^2 b^3 x^3+51051 a b^4 x^4+9009 b^5 x^5\right) (19 A b-7 a B)}{153153}+B x^{7/2} (a+b x)^6\right)}{19 b (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{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{2 b^5 B x^{19/2} \sqrt{a^2+2 a b x+b^2 x^2}}{19 (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 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{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)}",1,"(2*Sqrt[(a + b*x)^2]*(B*x^(7/2)*(a + b*x)^6 + ((19*A*b - 7*a*B)*x^(7/2)*(21879*a^5 + 85085*a^4*b*x + 139230*a^3*b^2*x^2 + 117810*a^2*b^3*x^3 + 51051*a*b^4*x^4 + 9009*b^5*x^5))/153153))/(19*b*(a + b*x))","A",1
802,1,127,320,0.0506812,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 x^{5/2} \sqrt{(a+b x)^2} \left(21879 a^5 (7 A+5 B x)+60775 a^4 b x (9 A+7 B x)+77350 a^3 b^2 x^2 (11 A+9 B x)+53550 a^2 b^3 x^3 (13 A+11 B x)+19635 a b^4 x^4 (15 A+13 B x)+3003 b^5 x^5 (17 A+15 B x)\right)}{765765 (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{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{2 b^5 B x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2}}{17 (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 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{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)}",1,"(2*x^(5/2)*Sqrt[(a + b*x)^2]*(21879*a^5*(7*A + 5*B*x) + 60775*a^4*b*x*(9*A + 7*B*x) + 77350*a^3*b^2*x^2*(11*A + 9*B*x) + 53550*a^2*b^3*x^3*(13*A + 11*B*x) + 19635*a*b^4*x^4*(15*A + 13*B*x) + 3003*b^5*x^5*(17*A + 15*B*x)))/(765765*(a + b*x))","A",1
803,1,127,320,0.0490721,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 x^{3/2} \sqrt{(a+b x)^2} \left(3003 a^5 (5 A+3 B x)+6435 a^4 b x (7 A+5 B x)+7150 a^3 b^2 x^2 (9 A+7 B x)+4550 a^2 b^3 x^3 (11 A+9 B x)+1575 a b^4 x^4 (13 A+11 B x)+231 b^5 x^5 (15 A+13 B x)\right)}{45045 (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{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{2 b^5 B x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}{15 (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 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{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)}",1,"(2*x^(3/2)*Sqrt[(a + b*x)^2]*(3003*a^5*(5*A + 3*B*x) + 6435*a^4*b*x*(7*A + 5*B*x) + 7150*a^3*b^2*x^2*(9*A + 7*B*x) + 4550*a^2*b^3*x^3*(11*A + 9*B*x) + 1575*a*b^4*x^4*(13*A + 11*B*x) + 231*b^5*x^5*(15*A + 13*B*x)))/(45045*(a + b*x))","A",1
804,1,126,316,0.0567665,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/Sqrt[x],x]","\frac{2 \sqrt{x} \sqrt{(a+b x)^2} \left(3003 a^5 (3 A+B x)+3003 a^4 b x (5 A+3 B x)+2574 a^3 b^2 x^2 (7 A+5 B x)+1430 a^2 b^3 x^3 (9 A+7 B x)+455 a b^4 x^4 (11 A+9 B x)+63 b^5 x^5 (13 A+11 B x)\right)}{9009 (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 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{2 b^5 B x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (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 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^3 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}",1,"(2*Sqrt[x]*Sqrt[(a + b*x)^2]*(3003*a^5*(3*A + B*x) + 3003*a^4*b*x*(5*A + 3*B*x) + 2574*a^3*b^2*x^2*(7*A + 5*B*x) + 1430*a^2*b^3*x^3*(9*A + 7*B*x) + 455*a*b^4*x^4*(11*A + 9*B*x) + 63*b^5*x^5*(13*A + 11*B*x)))/(9009*(a + b*x))","A",1
805,1,124,314,0.0442871,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-693 a^5 (A-B x)+1155 a^4 b x (3 A+B x)+462 a^3 b^2 x^2 (5 A+3 B x)+198 a^2 b^3 x^3 (7 A+5 B x)+55 a b^4 x^4 (9 A+7 B x)+7 b^5 x^5 (11 A+9 B x)\right)}{693 \sqrt{x} (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{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{2 b^5 B x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (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 a^4 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 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)}",1,"(2*Sqrt[(a + b*x)^2]*(-693*a^5*(A - B*x) + 1155*a^4*b*x*(3*A + B*x) + 462*a^3*b^2*x^2*(5*A + 3*B*x) + 198*a^2*b^3*x^3*(7*A + 5*B*x) + 55*a*b^4*x^4*(9*A + 7*B*x) + 7*b^5*x^5*(11*A + 9*B*x)))/(693*Sqrt[x]*(a + b*x))","A",1
806,1,122,314,0.0436347,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^(5/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(21 a^5 (A+3 B x)+315 a^4 b x (A-B x)-210 a^3 b^2 x^2 (3 A+B x)-42 a^2 b^3 x^3 (5 A+3 B x)-9 a b^4 x^4 (7 A+5 B x)-b^5 x^5 (9 A+7 B x)\right)}{63 x^{3/2} (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 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 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^5 B x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (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 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}",1,"(-2*Sqrt[(a + b*x)^2]*(315*a^4*b*x*(A - B*x) - 210*a^3*b^2*x^2*(3*A + B*x) + 21*a^5*(A + 3*B*x) - 42*a^2*b^3*x^3*(5*A + 3*B*x) - 9*a*b^4*x^4*(7*A + 5*B*x) - b^5*x^5*(9*A + 7*B*x)))/(63*x^(3/2)*(a + b*x))","A",1
807,1,122,316,0.0449974,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^(7/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(7 a^5 (3 A+5 B x)+175 a^4 b x (A+3 B x)+1050 a^3 b^2 x^2 (A-B x)-350 a^2 b^3 x^3 (3 A+B x)-35 a b^4 x^4 (5 A+3 B x)-3 b^5 x^5 (7 A+5 B x)\right)}{105 x^{5/2} (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{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{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^5 B x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (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 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)}",1,"(-2*Sqrt[(a + b*x)^2]*(1050*a^3*b^2*x^2*(A - B*x) - 350*a^2*b^3*x^3*(3*A + B*x) + 175*a^4*b*x*(A + 3*B*x) - 35*a*b^4*x^4*(5*A + 3*B*x) + 7*a^5*(3*A + 5*B*x) - 3*b^5*x^5*(7*A + 5*B*x)))/(105*x^(5/2)*(a + b*x))","A",1
808,1,122,316,0.0457183,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^(9/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(3 a^5 (5 A+7 B x)+35 a^4 b x (3 A+5 B x)+350 a^3 b^2 x^2 (A+3 B x)+1050 a^2 b^3 x^3 (A-B x)-175 a b^4 x^4 (3 A+B x)-7 b^5 x^5 (5 A+3 B x)\right)}{105 x^{7/2} (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{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{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^5 B x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (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 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)}",1,"(-2*Sqrt[(a + b*x)^2]*(1050*a^2*b^3*x^3*(A - B*x) - 175*a*b^4*x^4*(3*A + B*x) + 350*a^3*b^2*x^2*(A + 3*B*x) - 7*b^5*x^5*(5*A + 3*B*x) + 35*a^4*b*x*(3*A + 5*B*x) + 3*a^5*(5*A + 7*B*x)))/(105*x^(7/2)*(a + b*x))","A",1
809,1,139,286,0.0803718,"\int \frac{x^{7/2} (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(x^(7/2)*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \left(\sqrt{b} \sqrt{x} \left(315 a^4 B-105 a^3 b (3 A+B x)+21 a^2 b^2 x (5 A+3 B x)-9 a b^3 x^2 (7 A+5 B x)+5 b^4 x^3 (9 A+7 B x)\right)-315 a^{7/2} (a B-A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{315 b^{11/2} \sqrt{(a+b 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^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 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 B x^{9/2} (a+b x)}{9 b \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 a^3 \sqrt{x} (a+b x) (A b-a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(a + b*x)*(Sqrt[b]*Sqrt[x]*(315*a^4*B - 105*a^3*b*(3*A + B*x) + 21*a^2*b^2*x*(5*A + 3*B*x) - 9*a*b^3*x^2*(7*A + 5*B*x) + 5*b^4*x^3*(9*A + 7*B*x)) - 315*a^(7/2)*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(315*b^(11/2)*Sqrt[(a + b*x)^2])","A",1
810,1,120,238,0.0625855,"\int \frac{x^{5/2} (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(x^(5/2)*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \left(105 a^{5/2} (a B-A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{b} \sqrt{x} \left(-105 a^3 B+35 a^2 b (3 A+B x)-7 a b^2 x (5 A+3 B x)+3 b^3 x^2 (7 A+5 B x)\right)\right)}{105 b^{9/2} \sqrt{(a+b 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^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 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 B x^{7/2} (a+b x)}{7 b \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}}",1,"(2*(a + b*x)*(Sqrt[b]*Sqrt[x]*(-105*a^3*B + 35*a^2*b*(3*A + B*x) - 7*a*b^2*x*(5*A + 3*B*x) + 3*b^3*x^2*(7*A + 5*B*x)) + 105*a^(5/2)*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(105*b^(9/2)*Sqrt[(a + b*x)^2])","A",1
811,1,100,190,0.0523263,"\int \frac{x^{3/2} (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(x^(3/2)*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \left(\sqrt{b} \sqrt{x} \left(15 a^2 B-5 a b (3 A+B x)+b^2 x (5 A+3 B x)\right)-15 a^{3/2} (a B-A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{15 b^{7/2} \sqrt{(a+b 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 B x^{5/2} (a+b x)}{5 b \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}}",1,"(2*(a + b*x)*(Sqrt[b]*Sqrt[x]*(15*a^2*B - 5*a*b*(3*A + B*x) + b^2*x*(5*A + 3*B*x)) - 15*a^(3/2)*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(15*b^(7/2)*Sqrt[(a + b*x)^2])","A",1
812,1,82,144,0.0398697,"\int \frac{\sqrt{x} (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(Sqrt[x]*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \left(\sqrt{b} \sqrt{x} (-3 a B+3 A b+b B x)+3 \sqrt{a} (a B-A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{3 b^{5/2} \sqrt{(a+b 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*x)*(Sqrt[b]*Sqrt[x]*(3*A*b - 3*a*B + b*B*x) + 3*Sqrt[a]*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(3*b^(5/2)*Sqrt[(a + b*x)^2])","A",1
813,1,72,99,0.0364825,"\int \frac{A+B x}{\sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 (a+b x) \left((A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{a} \sqrt{b} B \sqrt{x}\right)}{\sqrt{a} b^{3/2} \sqrt{(a+b 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*(a + b*x)*(Sqrt[a]*Sqrt[b]*B*Sqrt[x] + (A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(Sqrt[a]*b^(3/2)*Sqrt[(a + b*x)^2])","A",1
814,1,79,99,0.0307644,"\int \frac{A+B x}{x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 (a+b x) \left(-\sqrt{x} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-\sqrt{a} A \sqrt{b}\right)}{a^{3/2} \sqrt{b} \sqrt{x} \sqrt{(a+b 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}}",1,"(2*(a + b*x)*(-(Sqrt[a]*A*Sqrt[b]) - (A*b - a*B)*Sqrt[x]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(a^(3/2)*Sqrt[b]*Sqrt[x]*Sqrt[(a + b*x)^2])","A",1
815,1,59,144,0.0207354,"\int \frac{A+B x}{x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 (a+b x) \left(\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x}{a}\right) (3 a B x-3 A b x)+a A\right)}{3 a^2 x^{3/2} \sqrt{(a+b 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 A (a+b x)}{3 a x^{3/2} \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}}",1,"(-2*(a + b*x)*(a*A + (-3*A*b*x + 3*a*B*x)*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x)/a)]))/(3*a^2*x^(3/2)*Sqrt[(a + b*x)^2])","C",1
816,1,60,190,0.0231353,"\int \frac{A+B x}{x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 (a+b x) \left(\, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b x}{a}\right) (5 a B x-5 A b x)+3 a A\right)}{15 a^2 x^{5/2} \sqrt{(a+b 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 A (a+b x)}{5 a x^{5/2} \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 b (a+b x) (A b-a B)}{a^3 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*(a + b*x)*(3*a*A + (-5*A*b*x + 5*a*B*x)*Hypergeometric2F1[-3/2, 1, -1/2, -((b*x)/a)]))/(15*a^2*x^(5/2)*Sqrt[(a + b*x)^2])","C",1
817,1,60,238,0.0219363,"\int \frac{A+B x}{x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 (a+b x) \left(\, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{b x}{a}\right) (7 a B x-7 A b x)+5 a A\right)}{35 a^2 x^{7/2} \sqrt{(a+b 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 A (a+b x)}{7 a x^{7/2} \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 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}}",1,"(-2*(a + b*x)*(5*a*A + (-7*A*b*x + 7*a*B*x)*Hypergeometric2F1[-5/2, 1, -3/2, -((b*x)/a)]))/(35*a^2*x^(7/2)*Sqrt[(a + b*x)^2])","C",1
818,1,79,302,0.0337896,"\int \frac{x^{7/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^{9/2} \left(9 a^2 (A b-a B)+(a+b x)^2 (9 a B-5 A b) \, _2F_1\left(2,\frac{9}{2};\frac{11}{2};-\frac{b x}{a}\right)\right)}{18 a^3 b (a+b x) \sqrt{(a+b 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 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 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 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 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,"(x^(9/2)*(9*a^2*(A*b - a*B) + (-5*A*b + 9*a*B)*(a + b*x)^2*Hypergeometric2F1[2, 9/2, 11/2, -((b*x)/a)]))/(18*a^3*b*(a + b*x)*Sqrt[(a + b*x)^2])","C",1
819,1,79,255,0.0300935,"\int \frac{x^{5/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^{7/2} \left(7 a^2 (A b-a B)+(a+b x)^2 (7 a B-3 A b) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{b x}{a}\right)\right)}{14 a^3 b (a+b x) \sqrt{(a+b 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 \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{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 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}}",1,"(x^(7/2)*(7*a^2*(A*b - a*B) + (-3*A*b + 7*a*B)*(a + b*x)^2*Hypergeometric2F1[2, 7/2, 9/2, -((b*x)/a)]))/(14*a^3*b*(a + b*x)*Sqrt[(a + b*x)^2])","C",1
820,1,79,206,0.0320685,"\int \frac{x^{3/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^{5/2} \left(5 a^2 (A b-a B)+(a+b x)^2 (5 a B-A b) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};-\frac{b x}{a}\right)\right)}{10 a^3 b (a+b x) \sqrt{(a+b 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 (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{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}}",1,"(x^(5/2)*(5*a^2*(A*b - a*B) + (-(A*b) + 5*a*B)*(a + b*x)^2*Hypergeometric2F1[2, 5/2, 7/2, -((b*x)/a)]))/(10*a^3*b*(a + b*x)*Sqrt[(a + b*x)^2])","C",1
821,1,105,158,0.0497662,"\int \frac{\sqrt{x} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\sqrt{a} \sqrt{b} \sqrt{x} \left(-3 a^2 B-a b (A+5 B x)+A b^2 x\right)+(a+b x)^2 (3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{3/2} b^{5/2} (a+b x) \sqrt{(a+b 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{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{(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,"(Sqrt[a]*Sqrt[b]*Sqrt[x]*(-3*a^2*B + A*b^2*x - a*b*(A + 5*B*x)) + (A*b + 3*a*B)*(a + b*x)^2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(3/2)*b^(5/2)*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
822,1,106,158,0.0492454,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{\sqrt{a} \sqrt{b} \sqrt{x} \left(a^2 (-B)+a b (5 A+B x)+3 A b^2 x\right)+(a+b x)^2 (a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} b^{3/2} (a+b x) \sqrt{(a+b 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,"(Sqrt[a]*Sqrt[b]*Sqrt[x]*(-(a^2*B) + 3*A*b^2*x + a*b*(5*A + B*x)) + (3*A*b + a*B)*(a + b*x)^2*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(5/2)*b^(3/2)*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
823,1,77,209,0.0323837,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{a^2 (A b-a B)+(a+b x)^2 (a B-5 A b) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{b x}{a}\right)}{2 a^3 b \sqrt{x} (a+b x) \sqrt{(a+b 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{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{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}}",1,"(a^2*(A*b - a*B) + (-5*A*b + a*B)*(a + b*x)^2*Hypergeometric2F1[-1/2, 2, 1/2, -((b*x)/a)])/(2*a^3*b*Sqrt[x]*(a + b*x)*Sqrt[(a + b*x)^2])","C",1
824,1,79,255,0.0308871,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{3 a^2 (A b-a B)+(a+b x)^2 (3 a B-7 A b) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\frac{b x}{a}\right)}{6 a^3 b x^{3/2} (a+b x) \sqrt{(a+b 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}}",1,"(3*a^2*(A*b - a*B) + (-7*A*b + 3*a*B)*(a + b*x)^2*Hypergeometric2F1[-3/2, 2, -1/2, -((b*x)/a)])/(6*a^3*b*x^(3/2)*(a + b*x)*Sqrt[(a + b*x)^2])","C",1
825,1,79,302,0.0312517,"\int \frac{A+B x}{x^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{5 a^2 (A b-a B)+(a+b x)^2 (5 a B-9 A b) \, _2F_1\left(-\frac{5}{2},2;-\frac{3}{2};-\frac{b x}{a}\right)}{10 a^3 b x^{5/2} (a+b x) \sqrt{(a+b 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}}",1,"(5*a^2*(A*b - a*B) + (-9*A*b + 5*a*B)*(a + b*x)^2*Hypergeometric2F1[-5/2, 2, -3/2, -((b*x)/a)])/(10*a^3*b*x^(5/2)*(a + b*x)*Sqrt[(a + b*x)^2])","C",1
826,1,80,404,0.0379978,"\int \frac{x^{11/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(x^(11/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{13/2} \left(13 a^4 (A b-a B)-(a+b x)^4 (5 A b-13 a B) \, _2F_1\left(4,\frac{13}{2};\frac{15}{2};-\frac{b x}{a}\right)\right)}{52 a^5 b (a+b x)^3 \sqrt{(a+b 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{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{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 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{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{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{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,"(x^(13/2)*(13*a^4*(A*b - a*B) - (5*A*b - 13*a*B)*(a + b*x)^4*Hypergeometric2F1[4, 13/2, 15/2, -((b*x)/a)]))/(52*a^5*b*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
827,1,80,357,0.0310443,"\int \frac{x^{9/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(x^(9/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{11/2} \left(11 a^4 (A b-a B)-(a+b x)^4 (3 A b-11 a B) \, _2F_1\left(4,\frac{11}{2};\frac{13}{2};-\frac{b x}{a}\right)\right)}{44 a^5 b (a+b x)^3 \sqrt{(a+b 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{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{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{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{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{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}}",1,"(x^(11/2)*(11*a^4*(A*b - a*B) - (3*A*b - 11*a*B)*(a + b*x)^4*Hypergeometric2F1[4, 11/2, 13/2, -((b*x)/a)]))/(44*a^5*b*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
828,1,79,306,0.0326282,"\int \frac{x^{7/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{9/2} \left(9 a^4 (A b-a B)-(a+b x)^4 (A b-9 a B) \, _2F_1\left(4,\frac{9}{2};\frac{11}{2};-\frac{b x}{a}\right)\right)}{36 a^5 b (a+b x)^3 \sqrt{(a+b 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{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{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 x^{3/2} (A b-9 a B)}{192 a b^4 \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}}",1,"(x^(9/2)*(9*a^4*(A*b - a*B) - (A*b - 9*a*B)*(a + b*x)^4*Hypergeometric2F1[4, 9/2, 11/2, -((b*x)/a)]))/(36*a^5*b*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
829,1,146,258,0.0785521,"\int \frac{x^{5/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{15 (a+b x)^4 (7 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-\sqrt{a} \sqrt{b} \sqrt{x} \left(105 a^4 B+5 a^3 b (3 A+77 B x)+a^2 b^2 x (55 A+511 B x)+a b^3 x^2 (73 A+279 B x)-15 A b^4 x^3\right)}{192 a^{3/2} b^{9/2} (a+b x)^3 \sqrt{(a+b 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 \sqrt{x} (7 a B+A b)}{64 a b^4 \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 (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,"(-(Sqrt[a]*Sqrt[b]*Sqrt[x]*(105*a^4*B - 15*A*b^4*x^3 + 5*a^3*b*(3*A + 77*B*x) + a*b^3*x^2*(73*A + 279*B*x) + a^2*b^2*x*(55*A + 511*B*x))) + 15*(A*b + 7*a*B)*(a + b*x)^4*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(192*a^(3/2)*b^(9/2)*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
830,1,79,262,0.032412,"\int \frac{x^{3/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{5/2} \left(5 a^4 (A b-a B)+(a+b x)^4 (5 a B+3 A b) \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};-\frac{b x}{a}\right)\right)}{20 a^5 b (a+b x)^3 \sqrt{(a+b 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,"(x^(5/2)*(5*a^4*(A*b - a*B) + (3*A*b + 5*a*B)*(a + b*x)^4*Hypergeometric2F1[5/2, 4, 7/2, -((b*x)/a)]))/(20*a^5*b*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
831,1,79,262,0.032781,"\int \frac{\sqrt{x} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{3/2} \left(3 a^4 (A b-a B)+(a+b x)^4 (3 a B+5 A b) \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};-\frac{b x}{a}\right)\right)}{12 a^5 b (a+b x)^3 \sqrt{(a+b 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{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{(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{\sqrt{x} (3 a B+5 A b)}{64 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(x^(3/2)*(3*a^4*(A*b - a*B) + (5*A*b + 3*a*B)*(a + b*x)^4*Hypergeometric2F1[3/2, 4, 5/2, -((b*x)/a)]))/(12*a^5*b*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
832,1,77,258,0.034615,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{\sqrt{x} \left(a^4 (A b-a B)+(a+b x)^4 (a B+7 A b) \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};-\frac{b x}{a}\right)\right)}{4 a^5 b (a+b x)^3 \sqrt{(a+b 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{\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{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}}",1,"(Sqrt[x]*(a^4*(A*b - a*B) + (7*A*b + a*B)*(a + b*x)^4*Hypergeometric2F1[1/2, 4, 3/2, -((b*x)/a)]))/(4*a^5*b*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
833,1,79,311,0.034097,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{a^4 (A b-a B)-(a+b x)^4 (9 A b-a B) \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};-\frac{b x}{a}\right)}{4 a^5 b \sqrt{x} (a+b x)^3 \sqrt{(a+b 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{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{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}}",1,"(a^4*(A*b - a*B) - (9*A*b - a*B)*(a + b*x)^4*Hypergeometric2F1[-1/2, 4, 1/2, -((b*x)/a)])/(4*a^5*b*Sqrt[x]*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
834,1,80,357,0.0342263,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{3 a^4 (A b-a B)-(a+b x)^4 (11 A b-3 a B) \, _2F_1\left(-\frac{3}{2},4;-\frac{1}{2};-\frac{b x}{a}\right)}{12 a^5 b x^{3/2} (a+b x)^3 \sqrt{(a+b 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{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{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}}",1,"(3*a^4*(A*b - a*B) - (11*A*b - 3*a*B)*(a + b*x)^4*Hypergeometric2F1[-3/2, 4, -1/2, -((b*x)/a)])/(12*a^5*b*x^(3/2)*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
835,1,80,404,0.0340342,"\int \frac{A+B x}{x^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{5 a^4 (A b-a B)-(a+b x)^4 (13 A b-5 a B) \, _2F_1\left(-\frac{5}{2},4;-\frac{3}{2};-\frac{b x}{a}\right)}{20 a^5 b x^{5/2} (a+b x)^3 \sqrt{(a+b 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{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{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{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}}",1,"(5*a^4*(A*b - a*B) - (13*A*b - 5*a*B)*(a + b*x)^4*Hypergeometric2F1[-5/2, 4, -3/2, -((b*x)/a)])/(20*a^5*b*x^(5/2)*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
836,1,135,179,0.1975095,"\int x^m (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[x^m*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x^{m+1} \left(\left(\frac{a^6}{m+1}+\frac{6 a^5 b x}{m+2}+\frac{15 a^4 b^2 x^2}{m+3}+\frac{20 a^3 b^3 x^3}{m+4}+\frac{15 a^2 b^4 x^4}{m+5}+\frac{6 a b^5 x^5}{m+6}+\frac{b^6 x^6}{m+7}\right) (A b (m+8)-a B (m+1))+B (a+b x)^7\right)}{b (m+8)}","\frac{a^6 A x^{m+1}}{m+1}+\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{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{b^5 x^{m+7} (6 a B+A b)}{m+7}+\frac{3 a b^4 x^{m+6} (5 a B+2 A b)}{m+6}+\frac{b^6 B x^{m+8}}{m+8}",1,"(x^(1 + m)*(B*(a + b*x)^7 + (-(a*B*(1 + m)) + A*b*(8 + m))*(a^6/(1 + m) + (6*a^5*b*x)/(2 + m) + (15*a^4*b^2*x^2)/(3 + m) + (20*a^3*b^3*x^3)/(4 + m) + (15*a^2*b^4*x^4)/(5 + m) + (6*a*b^5*x^5)/(6 + m) + (b^6*x^6)/(7 + m))))/(b*(8 + m))","A",1
837,1,103,125,0.132731,"\int x^m (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[x^m*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{x^{m+1} \left(\left(\frac{a^4}{m+1}+\frac{4 a^3 b x}{m+2}+\frac{6 a^2 b^2 x^2}{m+3}+\frac{4 a b^3 x^3}{m+4}+\frac{b^4 x^4}{m+5}\right) (A b (m+6)-a B (m+1))+B (a+b x)^5\right)}{b (m+6)}","\frac{a^4 A x^{m+1}}{m+1}+\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{b^3 x^{m+5} (4 a B+A b)}{m+5}+\frac{2 a b^2 x^{m+4} (3 a B+2 A b)}{m+4}+\frac{b^4 B x^{m+6}}{m+6}",1,"(x^(1 + m)*(B*(a + b*x)^5 + (-(a*B*(1 + m)) + A*b*(6 + m))*(a^4/(1 + m) + (4*a^3*b*x)/(2 + m) + (6*a^2*b^2*x^2)/(3 + m) + (4*a*b^3*x^3)/(4 + m) + (b^4*x^4)/(5 + m))))/(b*(6 + m))","A",1
838,1,71,71,0.0893925,"\int x^m (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[x^m*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{x^{m+1} \left(\left(\frac{a^2}{m+1}+\frac{2 a b x}{m+2}+\frac{b^2 x^2}{m+3}\right) (A b (m+4)-a B (m+1))+B (a+b x)^3\right)}{b (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,"(x^(1 + m)*(B*(a + b*x)^3 + (-(a*B*(1 + m)) + A*b*(4 + m))*(a^2/(1 + m) + (2*a*b*x)/(2 + m) + (b^2*x^2)/(3 + m))))/(b*(4 + m))","A",1
839,1,63,73,0.0387812,"\int \frac{x^m (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(x^m*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{x^{m+1} \left(\frac{(a B (m+1)-A b m) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{m+1}+\frac{a (A b-a B)}{a+b x}\right)}{a^2 b}","\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,"(x^(1 + m)*((a*(A*b - a*B))/(a + b*x) + ((-(A*b*m) + a*B*(1 + m))*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)])/(1 + m)))/(a^2*b)","A",1
840,1,71,81,0.034467,"\int \frac{x^m (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(x^m*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{x^{m+1} \left(\frac{a^3 (A b-a B)}{(a+b x)^3}-\frac{(A b (m-2)-a B (m+1)) \, _2F_1\left(3,m+1;m+2;-\frac{b x}{a}\right)}{m+1}\right)}{3 a^4 b}","\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,"(x^(1 + m)*((a^3*(A*b - a*B))/(a + b*x)^3 - ((A*b*(-2 + m) - a*B*(1 + m))*Hypergeometric2F1[3, 1 + m, 2 + m, -((b*x)/a)])/(1 + m)))/(3*a^4*b)","A",1
841,1,119,143,0.051552,"\int x^m (1+x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^m*(1 + x)*(1 + 2*x + x^2)^5,x]","x^{m+1} \left(\frac{x^{11}}{m+12}+\frac{11 x^{10}}{m+11}+\frac{55 x^9}{m+10}+\frac{165 x^8}{m+9}+\frac{330 x^7}{m+8}+\frac{462 x^6}{m+7}+\frac{462 x^5}{m+6}+\frac{330 x^4}{m+5}+\frac{165 x^3}{m+4}+\frac{55 x^2}{m+3}+\frac{11 x}{m+2}+\frac{1}{m+1}\right)","\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)^(-1) + (11*x)/(2 + m) + (55*x^2)/(3 + m) + (165*x^3)/(4 + m) + (330*x^4)/(5 + m) + (462*x^5)/(6 + m) + (462*x^6)/(7 + m) + (330*x^7)/(8 + m) + (165*x^8)/(9 + m) + (55*x^9)/(10 + m) + (11*x^10)/(11 + m) + x^11/(12 + m))","A",1
842,1,135,209,0.6632618,"\int x^m (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Integrate[x^m*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{x^{m+1} \left(\left(\frac{x^{10}}{m+11}+\frac{10 x^9}{m+10}+\frac{45 x^8}{m+9}+\frac{120 x^7}{m+8}+\frac{210 x^6}{m+7}+\frac{252 x^5}{m+6}+\frac{210 x^4}{m+5}+\frac{120 x^3}{m+4}+\frac{45 x^2}{m+3}+\frac{10 x}{m+2}+\frac{1}{m+1}\right) (d (m+12)-e (m+1))+e (x+1)^{11}\right)}{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,"(x^(1 + m)*(e*(1 + x)^11 + (-(e*(1 + m)) + d*(12 + m))*((1 + m)^(-1) + (10*x)/(2 + m) + (45*x^2)/(3 + m) + (120*x^3)/(4 + m) + (210*x^4)/(5 + m) + (252*x^5)/(6 + m) + (210*x^6)/(7 + m) + (120*x^7)/(8 + m) + (45*x^8)/(9 + m) + (10*x^9)/(10 + m) + x^10/(11 + m))))/(12 + m)","A",1
843,1,47,47,0.0105612,"\int x^3 (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[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",1
844,1,47,47,0.0149083,"\int x^2 (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[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",1
845,1,41,47,0.0139322,"\int x (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[x*(A + B*x)*(a + b*x + c*x^2),x]","\frac{1}{60} x^2 \left(20 x (a B+A b)+30 a A+15 x^2 (A c+b B)+12 B c x^3\right)","\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,"(x^2*(30*a*A + 20*(A*b + a*B)*x + 15*(b*B + A*c)*x^2 + 12*B*c*x^3))/60","A",1
846,1,42,42,0.0125153,"\int (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[(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",1
847,1,38,38,0.0106927,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x} \, dx","Integrate[((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",1
848,1,36,36,0.0167218,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^2} \, dx","Integrate[((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",1
849,1,37,36,0.0196528,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^3} \, dx","Integrate[((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,"-1/2*(a*A)/x^2 + (-(A*b) - a*B)/x + B*c*x + (b*B + A*c)*Log[x]","A",1
850,1,41,41,0.0266041,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^4} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/x^4,x]","B c \log (x)-\frac{a (2 A+3 B x)+3 x (A b+2 A c x+2 b B x)}{6 x^3}","-\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,"-1/6*(a*(2*A + 3*B*x) + 3*x*(A*b + 2*b*B*x + 2*A*c*x))/x^3 + B*c*Log[x]","A",1
851,1,42,45,0.0153776,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^5} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/x^5,x]","-\frac{a (3 A+4 B x)+2 x (A (2 b+3 c x)+3 B x (b+2 c x))}{12 x^4}","-\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,"-1/12*(a*(3*A + 4*B*x) + 2*x*(3*B*x*(b + 2*c*x) + A*(2*b + 3*c*x)))/x^4","A",1
852,1,44,47,0.0153747,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^6} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/x^6,x]","-\frac{3 a (4 A+5 B x)+5 x \left(3 A b+4 A c x+4 b B x+6 B c x^2\right)}{60 x^5}","-\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,"-1/60*(3*a*(4*A + 5*B*x) + 5*x*(3*A*b + 4*b*B*x + 4*A*c*x + 6*B*c*x^2))/x^5","A",1
853,1,45,47,0.0155788,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^7} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/x^7,x]","-\frac{2 a (5 A+6 B x)+x (3 A (4 b+5 c x)+5 B x (3 b+4 c x))}{60 x^6}","-\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,"-1/60*(2*a*(5*A + 6*B*x) + x*(5*B*x*(3*b + 4*c*x) + 3*A*(4*b + 5*c*x)))/x^6","A",1
854,1,46,47,0.0177581,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^8} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/x^8,x]","-\frac{10 a (6 A+7 B x)+7 x (2 A (5 b+6 c x)+3 B x (4 b+5 c x))}{420 x^7}","-\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,"-1/420*(10*a*(6*A + 7*B*x) + 7*x*(3*B*x*(4*b + 5*c*x) + 2*A*(5*b + 6*c*x)))/x^7","A",1
855,1,101,101,0.0268624,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[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(2 a A c+2 a b B+A b^2\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 + ((A*b^2 + 2*a*b*B + 2*a*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",1
856,1,101,101,0.0215618,"\int x (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[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(2 a A c+2 a b B+A b^2\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 + ((A*b^2 + 2*a*b*B + 2*a*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",1
857,1,96,96,0.0200616,"\int (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[(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(2 a A c+2 a b B+A b^2\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 + ((A*b^2 + 2*a*b*B + 2*a*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",1
858,1,92,92,0.0339321,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x} \, dx","Integrate[((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(2 a A c+2 a b B+A b^2\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 + ((A*b^2 + 2*a*b*B + 2*a*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",1
859,1,87,90,0.060322,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^2} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^2,x]","-\frac{a^2 A}{x}+a x (2 A c+2 b B+B c x)+a \log (x) (a B+2 A b)+\frac{1}{12} x \left(4 A \left(3 b^2+3 b c x+c^2 x^2\right)+B x \left(6 b^2+8 b c x+3 c^2 x^2\right)\right)","-\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) + a*x*(2*b*B + 2*A*c + B*c*x) + (x*(4*A*(3*b^2 + 3*b*c*x + c^2*x^2) + B*x*(6*b^2 + 8*b*c*x + 3*c^2*x^2)))/12 + a*(2*A*b + a*B)*Log[x]","A",1
860,1,86,90,0.0503297,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^3} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^3,x]","-\frac{a^2 (A+2 B x)}{2 x^2}+A \log (x) \left(2 a c+b^2\right)+a \left(2 B c x-\frac{2 A b}{x}\right)+2 a b B \log (x)+b c x (2 A+B x)+\frac{1}{6} c^2 x^2 (3 A+2 B x)+b^2 B 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",1,"b^2*B*x + b*c*x*(2*A + B*x) - (a^2*(A + 2*B*x))/(2*x^2) + (c^2*x^2*(3*A + 2*B*x))/6 + a*((-2*A*b)/x + 2*B*c*x) + 2*a*b*B*Log[x] + A*(b^2 + 2*a*c)*Log[x]","A",1
861,1,90,90,0.049702,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^4} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^4,x]","-\frac{a^2 (2 A+3 B x)}{6 x^3}+\log (x) \left(2 a B c+2 A b c+b^2 B\right)-\frac{a (A b+2 A c x+2 b B x)}{x^2}-\frac{A b^2}{x}+A c^2 x+2 b B c x+\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*b^2)/x) + 2*b*B*c*x + A*c^2*x + (B*c^2*x^2)/2 - (a^2*(2*A + 3*B*x))/(6*x^3) - (a*(A*b + 2*b*B*x + 2*A*c*x))/x^2 + (b^2*B + 2*A*b*c + 2*a*B*c)*Log[x]","A",1
862,1,92,90,0.0490361,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^5} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^5,x]","-\frac{a^2 (3 A+4 B x)+4 a x (A (2 b+3 c x)+3 B x (b+2 c x))+6 x^2 \left(A b (b+4 c x)+2 B x \left(b^2-c^2 x^2\right)\right)-12 c x^4 \log (x) (A c+2 b B)}{12 x^4}","-\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,"-1/12*(a^2*(3*A + 4*B*x) + 4*a*x*(3*B*x*(b + 2*c*x) + A*(2*b + 3*c*x)) + 6*x^2*(A*b*(b + 4*c*x) + 2*B*x*(b^2 - c^2*x^2)) - 12*c*(2*b*B + A*c)*x^4*Log[x])/x^4","A",1
863,1,92,95,0.0565055,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^6} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^6,x]","B c^2 \log (x)-\frac{3 a^2 (4 A+5 B x)+10 a x \left(3 A b+4 A c x+4 b B x+6 B c x^2\right)+10 x^2 \left(2 A \left(b^2+3 b c x+3 c^2 x^2\right)+3 b B x (b+4 c x)\right)}{60 x^5}","-\frac{a^2 A}{5 x^5}-\frac{A \left(2 a c+b^2\right)+2 a b B}{3 x^3}-\frac{2 a B c+2 A b c+b^2 B}{2 x^2}-\frac{a (a B+2 A b)}{4 x^4}-\frac{c (A c+2 b B)}{x}+B c^2 \log (x)",1,"-1/60*(3*a^2*(4*A + 5*B*x) + 10*a*x*(3*A*b + 4*b*B*x + 4*A*c*x + 6*B*c*x^2) + 10*x^2*(3*b*B*x*(b + 4*c*x) + 2*A*(b^2 + 3*b*c*x + 3*c^2*x^2)))/x^5 + B*c^2*Log[x]","A",1
864,1,97,99,0.0348117,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^7} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^7,x]","-\frac{2 a^2 (5 A+6 B x)+2 a x (3 A (4 b+5 c x)+5 B x (3 b+4 c x))+5 x^2 \left(A \left(3 b^2+8 b c x+6 c^2 x^2\right)+4 B x \left(b^2+3 b c x+3 c^2 x^2\right)\right)}{60 x^6}","-\frac{a^2 A}{6 x^6}-\frac{A \left(2 a c+b^2\right)+2 a b B}{4 x^4}-\frac{2 a B c+2 A b c+b^2 B}{3 x^3}-\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,"-1/60*(2*a^2*(5*A + 6*B*x) + 2*a*x*(5*B*x*(3*b + 4*c*x) + 3*A*(4*b + 5*c*x)) + 5*x^2*(4*B*x*(b^2 + 3*b*c*x + 3*c^2*x^2) + A*(3*b^2 + 8*b*c*x + 6*c^2*x^2)))/x^6","A",1
865,1,100,101,0.0363077,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^8} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^8,x]","-\frac{10 a^2 (6 A+7 B x)+14 a x (2 A (5 b+6 c x)+3 B x (4 b+5 c x))+7 x^2 \left(2 A \left(6 b^2+15 b c x+10 c^2 x^2\right)+5 B x \left(3 b^2+8 b c x+6 c^2 x^2\right)\right)}{420 x^7}","-\frac{a^2 A}{7 x^7}-\frac{A \left(2 a c+b^2\right)+2 a b B}{5 x^5}-\frac{2 a B c+2 A b c+b^2 B}{4 x^4}-\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,"-1/420*(10*a^2*(6*A + 7*B*x) + 14*a*x*(3*B*x*(4*b + 5*c*x) + 2*A*(5*b + 6*c*x)) + 7*x^2*(5*B*x*(3*b^2 + 8*b*c*x + 6*c^2*x^2) + 2*A*(6*b^2 + 15*b*c*x + 10*c^2*x^2)))/x^7","A",1
866,1,99,101,0.0384393,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^9} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^9,x]","-\frac{15 a^2 (7 A+8 B x)+8 a x (5 A (6 b+7 c x)+7 B x (5 b+6 c x))+14 x^2 \left(A \left(10 b^2+24 b c x+15 c^2 x^2\right)+2 B x \left(6 b^2+15 b c x+10 c^2 x^2\right)\right)}{840 x^8}","-\frac{a^2 A}{8 x^8}-\frac{A \left(2 a c+b^2\right)+2 a b B}{6 x^6}-\frac{2 a B c+2 A b c+b^2 B}{5 x^5}-\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,"-1/840*(15*a^2*(7*A + 8*B*x) + 8*a*x*(7*B*x*(5*b + 6*c*x) + 5*A*(6*b + 7*c*x)) + 14*x^2*(2*B*x*(6*b^2 + 15*b*c*x + 10*c^2*x^2) + A*(10*b^2 + 24*b*c*x + 15*c^2*x^2)))/x^8","A",1
867,1,166,166,0.0479882,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[x^2*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{3} a^3 A x^3+\frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{3}{8} c x^8 \left(a B c+A b c+b^2 B\right)+\frac{3}{5} a x^5 \left(A \left(a c+b^2\right)+a b B\right)+\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{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{1}{9} c^2 x^9 (A c+3 b B)+\frac{1}{10} B c^3 x^{10}","\frac{1}{3} a^3 A x^3+\frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{3}{8} c x^8 \left(a B c+A b c+b^2 B\right)+\frac{3}{5} a x^5 \left(A \left(a c+b^2\right)+a b B\right)+\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{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{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",1
868,1,166,166,0.040089,"\int x (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[x*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{2} a^3 A x^2+\frac{1}{3} a^2 x^3 (a B+3 A b)+\frac{3}{7} c x^7 \left(a B c+A b c+b^2 B\right)+\frac{3}{4} a x^4 \left(A \left(a c+b^2\right)+a b B\right)+\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{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{1}{8} c^2 x^8 (A c+3 b B)+\frac{1}{9} B c^3 x^9","\frac{1}{2} a^3 A x^2+\frac{1}{3} a^2 x^3 (a B+3 A b)+\frac{3}{7} c x^7 \left(a B c+A b c+b^2 B\right)+\frac{3}{4} a x^4 \left(A \left(a c+b^2\right)+a b B\right)+\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{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{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",1
869,1,158,158,0.0340227,"\int (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(a + b*x + c*x^2)^3,x]","a^3 A x+\frac{1}{2} a^2 x^2 (a B+3 A b)+\frac{1}{2} c x^6 \left(a B c+A b c+b^2 B\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\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}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{8} B c^3 x^8","a^3 A x+\frac{1}{2} a^2 x^2 (a B+3 A b)+\frac{1}{2} c x^6 \left(a B c+A b c+b^2 B\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\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}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\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",1
870,1,157,157,0.0622642,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x,x]","a^3 A \log (x)+a^2 x (a B+3 A b)+\frac{3}{5} c x^5 \left(a B c+A b c+b^2 B\right)+\frac{3}{2} a x^2 \left(A \left(a c+b^2\right)+a b B\right)+\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{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{1}{6} c^2 x^6 (A c+3 b B)+\frac{1}{7} B c^3 x^7","a^3 A \log (x)+a^2 x (a B+3 A b)+\frac{3}{5} c x^5 \left(a B c+A b c+b^2 B\right)+\frac{3}{2} a x^2 \left(A \left(a c+b^2\right)+a b B\right)+\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{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{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",1
871,1,156,156,0.0846239,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^2} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^2,x]","-\frac{a^3 A}{x}+a^2 \log (x) (a B+3 A b)+\frac{3}{4} c x^4 \left(a B c+A b c+b^2 B\right)+3 a x \left(A \left(a c+b^2\right)+a b B\right)+\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{1}{2} x^2 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{1}{5} c^2 x^5 (A c+3 b B)+\frac{1}{6} B c^3 x^6","-\frac{a^3 A}{x}+a^2 \log (x) (a B+3 A b)+\frac{3}{4} c x^4 \left(a B c+A b c+b^2 B\right)+3 a x \left(A \left(a c+b^2\right)+a b B\right)+\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{1}{2} x^2 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\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",1
872,1,153,153,0.0767856,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^3} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^3,x]","-\frac{a^3 A}{2 x^2}-\frac{a^2 (a B+3 A b)}{x}+c x^3 \left(a B c+A b c+b^2 B\right)+3 a \log (x) \left(A \left(a c+b^2\right)+a b B\right)+\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)+x \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{1}{4} c^2 x^4 (A c+3 b B)+\frac{1}{5} B c^3 x^5","-\frac{a^3 A}{2 x^2}-\frac{a^2 (a B+3 A b)}{x}+c x^3 \left(a B c+A b c+b^2 B\right)+3 a \log (x) \left(A \left(a c+b^2\right)+a b B\right)+\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)+x \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{1}{4} c^2 x^4 (A c+3 b B)+\frac{1}{5} B c^3 x^5",1,"-1/2*(a^3*A)/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",1
873,1,160,155,0.0612664,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^4} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^4,x]","\frac{-2 a^3 (2 A+3 B x)-18 a^2 x (A (b+2 c x)+2 b B x)+18 a x^2 \left(B c x^2 (4 b+c x)-2 A \left(b^2-c^2 x^2\right)\right)+12 x^3 \log (x) \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+x^4 \left(18 b^2 c (2 A+B x)+6 b c^2 x (3 A+2 B x)+c^3 x^2 (4 A+3 B x)+12 b^3 B\right)}{12 x^3}","-\frac{a^3 A}{3 x^3}-\frac{a^2 (a B+3 A b)}{2 x^2}+\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}+x \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\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,"(-2*a^3*(2*A + 3*B*x) + x^4*(12*b^3*B + 18*b^2*c*(2*A + B*x) + 6*b*c^2*x*(3*A + 2*B*x) + c^3*x^2*(4*A + 3*B*x)) - 18*a^2*x*(2*b*B*x + A*(b + 2*c*x)) + 18*a*x^2*(B*c*x^2*(4*b + c*x) - 2*A*(b^2 - c^2*x^2)) + 12*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^3*Log[x])/(12*x^3)","A",1
874,1,154,156,0.058824,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^5} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^5,x]","\frac{-3 a^3 A-4 a^2 x (a B+3 A b)+36 c x^5 \left(a B c+A b c+b^2 B\right)-18 a x^2 \left(A \left(a c+b^2\right)+a b B\right)+12 x^4 \log (x) \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)-12 x^3 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+6 c^2 x^6 (A c+3 b B)+4 B c^3 x^7}{12 x^4}","-\frac{a^3 A}{4 x^4}-\frac{a^2 (a B+3 A b)}{3 x^3}-\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)+\log (x) \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 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,"(-3*a^3*A - 4*a^2*(3*A*b + a*B)*x - 18*a*(a*b*B + A*(b^2 + a*c))*x^2 - 12*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^3 + 36*c*(b^2*B + A*b*c + a*B*c)*x^5 + 6*c^2*(3*b*B + A*c)*x^6 + 4*B*c^3*x^7 + 12*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^4*Log[x])/(12*x^4)","A",1
875,1,161,154,0.0876949,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^6} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^6,x]","-\frac{a^3 (4 A+5 B x)+5 a^2 x \left(3 A b+4 A c x+4 b B x+6 B c x^2\right)+10 a x^2 \left(2 A \left(b^2+3 b c x+3 c^2 x^2\right)+3 b B x (b+4 c x)\right)-60 c x^5 \log (x) \left(a B c+A b c+b^2 B\right)+10 x^3 \left(A \left(b^3+6 b^2 c x-2 c^3 x^3\right)-B x \left(-2 b^3+6 b c^2 x^2+c^3 x^3\right)\right)}{20 x^5}","-\frac{a^3 A}{5 x^5}-\frac{a^2 (a B+3 A b)}{4 x^4}-\frac{a \left(A \left(a c+b^2\right)+a b B\right)}{x^3}+3 c \log (x) \left(a B c+A b c+b^2 B\right)-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{x}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{2 x^2}+c^2 x (A c+3 b B)+\frac{1}{2} B c^3 x^2",1,"-1/20*(a^3*(4*A + 5*B*x) + 5*a^2*x*(3*A*b + 4*b*B*x + 4*A*c*x + 6*B*c*x^2) + 10*a*x^2*(3*b*B*x*(b + 4*c*x) + 2*A*(b^2 + 3*b*c*x + 3*c^2*x^2)) + 10*x^3*(A*(b^3 + 6*b^2*c*x - 2*c^3*x^3) - B*x*(-2*b^3 + 6*b*c^2*x^2 + c^3*x^3)) - 60*c*(b^2*B + A*b*c + a*B*c)*x^5*Log[x])/x^5","A",1
876,1,169,155,0.0878168,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^7} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^7,x]","-\frac{2 a^3 (5 A+6 B x)+3 a^2 x (3 A (4 b+5 c x)+5 B x (3 b+4 c x))+15 a x^2 \left(A \left(3 b^2+8 b c x+6 c^2 x^2\right)+4 B x \left(b^2+3 b c x+3 c^2 x^2\right)\right)+10 x^3 \left(A b \left(2 b^2+9 b c x+18 c^2 x^2\right)+3 B x \left(b^3+6 b^2 c x-2 c^3 x^3\right)\right)-60 c^2 x^6 \log (x) (A c+3 b B)}{60 x^6}","-\frac{a^3 A}{6 x^6}-\frac{a^2 (a B+3 A b)}{5 x^5}-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{4 x^4}-\frac{3 c \left(a B c+A b c+b^2 B\right)}{x}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{2 x^2}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{3 x^3}+c^2 \log (x) (A c+3 b B)+B c^3 x",1,"-1/60*(2*a^3*(5*A + 6*B*x) + 3*a^2*x*(5*B*x*(3*b + 4*c*x) + 3*A*(4*b + 5*c*x)) + 15*a*x^2*(4*B*x*(b^2 + 3*b*c*x + 3*c^2*x^2) + A*(3*b^2 + 8*b*c*x + 6*c^2*x^2)) + 10*x^3*(A*b*(2*b^2 + 9*b*c*x + 18*c^2*x^2) + 3*B*x*(b^3 + 6*b^2*c*x - 2*c^3*x^3)) - 60*c^2*(3*b*B + A*c)*x^6*Log[x])/x^6","A",1
877,1,175,160,0.0802296,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^8} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^8,x]","-\frac{10 a^3 (6 A+7 B x)+21 a^2 x (2 A (5 b+6 c x)+3 B x (4 b+5 c x))+21 a x^2 \left(2 A \left(6 b^2+15 b c x+10 c^2 x^2\right)+5 B x \left(3 b^2+8 b c x+6 c^2 x^2\right)\right)+35 x^3 \left(3 A \left(b^3+4 b^2 c x+6 b c^2 x^2+4 c^3 x^3\right)+2 b B x \left(2 b^2+9 b c x+18 c^2 x^2\right)\right)-420 B c^3 x^7 \log (x)}{420 x^7}","-\frac{a^3 A}{7 x^7}-\frac{a^2 (a B+3 A b)}{6 x^6}-\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{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{3 x^3}-\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,"-1/420*(10*a^3*(6*A + 7*B*x) + 21*a^2*x*(3*B*x*(4*b + 5*c*x) + 2*A*(5*b + 6*c*x)) + 21*a*x^2*(5*B*x*(3*b^2 + 8*b*c*x + 6*c^2*x^2) + 2*A*(6*b^2 + 15*b*c*x + 10*c^2*x^2)) + 35*x^3*(2*b*B*x*(2*b^2 + 9*b*c*x + 18*c^2*x^2) + 3*A*(b^3 + 4*b^2*c*x + 6*b*c^2*x^2 + 4*c^3*x^3)) - 420*B*c^3*x^7*Log[x])/x^7","A",1
878,1,172,162,0.0578949,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^9} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^9,x]","-\frac{5 a^3 (7 A+8 B x)+4 a^2 x (5 A (6 b+7 c x)+7 B x (5 b+6 c x))+14 a x^2 \left(A \left(10 b^2+24 b c x+15 c^2 x^2\right)+2 B x \left(6 b^2+15 b c x+10 c^2 x^2\right)\right)+14 x^3 \left(A \left(4 b^3+15 b^2 c x+20 b c^2 x^2+10 c^3 x^3\right)+5 B x \left(b^3+4 b^2 c x+6 b c^2 x^2+4 c^3 x^3\right)\right)}{280 x^8}","-\frac{a^3 A}{8 x^8}-\frac{a^2 (a B+3 A b)}{7 x^7}-\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{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{4 x^4}-\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,"-1/280*(5*a^3*(7*A + 8*B*x) + 4*a^2*x*(7*B*x*(5*b + 6*c*x) + 5*A*(6*b + 7*c*x)) + 14*a*x^2*(2*B*x*(6*b^2 + 15*b*c*x + 10*c^2*x^2) + A*(10*b^2 + 24*b*c*x + 15*c^2*x^2)) + 14*x^3*(5*B*x*(b^3 + 4*b^2*c*x + 6*b*c^2*x^2 + 4*c^3*x^3) + A*(4*b^3 + 15*b^2*c*x + 20*b*c^2*x^2 + 10*c^3*x^3)))/x^8","A",1
879,1,175,166,0.0601454,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{10}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^10,x]","-\frac{35 a^3 (8 A+9 B x)+45 a^2 x (3 A (7 b+8 c x)+4 B x (6 b+7 c x))+18 a x^2 \left(4 A \left(15 b^2+35 b c x+21 c^2 x^2\right)+7 B x \left(10 b^2+24 b c x+15 c^2 x^2\right)\right)+42 x^3 \left(A \left(10 b^3+36 b^2 c x+45 b c^2 x^2+20 c^3 x^3\right)+3 B x \left(4 b^3+15 b^2 c x+20 b c^2 x^2+10 c^3 x^3\right)\right)}{2520 x^9}","-\frac{a^3 A}{9 x^9}-\frac{a^2 (a B+3 A b)}{8 x^8}-\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{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{5 x^5}-\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,"-1/2520*(35*a^3*(8*A + 9*B*x) + 45*a^2*x*(4*B*x*(6*b + 7*c*x) + 3*A*(7*b + 8*c*x)) + 18*a*x^2*(7*B*x*(10*b^2 + 24*b*c*x + 15*c^2*x^2) + 4*A*(15*b^2 + 35*b*c*x + 21*c^2*x^2)) + 42*x^3*(3*B*x*(4*b^3 + 15*b^2*c*x + 20*b*c^2*x^2 + 10*c^3*x^3) + A*(10*b^3 + 36*b^2*c*x + 45*b*c^2*x^2 + 20*c^3*x^3)))/x^9","A",1
880,1,176,166,0.0615031,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{11}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^11,x]","-\frac{28 a^3 (9 A+10 B x)+15 a^2 x (7 A (8 b+9 c x)+9 B x (7 b+8 c x))+9 a x^2 \left(5 A \left(21 b^2+48 b c x+28 c^2 x^2\right)+8 B x \left(15 b^2+35 b c x+21 c^2 x^2\right)\right)+6 x^3 \left(3 A \left(20 b^3+70 b^2 c x+84 b c^2 x^2+35 c^3 x^3\right)+7 B x \left(10 b^3+36 b^2 c x+45 b c^2 x^2+20 c^3 x^3\right)\right)}{2520 x^{10}}","-\frac{a^3 A}{10 x^{10}}-\frac{a^2 (a B+3 A b)}{9 x^9}-\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{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{6 x^6}-\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,"-1/2520*(28*a^3*(9*A + 10*B*x) + 15*a^2*x*(9*B*x*(7*b + 8*c*x) + 7*A*(8*b + 9*c*x)) + 9*a*x^2*(8*B*x*(15*b^2 + 35*b*c*x + 21*c^2*x^2) + 5*A*(21*b^2 + 48*b*c*x + 28*c^2*x^2)) + 6*x^3*(7*B*x*(10*b^3 + 36*b^2*c*x + 45*b*c^2*x^2 + 20*c^3*x^3) + 3*A*(20*b^3 + 70*b^2*c*x + 84*b*c^2*x^2 + 35*c^3*x^3)))/x^10","A",1
881,1,222,229,0.1353361,"\int \frac{x^4 (d+e x)}{a+b x+c x^2} \, dx","Integrate[(x^4*(d + e*x))/(a + b*x + c*x^2),x]","\frac{6 \left(a^2 c^2 e-3 a b^2 c e+2 a b c^2 d+b^4 e-b^3 c d\right) \log (a+x (b+c x))+\frac{12 \left(-5 a^2 b c^2 e+2 a^2 c^3 d+5 a b^3 c e-4 a b^2 c^2 d+b^5 (-e)+b^4 c d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}-6 c^2 x^2 \left(a c e+b^2 (-e)+b c d\right)-12 c x \left(-2 a b c e+a c^2 d+b^3 e-b^2 c d\right)+4 c^3 x^3 (c d-b e)+3 c^4 e x^4}{12 c^5}","-\frac{\left(-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^4 (-e)+b^3 c d\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+5 a b^3 c e-4 a b^2 c^2 d+b^5 (-e)+b^4 c d\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^3 (-e)+b^2 c d\right)}{c^4}+\frac{x^3 (c d-b e)}{3 c^2}+\frac{e x^4}{4 c}",1,"(-12*c*(-(b^2*c*d) + a*c^2*d + b^3*e - 2*a*b*c*e)*x - 6*c^2*(b*c*d - b^2*e + a*c*e)*x^2 + 4*c^3*(c*d - b*e)*x^3 + 3*c^4*e*x^4 + (12*(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)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + 6*(-(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 + x*(b + c*x)])/(12*c^5)","A",1
882,1,165,169,0.1019512,"\int \frac{x^3 (d+e x)}{a+b x+c x^2} \, dx","Integrate[(x^3*(d + e*x))/(a + b*x + c*x^2),x]","\frac{\frac{6 \left(2 a^2 c^2 e-4 a b^2 c e+3 a b c^2 d+b^4 e-b^3 c d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}-6 c x \left(a c e+b^2 (-e)+b c d\right)-3 \left(-2 a b c e+a c^2 d+b^3 e-b^2 c d\right) \log (a+x (b+c x))+3 c^2 x^2 (c d-b e)+2 c^3 e x^3}{6 c^4}","\frac{\left(-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^4 (-e)+b^3 c d\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{x \left(a c e+b^2 (-e)+b c d\right)}{c^3}+\frac{\left(2 a b c e-a c^2 d+b^3 (-e)+b^2 c d\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{x^2 (c d-b e)}{2 c^2}+\frac{e x^3}{3 c}",1,"(-6*c*(b*c*d - b^2*e + a*c*e)*x + 3*c^2*(c*d - b*e)*x^2 + 2*c^3*e*x^3 + (6*(-(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)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] - 3*(-(b^2*c*d) + a*c^2*d + b^3*e - 2*a*b*c*e)*Log[a + x*(b + c*x)])/(6*c^4)","A",1
883,1,119,121,0.080902,"\int \frac{x^2 (d+e x)}{a+b x+c x^2} \, dx","Integrate[(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 (a+x (b+c x))+\frac{2 \left(3 a b c e-2 a c^2 d+b^3 (-e)+b^2 c d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+2 c x (c d-b e)+c^2 e x^2}{2 c^3}","-\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^3 (-e)+b^2 c d\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,"(2*c*(c*d - b*e)*x + c^2*e*x^2 + (2*(b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + (-(b*c*d) + b^2*e - a*c*e)*Log[a + x*(b + c*x)])/(2*c^3)","A",1
884,1,86,85,0.0825076,"\int \frac{x (d+e x)}{a+b x+c x^2} \, dx","Integrate[(x*(d + e*x))/(a + b*x + c*x^2),x]","\frac{\frac{2 \left(-2 a c e+b^2 e-b c d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+(c d-b e) \log (a+x (b+c x))+2 c e x}{2 c^2}","\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,"(2*c*e*x + (2*(-(b*c*d) + b^2*e - 2*a*c*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + (c*d - b*e)*Log[a + x*(b + c*x)])/(2*c^2)","A",1
885,1,66,66,0.0562777,"\int \frac{d+e x}{a+b x+c x^2} \, dx","Integrate[(d + e*x)/(a + b*x + c*x^2),x]","\frac{e \log (a+x (b+c x))-\frac{2 (b e-2 c d) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}}{2 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*(-2*c*d + b*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + e*Log[a + x*(b + c*x)])/(2*c)","A",1
886,1,71,71,0.1090396,"\int \frac{d+e x}{x \left(a+b x+c x^2\right)} \, dx","Integrate[(d + e*x)/(x*(a + b*x + c*x^2)),x]","-\frac{\frac{2 (b d-2 a e) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+d (\log (a+x (b+c x))-2 \log (x))}{2 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,"-1/2*((2*(b*d - 2*a*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + d*(-2*Log[x] + Log[a + x*(b + c*x)]))/a","A",1
887,1,100,104,0.0826026,"\int \frac{d+e x}{x^2 \left(a+b x+c x^2\right)} \, dx","Integrate[(d + e*x)/(x^2*(a + b*x + c*x^2)),x]","\frac{\frac{2 \left(-a b e-2 a c d+b^2 d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+(b d-a e) \log (a+x (b+c x))+2 \log (x) (a e-b d)-\frac{2 a d}{x}}{2 a^2}","-\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,"((-2*a*d)/x + (2*(b^2*d - 2*a*c*d - a*b*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + 2*(-(b*d) + a*e)*Log[x] + (b*d - a*e)*Log[a + x*(b + c*x)])/(2*a^2)","A",1
888,1,141,145,0.134849,"\int \frac{d+e x}{x^3 \left(a+b x+c x^2\right)} \, dx","Integrate[(d + e*x)/(x^3*(a + b*x + c*x^2)),x]","\frac{\frac{2 \left(-2 a^2 c e+a b^2 e+3 a b c d+b^3 (-d)\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}-\frac{a^2 d}{x^2}+2 \log (x) \left(-a b e-a c d+b^2 d\right)+\left(a b e+a c d+b^2 (-d)\right) \log (a+x (b+c x))+\frac{2 a (b d-a e)}{x}}{2 a^3}","-\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{b d-a e}{a^2 x}+\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{d}{2 a x^2}",1,"(-((a^2*d)/x^2) + (2*a*(b*d - a*e))/x + (2*(-(b^3*d) + 3*a*b*c*d + a*b^2*e - 2*a^2*c*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + 2*(b^2*d - a*c*d - a*b*e)*Log[x] + (-(b^2*d) + a*c*d + a*b*e)*Log[a + x*(b + c*x)])/(2*a^3)","A",1
889,1,196,204,0.1437628,"\int \frac{d+e x}{x^4 \left(a+b x+c x^2\right)} \, dx","Integrate[(d + e*x)/(x^4*(a + b*x + c*x^2)),x]","\frac{-\frac{2 a^3 d}{x^3}-6 \log (x) \left(a^2 c e-a b^2 e-2 a b c d+b^3 d\right)+3 \left(a^2 c e-a b^2 e-2 a b c d+b^3 d\right) \log (a+x (b+c x))+\frac{6 \left(3 a^2 b c e+2 a^2 c^2 d-a b^3 e-4 a b^2 c d+b^4 d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+\frac{3 a^2 (b d-a e)}{x^2}+\frac{6 a \left(a b e+a c d+b^2 (-d)\right)}{x}}{6 a^4}","-\frac{-a b e-a c d+b^2 d}{a^3 x}+\frac{b d-a e}{2 a^2 x^2}+\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{\log (x) \left(a^2 c e-a b^2 e-2 a b c d+b^3 d\right)}{a^4}-\frac{\left(3 a^2 b c e+2 a^2 c^2 d-a b^3 e-4 a b^2 c d+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{d}{3 a x^3}",1,"((-2*a^3*d)/x^3 + (3*a^2*(b*d - a*e))/x^2 + (6*a*(-(b^2*d) + a*c*d + a*b*e))/x + (6*(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)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] - 6*(b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e)*Log[x] + 3*(b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e)*Log[a + x*(b + c*x)])/(6*a^4)","A",1
890,1,249,262,0.3608349,"\int \frac{x^4 (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(x^4*(d + e*x))/(a + b*x + c*x^2)^2,x]","\frac{\frac{2 \left(30 a^2 b c^2 e-12 a^2 c^3 d-20 a b^3 c e+12 a b^2 c^2 d+3 b^5 e-2 b^4 c d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}+\frac{2 \left(2 a^3 c^2 e+a^2 c \left(-4 b^2 e+b c (3 d+5 e x)-2 c^2 d x\right)+a b^2 \left(b^2 e-b c (d+5 e x)+4 c^2 d x\right)+b^4 x (b e-c d)\right)}{\left(b^2-4 a c\right) (a+x (b+c x))}+\left(-2 a c e+3 b^2 e-2 b c d\right) \log (a+x (b+c x))+2 c x (c d-2 b e)+c^2 e x^2}{2 c^4}","-\frac{\left(-30 a^2 b c^2 e+12 a^2 c^3 d+20 a b^3 c e-12 a b^2 c^2 d-3 b^5 e+2 b^4 c d\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{\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^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{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{x \left(11 a b c e-6 a c^2 d-3 b^3 e+2 b^2 c d\right)}{c^3 \left(b^2-4 a c\right)}",1,"(2*c*(c*d - 2*b*e)*x + c^2*e*x^2 + (2*(2*a^3*c^2*e + b^4*(-(c*d) + b*e)*x + a*b^2*(b^2*e + 4*c^2*d*x - b*c*(d + 5*e*x)) + a^2*c*(-4*b^2*e - 2*c^2*d*x + b*c*(3*d + 5*e*x))))/((b^2 - 4*a*c)*(a + x*(b + 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)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2) + (-2*b*c*d + 3*b^2*e - 2*a*c*e)*Log[a + x*(b + c*x)])/(2*c^4)","A",1
891,1,190,192,0.2856699,"\int \frac{x^3 (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(x^3*(d + e*x))/(a + b*x + c*x^2)^2,x]","\frac{\frac{2 \left(a^2 c (3 b e-2 c (d+e x))+a b \left(b^2 (-e)+b c (d+4 e x)-3 c^2 d x\right)+b^3 x (c d-b e)\right)}{\left(b^2-4 a c\right) (a+x (b+c x))}-\frac{2 \left(12 a^2 c^2 e-12 a b^2 c e+6 a b c^2 d+2 b^4 e-b^3 c d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}+(c d-2 b e) \log (a+x (b+c x))+2 c e x}{2 c^3}","\frac{\left(-12 a^2 c^2 e+12 a b^2 c e-6 a b c^2 d-2 b^4 e+b^3 c d\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,"(2*c*e*x + (2*(b^3*(c*d - b*e)*x + a^2*c*(3*b*e - 2*c*(d + e*x)) + a*b*(-(b^2*e) - 3*c^2*d*x + b*c*(d + 4*e*x))))/((b^2 - 4*a*c)*(a + x*(b + 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)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2) + (c*d - 2*b*e)*Log[a + x*(b + c*x)])/(2*c^3)","A",1
892,1,146,132,0.1941505,"\int \frac{x^2 (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(x^2*(d + e*x))/(a + b*x + c*x^2)^2,x]","\frac{-\frac{2 \left(2 a^2 c e+a \left(b^2 (-e)+b c (d+3 e x)-2 c^2 d x\right)+b^2 x (c d-b e)\right)}{\left(b^2-4 a c\right) (a+x (b+c x))}+\frac{2 \left(2 a c (2 c d-3 b e)+b^3 e\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}+e \log (a+x (b+c x))}{2 c^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{\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{e \log \left(a+b x+c x^2\right)}{2 c^2}",1,"((-2*(2*a^2*c*e + b^2*(c*d - b*e)*x + a*(-(b^2*e) - 2*c^2*d*x + b*c*(d + 3*e*x))))/((b^2 - 4*a*c)*(a + x*(b + c*x))) + (2*(b^3*e + 2*a*c*(2*c*d - 3*b*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2) + e*Log[a + x*(b + c*x)])/(2*c^2)","A",1
893,1,99,99,0.0758979,"\int \frac{x (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(x*(d + e*x))/(a + b*x + c*x^2)^2,x]","\frac{a b e-2 a c (d+e x)+b x (b e-c d)}{c \left(4 a c-b^2\right) (a+x (b+c x))}-\frac{2 (b d-2 a e) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\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*b*e + b*(-(c*d) + b*e)*x - 2*a*c*(d + e*x))/(c*(-b^2 + 4*a*c)*(a + x*(b + c*x))) - (2*(b*d - 2*a*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2)","A",1
894,1,88,87,0.0735754,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(d + e*x)/(a + b*x + c*x^2)^2,x]","\frac{\frac{2 (b e-2 c d) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+\frac{2 a e-b d+b e x-2 c d x}{a+x (b+c x)}}{b^2-4 a c}","\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*x + b*e*x)/(a + x*(b + c*x)) + (2*(-2*c*d + b*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c])/(b^2 - 4*a*c)","A",1
895,1,134,135,0.2038358,"\int \frac{d+e x}{x \left(a+b x+c x^2\right)^2} \, dx","Integrate[(d + e*x)/(x*(a + b*x + c*x^2)^2),x]","\frac{\frac{2 \left(4 a^2 c e-6 a b c d+b^3 d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}-\frac{2 a \left(b (a e-c d x)+2 a c (d+e x)+b^2 (-d)\right)}{\left(b^2-4 a c\right) (a+x (b+c x))}-d \log (a+x (b+c x))+2 d \log (x)}{2 a^2}","\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,"((-2*a*(-(b^2*d) + b*(a*e - c*d*x) + 2*a*c*(d + e*x)))/((b^2 - 4*a*c)*(a + x*(b + c*x))) + (2*(b^3*d - 6*a*b*c*d + 4*a^2*c*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2) + 2*d*Log[x] - d*Log[a + x*(b + c*x)])/(2*a^2)","A",1
896,1,192,211,0.3411829,"\int \frac{d+e x}{x^2 \left(a+b x+c x^2\right)^2} \, dx","Integrate[(d + e*x)/(x^2*(a + b*x + c*x^2)^2),x]","\frac{-\frac{2 \left(6 a^2 b c e+12 a^2 c^2 d-a b^3 e-12 a b^2 c d+2 b^4 d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}-\frac{2 a \left(b^2 (c d x-a e)-a b c (3 d+e x)+2 a c (a e-c d x)+b^3 d\right)}{\left(b^2-4 a c\right) (a+x (b+c x))}+(2 b d-a e) \log (a+x (b+c x))+2 \log (x) (a e-2 b d)-\frac{2 a d}{x}}{2 a^3}","\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{-a b e-6 a c d+2 b^2 d}{a^2 x \left(b^2-4 a c\right)}-\frac{\left(6 a^2 b c e+12 a^2 c^2 d-a b^3 e-12 a b^2 c d+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{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*a*d)/x - (2*a*(b^3*d + 2*a*c*(a*e - c*d*x) + b^2*(-(a*e) + c*d*x) - a*b*c*(3*d + e*x)))/((b^2 - 4*a*c)*(a + x*(b + 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)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2) + 2*(-2*b*d + a*e)*Log[x] + (2*b*d - a*e)*Log[a + x*(b + c*x)])/(2*a^3)","A",1
897,1,253,283,0.4465415,"\int \frac{d+e x}{x^3 \left(a+b x+c x^2\right)^2} \, dx","Integrate[(d + e*x)/(x^3*(a + b*x + c*x^2)^2),x]","\frac{\frac{2 a \left(2 a^2 c^2 (d+e x)+b^3 (c d x-a e)-a b^2 c (4 d+e x)+3 a b c (a e-c d x)+b^4 d\right)}{\left(b^2-4 a c\right) (a+x (b+c x))}-\frac{a^2 d}{x^2}+\frac{2 \left(-12 a^3 c^2 e+12 a^2 b^2 c e+30 a^2 b c^2 d-2 a b^4 e-20 a b^3 c d+3 b^5 d\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}+2 \log (x) \left(-2 a b e-2 a c d+3 b^2 d\right)+\left(2 a b e+2 a c d-3 b^2 d\right) \log (a+x (b+c x))-\frac{2 a (a e-2 b d)}{x}}{2 a^4}","-\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{\log (x) \left(-2 a b e-2 a c d+3 b^2 d\right)}{a^4}-\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{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{\left(-12 a^3 c^2 e+12 a^2 b^2 c e+30 a^2 b c^2 d-2 a b^4 e-20 a b^3 c d+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{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,"(-((a^2*d)/x^2) - (2*a*(-2*b*d + a*e))/x + (2*a*(b^4*d + 3*a*b*c*(a*e - c*d*x) + b^3*(-(a*e) + c*d*x) + 2*a^2*c^2*(d + e*x) - a*b^2*c*(4*d + e*x)))/((b^2 - 4*a*c)*(a + x*(b + 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)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2) + 2*(3*b^2*d - 2*a*c*d - 2*a*b*e)*Log[x] + (-3*b^2*d + 2*a*c*d + 2*a*b*e)*Log[a + x*(b + c*x)])/(2*a^4)","A",1
898,1,9,9,0.0023009,"\int \frac{5+2 x}{4+5 x+x^2} \, dx","Integrate[(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
899,1,17,17,0.004311,"\int \frac{7+3 x}{8+6 x+x^2} \, dx","Integrate[(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",1
900,1,14,14,0.0044635,"\int \frac{5+2 x}{5+4 x+x^2} \, dx","Integrate[(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",1
901,1,35,33,0.0141272,"\int \frac{-2+7 x}{42-16 x+2 x^2} \, dx","Integrate[(-2 + 7*x)/(42 - 16*x + 2*x^2),x]","\frac{1}{2} \left(\frac{7}{2} \log \left(x^2-8 x+21\right)+\frac{26 \tan ^{-1}\left(\frac{x-4}{\sqrt{5}}\right)}{\sqrt{5}}\right)","\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,"((26*ArcTan[(-4 + x)/Sqrt[5]])/Sqrt[5] + (7*Log[21 - 8*x + x^2])/2)/2","A",1
902,1,49,51,0.0267883,"\int \frac{3+x}{1+3 x+x^2} \, dx","Integrate[(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",1
903,1,44,49,0.0226465,"\int \frac{-1+2 x}{1+8 x+4 x^2} \, dx","Integrate[(-1 + 2*x)/(1 + 8*x + 4*x^2),x]","\frac{1}{4} \left(\left(1+\sqrt{3}\right) \log \left(2 x+\sqrt{3}+2\right)-\left(\sqrt{3}-1\right) \log \left(-2 x+\sqrt{3}-2\right)\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]) + (1 + Sqrt[3])*Log[2 + Sqrt[3] + 2*x])/4","A",1
904,1,16,16,0.0061075,"\int \frac{3+2 x}{\left(13+12 x+4 x^2\right)^2} \, dx","Integrate[(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*1/(13 + 12*x + 4*x^2)","A",1
905,1,24,24,0.0114957,"\int \frac{4+x}{\left(5+4 x+x^2\right)^2} \, dx","Integrate[(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",1
906,1,39,39,0.0242765,"\int \frac{-1+3 x}{\left(1+x+x^2\right)^2} \, dx","Integrate[(-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",1
907,1,49,58,0.0288299,"\int \frac{1+x}{\left(1-x+x^2\right)^3} \, dx","Integrate[(1 + x)/(1 - x + x^2)^3,x]","\frac{2 x^3-3 x^2+4 x-2}{2 \left(x^2-x+1\right)^2}+\frac{2 \tan ^{-1}\left(\frac{2 x-1}{\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,"(-2 + 4*x - 3*x^2 + 2*x^3)/(2*(1 - x + x^2)^2) + (2*ArcTan[(-1 + 2*x)/Sqrt[3]])/Sqrt[3]","A",1
908,1,10,10,0.0010012,"\int \frac{1}{A+B x} \, dx","Integrate[(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
909,1,10,10,0.0010998,"\int \frac{A+B x}{A^2+2 A B x+B^2 x^2} \, dx","Integrate[(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",1
910,1,312,367,0.5431034,"\int x^4 (A+B x) \sqrt{a+b x+c x^2} \, dx","Integrate[x^4*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{\frac{7 \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) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{2048 c^{11/2}}+\frac{x^2 (a+x (b+c x))^{3/2} \left(-32 a B c-42 A b c+33 b^2 B\right)}{40 c^2}+\frac{(a+x (b+c x))^{3/2} \left(252 b^2 c (7 A c x-13 a B)+8 a b c^2 (343 A+333 B x)+16 a c^2 (64 a B-105 A c x)-42 b^3 c (35 A+33 B x)+1155 b^4 B\right)}{1920 c^4}+\frac{x^3 (a+x (b+c x))^{3/2} (14 A c-11 b B)}{12 c}+B x^4 (a+x (b+c x))^{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{\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{(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{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^2*B - 42*A*b*c - 32*a*B*c)*x^2*(a + x*(b + c*x))^(3/2))/(40*c^2) + ((-11*b*B + 14*A*c)*x^3*(a + x*(b + c*x))^(3/2))/(12*c) + B*x^4*(a + x*(b + c*x))^(3/2) + ((a + x*(b + c*x))^(3/2)*(1155*b^4*B - 42*b^3*c*(35*A + 33*B*x) + 8*a*b*c^2*(343*A + 333*B*x) + 16*a*c^2*(64*a*B - 105*A*c*x) + 252*b^2*c*(-13*a*B + 7*A*c*x)))/(1920*c^4) + (7*(-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)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(2048*c^(11/2)))/(7*c)","A",1
911,1,241,280,0.3623603,"\int x^3 (A+B x) \sqrt{a+b x+c x^2} \, dx","Integrate[x^3*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{\frac{3 \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) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{512 c^{9/2}}+\frac{(a+x (b+c x))^{3/2} \left(28 b c (7 a B-6 A c x)-8 a c^2 (16 A+15 B x)+14 b^2 c (10 A+9 B x)-105 b^3 B\right)}{160 c^3}+\frac{3 x^2 (a+x (b+c x))^{3/2} (4 A c-3 b B)}{10 c}+B x^3 (a+x (b+c x))^{3/2}}{6 c}","-\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{(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(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,"((3*(-3*b*B + 4*A*c)*x^2*(a + x*(b + c*x))^(3/2))/(10*c) + B*x^3*(a + x*(b + c*x))^(3/2) + ((a + x*(b + c*x))^(3/2)*(-105*b^3*B + 14*b^2*c*(10*A + 9*B*x) - 8*a*c^2*(16*A + 15*B*x) + 28*b*c*(7*a*B - 6*A*c*x)))/(160*c^3) + (3*(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)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(512*c^(9/2)))/(6*c)","A",1
912,1,179,205,0.2296881,"\int x^2 (A+B x) \sqrt{a+b x+c x^2} \, dx","Integrate[x^2*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{\frac{(a+x (b+c x))^{3/2} \left(4 c (15 A c x-8 a B)-2 b c (25 A+21 B x)+35 b^2 B\right)}{48 c^2}+\frac{5 \left(8 a A c^2-12 a b B c-10 A b^2 c+7 b^3 B\right) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{256 c^{7/2}}+B x^2 (a+x (b+c x))^{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{\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+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{B x^2 \left(a+b x+c x^2\right)^{3/2}}{5 c}",1,"(B*x^2*(a + x*(b + c*x))^(3/2) + ((a + x*(b + c*x))^(3/2)*(35*b^2*B - 2*b*c*(25*A + 21*B*x) + 4*c*(-8*a*B + 15*A*c*x)))/(48*c^2) + (5*(7*b^3*B - 10*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(256*c^(7/2)))/(5*c)","A",1
913,1,127,144,0.1331221,"\int x (A+B x) \sqrt{a+b x+c x^2} \, dx","Integrate[x*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{(a+x (b+c x))^{3/2} (8 A c-5 b B+6 B c x)-\frac{3 \left(-4 a B c-8 A b c+5 b^2 B\right) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{16 c^{3/2}}}{24 c^2}","-\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{(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(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*B + 8*A*c + 6*B*c*x)*(a + x*(b + c*x))^(3/2) - (3*(5*b^2*B - 8*A*b*c - 4*a*B*c)*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(16*c^(3/2)))/(24*c^2)","A",1
914,1,114,113,0.1050313,"\int (A+B x) \sqrt{a+b x+c x^2} \, dx","Integrate[(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{c} \sqrt{a+x (b+c x)} \left(4 c (2 a B+c x (3 A+2 B x))+2 b c (3 A+B x)-3 b^2 B\right)+3 \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+x (b+c x)}}\right)}{48 c^{5/2}}","\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,"(2*Sqrt[c]*Sqrt[a + x*(b + c*x)]*(-3*b^2*B + 2*b*c*(3*A + B*x) + 4*c*(2*a*B + c*x*(3*A + 2*B*x))) + 3*(b^2 - 4*a*c)*(b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(48*c^(5/2))","A",1
915,1,127,129,0.1657643,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x} \, dx","Integrate[((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+x (b+c x)}}\right)}{8 c^{3/2}}+\frac{\sqrt{a+x (b+c x)} (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+x (b+c x)}}\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 + x*(b + c*x)])/(4*c) - Sqrt[a]*A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])] + ((-(b^2*B) + 4*A*b*c + 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(8*c^(3/2))","A",1
916,1,118,121,0.1745555,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^2} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^2,x]","\frac{(B x-A) \sqrt{a+x (b+c x)}}{x}-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{2 \sqrt{a}}+\frac{(2 A c+b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\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 + x*(b + c*x)])/x - ((A*b + 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(2*Sqrt[a]) + ((b*B + 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(2*Sqrt[c])","A",1
917,1,129,133,0.3535895,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^3} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^3,x]","\frac{\left(A \left(b^2-4 a c\right)-4 a b B\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{8 a^{3/2}}-\frac{\sqrt{a+x (b+c x)} (2 a (A+2 B x)+A b x)}{4 a x^2}+B \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\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,"-1/4*((A*b*x + 2*a*(A + 2*B*x))*Sqrt[a + x*(b + c*x)])/(a*x^2) + ((-4*a*b*B + A*(b^2 - 4*a*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(8*a^(3/2)) + B*Sqrt[c]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]","A",1
918,1,116,121,0.1611151,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^4} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^4,x]","\frac{3 x (A b-2 a B) \left(2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)}-x^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)\right)-16 a^{3/2} A (a+x (b+c x))^{3/2}}{48 a^{5/2} 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,"(-16*a^(3/2)*A*(a + x*(b + c*x))^(3/2) + 3*(A*b - 2*a*B)*x*(2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*x^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])]))/(48*a^(5/2)*x^3)","A",1
919,1,153,172,0.1823784,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^5} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^5,x]","\frac{\frac{3 \left(-4 a A c-8 a b B+5 A b^2\right) \left(x^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)}\right)}{16 a^{3/2} x^2}+\frac{(5 A b-8 a B) (a+x (b+c x))^{3/2}}{x^3}-\frac{6 a A (a+x (b+c x))^{3/2}}{x^4}}{24 a^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{(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{(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,"((-6*a*A*(a + x*(b + c*x))^(3/2))/x^4 + ((5*A*b - 8*a*B)*(a + x*(b + c*x))^(3/2))/x^3 + (3*(5*A*b^2 - 8*a*b*B - 4*a*A*c)*(-2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*x^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])]))/(16*a^(3/2)*x^2))/(24*a^2)","A",1
920,1,206,235,0.3896047,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^6} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^6,x]","\frac{-\frac{5 \left(A \left(7 b^3-12 a b c\right)+2 a B \left(4 a c-5 b^2\right)\right) \left(x^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)}\right)}{32 a^{7/2} x^2}+\frac{(a+x (b+c x))^{3/2} \left(32 a A c+50 a b B-35 A b^2\right)}{6 a^2 x^3}+\frac{(7 A b-10 a B) (a+x (b+c x))^{3/2}}{a x^4}-\frac{8 A (a+x (b+c x))^{3/2}}{x^5}}{40 a}","\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{\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{(7 A b-10 a B) \left(a+b x+c x^2\right)^{3/2}}{40 a^2 x^4}+\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{A \left(a+b x+c x^2\right)^{3/2}}{5 a x^5}",1,"((-8*A*(a + x*(b + c*x))^(3/2))/x^5 + ((7*A*b - 10*a*B)*(a + x*(b + c*x))^(3/2))/(a*x^4) + ((-35*A*b^2 + 50*a*b*B + 32*a*A*c)*(a + x*(b + c*x))^(3/2))/(6*a^2*x^3) - (5*(2*a*B*(-5*b^2 + 4*a*c) + A*(7*b^3 - 12*a*b*c))*(-2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*x^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])]))/(32*a^(7/2)*x^2))/(40*a)","A",1
921,1,262,310,0.4433508,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^7} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^7,x]","\frac{\frac{2 x^3 (a+x (b+c x))^{3/2} \left(7 A \left(15 b^3-28 a b c\right)+4 a B \left(32 a c-35 b^2\right)\right)}{a^2}+\frac{15 x^4 \left(A \left(16 a^2 c^2-56 a b^2 c+21 b^4\right)+4 a b B \left(12 a c-7 b^2\right)\right) \left(x^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)}\right)}{8 a^{7/2}}+\frac{12 x^2 (a+x (b+c x))^{3/2} \left(20 a A c+28 a b B-21 A b^2\right)}{a}+96 x (3 A b-4 a B) (a+x (b+c x))^{3/2}-320 a A (a+x (b+c x))^{3/2}}{1920 a^2 x^6}","-\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{\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{(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(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{A \left(a+b x+c x^2\right)^{3/2}}{6 a x^6}",1,"(-320*a*A*(a + x*(b + c*x))^(3/2) + 96*(3*A*b - 4*a*B)*x*(a + x*(b + c*x))^(3/2) + (12*(-21*A*b^2 + 28*a*b*B + 20*a*A*c)*x^2*(a + x*(b + c*x))^(3/2))/a + (2*(4*a*B*(-35*b^2 + 32*a*c) + 7*A*(15*b^3 - 28*a*b*c))*x^3*(a + x*(b + c*x))^(3/2))/a^2 + (15*(4*a*b*B*(-7*b^2 + 12*a*c) + A*(21*b^4 - 56*a*b^2*c + 16*a^2*c^2))*x^4*(-2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*x^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])]))/(8*a^(7/2)))/(1920*a^2*x^6)","A",1
922,1,338,455,0.8220466,"\int x^4 (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[x^4*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{\frac{3 \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) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)} \left(4 c \left(5 a+2 c x^2\right)-3 b^2+8 b c x\right)+3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{65536 c^{13/2}}+\frac{x^2 (a+x (b+c x))^{5/2} \left(-128 a B c-198 A b c+143 b^2 B\right)}{224 c^2}+\frac{(a+x (b+c x))^{5/2} \left(396 b^2 c (15 A c x-19 a B)+8 a b c^2 (837 A+935 B x)+16 a c^2 (128 a B-315 A c x)-66 b^3 c (63 A+65 B x)+3003 b^4 B\right)}{8960 c^4}+\frac{x^3 (a+x (b+c x))^{5/2} (18 A c-13 b B)}{16 c}+B x^4 (a+x (b+c x))^{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{\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{\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{(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{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,"(((143*b^2*B - 198*A*b*c - 128*a*B*c)*x^2*(a + x*(b + c*x))^(5/2))/(224*c^2) + ((-13*b*B + 18*A*c)*x^3*(a + x*(b + c*x))^(5/2))/(16*c) + B*x^4*(a + x*(b + c*x))^(5/2) + ((a + x*(b + c*x))^(5/2)*(3003*b^4*B - 66*b^3*c*(63*A + 65*B*x) + 8*a*b*c^2*(837*A + 935*B*x) + 16*a*c^2*(128*a*B - 315*A*c*x) + 396*b^2*c*(-19*a*B + 15*A*c*x)))/(8960*c^4) + (3*(-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)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)]*(-3*b^2 + 8*b*c*x + 4*c*(5*a + 2*c*x^2)) + 3*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(65536*c^(13/2)))/(9*c)","A",1
923,1,267,356,0.5187109,"\int x^3 (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[x^3*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{\frac{\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) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)} \left(4 c \left(5 a+2 c x^2\right)-3 b^2+8 b c x\right)+3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{4096 c^{11/2}}+\frac{(a+x (b+c x))^{5/2} \left(12 b c (31 a B-40 A c x)-8 a c^2 (32 A+35 B x)+6 b^2 c (56 A+55 B x)-231 b^3 B\right)}{560 c^3}+\frac{x^2 (a+x (b+c x))^{5/2} (16 A c-11 b B)}{14 c}+B x^3 (a+x (b+c x))^{5/2}}{8 c}","\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{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{(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{\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,"(((-11*b*B + 16*A*c)*x^2*(a + x*(b + c*x))^(5/2))/(14*c) + B*x^3*(a + x*(b + c*x))^(5/2) + ((a + x*(b + c*x))^(5/2)*(-231*b^3*B - 8*a*c^2*(32*A + 35*B*x) + 6*b^2*c*(56*A + 55*B*x) + 12*b*c*(31*a*B - 40*A*c*x)))/(560*c^3) + ((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)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)]*(-3*b^2 + 8*b*c*x + 4*c*(5*a + 2*c*x^2)) + 3*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(4096*c^(11/2)))/(8*c)","A",1
924,1,206,269,0.3267081,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[x^2*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{\frac{(a+x (b+c x))^{5/2} \left(4 c (35 A c x-12 a B)-2 b c (49 A+45 B x)+63 b^2 B\right)}{120 c^2}-\frac{7 \left(8 a A c^2-12 a b B c-14 A b^2 c+9 b^3 B\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)} \left(4 c \left(5 a+2 c x^2\right)-3 b^2+8 b c x\right)+3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{6144 c^{9/2}}+B x^2 (a+x (b+c x))^{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{\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{\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{(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{B x^2 \left(a+b x+c x^2\right)^{5/2}}{7 c}",1,"(B*x^2*(a + x*(b + c*x))^(5/2) + ((a + x*(b + c*x))^(5/2)*(63*b^2*B - 2*b*c*(49*A + 45*B*x) + 4*c*(-12*a*B + 35*A*c*x)))/(120*c^2) - (7*(9*b^3*B - 14*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)]*(-3*b^2 + 8*b*c*x + 4*c*(5*a + 2*c*x^2)) + 3*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(6144*c^(9/2)))/(7*c)","A",1
925,1,156,198,0.2061685,"\int x (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[x*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{\frac{5 \left(-4 a B c-12 A b c+7 b^2 B\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)} \left(4 c \left(5 a+2 c x^2\right)-3 b^2+8 b c x\right)+3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{256 c^{5/2}}+(a+x (b+c x))^{5/2} (2 c (6 A+5 B x)-7 b B)}{60 c^2}","\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(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{(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(a+b x+c x^2\right)^{5/2} (-12 A c+7 b B-10 B c x)}{60 c^2}",1,"((-7*b*B + 2*c*(6*A + 5*B*x))*(a + x*(b + c*x))^(5/2) + (5*(7*b^2*B - 12*A*b*c - 4*a*B*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)]*(-3*b^2 + 8*b*c*x + 4*c*(5*a + 2*c*x^2)) + 3*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(256*c^(5/2)))/(60*c^2)","A",1
926,1,144,158,0.2834972,"\int (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{5 (2 A c-b B) \left(\frac{3 \left(b^2-4 a c\right) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{128 c^{5/2}}+\frac{(b+2 c x) (a+x (b+c x))^{3/2}}{8 c}\right)+2 B (a+x (b+c x))^{5/2}}{10 c}","-\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{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{(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,"(2*B*(a + x*(b + c*x))^(5/2) + 5*(-(b*B) + 2*A*c)*(((b + 2*c*x)*(a + x*(b + c*x))^(3/2))/(8*c) + (3*(b^2 - 4*a*c)*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(128*c^(5/2))))/(10*c)","A",1
927,1,206,218,0.3394471,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x} \, dx","Integrate[((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+x (b+c x)}}\right)+\frac{\left(48 a^2 B c^2+96 a A b c^2-24 a b^2 B c-8 A b^3 c+3 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{128 c^{5/2}}+\frac{\sqrt{a+x (b+c x)} \left(4 b c (15 a B+2 c x (14 A+9 B x))+8 c^2 \left(32 a A+15 a B x+8 A c x^2+6 B c x^3\right)+6 b^2 c (4 A+B x)-9 b^3 B\right)}{192 c^2}","a^{3/2} (-A) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)+\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{\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(a+b x+c x^2\right)^{3/2} (8 A c+3 b B+6 B c x)}{24 c}",1,"(Sqrt[a + x*(b + c*x)]*(-9*b^3*B + 6*b^2*c*(4*A + B*x) + 8*c^2*(32*a*A + 15*a*B*x + 8*A*c*x^2 + 6*B*c*x^3) + 4*b*c*(15*a*B + 2*c*x*(14*A + 9*B*x))))/(192*c^2) - a^(3/2)*A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])] + ((3*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 + x*(b + c*x)])])/(128*c^(5/2))","A",1
928,1,183,193,0.3221021,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^2} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^2,x]","\frac{1}{48} \left(\frac{2 \sqrt{a+x (b+c x)} \left(x \left(2 b c (15 A+7 B x)+4 c^2 x (3 A+2 B x)+3 b^2 B\right)-8 a c (3 A-4 B x)\right)}{c x}+\frac{3 \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+x (b+c x)}}\right)}{c^{3/2}}-24 \sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)\right)","\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{\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{(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,"((2*Sqrt[a + x*(b + c*x)]*(-8*a*c*(3*A - 4*B*x) + x*(3*b^2*B + 4*c^2*x*(3*A + 2*B*x) + 2*b*c*(15*A + 7*B*x))))/(c*x) - 24*Sqrt[a]*(3*A*b + 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])] + (3*(-(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 + x*(b + c*x)])])/c^(3/2))/48","A",1
929,1,162,179,0.4443547,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^3} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^3,x]","\frac{1}{8} \left(-\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+x (b+c x)}}\right)}{\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+x (b+c x)}}\right)}{\sqrt{c}}+\frac{2 \sqrt{a+x (b+c x)} (x (A (4 c x-5 b)+B x (5 b+2 c x))-2 a (A+2 B x))}{x^2}\right)","-\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,"((2*Sqrt[a + x*(b + c*x)]*(-2*a*(A + 2*B*x) + x*(B*x*(5*b + 2*c*x) + A*(-5*b + 4*c*x))))/x^2 - (3*(4*a*b*B + A*(b^2 + 4*a*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/Sqrt[a] + (3*(b^2*B + 4*A*b*c + 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/Sqrt[c])/8","A",1
930,1,182,206,0.5018711,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^4} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^4,x]","\frac{1}{48} \left(\frac{3 \left(A \left(b^3-12 a b c\right)-6 a B \left(4 a c+b^2\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{a^{3/2}}-\frac{2 \sqrt{a+x (b+c x)} \left(4 a^2 (2 A+3 B x)+2 a x (A (7 b+16 c x)+3 B x (5 b-4 c x))+3 A b^2 x^2\right)}{a x^3}+24 \sqrt{c} (2 A c+3 b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\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{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(a+b x+c x^2\right)^{3/2} (3 x (2 a B+A b)+4 a A)}{12 a x^3}",1,"((-2*Sqrt[a + x*(b + c*x)]*(3*A*b^2*x^2 + 4*a^2*(2*A + 3*B*x) + 2*a*x*(3*B*x*(5*b - 4*c*x) + A*(7*b + 16*c*x))))/(a*x^3) + (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 + x*(b + c*x)])])/a^(3/2) + 24*Sqrt[c]*(3*b*B + 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/48","A",1
931,1,202,217,0.6309356,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^5} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^5,x]","-\frac{\left(3 A \left(b^2-4 a c\right)^2+8 a b B \left(12 a c-b^2\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{128 a^{5/2}}-\frac{\sqrt{a+x (b+c x)} \left(16 a^3 (3 A+4 B x)+8 a^2 x (3 A (3 b+5 c x)+2 B x (7 b+16 c x))+6 a b x^2 (A (b+10 c x)+4 b B x)-9 A b^3 x^3\right)}{192 a^2 x^4}+B c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)","\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{\sqrt{a+b x+c x^2} \left(2 a \left(8 a b B-3 A \left(b^2-4 a c\right)\right)+x \left(8 a B \left(8 a c+b^2\right)-3 A \left(b^3-4 a b c\right)\right)\right)}{64 a^2 x^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,"-1/192*(Sqrt[a + x*(b + c*x)]*(-9*A*b^3*x^3 + 16*a^3*(3*A + 4*B*x) + 6*a*b*x^2*(4*b*B*x + A*(b + 10*c*x)) + 8*a^2*x*(3*A*(3*b + 5*c*x) + 2*B*x*(7*b + 16*c*x))))/(a^2*x^4) - ((3*A*(b^2 - 4*a*c)^2 + 8*a*b*B*(-b^2 + 12*a*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(128*a^(5/2)) + B*c^(3/2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]","A",1
932,1,157,170,0.2591152,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^6} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^6,x]","\frac{(A b-2 a B) \left(16 a^{3/2} (2 a+b x) (a+x (b+c x))^{3/2}-3 x^2 \left(b^2-4 a c\right) \left(2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)}-x^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)\right)\right)}{256 a^{7/2} x^4}-\frac{A (a+x (b+c x))^{5/2}}{5 a x^5}","\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{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{(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,"-1/5*(A*(a + x*(b + c*x))^(5/2))/(a*x^5) + ((A*b - 2*a*B)*(16*a^(3/2)*(2*a + b*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*x^2*(2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*x^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])))/(256*a^(7/2)*x^4)","A",1
933,1,182,230,0.3267595,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^7} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^7,x]","\frac{-\frac{5 \left(-4 a A c-12 a b B+7 A b^2\right) \left(2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)} \left(8 a^2+4 a x (2 b+5 c x)-3 b^2 x^2\right)+3 x^4 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)\right)}{256 a^{5/2} x^4}+\frac{(7 A b-12 a B) (a+x (b+c x))^{5/2}}{x^5}-\frac{10 a A (a+x (b+c x))^{5/2}}{x^6}}{60 a^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{\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{(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{(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,"((-10*a*A*(a + x*(b + c*x))^(5/2))/x^6 + ((7*A*b - 12*a*B)*(a + x*(b + c*x))^(5/2))/x^5 - (5*(7*A*b^2 - 12*a*b*B - 4*a*A*c)*(2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)]*(8*a^2 - 3*b^2*x^2 + 4*a*x*(2*b + 5*c*x)) + 3*(b^2 - 4*a*c)^2*x^4*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])]))/(256*a^(5/2)*x^4))/(60*a^2)","A",1
934,1,234,303,0.5636947,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^8} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^8,x]","\frac{\frac{7 \left(3 A \left(3 b^3-4 a b c\right)+2 a B \left(4 a c-7 b^2\right)\right) \left(2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)} \left(8 a^2+4 a x (2 b+5 c x)-3 b^2 x^2\right)+3 x^4 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)\right)}{512 a^{7/2} x^4}+\frac{(a+x (b+c x))^{5/2} \left(48 a A c+98 a b B-63 A b^2\right)}{10 a x^5}+\frac{(9 A b-14 a B) (a+x (b+c x))^{5/2}}{x^6}-\frac{12 a A (a+x (b+c x))^{5/2}}{x^7}}{84 a^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{\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{(9 A b-14 a B) \left(a+b x+c x^2\right)^{5/2}}{84 a^2 x^6}-\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{(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{A \left(a+b x+c x^2\right)^{5/2}}{7 a x^7}",1,"((-12*a*A*(a + x*(b + c*x))^(5/2))/x^7 + ((9*A*b - 14*a*B)*(a + x*(b + c*x))^(5/2))/x^6 + ((-63*A*b^2 + 98*a*b*B + 48*a*A*c)*(a + x*(b + c*x))^(5/2))/(10*a*x^5) + (7*(2*a*B*(-7*b^2 + 4*a*c) + 3*A*(3*b^3 - 4*a*b*c))*(2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)]*(8*a^2 - 3*b^2*x^2 + 4*a*x*(2*b + 5*c*x)) + 3*(b^2 - 4*a*c)^2*x^4*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])]))/(512*a^(7/2)*x^4))/(84*a^2)","A",1
935,1,386,543,1.0067437,"\int x^4 (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[x^4*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{\frac{11 \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) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)} \left(16 c^2 \left(33 a^2+26 a c x^2+8 c^2 x^4\right)+8 b^2 c \left(11 c x^2-20 a\right)+32 b c^2 x \left(13 a+8 c x^2\right)+15 b^4-40 b^3 c x\right)-15 \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{7864320 c^{15/2}}+\frac{x^2 (a+x (b+c x))^{7/2} \left(-160 a B c-286 A b c+195 b^2 B\right)}{360 c^2}+\frac{(a+x (b+c x))^{7/2} \left(572 b^2 c (77 A c x-75 a B)+8 a b c^2 (4961 A+5915 B x)+16 a c^2 (640 a B-2079 A c x)-858 b^3 c (33 A+35 B x)+19305 b^4 B\right)}{80640 c^4}+\frac{x^3 (a+x (b+c x))^{7/2} (22 A c-15 b B)}{20 c}+B x^4 (a+x (b+c x))^{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{\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{\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) (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{(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{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,"(((195*b^2*B - 286*A*b*c - 160*a*B*c)*x^2*(a + x*(b + c*x))^(7/2))/(360*c^2) + ((-15*b*B + 22*A*c)*x^3*(a + x*(b + c*x))^(7/2))/(20*c) + B*x^4*(a + x*(b + c*x))^(7/2) + ((a + x*(b + c*x))^(7/2)*(19305*b^4*B - 858*b^3*c*(33*A + 35*B*x) + 8*a*b*c^2*(4961*A + 5915*B*x) + 16*a*c^2*(640*a*B - 2079*A*c*x) + 572*b^2*c*(-75*a*B + 77*A*c*x)))/(80640*c^4) + (11*(-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)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)]*(15*b^4 - 40*b^3*c*x + 32*b*c^2*x*(13*a + 8*c*x^2) + 8*b^2*c*(-20*a + 11*c*x^2) + 16*c^2*(33*a^2 + 26*a*c*x^2 + 8*c^2*x^4)) - 15*(b^2 - 4*a*c)^3*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(7864320*c^(15/2)))/(11*c)","A",1
936,1,315,432,0.7630299,"\int x^3 (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[x^3*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{\frac{\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) \left(256 c^{5/2} (b+2 c x) (a+x (b+c x))^{5/2}-5 \left(b^2-4 a c\right) \left(16 c^{3/2} (b+2 c x) (a+x (b+c x))^{3/2}-3 \left(b^2-4 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{393216 c^{13/2}}+\frac{(a+x (b+c x))^{7/2} \left(44 b c (41 a B-70 A c x)-8 a c^2 (160 A+189 B x)+22 b^2 c (90 A+91 B x)-1287 b^3 B\right)}{4032 c^3}+\frac{x^2 (a+x (b+c x))^{7/2} (20 A c-13 b B)}{18 c}+B x^3 (a+x (b+c x))^{7/2}}{10 c}","-\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(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) (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{(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(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,"(((-13*b*B + 20*A*c)*x^2*(a + x*(b + c*x))^(7/2))/(18*c) + B*x^3*(a + x*(b + c*x))^(7/2) + ((a + x*(b + c*x))^(7/2)*(-1287*b^3*B + 22*b^2*c*(90*A + 91*B*x) - 8*a*c^2*(160*A + 189*B*x) + 44*b*c*(41*a*B - 70*A*c*x)))/(4032*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)*(256*c^(5/2)*(b + 2*c*x)*(a + x*(b + c*x))^(5/2) - 5*(b^2 - 4*a*c)*(16*c^(3/2)*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))))/(393216*c^(13/2)))/(10*c)","A",1
937,1,254,333,0.4497686,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[x^2*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{\frac{(a+x (b+c x))^{7/2} \left(4 c (63 A c x-16 a B)-2 b c (81 A+77 B x)+99 b^2 B\right)}{224 c^2}+\frac{3 \left(-8 a A c^2+12 a b B c+18 A b^2 c-11 b^3 B\right) \left(256 c^{5/2} (b+2 c x) (a+x (b+c x))^{5/2}-5 \left(b^2-4 a c\right) \left(16 c^{3/2} (b+2 c x) (a+x (b+c x))^{3/2}-3 \left(b^2-4 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{65536 c^{11/2}}+B x^2 (a+x (b+c x))^{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{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{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) (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{(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{B x^2 \left(a+b x+c x^2\right)^{7/2}}{9 c}",1,"(B*x^2*(a + x*(b + c*x))^(7/2) + ((a + x*(b + c*x))^(7/2)*(99*b^2*B - 2*b*c*(81*A + 77*B*x) + 4*c*(-16*a*B + 63*A*c*x)))/(224*c^2) + (3*(-11*b^3*B + 18*A*b^2*c + 12*a*b*B*c - 8*a*A*c^2)*(256*c^(5/2)*(b + 2*c*x)*(a + x*(b + c*x))^(5/2) - 5*(b^2 - 4*a*c)*(16*c^(3/2)*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))))/(65536*c^(11/2)))/(9*c)","A",1
938,1,205,252,0.6034549,"\int x (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[x*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{\frac{7 \left(-2 a B c-8 A b c+\frac{9 b^2 B}{2}\right) \left(2 (b+2 c x) (a+x (b+c x))^{5/2}-5 \left(b^2-4 a c\right) \left(\frac{3 \left(b^2-4 a c\right) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{128 c^{5/2}}+\frac{(b+2 c x) (a+x (b+c x))^{3/2}}{8 c}\right)\right)}{24 c}+(a+x (b+c x))^{7/2} (2 c (8 A+7 B x)-9 b B)}{112 c^2}","-\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{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) (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{(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{\left(a+b x+c x^2\right)^{7/2} (-16 A c+9 b B-14 B c x)}{112 c^2}",1,"((-9*b*B + 2*c*(8*A + 7*B*x))*(a + x*(b + c*x))^(7/2) + (7*((9*b^2*B)/2 - 8*A*b*c - 2*a*B*c)*(2*(b + 2*c*x)*(a + x*(b + c*x))^(5/2) - 5*(b^2 - 4*a*c)*(((b + 2*c*x)*(a + x*(b + c*x))^(3/2))/(8*c) + (3*(b^2 - 4*a*c)*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(128*c^(5/2)))))/(24*c))/(112*c^2)","A",1
939,1,179,203,0.2892742,"\int (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{B (a+x (b+c x))^{7/2}}{7 c}-\frac{(b B-2 A c) \left(256 c^{5/2} (b+2 c x) (a+x (b+c x))^{5/2}-5 \left(b^2-4 a c\right) \left(16 c^{3/2} (b+2 c x) (a+x (b+c x))^{3/2}-3 \left(b^2-4 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{6144 c^{9/2}}","\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{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) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (b B-2 A c)}{384 c^3}-\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,"(B*(a + x*(b + c*x))^(7/2))/(7*c) - ((b*B - 2*A*c)*(256*c^(5/2)*(b + 2*c*x)*(a + x*(b + c*x))^(5/2) - 5*(b^2 - 4*a*c)*(16*c^(3/2)*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))))/(6144*c^(9/2))","A",1
940,1,349,350,0.4599047,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x,x]","a^{5/2} (-A) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)+\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+x (b+c x)}}\right)}{1024 c^{7/2}}+\frac{\sqrt{a+x (b+c x)} \left(32 a^2 c^3 (16 A+5 B x)-8 b^3 c (5 a B+3 A c x)+16 a b^2 c^2 (7 A-5 B x)+16 a b c^2 (5 a B+14 A c x)-2 b^4 c (6 A-5 B x)+5 b^5 B\right)}{512 c^3}+\frac{(a+x (b+c x))^{3/2} \left(4 b c (5 a B+6 A c x)+8 a c^2 (8 A+5 B x)+2 b^2 c (6 A-5 B x)-5 b^3 B\right)}{192 c^2}+\frac{(a+x (b+c x))^{5/2} (2 c (6 A+5 B x)+5 b B)}{60 c}","a^{5/2} (-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(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}}-\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,"((5*b*B + 2*c*(6*A + 5*B*x))*(a + x*(b + c*x))^(5/2))/(60*c) + ((a + x*(b + c*x))^(3/2)*(-5*b^3*B + 2*b^2*c*(6*A - 5*B*x) + 8*a*c^2*(8*A + 5*B*x) + 4*b*c*(5*a*B + 6*A*c*x)))/(192*c^2) + (Sqrt[a + x*(b + c*x)]*(5*b^5*B - 2*b^4*c*(6*A - 5*B*x) + 16*a*b^2*c^2*(7*A - 5*B*x) + 32*a^2*c^3*(16*A + 5*B*x) - 8*b^3*c*(5*a*B + 3*A*c*x) + 16*a*b*c^2*(5*a*B + 14*A*c*x)))/(512*c^3) - a^(5/2)*A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])] + ((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 + x*(b + c*x)])])/(1024*c^(7/2))","A",1
941,1,288,310,0.5204378,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^2} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^2,x]","-\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+x (b+c x)}}\right)+\frac{\sqrt{a+x (b+c x)} \left(-128 a^2 c^2 (15 A-23 B x)+4 a c x \left(2 b c (695 A+311 B x)+4 c^2 x (135 A+88 B x)+135 b^2 B\right)+x \left(30 b^3 c (5 A+B x)+4 b^2 c^2 x (295 A+186 B x)+16 b c^3 x^2 (85 A+63 B x)+96 c^4 x^3 (5 A+4 B x)-45 b^4 B\right)\right)}{1920 c^2 x}+\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+x (b+c x)}}\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{\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{\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,"(Sqrt[a + x*(b + c*x)]*(-128*a^2*c^2*(15*A - 23*B*x) + x*(-45*b^4*B + 30*b^3*c*(5*A + B*x) + 96*c^4*x^3*(5*A + 4*B*x) + 16*b*c^3*x^2*(85*A + 63*B*x) + 4*b^2*c^2*x*(295*A + 186*B*x)) + 4*a*c*x*(135*b^2*B + 4*c^2*x*(135*A + 88*B*x) + 2*b*c*(695*A + 311*B*x))))/(1920*c^2*x) - (a^(3/2)*(5*A*b + 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/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 + x*(b + c*x)])])/(256*c^(5/2))","A",1
942,1,254,273,0.460206,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^3} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^3,x]","\frac{\sqrt{a+x (b+c x)} \left(-96 a^2 c (A+2 B x)+4 a c x (B x (139 b+54 c x)-4 A (27 b-28 c x))+x^2 \left(2 b^2 c (132 A+59 B x)+8 b c^2 x (26 A+17 B x)+16 c^3 x^2 (4 A+3 B x)+15 b^3 B\right)\right)}{192 c x^2}+\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+x (b+c x)}}\right)}{128 c^{3/2}}-\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+x (b+c x)}}\right)","-\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}{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{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{(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,"(Sqrt[a + x*(b + c*x)]*(-96*a^2*c*(A + 2*B*x) + x^2*(15*b^3*B + 16*c^3*x^2*(4*A + 3*B*x) + 8*b*c^2*x*(26*A + 17*B*x) + 2*b^2*c*(132*A + 59*B*x)) + 4*a*c*x*(-4*A*(27*b - 28*c*x) + B*x*(139*b + 54*c*x))))/(192*c*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 + x*(b + c*x)])])/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 + x*(b + c*x)])])/(128*c^(3/2))","A",1
943,1,236,255,0.7155489,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^4} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^4,x]","\frac{1}{48} \left(\frac{2 \sqrt{a+x (b+c x)} \left(-4 a^2 (2 A+3 B x)-2 a x (A (13 b+28 c x)+B x (27 b-28 c x))+x^2 \left(A \left(-33 b^2+54 b c x+12 c^2 x^2\right)+B x \left(33 b^2+26 b c x+8 c^2 x^2\right)\right)\right)}{x^3}+\frac{15 \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+x (b+c x)}}\right)}{\sqrt{c}}-\frac{15 \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+x (b+c x)}}\right)}{\sqrt{a}}\right)","-\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(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 \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{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{(A-B x) \left(a+b x+c x^2\right)^{5/2}}{3 x^3}",1,"((2*Sqrt[a + x*(b + c*x)]*(-4*a^2*(2*A + 3*B*x) - 2*a*x*(B*x*(27*b - 28*c*x) + A*(13*b + 28*c*x)) + x^2*(B*x*(33*b^2 + 26*b*c*x + 8*c^2*x^2) + A*(-33*b^2 + 54*b*c*x + 12*c^2*x^2))))/x^3 - (15*(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 + x*(b + c*x)])])/Sqrt[a] + (15*(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 + x*(b + c*x)])])/Sqrt[c])/48","A",1
944,1,255,284,0.6908801,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^5} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^5,x]","\frac{5 \left(A \left(-48 a^2 c^2-24 a b^2 c+b^4\right)-8 a b B \left(12 a c+b^2\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{128 a^{3/2}}-\frac{\sqrt{a+x (b+c x)} \left(16 a^3 (3 A+4 B x)+8 a^2 x \left(17 A b+27 A c x+26 b B x+56 B c x^2\right)+2 a x^2 \left(A \left(59 b^2+278 b c x-96 c^2 x^2\right)-12 B x \left(-11 b^2+18 b c x+4 c^2 x^2\right)\right)+15 A b^3 x^3\right)}{192 a x^4}+\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+x (b+c x)}}\right)","-\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}{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{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(-A \left(b^3-20 a b c\right)-2 c x \left(A \left(12 a c+b^2\right)+16 a b B\right)+8 a B \left(4 a c+b^2\right)\right)}{64 a x}-\frac{(A-2 B x) \left(a+b x+c x^2\right)^{5/2}}{4 x^4}",1,"-1/192*(Sqrt[a + x*(b + c*x)]*(15*A*b^3*x^3 + 16*a^3*(3*A + 4*B*x) + 8*a^2*x*(17*A*b + 26*b*B*x + 27*A*c*x + 56*B*c*x^2) + 2*a*x^2*(A*(59*b^2 + 278*b*c*x - 96*c^2*x^2) - 12*B*x*(-11*b^2 + 18*b*c*x + 4*c^2*x^2))))/(a*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 + x*(b + c*x)])])/(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 + x*(b + c*x)])])/8","A",1
945,1,289,346,0.8454813,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^6} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^6,x]","-\frac{\left(A \left(240 a^2 b c^2-40 a b^3 c+3 b^5\right)+10 a B \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+x (b+c x)}}\right)}{256 a^{5/2}}-\frac{\sqrt{a+x (b+c x)} \left(96 a^4 (4 A+5 B x)+16 a^3 x (A (63 b+88 c x)+5 B x (17 b+27 c x))+4 a^2 x^2 \left(2 A \left(93 b^2+311 b c x+368 c^2 x^2\right)+5 B x \left(59 b^2+278 b c x-96 c^2 x^2\right)\right)+30 a b^2 x^3 (A (b+18 c x)+5 b B x)-45 A b^4 x^4\right)}{1920 a^2 x^5}+\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+x (b+c x)}}\right)","\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{\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{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,"-1/1920*(Sqrt[a + x*(b + c*x)]*(-45*A*b^4*x^4 + 96*a^4*(4*A + 5*B*x) + 30*a*b^2*x^3*(5*b*B*x + A*(b + 18*c*x)) + 16*a^3*x*(5*B*x*(17*b + 27*c*x) + A*(63*b + 88*c*x)) + 4*a^2*x^2*(5*B*x*(59*b^2 + 278*b*c*x - 96*c^2*x^2) + 2*A*(93*b^2 + 311*b*c*x + 368*c^2*x^2))))/(a^2*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 + x*(b + c*x)])])/(256*a^(5/2)) + (c^(3/2)*(5*b*B + 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/2","A",1
946,1,308,332,0.9775151,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^7} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^7,x]","\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+x (b+c x)}}\right)}{1024 a^{7/2}}-\frac{\sqrt{a+x (b+c x)} \left(256 a^5 (5 A+6 B x)+64 a^4 x (A (50 b+65 c x)+B x (63 b+88 c x))+16 a^3 x^2 \left(15 A \left(9 b^2+26 b c x+22 c^2 x^2\right)+2 B x \left(93 b^2+311 b c x+368 c^2 x^2\right)\right)+40 a^2 b x^3 \left(A \left(b^2+12 b c x+66 c^2 x^2\right)+3 b B x (b+18 c x)\right)-10 a b^3 x^4 (5 A (b+16 c x)+18 b B x)+75 A b^5 x^5\right)}{7680 a^3 x^6}+B c^{5/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)","-\frac{\left(a+b x+c x^2\right)^{3/2} \left(2 a \left(12 a b B-5 A \left(b^2-4 a c\right)\right)+x \left(4 a B \left(16 a c+3 b^2\right)-5 A \left(b^3-4 a b c\right)\right)\right)}{192 a^2 x^4}+\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{\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(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,"-1/7680*(Sqrt[a + x*(b + c*x)]*(75*A*b^5*x^5 + 256*a^5*(5*A + 6*B*x) - 10*a*b^3*x^4*(18*b*B*x + 5*A*(b + 16*c*x)) + 64*a^4*x*(A*(50*b + 65*c*x) + B*x*(63*b + 88*c*x)) + 40*a^2*b*x^3*(3*b*B*x*(b + 18*c*x) + A*(b^2 + 12*b*c*x + 66*c^2*x^2)) + 16*a^3*x^2*(15*A*(9*b^2 + 26*b*c*x + 22*c^2*x^2) + 2*B*x*(93*b^2 + 311*b*c*x + 368*c^2*x^2))))/(a^3*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 + x*(b + c*x)])])/(1024*a^(7/2)) + B*c^(5/2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]","A",1
947,1,198,219,0.4706388,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^8} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^8,x]","\frac{(A b-2 a B) \left(256 a^{5/2} (2 a+b x) (a+x (b+c x))^{5/2}-5 x^2 \left(b^2-4 a c\right) \left(16 a^{3/2} (2 a+b x) (a+x (b+c x))^{3/2}-3 x^2 \left(b^2-4 a c\right) \left(2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)}-x^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{6144 a^{9/2} x^6}-\frac{A (a+x (b+c x))^{7/2}}{7 a x^7}","-\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{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) (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{(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,"-1/7*(A*(a + x*(b + c*x))^(7/2))/(a*x^7) + ((A*b - 2*a*B)*(256*a^(5/2)*(2*a + b*x)*(a + x*(b + c*x))^(5/2) - 5*(b^2 - 4*a*c)*x^2*(16*a^(3/2)*(2*a + b*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*x^2*(2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*x^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])]))))/(6144*a^(9/2)*x^6)","A",1
948,1,242,288,0.7471336,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^9} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^9,x]","-\frac{\frac{\left(-2 a A c-8 a b B+\frac{9 A b^2}{2}\right) \left(256 a^{5/2} (2 a+b x) (a+x (b+c x))^{5/2}-5 x^2 \left(b^2-4 a c\right) \left(16 a^{3/2} (2 a+b x) (a+x (b+c x))^{3/2}-3 x^2 \left(b^2-4 a c\right) \left(2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)}-x^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{6144 a^{9/2} x^6}+\frac{(16 a B-9 A b) (a+x (b+c x))^{7/2}}{14 a x^7}+\frac{A (a+x (b+c x))^{7/2}}{x^8}}{8 a}","\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{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) (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{(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{(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,"-1/8*((A*(a + x*(b + c*x))^(7/2))/x^8 + ((-9*A*b + 16*a*B)*(a + x*(b + c*x))^(7/2))/(14*a*x^7) + (((9*A*b^2)/2 - 8*a*b*B - 2*a*A*c)*(256*a^(5/2)*(2*a + b*x)*(a + x*(b + c*x))^(5/2) - 5*(b^2 - 4*a*c)*x^2*(16*a^(3/2)*(2*a + b*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*x^2*(2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*x^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])]))))/(6144*a^(9/2)*x^6))/a","A",1
949,1,292,375,0.7277607,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^{10}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^10,x]","\frac{\frac{3 \left(A \left(11 b^3-12 a b c\right)+2 a B \left(4 a c-9 b^2\right)\right) \left(256 a^{5/2} (2 a+b x) (a+x (b+c x))^{5/2}-5 x^2 \left(b^2-4 a c\right) \left(16 a^{3/2} (2 a+b x) (a+x (b+c x))^{3/2}-3 x^2 \left(b^2-4 a c\right) \left(2 \sqrt{a} (2 a+b x) \sqrt{a+x (b+c x)}-x^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{65536 a^{11/2} x^6}+\frac{(a+x (b+c x))^{7/2} \left(64 a A c+162 a b B-99 A b^2\right)}{224 a^2 x^7}+\frac{(11 A b-18 a B) (a+x (b+c x))^{7/2}}{16 a x^8}-\frac{A (a+x (b+c x))^{7/2}}{x^9}}{9 a}","\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{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) (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{\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{(11 A b-18 a B) \left(a+b x+c x^2\right)^{7/2}}{144 a^2 x^8}+\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{A \left(a+b x+c x^2\right)^{7/2}}{9 a x^9}",1,"(-((A*(a + x*(b + c*x))^(7/2))/x^9) + ((11*A*b - 18*a*B)*(a + x*(b + c*x))^(7/2))/(16*a*x^8) + ((-99*A*b^2 + 162*a*b*B + 64*a*A*c)*(a + x*(b + c*x))^(7/2))/(224*a^2*x^7) + (3*(2*a*B*(-9*b^2 + 4*a*c) + A*(11*b^3 - 12*a*b*c))*(256*a^(5/2)*(2*a + b*x)*(a + x*(b + c*x))^(5/2) - 5*(b^2 - 4*a*c)*x^2*(16*a^(3/2)*(2*a + b*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*x^2*(2*Sqrt[a]*(2*a + b*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*x^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])]))))/(65536*a^(11/2)*x^6))/(9*a)","A",1
950,1,225,281,0.3901196,"\int \frac{x^4 (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(x^4*(A + B*x))/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+x (b+c x)} \left(16 c^2 \left(64 a^2 B-a c x (45 A+32 B x)+6 c^2 x^3 (5 A+4 B x)\right)+28 b^2 c (c x (25 A+18 B x)-105 a B)+8 b c^2 \left(a (275 A+161 B x)-2 c x^2 (35 A+27 B x)\right)-210 b^3 c (5 A+3 B x)+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+x (b+c x)}}\right)}{256 c^{11/2}}","\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,"(Sqrt[a + x*(b + c*x)]*(945*b^4*B - 210*b^3*c*(5*A + 3*B*x) + 28*b^2*c*(-105*a*B + c*x*(25*A + 18*B*x)) + 16*c^2*(64*a^2*B + 6*c^2*x^3*(5*A + 4*B*x) - a*c*x*(45*A + 32*B*x)) + 8*b*c^2*(-2*c*x^2*(35*A + 27*B*x) + a*(275*A + 161*B*x))))/(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 + x*(b + c*x)])])/(256*c^(11/2))","A",1
951,1,169,206,0.268709,"\int \frac{x^3 (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(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+x (b+c x)}}\right)}{128 c^{9/2}}+\frac{\sqrt{a+x (b+c x)} \left(4 b c (55 a B-2 c x (10 A+7 B x))+8 c^2 \left(-16 a A-9 a B x+8 A c x^2+6 B c x^3\right)+10 b^2 c (12 A+7 B x)-105 b^3 B\right)}{192 c^4}","\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,"(Sqrt[a + x*(b + c*x)]*(-105*b^3*B + 10*b^2*c*(12*A + 7*B*x) + 8*c^2*(-16*a*A - 9*a*B*x + 8*A*c*x^2 + 6*B*c*x^3) + 4*b*c*(55*a*B - 2*c*x*(10*A + 7*B*x))))/(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 + x*(b + c*x)])])/(128*c^(9/2))","A",1
952,1,126,143,0.1480728,"\int \frac{x^2 (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(x^2*(A + B*x))/Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{c} \sqrt{a+x (b+c x)} \left(4 c (c x (3 A+2 B x)-4 a B)-2 b c (9 A+5 B x)+15 b^2 B\right)-3 \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+x (b+c x)}}\right)}{48 c^{7/2}}","\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,"(2*Sqrt[c]*Sqrt[a + x*(b + c*x)]*(15*b^2*B - 2*b*c*(9*A + 5*B*x) + 4*c*(-4*a*B + c*x*(3*A + 2*B*x))) - 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 + x*(b + c*x)])])/(48*c^(7/2))","A",1
953,1,90,92,0.1214744,"\int \frac{x (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(x*(A + B*x))/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+x (b+c x)} (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+x (b+c x)}}\right)}{8 c^{5/2}}","\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 + x*(b + c*x)])/(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 + x*(b + c*x)])])/(8*c^(5/2))","A",1
954,1,66,67,0.084153,"\int \frac{A+B x}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/Sqrt[a + b*x + c*x^2],x]","\frac{(2 A c-b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{2 c^{3/2}}+\frac{B \sqrt{a+x (b+c x)}}{c}","\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 + x*(b + c*x)])/c + ((-(b*B) + 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(2*c^(3/2))","A",1
955,1,75,77,0.023354,"\int \frac{A+B x}{x \sqrt{a+b x+c x^2}} \, dx","Integrate[(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+x (b+c x)}}\right)}{\sqrt{c}}-\frac{A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\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 + x*(b + c*x)])])/Sqrt[a]) + (B*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/Sqrt[c]","A",1
956,1,70,72,0.0853268,"\int \frac{A+B x}{x^2 \sqrt{a+b x+c x^2}} \, dx","Integrate[(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+x (b+c x)}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+x (b+c x)}}{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 + x*(b + c*x)])/(a*x)) + ((A*b - 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(2*a^(3/2))","A",1
957,1,95,116,0.1302183,"\int \frac{A+B x}{x^3 \sqrt{a+b x+c x^2}} \, dx","Integrate[(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+x (b+c x)}}\right)}{8 a^{5/2}}+\frac{\sqrt{a+x (b+c x)} (3 A b x-2 a (A+2 B x))}{4 a^2 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,"((3*A*b*x - 2*a*(A + 2*B*x))*Sqrt[a + x*(b + c*x)])/(4*a^2*x^2) + ((-3*A*b^2 + 4*a*b*B + 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(8*a^(5/2))","A",1
958,1,132,167,0.1400825,"\int \frac{A+B x}{x^4 \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^4*Sqrt[a + b*x + c*x^2]),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+x (b+c x)}}\right)}{16 a^{7/2}}-\frac{\sqrt{a+x (b+c x)} \left(4 a^2 (2 A+3 B x)-2 a x (5 A b+8 A c x+9 b B x)+15 A b^2 x^2\right)}{24 a^3 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{(5 A b-6 a B) \sqrt{a+b x+c x^2}}{12 a^2 x^2}+\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{A \sqrt{a+b x+c x^2}}{3 a x^3}",1,"-1/24*(Sqrt[a + x*(b + c*x)]*(15*A*b^2*x^2 + 4*a^2*(2*A + 3*B*x) - 2*a*x*(5*A*b + 9*b*B*x + 8*A*c*x)))/(a^3*x^3) + ((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 + x*(b + c*x)])])/(16*a^(7/2))","A",1
959,1,176,231,0.2291286,"\int \frac{A+B x}{x^5 \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^5*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+x (b+c x)} \left(-16 a^3 (3 A+4 B x)+8 a^2 x (A (7 b+9 c x)+2 B x (5 b+8 c x))-10 a b x^2 (7 A b+22 A c x+12 b B x)+105 A b^3 x^3\right)}{192 a^4 x^4}-\frac{\left(A \left(48 a^2 c^2-120 a b^2 c+35 b^4\right)+8 a b B \left(12 a c-5 b^2\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{128 a^{9/2}}","-\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{\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{A \sqrt{a+b x+c x^2}}{4 a x^4}",1,"(Sqrt[a + x*(b + c*x)]*(105*A*b^3*x^3 - 16*a^3*(3*A + 4*B*x) - 10*a*b*x^2*(7*A*b + 12*b*B*x + 22*A*c*x) + 8*a^2*x*(2*B*x*(5*b + 8*c*x) + A*(7*b + 9*c*x))))/(192*a^4*x^4) - ((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 + x*(b + c*x)])])/(128*a^(9/2))","A",1
960,1,233,306,0.2988285,"\int \frac{A+B x}{x^6 \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/(x^6*Sqrt[a + b*x + c*x^2]),x]","\frac{\left(A \left(240 a^2 b c^2-280 a b^3 c+63 b^5\right)-2 a B \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+x (b+c x)}}\right)}{256 a^{11/2}}-\frac{\sqrt{a+x (b+c x)} \left(96 a^4 (4 A+5 B x)-16 a^3 x (A (27 b+32 c x)+5 B x (7 b+9 c x))+4 a^2 x^2 \left(2 A \left(63 b^2+161 b c x+128 c^2 x^2\right)+25 b B x (7 b+22 c x)\right)-210 a b^2 x^3 (3 A b+14 A c x+5 b B x)+945 A b^4 x^4\right)}{1920 a^5 x^5}","-\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{\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(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{\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{A \sqrt{a+b x+c x^2}}{5 a x^5}",1,"-1/1920*(Sqrt[a + x*(b + c*x)]*(945*A*b^4*x^4 + 96*a^4*(4*A + 5*B*x) - 210*a*b^2*x^3*(3*A*b + 5*b*B*x + 14*A*c*x) - 16*a^3*x*(5*B*x*(7*b + 9*c*x) + A*(27*b + 32*c*x)) + 4*a^2*x^2*(25*b*B*x*(7*b + 22*c*x) + 2*A*(63*b^2 + 161*b*c*x + 128*c^2*x^2))))/(a^5*x^5) + ((-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 + x*(b + c*x)])])/(256*a^(11/2))","A",1
961,1,300,280,0.4277223,"\int \frac{x^4 (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^4*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{c} \left(-256 a^3 B c^2+4 a^2 c \left(-2 b c (39 A+61 B x)+4 c^2 x (9 A-8 B x)+115 b^2 B\right)+a \left(10 b^3 c (9 A+53 B x)+4 b^2 c^2 x (43 B x-93 A)-8 b c^3 x^2 (15 A+7 B x)+16 c^4 x^3 (3 A+2 B x)-105 b^4 B\right)+b^2 x \left(5 b^2 c (18 A-7 B x)+2 b c^2 x (15 A+7 B x)-4 c^3 x^2 (3 A+2 B x)-105 b^3 B\right)\right)+3 \left(b^2-4 a c\right) \sqrt{a+x (b+c x)} \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+x (b+c x)}}\right)}{48 c^{9/2} \left(4 a c-b^2\right) \sqrt{a+x (b+c 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{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{\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}}",1,"(2*Sqrt[c]*(-256*a^3*B*c^2 + b^2*x*(-105*b^3*B + 5*b^2*c*(18*A - 7*B*x) - 4*c^3*x^2*(3*A + 2*B*x) + 2*b*c^2*x*(15*A + 7*B*x)) + a*(-105*b^4*B + 16*c^4*x^3*(3*A + 2*B*x) - 8*b*c^3*x^2*(15*A + 7*B*x) + 4*b^2*c^2*x*(-93*A + 43*B*x) + 10*b^3*c*(9*A + 53*B*x)) + 4*a^2*c*(115*b^2*B + 4*c^2*x*(9*A - 8*B*x) - 2*b*c*(39*A + 61*B*x))) + 3*(b^2 - 4*a*c)*(35*b^3*B - 30*A*b^2*c - 60*a*b*B*c + 24*a*A*c^2)*Sqrt[a + x*(b + c*x)]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(48*c^(9/2)*(-b^2 + 4*a*c)*Sqrt[a + x*(b + c*x)])","A",1
962,1,221,197,0.2751593,"\int \frac{x^3 (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^3*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{c} \left(4 a^2 c (8 A c-13 b B+6 B c x)+a \left(-2 b^2 c (6 A+31 B x)-20 b c^2 x (B x-2 A)+8 c^3 x^2 (2 A+B x)+15 b^3 B\right)+b^2 x \left(b (5 B c x-12 A c)-2 c^2 x (2 A+B x)+15 b^2 B\right)\right)-3 \left(b^2-4 a c\right) \sqrt{a+x (b+c x)} \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+x (b+c x)}}\right)}{8 c^{7/2} \left(4 a c-b^2\right) \sqrt{a+x (b+c x)}}","\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)}",1,"(2*Sqrt[c]*(4*a^2*c*(-13*b*B + 8*A*c + 6*B*c*x) + a*(15*b^3*B - 20*b*c^2*x*(-2*A + B*x) + 8*c^3*x^2*(2*A + B*x) - 2*b^2*c*(6*A + 31*B*x)) + b^2*x*(15*b^2*B - 2*c^2*x*(2*A + B*x) + b*(-12*A*c + 5*B*c*x))) - 3*(b^2 - 4*a*c)*(5*b^2*B - 4*A*b*c - 4*a*B*c)*Sqrt[a + x*(b + c*x)]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(8*c^(7/2)*(-b^2 + 4*a*c)*Sqrt[a + x*(b + c*x)])","A",1
963,1,148,153,0.2310164,"\int \frac{x^2 (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(x^2*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{\frac{2 \sqrt{c} \left(8 a^2 B c+a \left(2 b c (A+5 B x)+4 c^2 x (B x-A)-3 b^2 B\right)-b^2 x (-2 A c+3 b B+B c x)\right)}{\sqrt{a+x (b+c x)}}+\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+x (b+c x)}}\right)}{2 c^{5/2} \left(4 a c-b^2\right)}","\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*Sqrt[c]*(8*a^2*B*c - b^2*x*(3*b*B - 2*A*c + B*c*x) + a*(-3*b^2*B + 4*c^2*x*(-A + B*x) + 2*b*c*(A + 5*B*x))))/Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*(3*b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(2*c^(5/2)*(-b^2 + 4*a*c))","A",1
964,1,102,96,0.2819217,"\int \frac{x (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(x*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{\frac{2 \sqrt{c} (-2 a c (A+B x)+a b B+b x (b B-A c))}{\sqrt{a+x (b+c x)}}-B \left(b^2-4 a c\right) \log \left(2 \sqrt{c} \sqrt{a+x (b+c x)}+b+2 c x\right)}{c^{3/2} \left(4 a c-b^2\right)}","\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*Sqrt[c]*(a*b*B + b*(b*B - A*c)*x - 2*a*c*(A + B*x)))/Sqrt[a + x*(b + c*x)] - B*(b^2 - 4*a*c)*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/(c^(3/2)*(-b^2 + 4*a*c))","A",1
965,1,44,45,0.1606246,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(a + b*x + c*x^2)^(3/2),x]","\frac{2 B (2 a+b x)-2 A (b+2 c x)}{\left(b^2-4 a c\right) \sqrt{a+x (b+c 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}}",1,"(2*B*(2*a + b*x) - 2*A*(b + 2*c*x))/((b^2 - 4*a*c)*Sqrt[a + x*(b + c*x)])","A",1
966,1,104,96,0.1249524,"\int \frac{A+B x}{x \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x*(a + b*x + c*x^2)^(3/2)),x]","\frac{\frac{2 \sqrt{a} \left(a B (b+2 c x)-A \left(-2 a c+b^2+b c x\right)\right)}{\sqrt{a+x (b+c x)}}+A \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{a^{3/2} \left(4 a c-b^2\right)}","\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*Sqrt[a]*(a*B*(b + 2*c*x) - A*(b^2 - 2*a*c + b*c*x)))/Sqrt[a + x*(b + c*x)] + A*(b^2 - 4*a*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(a^(3/2)*(-b^2 + 4*a*c))","A",1
967,1,150,158,0.1826701,"\int \frac{A+B x}{x^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^2*(a + b*x + c*x^2)^(3/2)),x]","\frac{\frac{2 \sqrt{a} \left(-4 a^2 c (A-B x)+a A \left(b^2-10 b c x-8 c^2 x^2\right)-2 a b B x (b+c x)+3 A b^2 x (b+c x)\right)}{x \sqrt{a+x (b+c x)}}-\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+x (b+c x)}}\right)}{2 a^{5/2} \left(4 a c-b^2\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{\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{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*Sqrt[a]*(-4*a^2*c*(A - B*x) + 3*A*b^2*x*(b + c*x) - 2*a*b*B*x*(b + c*x) + a*A*(b^2 - 10*b*c*x - 8*c^2*x^2)))/(x*Sqrt[a + x*(b + c*x)]) - (3*A*b - 2*a*B)*(b^2 - 4*a*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(2*a^(5/2)*(-b^2 + 4*a*c))","A",1
968,1,214,231,0.2889333,"\int \frac{A+B x}{x^3 \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^3*(a + b*x + c*x^2)^(3/2)),x]","\frac{3 \left(b^2-4 a c\right) \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+x (b+c x)}}\right)-\frac{2 \sqrt{a} \left(8 a^3 c (A+2 B x)+a^2 \left(4 B x \left(-b^2+10 b c x+8 c^2 x^2\right)-2 A \left(b^2+10 b c x-12 c^2 x^2\right)\right)-a b x \left(A \left(-5 b^2+62 b c x+52 c^2 x^2\right)+12 b B x (b+c x)\right)+15 A b^3 x^2 (b+c x)\right)}{x^2 \sqrt{a+x (b+c x)}}}{8 a^{7/2} \left(4 a c-b^2\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{\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{\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{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*Sqrt[a]*(8*a^3*c*(A + 2*B*x) + 15*A*b^3*x^2*(b + c*x) + a^2*(-2*A*(b^2 + 10*b*c*x - 12*c^2*x^2) + 4*B*x*(-b^2 + 10*b*c*x + 8*c^2*x^2)) - a*b*x*(12*b*B*x*(b + c*x) + A*(-5*b^2 + 62*b*c*x + 52*c^2*x^2))))/(x^2*Sqrt[a + x*(b + c*x)]) + 3*(b^2 - 4*a*c)*(5*A*b^2 - 4*a*b*B - 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(8*a^(7/2)*(-b^2 + 4*a*c))","A",1
969,1,294,317,0.4296619,"\int \frac{A+B x}{x^4 \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(x^4*(a + b*x + c*x^2)^(3/2)),x]","\frac{\frac{2 \sqrt{a} \left(-16 a^4 c (2 A+3 B x)+4 a^3 \left(2 A \left(b^2+7 b c x+16 c^2 x^2\right)+3 B x \left(b^2+10 b c x-12 c^2 x^2\right)\right)+2 a^2 x \left(A \left(-7 b^3-86 b^2 c x+244 b c^2 x^2+128 c^3 x^3\right)+3 b B x \left(-5 b^2+62 b c x+52 c^2 x^2\right)\right)-5 a b^2 x^2 \left(A \left(-7 b^2+106 b c x+92 c^2 x^2\right)+18 b B x (b+c x)\right)+105 A b^4 x^3 (b+c x)\right)}{x^3 \sqrt{a+x (b+c x)}}-3 \left(b^2-4 a c\right) \left(5 A \left(7 b^3-12 a b c\right)+6 a B \left(4 a c-5 b^2\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{48 a^{9/2} \left(4 a c-b^2\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{\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{\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 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{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*Sqrt[a]*(-16*a^4*c*(2*A + 3*B*x) + 105*A*b^4*x^3*(b + c*x) + 4*a^3*(3*B*x*(b^2 + 10*b*c*x - 12*c^2*x^2) + 2*A*(b^2 + 7*b*c*x + 16*c^2*x^2)) - 5*a*b^2*x^2*(18*b*B*x*(b + c*x) + A*(-7*b^2 + 106*b*c*x + 92*c^2*x^2)) + 2*a^2*x*(3*b*B*x*(-5*b^2 + 62*b*c*x + 52*c^2*x^2) + A*(-7*b^3 - 86*b^2*c*x + 244*b*c^2*x^2 + 128*c^3*x^3))))/(x^3*Sqrt[a + x*(b + c*x)]) - 3*(b^2 - 4*a*c)*(6*a*B*(-5*b^2 + 4*a*c) + 5*A*(7*b^3 - 12*a*b*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(48*a^(9/2)*(-b^2 + 4*a*c))","A",1
970,1,414,285,0.7928096,"\int \frac{x^4 (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^4*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","\frac{2 \left(\frac{x^5 \left(A \left(16 a^2 c^2-28 a b^2 c-20 a b c^2 x+7 b^4+7 b^3 c x\right)+2 a B \left(16 a b c+12 a c^2 x-5 b^3-5 b^2 c x\right)\right)}{a \left(4 a c-b^2\right) \sqrt{a+x (b+c x)}}+\frac{3 a^2 \left(b^2-4 a c\right)^2 (5 b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} \sqrt{a+x (b+c x)} \left(128 a^4 B c^2-4 a^3 c \left(-2 b c (5 A+7 B x)+4 c^2 x (3 A+4 B x)+25 b^2 B\right)+a^2 \left(-2 b^3 c (3 A+5 B x)+4 b^2 c^2 x (A+2 B x)+16 b c^3 x^2 (A+B x)+16 c^4 x^3 (2 A+3 B x)+15 b^4 B\right)-4 a b c^3 x^3 (4 A b+10 A c x+5 b B x)+14 A b^3 c^3 x^4\right)}{4 a c^{7/2} \left(4 a c-b^2\right)}+\frac{x^5 \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{(a+x (b+c x))^{3/2}}\right)}{3 a \left(b^2-4 a c\right)}","-\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^5*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x))^(3/2) + (x^5*(2*a*B*(-5*b^3 + 16*a*b*c - 5*b^2*c*x + 12*a*c^2*x) + A*(7*b^4 - 28*a*b^2*c + 16*a^2*c^2 + 7*b^3*c*x - 20*a*b*c^2*x)))/(a*(-b^2 + 4*a*c)*Sqrt[a + x*(b + c*x)]) + (-2*Sqrt[c]*Sqrt[a + x*(b + c*x)]*(128*a^4*B*c^2 + 14*A*b^3*c^3*x^4 - 4*a*b*c^3*x^3*(4*A*b + 5*b*B*x + 10*A*c*x) + a^2*(15*b^4*B + 16*b*c^3*x^2*(A + B*x) + 4*b^2*c^2*x*(A + 2*B*x) + 16*c^4*x^3*(2*A + 3*B*x) - 2*b^3*c*(3*A + 5*B*x)) - 4*a^3*c*(25*b^2*B + 4*c^2*x*(3*A + 4*B*x) - 2*b*c*(5*A + 7*B*x))) + 3*a^2*(b^2 - 4*a*c)^2*(5*b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(4*a*c^(7/2)*(-b^2 + 4*a*c))))/(3*a*(b^2 - 4*a*c))","A",1
971,1,201,189,0.39448,"\int \frac{x^3 (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^3*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{c^{5/2}}-\frac{2 \left(4 a^3 c (4 A c-5 b B+6 B c x)+a^2 \left(24 A b c^2 x+8 c^3 x^2 (3 A+4 B x)+3 b^3 B-42 b^2 B c x\right)+2 a b x \left(b c^2 x (3 A-14 B x)+6 A c^3 x^2+3 b^3 B-9 b^2 B c x\right)+b^3 x^2 \left(-A c^2 x+3 b^2 B+4 b B c x\right)\right)}{3 c^2 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{3/2}}","-\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*(4*a^3*c*(-5*b*B + 4*A*c + 6*B*c*x) + b^3*x^2*(3*b^2*B + 4*b*B*c*x - A*c^2*x) + 2*a*b*x*(3*b^3*B - 9*b^2*B*c*x + 6*A*c^3*x^2 + b*c^2*x*(3*A - 14*B*x)) + a^2*(3*b^3*B - 42*b^2*B*c*x + 24*A*b*c^2*x + 8*c^3*x^2*(3*A + 4*B*x))))/(3*c^2*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2)) + (B*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/c^(5/2)","A",1
972,1,110,94,0.2497917,"\int \frac{x^2 (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(x^2*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","\frac{2 \left(-16 a^3 B+8 a^2 (A b-3 B x (b+c x))+2 a x \left(A \left(6 b^2+6 b c x+4 c^2 x^2\right)-3 b B x (b+2 c x)\right)+b^2 x^2 (3 A b+2 A c x+b B x)\right)}{3 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{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*(-16*a^3*B + b^2*x^2*(3*A*b + b*B*x + 2*A*c*x) + 8*a^2*(A*b - 3*B*x*(b + c*x)) + 2*a*x*(-3*b*B*x*(b + 2*c*x) + A*(6*b^2 + 6*b*c*x + 4*c^2*x^2))))/(3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2))","A",1
973,1,114,114,0.1701358,"\int \frac{x (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(x*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","\frac{2 \left(8 a^2 (b B-A c)-2 a A b (b+6 c x)+4 a B x \left(3 b^2+3 b c x+2 c^2 x^2\right)+b x \left(b B x (3 b+2 c x)-A \left(3 b^2+12 b c x+8 c^2 x^2\right)\right)\right)}{3 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{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*(8*a^2*(b*B - A*c) - 2*a*A*b*(b + 6*c*x) + 4*a*B*x*(3*b^2 + 3*b*c*x + 2*c^2*x^2) + b*x*(b*B*x*(3*b + 2*c*x) - A*(3*b^2 + 12*b*c*x + 8*c^2*x^2))))/(3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2))","A",1
974,1,99,90,0.1011869,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \left(B \left(8 a^2 c+2 a b (b+6 c x)+b x \left(3 b^2+12 b c x+8 c^2 x^2\right)\right)+A (b+2 c x) \left(-4 c \left(3 a+2 c x^2\right)+b^2-8 b c x\right)\right)}{3 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{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*c*x)*(b^2 - 8*b*c*x - 4*c*(3*a + 2*c*x^2)) + B*(8*a^2*c + 2*a*b*(b + 6*c*x) + b*x*(3*b^2 + 12*b*c*x + 8*c^2*x^2))))/(3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2))","A",1
975,1,179,184,0.1275763,"\int \frac{A+B x}{x \left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x*(a + b*x + c*x^2)^(5/2)),x]","-\frac{A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{a^{5/2}}+\frac{A \left(48 a^2 c^2-44 a b^2 c-40 a b c^2 x+6 b^4+6 b^3 c x\right)+16 a^2 B c (b+2 c x)}{3 a^2 \left(b^2-4 a c\right)^2 \sqrt{a+x (b+c x)}}+\frac{2 a B (b+2 c x)-2 A \left(-2 a c+b^2+b c x\right)}{3 a \left(4 a c-b^2\right) (a+x (b+c x))^{3/2}}","-\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 \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{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*(b + 2*c*x) - 2*A*(b^2 - 2*a*c + b*c*x))/(3*a*(-b^2 + 4*a*c)*(a + x*(b + c*x))^(3/2)) + (16*a^2*B*c*(b + 2*c*x) + A*(6*b^4 - 44*a*b^2*c + 48*a^2*c^2 + 6*b^3*c*x - 40*a*b*c^2*x))/(3*a^2*(b^2 - 4*a*c)^2*Sqrt[a + x*(b + c*x)]) - (A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/a^(5/2)","A",1
976,1,285,288,0.4347132,"\int \frac{A+B x}{x^2 \left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^2*(a + b*x + c*x^2)^(5/2)),x]","\frac{2 \left(\frac{3 \left(b^2-4 a c\right) (5 A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+x (b+c x)}}\right)}{4 a^{5/2}}-\frac{\sqrt{a+x (b+c x)} \left(A \left(128 a^2 c^2-100 a b^2 c+15 b^4\right)+2 a b B \left(20 a c-3 b^2\right)\right)}{2 a^2 x \left(b^2-4 a c\right)}+\frac{A \left(-32 a^2 c^2+32 a b^2 c+28 a b c^2 x-5 b^4-5 b^3 c x\right)+2 a B \left(-8 a b c-12 a c^2 x+b^3+b^2 c x\right)}{a x \left(4 a c-b^2\right) \sqrt{a+x (b+c x)}}+\frac{A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)}{x (a+x (b+c x))^{3/2}}\right)}{3 a \left(b^2-4 a c\right)}","\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(-A \left(32 a^2 c^2-32 a b^2 c+5 b^4\right)-c x \left(24 a^2 B c-28 a A b c-2 a b^2 B+5 A b^3\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{\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 (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*(-1/2*((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 + x*(b + c*x)])/(a^2*(b^2 - 4*a*c)*x) + (-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x))/(x*(a + x*(b + c*x))^(3/2)) + (2*a*B*(b^3 - 8*a*b*c + b^2*c*x - 12*a*c^2*x) + A*(-5*b^4 + 32*a*b^2*c - 32*a^2*c^2 - 5*b^3*c*x + 28*a*b*c^2*x))/(a*(-b^2 + 4*a*c)*x*Sqrt[a + x*(b + c*x)]) + (3*(5*A*b - 2*a*B)*(b^2 - 4*a*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(4*a^(5/2))))/(3*a*(b^2 - 4*a*c))","A",1
977,1,343,381,0.7315199,"\int \frac{A+B x}{x^3 \left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(x^3*(a + b*x + c*x^2)^(5/2)),x]","\frac{-\frac{8 \left(A \left(40 a^2 c^2-42 a b^2 c-36 a b c^2 x+7 b^4+7 b^3 c x\right)+4 a B \left(6 a b c+8 a c^2 x-b^3-b^2 c x\right)\right)}{a \left(4 a c-b^2\right) \sqrt{a+x (b+c x)}}+\frac{2 \sqrt{a} \sqrt{a+x (b+c x)} \left(32 a^3 c (15 A c+7 b B+16 B c x)-8 a^2 b \left(54 A b c+162 A c^2 x+5 b^2 B+50 b B c x\right)+10 a b^3 (7 A b+76 A c x+6 b B x)-105 A b^5 x\right)+15 x^2 \left(b^2-4 a c\right)^2 \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+x (b+c x)}}\right)}{2 a^{7/2} \left(4 a c-b^2\right)}+\frac{8 A \left(-2 a c+b^2+b c x\right)-8 a B (b+2 c x)}{(a+x (b+c x))^{3/2}}}{12 a x^2 \left(b^2-4 a c\right)}","-\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(-A \left(40 a^2 c^2-42 a b^2 c+7 b^4\right)-c x \left(32 a^2 B c-36 a A b c-4 a b^2 B+7 A b^3\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{\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{\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{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,"((-8*a*B*(b + 2*c*x) + 8*A*(b^2 - 2*a*c + b*c*x))/(a + x*(b + c*x))^(3/2) - (8*(4*a*B*(-b^3 + 6*a*b*c - b^2*c*x + 8*a*c^2*x) + A*(7*b^4 - 42*a*b^2*c + 40*a^2*c^2 + 7*b^3*c*x - 36*a*b*c^2*x)))/(a*(-b^2 + 4*a*c)*Sqrt[a + x*(b + c*x)]) + (2*Sqrt[a]*Sqrt[a + x*(b + c*x)]*(-105*A*b^5*x + 10*a*b^3*(7*A*b + 6*b*B*x + 76*A*c*x) + 32*a^3*c*(7*b*B + 15*A*c + 16*B*c*x) - 8*a^2*b*(5*b^2*B + 54*A*b*c + 50*b*B*c*x + 162*A*c^2*x)) + 15*(b^2 - 4*a*c)^2*(7*A*b^2 - 4*a*b*B - 4*a*A*c)*x^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + x*(b + c*x)])])/(2*a^(7/2)*(-b^2 + 4*a*c)))/(12*a*(b^2 - 4*a*c)*x^2)","A",1
978,1,119,135,0.2395683,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[(d + e*x)/(a + b*x + c*x^2)^(7/2),x]","\frac{2 \left(3 \left(b^2-4 a c\right)^2 (2 a e-b d+b e x-2 c d x)-8 \left(b^2-4 a c\right) (b+2 c x) (a+x (b+c x)) (b e-2 c d)+64 c (b+2 c x) (a+x (b+c x))^2 (b e-2 c d)\right)}{15 \left(b^2-4 a c\right)^3 (a+x (b+c x))^{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*(3*(b^2 - 4*a*c)^2*(-(b*d) + 2*a*e - 2*c*d*x + b*e*x) - 8*(b^2 - 4*a*c)*(-2*c*d + b*e)*(b + 2*c*x)*(a + x*(b + c*x)) + 64*c*(-2*c*d + b*e)*(b + 2*c*x)*(a + x*(b + c*x))^2))/(15*(b^2 - 4*a*c)^3*(a + x*(b + c*x))^(5/2))","A",1
979,1,159,181,0.188894,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^{9/2}} \, dx","Integrate[(d + e*x)/(a + b*x + c*x^2)^(9/2),x]","\frac{2 \left(5 \left(b^2-4 a c\right)^3 (2 a e-b d+b e x-2 c d x)-12 \left(b^2-4 a c\right)^2 (b+2 c x) (a+x (b+c x)) (b e-2 c d)+64 c \left(b^2-4 a c\right) (b+2 c x) (a+x (b+c x))^2 (b e-2 c d)-512 c^2 (b+2 c x) (a+x (b+c x))^3 (b e-2 c d)\right)}{35 \left(b^2-4 a c\right)^4 (a+x (b+c x))^{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*(5*(b^2 - 4*a*c)^3*(-(b*d) + 2*a*e - 2*c*d*x + b*e*x) - 12*(b^2 - 4*a*c)^2*(-2*c*d + b*e)*(b + 2*c*x)*(a + x*(b + c*x)) + 64*c*(b^2 - 4*a*c)*(-2*c*d + b*e)*(b + 2*c*x)*(a + x*(b + c*x))^2 - 512*c^2*(-2*c*d + b*e)*(b + 2*c*x)*(a + x*(b + c*x))^3))/(35*(b^2 - 4*a*c)^4*(a + x*(b + c*x))^(7/2))","A",1
980,1,49,19,0.0065162,"\int \frac{1-x}{x \sqrt{1+3 x+x^2}} \, dx","Integrate[(1 - x)/(x*Sqrt[1 + 3*x + x^2]),x]","-\tanh ^{-1}\left(\frac{2 x+3}{2 \sqrt{x^2+3 x+1}}\right)-\tanh ^{-1}\left(\frac{3 x+2}{2 \sqrt{x^2+3 x+1}}\right)","-2 \tanh ^{-1}\left(\frac{x+1}{\sqrt{x^2+3 x+1}}\right)",1,"-ArcTanh[(3 + 2*x)/(2*Sqrt[1 + 3*x + x^2])] - ArcTanh[(2 + 3*x)/(2*Sqrt[1 + 3*x + x^2])]","B",1
981,1,47,55,0.047044,"\int x^{7/2} (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[x^(7/2)*(A + B*x)*(a + b*x + c*x^2),x]","\frac{2 x^{9/2} \left(65 a (11 A+9 B x)+45 A x (13 b+11 c x)+33 B x^2 (15 b+13 c x)\right)}{6435}","\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*x^(9/2)*(65*a*(11*A + 9*B*x) + 45*A*x*(13*b + 11*c*x) + 33*B*x^2*(15*b + 13*c*x)))/6435","A",1
982,1,48,55,0.0480732,"\int x^{5/2} (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[x^(5/2)*(A + B*x)*(a + b*x + c*x^2),x]","\frac{2 x^{7/2} (143 a (9 A+7 B x)+7 x (13 A (11 b+9 c x)+9 B x (13 b+11 c x)))}{9009}","\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*x^(7/2)*(143*a*(9*A + 7*B*x) + 7*x*(13*A*(11*b + 9*c*x) + 9*B*x*(13*b + 11*c*x))))/9009","A",1
983,1,48,55,0.0462322,"\int x^{3/2} (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[x^(3/2)*(A + B*x)*(a + b*x + c*x^2),x]","\frac{2 x^{5/2} (99 a (7 A+5 B x)+5 x (11 A (9 b+7 c x)+7 B x (11 b+9 c x)))}{3465}","\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*x^(5/2)*(99*a*(7*A + 5*B*x) + 5*x*(11*A*(9*b + 7*c*x) + 7*B*x*(11*b + 9*c*x))))/3465","A",1
984,1,47,55,0.0447424,"\int \sqrt{x} (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[Sqrt[x]*(A + B*x)*(a + b*x + c*x^2),x]","\frac{2}{315} x^{3/2} (21 a (5 A+3 B x)+x (9 A (7 b+5 c x)+5 B x (9 b+7 c 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}",1,"(2*x^(3/2)*(21*a*(5*A + 3*B*x) + x*(9*A*(7*b + 5*c*x) + 5*B*x*(9*b + 7*c*x))))/315","A",1
985,1,46,53,0.0452602,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/Sqrt[x],x]","\frac{2}{105} \sqrt{x} (35 a (3 A+B x)+x (7 A (5 b+3 c x)+3 B x (7 b+5 c 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}",1,"(2*Sqrt[x]*(35*a*(3*A + B*x) + x*(7*A*(5*b + 3*c*x) + 3*B*x*(7*b + 5*c*x))))/105","A",1
986,1,44,51,0.0428849,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/x^(3/2),x]","\frac{2 x (5 A (3 b+c x)+B x (5 b+3 c x))-30 a (A-B x)}{15 \sqrt{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}",1,"(-30*a*(A - B*x) + 2*x*(5*A*(3*b + c*x) + B*x*(5*b + 3*c*x)))/(15*Sqrt[x])","A",1
987,1,42,51,0.0545343,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/x^(5/2),x]","\frac{2 x (B x (3 b+c x)-3 A (b-c x))-2 a (A+3 B x)}{3 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*B*x) + 2*x*(-3*A*(b - c*x) + B*x*(3*b + c*x)))/(3*x^(3/2))","A",1
988,1,42,51,0.0430954,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/x^(7/2),x]","-\frac{2 (a (3 A+5 B x)+5 x (A (b+3 c x)+3 B x (b-c x)))}{15 x^{5/2}}","-\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*(3*A + 5*B*x) + 5*x*(3*B*x*(b - c*x) + A*(b + 3*c*x))))/(15*x^(5/2))","A",1
989,1,45,53,0.0453988,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/x^(9/2),x]","-\frac{2 (3 a (5 A+7 B x)+7 x (A (3 b+5 c x)+5 B x (b+3 c x)))}{105 x^{7/2}}","-\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*(3*a*(5*A + 7*B*x) + 7*x*(5*B*x*(b + 3*c*x) + A*(3*b + 5*c*x))))/(105*x^(7/2))","A",1
990,1,102,113,0.1015948,"\int x^{7/2} (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[x^(7/2)*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{2 x^{9/2} \left(20995 a^2 (11 A+9 B x)+1938 a x (15 A (13 b+11 c x)+11 B x (15 b+13 c x))+33 x^2 \left(19 A \left(255 b^2+442 b c x+195 c^2 x^2\right)+13 B x \left(323 b^2+570 b c x+255 c^2 x^2\right)\right)\right)}{2078505}","\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*x^(9/2)*(20995*a^2*(11*A + 9*B*x) + 1938*a*x*(15*A*(13*b + 11*c*x) + 11*B*x*(15*b + 13*c*x)) + 33*x^2*(19*A*(255*b^2 + 442*b*c*x + 195*c^2*x^2) + 13*B*x*(323*b^2 + 570*b*c*x + 255*c^2*x^2))))/2078505","A",1
991,1,102,113,0.0964496,"\int x^{5/2} (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[x^(5/2)*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{2 x^{7/2} \left(12155 a^2 (9 A+7 B x)+1190 a x (13 A (11 b+9 c x)+9 B x (13 b+11 c x))+21 x^2 \left(17 A \left(195 b^2+330 b c x+143 c^2 x^2\right)+11 B x \left(255 b^2+442 b c x+195 c^2 x^2\right)\right)\right)}{765765}","\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*x^(7/2)*(12155*a^2*(9*A + 7*B*x) + 1190*a*x*(13*A*(11*b + 9*c*x) + 9*B*x*(13*b + 11*c*x)) + 21*x^2*(17*A*(195*b^2 + 330*b*c*x + 143*c^2*x^2) + 11*B*x*(255*b^2 + 442*b*c*x + 195*c^2*x^2))))/765765","A",1
992,1,102,113,0.1167525,"\int x^{3/2} (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[x^(3/2)*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{2 x^{5/2} \left(1287 a^2 (7 A+5 B x)+130 a x (11 A (9 b+7 c x)+7 B x (11 b+9 c x))+7 x^2 \left(5 A \left(143 b^2+234 b c x+99 c^2 x^2\right)+3 B x \left(195 b^2+330 b c x+143 c^2 x^2\right)\right)\right)}{45045}","\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*x^(5/2)*(1287*a^2*(7*A + 5*B*x) + 130*a*x*(11*A*(9*b + 7*c*x) + 7*B*x*(11*b + 9*c*x)) + 7*x^2*(5*A*(143*b^2 + 234*b*c*x + 99*c^2*x^2) + 3*B*x*(195*b^2 + 330*b*c*x + 143*c^2*x^2))))/45045","A",1
993,1,102,113,0.0927137,"\int \sqrt{x} (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[Sqrt[x]*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{2 x^{3/2} \left(3003 a^2 (5 A+3 B x)+286 a x (9 A (7 b+5 c x)+5 B x (9 b+7 c x))+5 x^2 \left(13 A \left(99 b^2+154 b c x+63 c^2 x^2\right)+7 B x \left(143 b^2+234 b c x+99 c^2 x^2\right)\right)\right)}{45045}","\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*x^(3/2)*(3003*a^2*(5*A + 3*B*x) + 286*a*x*(9*A*(7*b + 5*c*x) + 5*B*x*(9*b + 7*c*x)) + 5*x^2*(13*A*(99*b^2 + 154*b*c*x + 63*c^2*x^2) + 7*B*x*(143*b^2 + 234*b*c*x + 99*c^2*x^2))))/45045","A",1
994,1,100,111,0.1185413,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/Sqrt[x],x]","\frac{2 \sqrt{x} \left(1155 a^2 (3 A+B x)+66 a x (7 A (5 b+3 c x)+3 B x (7 b+5 c x))+x^2 \left(11 A \left(63 b^2+90 b c x+35 c^2 x^2\right)+5 B x \left(99 b^2+154 b c x+63 c^2 x^2\right)\right)\right)}{3465}","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*Sqrt[x]*(1155*a^2*(3*A + B*x) + 66*a*x*(7*A*(5*b + 3*c*x) + 3*B*x*(7*b + 5*c*x)) + x^2*(11*A*(63*b^2 + 90*b*c*x + 35*c^2*x^2) + 5*B*x*(99*b^2 + 154*b*c*x + 63*c^2*x^2))))/3465","A",1
995,1,97,109,0.118706,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^(3/2),x]","\frac{-630 a^2 (A-B x)+84 a x (5 A (3 b+c x)+B x (5 b+3 c x))+2 x^2 \left(3 A \left(35 b^2+42 b c x+15 c^2 x^2\right)+B x \left(63 b^2+90 b c x+35 c^2 x^2\right)\right)}{315 \sqrt{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}",1,"(-630*a^2*(A - B*x) + 84*a*x*(5*A*(3*b + c*x) + B*x*(5*b + 3*c*x)) + 2*x^2*(3*A*(35*b^2 + 42*b*c*x + 15*c^2*x^2) + B*x*(63*b^2 + 90*b*c*x + 35*c^2*x^2)))/(315*Sqrt[x])","A",1
996,1,94,109,0.1174987,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^(5/2),x]","\frac{2 \left(-35 a^2 (A+3 B x)+70 a x (B x (3 b+c x)-3 A (b-c x))+x^2 \left(7 A \left(15 b^2+10 b c x+3 c^2 x^2\right)+B x \left(35 b^2+42 b c x+15 c^2 x^2\right)\right)\right)}{105 x^{3/2}}","-\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*(-35*a^2*(A + 3*B*x) + 70*a*x*(-3*A*(b - c*x) + B*x*(3*b + c*x)) + x^2*(7*A*(15*b^2 + 10*b*c*x + 3*c^2*x^2) + B*x*(35*b^2 + 42*b*c*x + 15*c^2*x^2))))/(105*x^(3/2))","A",1
997,1,95,109,0.1129308,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^(7/2),x]","\frac{-2 a^2 (3 A+5 B x)-20 a x (A (b+3 c x)+3 B x (b-c x))+2 x^2 \left(5 A \left(-3 b^2+6 b c x+c^2 x^2\right)+B x \left(15 b^2+10 b c x+3 c^2 x^2\right)\right)}{15 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*(3*A + 5*B*x) - 20*a*x*(3*B*x*(b - c*x) + A*(b + 3*c*x)) + 2*x^2*(5*A*(-3*b^2 + 6*b*c*x + c^2*x^2) + B*x*(15*b^2 + 10*b*c*x + 3*c^2*x^2)))/(15*x^(5/2))","A",1
998,1,95,109,0.084998,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^(9/2),x]","-\frac{2 \left(3 a^2 (5 A+7 B x)+14 a x (A (3 b+5 c x)+5 B x (b+3 c x))+35 x^2 \left(A \left(b^2+6 b c x-3 c^2 x^2\right)-B x \left(-3 b^2+6 b c x+c^2 x^2\right)\right)\right)}{105 x^{7/2}}","-\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*(3*a^2*(5*A + 7*B*x) + 14*a*x*(5*B*x*(b + 3*c*x) + A*(3*b + 5*c*x)) + 35*x^2*(A*(b^2 + 6*b*c*x - 3*c^2*x^2) - B*x*(-3*b^2 + 6*b*c*x + c^2*x^2))))/(105*x^(7/2))","A",1
999,1,178,182,0.1989369,"\int x^{7/2} (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[x^(7/2)*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{2 x^{9/2} \left(3380195 a^3 (11 A+9 B x)+468027 a^2 x (15 A (13 b+11 c x)+11 B x (15 b+13 c x))+15939 a x^2 \left(19 A \left(255 b^2+442 b c x+195 c^2 x^2\right)+13 B x \left(323 b^2+570 b c x+255 c^2 x^2\right)\right)+429 x^3 \left(23 A \left(2261 b^3+5985 b^2 c x+5355 b c^2 x^2+1615 c^3 x^3\right)+15 B x \left(3059 b^3+8211 b^2 c x+7429 b c^2 x^2+2261 c^3 x^3\right)\right)\right)}{334639305}","\frac{2}{9} a^3 A x^{9/2}+\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{6}{19} c x^{19/2} \left(a B c+A b c+b^2 B\right)+\frac{6}{13} a x^{13/2} \left(A \left(a c+b^2\right)+a b B\right)+\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{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{2}{21} c^2 x^{21/2} (A c+3 b B)+\frac{2}{23} B c^3 x^{23/2}",1,"(2*x^(9/2)*(3380195*a^3*(11*A + 9*B*x) + 468027*a^2*x*(15*A*(13*b + 11*c*x) + 11*B*x*(15*b + 13*c*x)) + 15939*a*x^2*(19*A*(255*b^2 + 442*b*c*x + 195*c^2*x^2) + 13*B*x*(323*b^2 + 570*b*c*x + 255*c^2*x^2)) + 429*x^3*(23*A*(2261*b^3 + 5985*b^2*c*x + 5355*b*c^2*x^2 + 1615*c^3*x^3) + 15*B*x*(3059*b^3 + 8211*b^2*c*x + 7429*b*c^2*x^2 + 2261*c^3*x^3))))/334639305","A",1
1000,1,178,182,0.225449,"\int x^{5/2} (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[x^(5/2)*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{2 x^{7/2} \left(230945 a^3 (9 A+7 B x)+33915 a^2 x (13 A (11 b+9 c x)+9 B x (13 b+11 c x))+1197 a x^2 \left(17 A \left(195 b^2+330 b c x+143 c^2 x^2\right)+11 B x \left(255 b^2+442 b c x+195 c^2 x^2\right)\right)+33 x^3 \left(21 A \left(1615 b^3+4199 b^2 c x+3705 b c^2 x^2+1105 c^3 x^3\right)+13 B x \left(2261 b^3+5985 b^2 c x+5355 b c^2 x^2+1615 c^3 x^3\right)\right)\right)}{14549535}","\frac{2}{7} a^3 A x^{7/2}+\frac{2}{9} a^2 x^{9/2} (a B+3 A b)+\frac{6}{17} c x^{17/2} \left(a B c+A b c+b^2 B\right)+\frac{6}{11} a x^{11/2} \left(A \left(a c+b^2\right)+a b B\right)+\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{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{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{2}{21} B c^3 x^{21/2}",1,"(2*x^(7/2)*(230945*a^3*(9*A + 7*B*x) + 33915*a^2*x*(13*A*(11*b + 9*c*x) + 9*B*x*(13*b + 11*c*x)) + 1197*a*x^2*(17*A*(195*b^2 + 330*b*c*x + 143*c^2*x^2) + 11*B*x*(255*b^2 + 442*b*c*x + 195*c^2*x^2)) + 33*x^3*(21*A*(1615*b^3 + 4199*b^2*c*x + 3705*b*c^2*x^2 + 1105*c^3*x^3) + 13*B*x*(2261*b^3 + 5985*b^2*c*x + 5355*b*c^2*x^2 + 1615*c^3*x^3))))/14549535","A",1
1001,1,178,182,0.1919945,"\int x^{3/2} (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[x^(3/2)*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{2 x^{5/2} \left(138567 a^3 (7 A+5 B x)+20995 a^2 x (11 A (9 b+7 c x)+7 B x (11 b+9 c x))+2261 a x^2 \left(5 A \left(143 b^2+234 b c x+99 c^2 x^2\right)+3 B x \left(195 b^2+330 b c x+143 c^2 x^2\right)\right)+21 x^3 \left(19 A \left(1105 b^3+2805 b^2 c x+2431 b c^2 x^2+715 c^3 x^3\right)+11 B x \left(1615 b^3+4199 b^2 c x+3705 b c^2 x^2+1105 c^3 x^3\right)\right)\right)}{4849845}","\frac{2}{5} a^3 A x^{5/2}+\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+\frac{2}{5} c x^{15/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{3} a x^{9/2} \left(A \left(a c+b^2\right)+a b B\right)+\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}{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}{17} c^2 x^{17/2} (A c+3 b B)+\frac{2}{19} B c^3 x^{19/2}",1,"(2*x^(5/2)*(138567*a^3*(7*A + 5*B*x) + 20995*a^2*x*(11*A*(9*b + 7*c*x) + 7*B*x*(11*b + 9*c*x)) + 2261*a*x^2*(5*A*(143*b^2 + 234*b*c*x + 99*c^2*x^2) + 3*B*x*(195*b^2 + 330*b*c*x + 143*c^2*x^2)) + 21*x^3*(19*A*(1105*b^3 + 2805*b^2*c*x + 2431*b*c^2*x^2 + 715*c^3*x^3) + 11*B*x*(1615*b^3 + 4199*b^2*c*x + 3705*b*c^2*x^2 + 1105*c^3*x^3))))/4849845","A",1
1002,1,178,182,0.2027922,"\int \sqrt{x} (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[Sqrt[x]*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{2 x^{3/2} \left(51051 a^3 (5 A+3 B x)+7293 a^2 x (9 A (7 b+5 c x)+5 B x (9 b+7 c x))+255 a x^2 \left(13 A \left(99 b^2+154 b c x+63 c^2 x^2\right)+7 B x \left(143 b^2+234 b c x+99 c^2 x^2\right)\right)+7 x^3 \left(17 A \left(715 b^3+1755 b^2 c x+1485 b c^2 x^2+429 c^3 x^3\right)+9 B x \left(1105 b^3+2805 b^2 c x+2431 b c^2 x^2+715 c^3 x^3\right)\right)\right)}{765765}","\frac{2}{3} a^3 A x^{3/2}+\frac{2}{5} a^2 x^{5/2} (a B+3 A b)+\frac{6}{13} c x^{13/2} \left(a B c+A b c+b^2 B\right)+\frac{6}{7} a x^{7/2} \left(A \left(a c+b^2\right)+a b B\right)+\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{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{2}{15} c^2 x^{15/2} (A c+3 b B)+\frac{2}{17} B c^3 x^{17/2}",1,"(2*x^(3/2)*(51051*a^3*(5*A + 3*B*x) + 7293*a^2*x*(9*A*(7*b + 5*c*x) + 5*B*x*(9*b + 7*c*x)) + 255*a*x^2*(13*A*(99*b^2 + 154*b*c*x + 63*c^2*x^2) + 7*B*x*(143*b^2 + 234*b*c*x + 99*c^2*x^2)) + 7*x^3*(17*A*(715*b^3 + 1755*b^2*c*x + 1485*b*c^2*x^2 + 429*c^3*x^3) + 9*B*x*(1105*b^3 + 2805*b^2*c*x + 2431*b*c^2*x^2 + 715*c^3*x^3))))/765765","A",1
1003,1,176,180,0.1959135,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{\sqrt{x}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/Sqrt[x],x]","\frac{2 \sqrt{x} \left(15015 a^3 (3 A+B x)+1287 a^2 x (7 A (5 b+3 c x)+3 B x (7 b+5 c x))+39 a x^2 \left(11 A \left(63 b^2+90 b c x+35 c^2 x^2\right)+5 B x \left(99 b^2+154 b c x+63 c^2 x^2\right)\right)+x^3 \left(15 A \left(429 b^3+1001 b^2 c x+819 b c^2 x^2+231 c^3 x^3\right)+7 B x \left(715 b^3+1755 b^2 c x+1485 b c^2 x^2+429 c^3 x^3\right)\right)\right)}{45045}","2 a^3 A \sqrt{x}+\frac{2}{3} a^2 x^{3/2} (a B+3 A b)+\frac{6}{11} c x^{11/2} \left(a B c+A b c+b^2 B\right)+\frac{6}{5} a x^{5/2} \left(A \left(a c+b^2\right)+a b B\right)+\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{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{2}{13} c^2 x^{13/2} (A c+3 b B)+\frac{2}{15} B c^3 x^{15/2}",1,"(2*Sqrt[x]*(15015*a^3*(3*A + B*x) + 1287*a^2*x*(7*A*(5*b + 3*c*x) + 3*B*x*(7*b + 5*c*x)) + 39*a*x^2*(11*A*(63*b^2 + 90*b*c*x + 35*c^2*x^2) + 5*B*x*(99*b^2 + 154*b*c*x + 63*c^2*x^2)) + x^3*(15*A*(429*b^3 + 1001*b^2*c*x + 819*b*c^2*x^2 + 231*c^3*x^3) + 7*B*x*(715*b^3 + 1755*b^2*c*x + 1485*b*c^2*x^2 + 429*c^3*x^3))))/45045","A",1
1004,1,173,176,0.1941215,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{3/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^(3/2),x]","\frac{-30030 a^3 (A-B x)+6006 a^2 x (5 A (3 b+c x)+B x (5 b+3 c x))+286 a x^2 \left(3 A \left(35 b^2+42 b c x+15 c^2 x^2\right)+B x \left(63 b^2+90 b c x+35 c^2 x^2\right)\right)+2 x^3 \left(13 A \left(231 b^3+495 b^2 c x+385 b c^2 x^2+105 c^3 x^3\right)+5 B x \left(429 b^3+1001 b^2 c x+819 b c^2 x^2+231 c^3 x^3\right)\right)}{15015 \sqrt{x}}","-\frac{2 a^3 A}{\sqrt{x}}+2 a^2 \sqrt{x} (a B+3 A b)+\frac{2}{3} c x^{9/2} \left(a B c+A b c+b^2 B\right)+2 a x^{3/2} \left(A \left(a c+b^2\right)+a b B\right)+\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}{5} x^{5/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{2}{11} c^2 x^{11/2} (A c+3 b B)+\frac{2}{13} B c^3 x^{13/2}",1,"(-30030*a^3*(A - B*x) + 6006*a^2*x*(5*A*(3*b + c*x) + B*x*(5*b + 3*c*x)) + 286*a*x^2*(3*A*(35*b^2 + 42*b*c*x + 15*c^2*x^2) + B*x*(63*b^2 + 90*b*c*x + 35*c^2*x^2)) + 2*x^3*(13*A*(231*b^3 + 495*b^2*c*x + 385*b*c^2*x^2 + 105*c^3*x^3) + 5*B*x*(429*b^3 + 1001*b^2*c*x + 819*b*c^2*x^2 + 231*c^3*x^3)))/(15015*Sqrt[x])","A",1
1005,1,170,178,0.1597795,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{5/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^(5/2),x]","\frac{2 \left(-1155 a^3 (A+3 B x)+3465 a^2 x (B x (3 b+c x)-3 A (b-c x))+99 a x^2 \left(7 A \left(15 b^2+10 b c x+3 c^2 x^2\right)+B x \left(35 b^2+42 b c x+15 c^2 x^2\right)\right)+x^3 \left(11 A \left(105 b^3+189 b^2 c x+135 b c^2 x^2+35 c^3 x^3\right)+3 B x \left(231 b^3+495 b^2 c x+385 b c^2 x^2+105 c^3 x^3\right)\right)\right)}{3465 x^{3/2}}","-\frac{2 a^3 A}{3 x^{3/2}}-\frac{2 a^2 (a B+3 A b)}{\sqrt{x}}+\frac{6}{7} c x^{7/2} \left(a B c+A b c+b^2 B\right)+6 a \sqrt{x} \left(A \left(a c+b^2\right)+a b B\right)+\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{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)+\frac{2}{9} c^2 x^{9/2} (A c+3 b B)+\frac{2}{11} B c^3 x^{11/2}",1,"(2*(-1155*a^3*(A + 3*B*x) + 3465*a^2*x*(-3*A*(b - c*x) + B*x*(3*b + c*x)) + 99*a*x^2*(7*A*(15*b^2 + 10*b*c*x + 3*c^2*x^2) + B*x*(35*b^2 + 42*b*c*x + 15*c^2*x^2)) + x^3*(11*A*(105*b^3 + 189*b^2*c*x + 135*b*c^2*x^2 + 35*c^3*x^3) + 3*B*x*(231*b^3 + 495*b^2*c*x + 385*b*c^2*x^2 + 105*c^3*x^3))))/(3465*x^(3/2))","A",1
1006,1,169,178,0.1840901,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{7/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^(7/2),x]","\frac{2 \left(-21 a^3 (3 A+5 B x)-315 a^2 x (A (b+3 c x)+3 B x (b-c x))+63 a x^2 \left(5 A \left(-3 b^2+6 b c x+c^2 x^2\right)+B x \left(15 b^2+10 b c x+3 c^2 x^2\right)\right)+x^3 \left(9 A \left(35 b^3+35 b^2 c x+21 b c^2 x^2+5 c^3 x^3\right)+B x \left(105 b^3+189 b^2 c x+135 b c^2 x^2+35 c^3 x^3\right)\right)\right)}{315 x^{5/2}}","-\frac{2 a^3 A}{5 x^{5/2}}-\frac{2 a^2 (a B+3 A b)}{3 x^{3/2}}+\frac{6}{5} c x^{5/2} \left(a B c+A b c+b^2 B\right)-\frac{6 a \left(A \left(a c+b^2\right)+a b B\right)}{\sqrt{x}}+\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)+2 \sqrt{x} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{2}{7} c^2 x^{7/2} (A c+3 b B)+\frac{2}{9} B c^3 x^{9/2}",1,"(2*(-21*a^3*(3*A + 5*B*x) - 315*a^2*x*(3*B*x*(b - c*x) + A*(b + 3*c*x)) + 63*a*x^2*(5*A*(-3*b^2 + 6*b*c*x + c^2*x^2) + B*x*(15*b^2 + 10*b*c*x + 3*c^2*x^2)) + x^3*(9*A*(35*b^3 + 35*b^2*c*x + 21*b*c^2*x^2 + 5*c^3*x^3) + B*x*(105*b^3 + 189*b^2*c*x + 135*b*c^2*x^2 + 35*c^3*x^3))))/(315*x^(5/2))","A",1
1007,1,168,174,0.1873589,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{9/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^(9/2),x]","\frac{2 \left(-\left(a^3 (5 A+7 B x)\right)-7 a^2 x (A (3 b+5 c x)+5 B x (b+3 c x))-35 a x^2 \left(A \left(b^2+6 b c x-3 c^2 x^2\right)-B x \left(-3 b^2+6 b c x+c^2 x^2\right)\right)+x^3 \left(7 A \left(-5 b^3+15 b^2 c x+5 b c^2 x^2+c^3 x^3\right)+B x \left(35 b^3+35 b^2 c x+21 b c^2 x^2+5 c^3 x^3\right)\right)\right)}{35 x^{7/2}}","-\frac{2 a^3 A}{7 x^{7/2}}-\frac{2 a^2 (a B+3 A b)}{5 x^{5/2}}+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}}+2 \sqrt{x} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)-\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*(5*A + 7*B*x)) - 7*a^2*x*(5*B*x*(b + 3*c*x) + A*(3*b + 5*c*x)) - 35*a*x^2*(A*(b^2 + 6*b*c*x - 3*c^2*x^2) - B*x*(-3*b^2 + 6*b*c*x + c^2*x^2)) + x^3*(7*A*(-5*b^3 + 15*b^2*c*x + 5*b*c^2*x^2 + c^3*x^3) + B*x*(35*b^3 + 35*b^2*c*x + 21*b*c^2*x^2 + 5*c^3*x^3))))/(35*x^(7/2))","A",1
1008,1,172,178,0.1953811,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{11/2}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/x^(11/2),x]","-\frac{2 \left(5 a^3 (7 A+9 B x)+9 a^2 x (3 A (5 b+7 c x)+7 B x (3 b+5 c x))+63 a x^2 \left(A \left(3 b^2+10 b c x+15 c^2 x^2\right)+5 B x \left(b^2+6 b c x-3 c^2 x^2\right)\right)+21 x^3 \left(5 A \left(b^3+9 b^2 c x-9 b c^2 x^2-c^3 x^3\right)-3 B x \left(-5 b^3+15 b^2 c x+5 b c^2 x^2+c^3 x^3\right)\right)\right)}{315 x^{9/2}}","-\frac{2 a^3 A}{9 x^{9/2}}-\frac{2 a^2 (a B+3 A b)}{7 x^{7/2}}-\frac{6 a \left(A \left(a c+b^2\right)+a b B\right)}{5 x^{5/2}}+6 c \sqrt{x} \left(a B c+A b c+b^2 B\right)-\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{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}}+\frac{2}{3} c^2 x^{3/2} (A c+3 b B)+\frac{2}{5} B c^3 x^{5/2}",1,"(-2*(5*a^3*(7*A + 9*B*x) + 9*a^2*x*(7*B*x*(3*b + 5*c*x) + 3*A*(5*b + 7*c*x)) + 63*a*x^2*(5*B*x*(b^2 + 6*b*c*x - 3*c^2*x^2) + A*(3*b^2 + 10*b*c*x + 15*c^2*x^2)) + 21*x^3*(5*A*(b^3 + 9*b^2*c*x - 9*b*c^2*x^2 - c^3*x^3) - 3*B*x*(-5*b^3 + 15*b^2*c*x + 5*b*c^2*x^2 + c^3*x^3))))/(315*x^(9/2))","A",1
1009,1,480,347,0.8842807,"\int \frac{x^{5/2} (A+B x)}{a+b x+c x^2} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + b*x + c*x^2),x]","\frac{\sqrt{2} B \left(\frac{\left(\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}+2 a b c-b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(-\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}+2 a b c-b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c^{7/2}}+\frac{\sqrt{2} A \left(\frac{3 a b c-b^3}{\sqrt{b^2-4 a c}}-a c+b^2\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} A \left(\frac{b^3-3 a b c}{\sqrt{b^2-4 a c}}-a c+b^2\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 B \sqrt{x} \left(b^2-a c\right)}{c^3}-\frac{2 A b \sqrt{x}}{c^2}+\frac{2 A x^{3/2}}{3 c}-\frac{2 b B x^{3/2}}{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*A*b*Sqrt[x])/c^2 + (2*B*(b^2 - a*c)*Sqrt[x])/c^3 - (2*b*B*x^(3/2))/(3*c^2) + (2*A*x^(3/2))/(3*c) + (2*B*x^(5/2))/(5*c) + (Sqrt[2]*A*(b^2 - a*c + (-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]]])/(c^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*A*(b^2 - a*c + (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]]])/(c^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*B*(((-b^3 + 2*a*b*c + (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]]])/Sqrt[b - Sqrt[b^2 - 4*a*c]] + ((-b^3 + 2*a*b*c - (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]]])/Sqrt[b + Sqrt[b^2 - 4*a*c]]))/c^(7/2)","A",1
1010,1,413,275,0.6386956,"\int \frac{x^{3/2} (A+B x)}{a+b x+c x^2} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + b*x + c*x^2),x]","\frac{\frac{3 \sqrt{2} A c \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}-b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \sqrt{2} A c \left(\frac{2 a c-b^2}{\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{\sqrt{b^2-4 a c}+b}}+3 \sqrt{2} B \left(\frac{\left(\frac{3 a b c-b^3}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b^3-3 a b c}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)+6 A c^{3/2} \sqrt{x}-6 b B \sqrt{c} \sqrt{x}+2 B c^{3/2} x^{3/2}}{3 c^{5/2}}","\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,"(-6*b*B*Sqrt[c]*Sqrt[x] + 6*A*c^(3/2)*Sqrt[x] + 2*B*c^(3/2)*x^(3/2) + (3*Sqrt[2]*A*c*(-b + (b^2 - 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[b - Sqrt[b^2 - 4*a*c]] + (3*Sqrt[2]*A*c*(-b + (-b^2 + 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[b + Sqrt[b^2 - 4*a*c]] + 3*Sqrt[2]*B*(((b^2 - a*c + (-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]]])/Sqrt[b - Sqrt[b^2 - 4*a*c]] + ((b^2 - a*c + (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]]])/Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(3*c^(5/2))","A",1
1011,1,264,221,0.2207647,"\int \frac{\sqrt{x} (A+B x)}{a+b x+c x^2} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + b*x + c*x^2),x]","-\frac{\sqrt{2} \left(-A c \sqrt{b^2-4 a c}+b B \sqrt{b^2-4 a c}+2 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^{3/2} \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \left(-A c \sqrt{b^2-4 a c}+b B \sqrt{b^2-4 a c}-2 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^{3/2} \sqrt{b^2-4 a c} \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^2*B) + A*b*c + 2*a*B*c + b*B*Sqrt[b^2 - 4*a*c] - A*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^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*(b^2*B - A*b*c - 2*a*B*c + b*B*Sqrt[b^2 - 4*a*c] - A*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^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",1
1012,1,181,180,0.2777124,"\int \frac{A+B x}{\sqrt{x} \left(a+b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + b*x + c*x^2)),x]","\frac{\sqrt{2} \left(\frac{\left(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{b-\sqrt{b^2-4 a c}}}+\frac{\left(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{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{c} \sqrt{b^2-4 a c}}","\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) + 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]]])/Sqrt[b - Sqrt[b^2 - 4*a*c]] + ((b*B - 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]]])/Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(Sqrt[c]*Sqrt[b^2 - 4*a*c])","A",1
1013,1,216,199,0.2059951,"\int \frac{A+B x}{x^{3/2} \left(a+b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + b*x + c*x^2)),x]","\frac{2 \left(-\frac{\sqrt{c} \left(A \left(\sqrt{b^2-4 a c}+b\right)-2 a B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(A \left(\sqrt{b^2-4 a c}-b\right)+2 a B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{A}{\sqrt{x}}\right)}{a}","-\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/Sqrt[x]) - (Sqrt[c]*(-2*a*B + A*(b + Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(2*a*B + A*(-b + Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])))/a","A",1
1014,1,258,284,0.5823805,"\int \frac{A+B x}{x^{5/2} \left(a+b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a + b*x + c*x^2)),x]","\frac{\frac{3 \sqrt{2} \sqrt{c} \left(\frac{\left(A \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right)-a B \left(\sqrt{b^2-4 a c}+b\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(A \left(b \sqrt{b^2-4 a c}+2 a c-b^2\right)+a B \left(b-\sqrt{b^2-4 a c}\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c}}+\frac{6 (A b-a B)}{\sqrt{x}}-\frac{2 a A}{x^{3/2}}}{3 a^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*A)/x^(3/2) + (6*(A*b - a*B))/Sqrt[x] + (3*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]]])/Sqrt[b - Sqrt[b^2 - 4*a*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]]])/Sqrt[b + Sqrt[b^2 - 4*a*c]]))/Sqrt[b^2 - 4*a*c])/(3*a^2)","A",1
1015,1,337,307,0.7894258,"\int \frac{A+B x}{x^{7/2} \left(a+b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a + b*x + c*x^2)),x]","\frac{-\frac{6 a^2 A}{x^{5/2}}+\frac{30 \left(a A c+a b B-A b^2\right)}{\sqrt{x}}-\frac{15 \sqrt{2} \sqrt{c} \left(-\frac{\left(a B \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right)-A \left(b^2 \sqrt{b^2-4 a c}-a c \sqrt{b^2-4 a c}-3 a b c+b^3\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(A \left(-b^2 \sqrt{b^2-4 a c}+a c \sqrt{b^2-4 a c}-3 a b c+b^3\right)+a B \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)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c}}+\frac{10 a (A b-a B)}{x^{3/2}}}{15 a^3}","-\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,"((-6*a^2*A)/x^(5/2) + (10*a*(A*b - a*B))/x^(3/2) + (30*(-(A*b^2) + a*b*B + a*A*c))/Sqrt[x] - (15*Sqrt[2]*Sqrt[c]*(-(((a*B*(b^2 - 2*a*c + b*Sqrt[b^2 - 4*a*c]) - A*(b^3 - 3*a*b*c + b^2*Sqrt[b^2 - 4*a*c] - a*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((a*B*(-b^2 + 2*a*c + b*Sqrt[b^2 - 4*a*c]) + A*(b^3 - 3*a*b*c - b^2*Sqrt[b^2 - 4*a*c] + a*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/Sqrt[b + Sqrt[b^2 - 4*a*c]]))/Sqrt[b^2 - 4*a*c])/(15*a^3)","A",1
1016,1,430,381,1.0694348,"\int \frac{A+B x}{x^{9/2} \left(a+b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(x^(9/2)*(a + b*x + c*x^2)),x]","\frac{-\frac{30 a^3 A}{x^{7/2}}+\frac{105 \sqrt{2} \sqrt{c} \left(\frac{\left(A \left(2 a^2 c^2-4 a b^2 c-2 a b c \sqrt{b^2-4 a c}+b^3 \sqrt{b^2-4 a c}+b^4\right)+a B \left(-b^2 \sqrt{b^2-4 a c}+a c \sqrt{b^2-4 a c}+3 a b c-b^3\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(A \left(-2 a^2 c^2+4 a b^2 c-2 a b c \sqrt{b^2-4 a c}+b^3 \sqrt{b^2-4 a c}-b^4\right)+a B \left(-b^2 \sqrt{b^2-4 a c}+a c \sqrt{b^2-4 a c}-3 a b c+b^3\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c}}+\frac{42 a^2 (A b-a B)}{x^{5/2}}+\frac{70 a \left(a A c+a b B-A b^2\right)}{x^{3/2}}+\frac{210 \left(A \left(b^3-2 a b c\right)+a B \left(a c-b^2\right)\right)}{\sqrt{x}}}{105 a^4}","-\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 \left(-a A c-a b B+A b^2\right)}{3 a^3 x^{3/2}}+\frac{2 (A b-a B)}{5 a^2 x^{5/2}}-\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 A}{7 a x^{7/2}}",1,"((-30*a^3*A)/x^(7/2) + (42*a^2*(A*b - a*B))/x^(5/2) + (70*a*(-(A*b^2) + a*b*B + a*A*c))/x^(3/2) + (210*(a*B*(-b^2 + a*c) + A*(b^3 - 2*a*b*c)))/Sqrt[x] + (105*Sqrt[2]*Sqrt[c]*(((a*B*(-b^3 + 3*a*b*c - b^2*Sqrt[b^2 - 4*a*c] + a*c*Sqrt[b^2 - 4*a*c]) + A*(b^4 - 4*a*b^2*c + 2*a^2*c^2 + b^3*Sqrt[b^2 - 4*a*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]]])/Sqrt[b - Sqrt[b^2 - 4*a*c]] + ((a*B*(b^3 - 3*a*b*c - b^2*Sqrt[b^2 - 4*a*c] + a*c*Sqrt[b^2 - 4*a*c]) + A*(-b^4 + 4*a*b^2*c - 2*a^2*c^2 + b^3*Sqrt[b^2 - 4*a*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]]])/Sqrt[b + Sqrt[b^2 - 4*a*c]]))/Sqrt[b^2 - 4*a*c])/(105*a^4)","A",1
1017,1,413,411,1.3989507,"\int \frac{x^{5/2} (A+B x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + b*x + c*x^2)^2,x]","\frac{\frac{a \left(-\frac{\sqrt{2} \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{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \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{\sqrt{b^2-4 a c}+b}}-2 \sqrt{c} \sqrt{x} \left(10 a B c+A b c-3 b^2 B\right)+2 c^{3/2} x^{3/2} (2 A c-b B)\right)}{2 c^{5/2}}+\frac{x^{7/2} \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{a+x (b+c x)}+x^{5/2} (2 a B-A b)}{a \left(b^2-4 a c\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,"((-(A*b) + 2*a*B)*x^(5/2) + (x^(7/2)*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x)) + (a*(-2*Sqrt[c]*(-3*b^2*B + A*b*c + 10*a*B*c)*Sqrt[x] + 2*c^(3/2)*(-(b*B) + 2*A*c)*x^(3/2) - (Sqrt[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[b - Sqrt[b^2 - 4*a*c]] - (Sqrt[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[b + Sqrt[b^2 - 4*a*c]]))/(2*c^(5/2)))/(a*(b^2 - 4*a*c))","A",1
1018,1,339,321,1.0800976,"\int \frac{x^{3/2} (A+B x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + b*x + c*x^2)^2,x]","\frac{\frac{x^{5/2} \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{a+x (b+c x)}+\frac{a \left(-\frac{\sqrt{2} \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{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \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{\sqrt{b^2-4 a c}+b}}+2 \sqrt{c} \sqrt{x} (2 A c-b B)\right)}{2 c^{3/2}}+x^{3/2} (2 a B-A b)}{a \left(b^2-4 a c\right)}","-\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}}",1,"((-(A*b) + 2*a*B)*x^(3/2) + (x^(5/2)*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x)) + (a*(2*Sqrt[c]*(-(b*B) + 2*A*c)*Sqrt[x] - (Sqrt[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[b - Sqrt[b^2 - 4*a*c]] - (Sqrt[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[b + Sqrt[b^2 - 4*a*c]]))/(2*c^(3/2)))/(a*(b^2 - 4*a*c))","A",1
1019,1,295,276,0.6821529,"\int \frac{\sqrt{x} (A+B x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + b*x + c*x^2)^2,x]","\frac{\frac{x^{3/2} \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{a+x (b+c x)}+\frac{a \left(\frac{\left(-2 A c \sqrt{b^2-4 a c}+b 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)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}-\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{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c}}+\sqrt{x} (2 a B-A b)}{a \left(b^2-4 a c\right)}","-\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,"((-(A*b) + 2*a*B)*Sqrt[x] + (x^(3/2)*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x)) + (a*(-(((-(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[b - Sqrt[b^2 - 4*a*c]]) + ((b^2*B - 4*A*b*c + 4*a*B*c + b*B*Sqrt[b^2 - 4*a*c] - 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[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])))/(Sqrt[2]*Sqrt[c]))/(a*(b^2 - 4*a*c))","A",1
1020,1,285,304,0.6342576,"\int \frac{A+B x}{\sqrt{x} \left(a+b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + b*x + c*x^2)^2),x]","\frac{\frac{\sqrt{x} \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{a+x (b+c x)}+\frac{\sqrt{c} \left(\frac{\left(A \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right)-2 a B \left(\sqrt{b^2-4 a c}-2 b\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(A \left(b \sqrt{b^2-4 a c}+12 a c-b^2\right)-2 a B \left(\sqrt{b^2-4 a c}+2 b\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{b^2-4 a c}}}{a \left(b^2-4 a c\right)}","\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*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x)) + (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[b - Sqrt[b^2 - 4*a*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[b + Sqrt[b^2 - 4*a*c]]))/(Sqrt[2]*Sqrt[b^2 - 4*a*c]))/(a*(b^2 - 4*a*c))","A",1
1021,1,367,406,0.9956244,"\int \frac{A+B x}{x^{3/2} \left(a+b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + b*x + c*x^2)^2),x]","\frac{\frac{10 a A c+a b B-3 A b^2}{a \sqrt{x}}+\frac{A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)}{\sqrt{x} (a+x (b+c x))}+\frac{\sqrt{c} \left(\frac{\left(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)+a B \left(b \sqrt{b^2-4 a c}-12 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)}{\sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(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)+a B \left(b \sqrt{b^2-4 a c}+12 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)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{b^2-4 a c}}}{a \left(b^2-4 a c\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*Sqrt[x]) + (-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x))/(Sqrt[x]*(a + x*(b + c*x))) + (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[b - Sqrt[b^2 - 4*a*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[b + Sqrt[b^2 - 4*a*c]]))/(Sqrt[2]*a*Sqrt[b^2 - 4*a*c]))/(a*(b^2 - 4*a*c))","A",1
1022,1,473,521,1.8339989,"\int \frac{A+B x}{x^{5/2} \left(a+b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a + b*x + c*x^2)^2),x]","\frac{\frac{\frac{3 \sqrt{c} \left(\frac{\left(A \left(28 a^2 c^2-29 a b^2 c-19 a b c \sqrt{b^2-4 a c}+5 b^3 \sqrt{b^2-4 a c}+5 b^4\right)+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)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(A \left(-28 a^2 c^2+29 a b^2 c-19 a b c \sqrt{b^2-4 a c}+5 b^3 \sqrt{b^2-4 a c}-5 b^4\right)+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)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{b^2-4 a c}}+\frac{3 \left(A \left(5 b^3-19 a b c\right)+a B \left(10 a c-3 b^2\right)\right)}{\sqrt{x}}}{a^2}+\frac{14 a A c+3 a b B-5 A b^2}{a x^{3/2}}+\frac{3 A \left(-2 a c+b^2+b c x\right)-3 a B (b+2 c x)}{x^{3/2} (a+x (b+c x))}}{3 a \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{-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{\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^2-29 a b^2 c-19 a b c \sqrt{b^2-4 a c}+5 b^3 \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^2-29 a b^2 c+19 a b c \sqrt{b^2-4 a c}-5 b^3 \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{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)/(a*x^(3/2)) + (-3*a*B*(b + 2*c*x) + 3*A*(b^2 - 2*a*c + b*c*x))/(x^(3/2)*(a + x*(b + c*x))) + ((3*(a*B*(-3*b^2 + 10*a*c) + A*(5*b^3 - 19*a*b*c)))/Sqrt[x] + (3*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[b - Sqrt[b^2 - 4*a*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[b + Sqrt[b^2 - 4*a*c]]))/(Sqrt[2]*Sqrt[b^2 - 4*a*c]))/a^2)/(3*a*(b^2 - 4*a*c))","A",1
1023,1,745,528,2.5817017,"\int \frac{x^{7/2} (A+B x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a + b*x + c*x^2)^3,x]","\frac{\frac{x^{9/2} \left(A \left(4 a^2 c^2-15 a b^2 c-8 a b c^2 x+5 b^4+5 b^3 c x\right)+3 a B \left(8 a b c+4 a c^2 x-3 b^3-3 b^2 c x\right)\right)}{2 a \left(4 a c-b^2\right) (a+x (b+c x))}+\frac{\frac{2 a^2 x^{3/2} \left(-28 a B c+12 A b c+b^2 B\right)}{c}-\frac{2 a^2 \sqrt{x} \left(20 a A c^2-24 a b B c+A b^2 c+3 b^3 B\right)}{c^2}+\frac{\sqrt{2} a^2 \left(4 a^2 c^2 \left(21 B \sqrt{b^2-4 a c}+10 A c\right)-4 a b c^2 \left(4 A \sqrt{b^2-4 a c}+33 a B\right)+9 a b^2 c \left(2 A c-3 B \sqrt{b^2-4 a c}\right)+b^4 \left(3 B \sqrt{b^2-4 a c}-A c\right)+b^3 c \left(A \sqrt{b^2-4 a c}+33 a B\right)-3 b^5 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^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} a^2 \left(4 a^2 c^2 \left(21 B \sqrt{b^2-4 a c}-10 A c\right)+4 a b c^2 \left(33 a B-4 A \sqrt{b^2-4 a c}\right)-9 a b^2 c \left(3 B \sqrt{b^2-4 a c}+2 A c\right)+b^4 \left(3 B \sqrt{b^2-4 a c}+A c\right)+b^3 \left(A c \sqrt{b^2-4 a c}-33 a B c\right)+3 b^5 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{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}+2 a x^{5/2} \left(4 a A c+12 a b B-7 A b^2\right)+2 x^{7/2} \left(A \left(5 b^3-8 a b c\right)+3 a B \left(4 a c-3 b^2\right)\right)}{4 a \left(b^2-4 a c\right)}+\frac{x^{9/2} \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{(a+x (b+c x))^2}}{2 a \left(b^2-4 a c\right)}","-\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^(9/2)*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x))^2 + (x^(9/2)*(3*a*B*(-3*b^3 + 8*a*b*c - 3*b^2*c*x + 4*a*c^2*x) + A*(5*b^4 - 15*a*b^2*c + 4*a^2*c^2 + 5*b^3*c*x - 8*a*b*c^2*x)))/(2*a*(-b^2 + 4*a*c)*(a + x*(b + c*x))) + ((-2*a^2*(3*b^3*B + A*b^2*c - 24*a*b*B*c + 20*a*A*c^2)*Sqrt[x])/c^2 + (2*a^2*(b^2*B + 12*A*b*c - 28*a*B*c)*x^(3/2))/c + 2*a*(-7*A*b^2 + 12*a*b*B + 4*a*A*c)*x^(5/2) + 2*(3*a*B*(-3*b^2 + 4*a*c) + A*(5*b^3 - 8*a*b*c))*x^(7/2) + (Sqrt[2]*a^2*(-3*b^5*B + b^3*c*(33*a*B + A*Sqrt[b^2 - 4*a*c]) - 4*a*b*c^2*(33*a*B + 4*A*Sqrt[b^2 - 4*a*c]) + 9*a*b^2*c*(2*A*c - 3*B*Sqrt[b^2 - 4*a*c]) + b^4*(-(A*c) + 3*B*Sqrt[b^2 - 4*a*c]) + 4*a^2*c^2*(10*A*c + 21*B*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^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*a^2*(3*b^5*B + 4*a*b*c^2*(33*a*B - 4*A*Sqrt[b^2 - 4*a*c]) + b^4*(A*c + 3*B*Sqrt[b^2 - 4*a*c]) - 9*a*b^2*c*(2*A*c + 3*B*Sqrt[b^2 - 4*a*c]) + 4*a^2*c^2*(-10*A*c + 21*B*Sqrt[b^2 - 4*a*c]) + b^3*(-33*a*B*c + A*c*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^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(4*a*(b^2 - 4*a*c)))/(2*a*(b^2 - 4*a*c))","A",1
1024,1,589,459,2.1457485,"\int \frac{x^{5/2} (A+B x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + b*x + c*x^2)^3,x]","\frac{\frac{x^{7/2} \left(A \left(-4 a^2 c^2-5 a b^2 c+3 b^4+3 b^3 c x\right)+a B \left(16 a b c+4 a c^2 x-7 b^3-7 b^2 c x\right)\right)}{2 a \left(4 a c-b^2\right) (a+x (b+c x))}+\frac{-\frac{2 a^2 \sqrt{x} \left(20 a B c-12 A b c+b^2 B\right)}{c}+\frac{\sqrt{2} a^2 \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)}{c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} a^2 \left(4 a c^2 \left(3 A \sqrt{b^2-4 a c}-10 a B\right)+3 b^2 c \left(A \sqrt{b^2-4 a c}-6 a B\right)+4 a b c \left(9 A c-4 B \sqrt{b^2-4 a c}\right)+b^3 \left(B \sqrt{b^2-4 a c}+3 A c\right)+b^4 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{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}-2 a x^{3/2} \left(4 a A c-12 a b B+5 A b^2\right)+2 a B x^{5/2} \left(4 a c-7 b^2\right)+6 A b^3 x^{5/2}}{4 a \left(b^2-4 a c\right)}+\frac{x^{7/2} \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{(a+x (b+c x))^2}}{2 a \left(b^2-4 a c\right)}","\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{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{\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)}",1,"((x^(7/2)*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x))^2 + (x^(7/2)*(A*(3*b^4 - 5*a*b^2*c - 4*a^2*c^2 + 3*b^3*c*x) + a*B*(-7*b^3 + 16*a*b*c - 7*b^2*c*x + 4*a*c^2*x)))/(2*a*(-b^2 + 4*a*c)*(a + x*(b + c*x))) + ((-2*a^2*(b^2*B - 12*A*b*c + 20*a*B*c)*Sqrt[x])/c - 2*a*(5*A*b^2 - 12*a*b*B + 4*a*A*c)*x^(3/2) + 6*A*b^3*x^(5/2) + 2*a*B*(-7*b^2 + 4*a*c)*x^(5/2) + (Sqrt[2]*a^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]]])/(c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*a^2*(b^4*B + 3*b^2*c*(-6*a*B + A*Sqrt[b^2 - 4*a*c]) + 4*a*c^2*(-10*a*B + 3*A*Sqrt[b^2 - 4*a*c]) + 4*a*b*c*(9*A*c - 4*B*Sqrt[b^2 - 4*a*c]) + b^3*(3*A*c + B*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^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(4*a*(b^2 - 4*a*c)))/(2*a*(b^2 - 4*a*c))","A",1
1025,1,558,414,1.6611052,"\int \frac{x^{3/2} (A+B x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + b*x + c*x^2)^3,x]","\frac{\frac{\frac{9 a^2 \left(b^2 \left(B \sqrt{b^2-4 a c}+6 A c\right)-4 b c \left(A \sqrt{b^2-4 a c}+3 a B\right)+4 a c \left(B \sqrt{b^2-4 a c}+2 A c\right)+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} \sqrt{c} \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{9 a^2 \left(b^2 \left(B \sqrt{b^2-4 a c}-6 A c\right)+4 b c \left(3 a B-A \sqrt{b^2-4 a c}\right)+4 a c \left(B \sqrt{b^2-4 a c}-2 A c\right)+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} \sqrt{c} \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}+36 a^2 b B \sqrt{x}+3 A x^{3/2} \left(8 a b c+b^3\right)-9 a A \sqrt{x} \left(4 a c+b^2\right)-3 a B x^{3/2} \left(4 a c+5 b^2\right)}{6 a \left(b^2-4 a c\right)}+\frac{x^{5/2} \left(A \left(-12 a^2 c^2+5 a b^2 c+8 a b c^2 x+b^4+b^3 c x\right)+a B \left(8 a b c-4 a c^2 x-5 b^3-5 b^2 c x\right)\right)}{2 a \left(4 a c-b^2\right) (a+x (b+c x))}+\frac{x^{5/2} \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{(a+x (b+c x))^2}}{2 a \left(b^2-4 a c\right)}","-\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}}",1,"((x^(5/2)*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x))^2 + (x^(5/2)*(a*B*(-5*b^3 + 8*a*b*c - 5*b^2*c*x - 4*a*c^2*x) + A*(b^4 + 5*a*b^2*c - 12*a^2*c^2 + b^3*c*x + 8*a*b*c^2*x)))/(2*a*(-b^2 + 4*a*c)*(a + x*(b + c*x))) + (36*a^2*b*B*Sqrt[x] - 9*a*A*(b^2 + 4*a*c)*Sqrt[x] - 3*a*B*(5*b^2 + 4*a*c)*x^(3/2) + 3*A*(b^3 + 8*a*b*c)*x^(3/2) + (9*a^2*(-(b^3*B) - 4*b*c*(3*a*B + A*Sqrt[b^2 - 4*a*c]) + 4*a*c*(2*A*c + B*Sqrt[b^2 - 4*a*c]) + b^2*(6*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]*Sqrt[c]*Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (9*a^2*(b^3*B + 4*b*c*(3*a*B - A*Sqrt[b^2 - 4*a*c]) + b^2*(-6*A*c + B*Sqrt[b^2 - 4*a*c]) + 4*a*c*(-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]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(6*a*(b^2 - 4*a*c)))/(2*a*(b^2 - 4*a*c))","A",1
1026,1,510,426,1.4351228,"\int \frac{\sqrt{x} (A+B x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + b*x + c*x^2)^3,x]","\frac{-\frac{x^{3/2} \left(A \left(20 a^2 c^2-15 a b^2 c-16 a b c^2 x+b^4+b^3 c x\right)+3 a B \left(4 a c^2 x+b^3+b^2 c x\right)\right)}{2 a \left(4 a c-b^2\right) (a+x (b+c x))}+\frac{x^{3/2} \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{(a+x (b+c x))^2}+\frac{-2 A \sqrt{x} \left(b^3-16 a b c\right)+\frac{\sqrt{2} a \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)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} a \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{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}-6 a B \sqrt{x} \left(4 a c+b^2\right)}{4 a \left(b^2-4 a c\right)}}{2 a \left(b^2-4 a c\right)}","-\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(-A \left(8 a b c+b^3\right)+c x \left(12 a b B-A \left(20 a c+b^2\right)\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(-A \left(20 a c+b^2\right)+\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}}+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,"((x^(3/2)*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x))^2 - (x^(3/2)*(3*a*B*(b^3 + b^2*c*x + 4*a*c^2*x) + A*(b^4 - 15*a*b^2*c + 20*a^2*c^2 + b^3*c*x - 16*a*b*c^2*x)))/(2*a*(-b^2 + 4*a*c)*(a + x*(b + c*x))) + (-6*a*B*(b^2 + 4*a*c)*Sqrt[x] - 2*A*(b^3 - 16*a*b*c)*Sqrt[x] + (Sqrt[2]*a*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]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*a*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]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(4*a*(b^2 - 4*a*c)))/(2*a*(b^2 - 4*a*c))","A",1
1027,1,440,468,1.6854469,"\int \frac{A+B x}{\sqrt{x} \left(a+b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + b*x + c*x^2)^3),x]","\frac{-\frac{2 \sqrt{x} \left(A \left(28 a^2 c^2-25 a b^2 c-24 a b c^2 x+3 b^4+3 b^3 c x\right)+a B \left(8 a b c+20 a c^2 x+b^3+b^2 c x\right)\right)}{a \left(4 a c-b^2\right) (a+x (b+c x))}+\frac{\sqrt{2} \sqrt{c} \left(\frac{\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)}{\sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\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)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a \left(b^2-4 a c\right)}+\frac{4 \sqrt{x} \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{(a+x (b+c x))^2}}{8 a \left(b^2-4 a c\right)}","\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,"((4*Sqrt[x]*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x))^2 - (2*Sqrt[x]*(a*B*(b^3 + 8*a*b*c + b^2*c*x + 20*a*c^2*x) + A*(3*b^4 - 25*a*b^2*c + 28*a^2*c^2 + 3*b^3*c*x - 24*a*b*c^2*x)))/(a*(-b^2 + 4*a*c)*(a + x*(b + c*x))) + (Sqrt[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]]])/Sqrt[b - Sqrt[b^2 - 4*a*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]]])/Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(a*(b^2 - 4*a*c)))/(8*a*(b^2 - 4*a*c))","A",1
1028,1,628,664,2.3105573,"\int \frac{A+B x}{x^{3/2} \left(a+b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + b*x + c*x^2)^3),x]","\frac{\frac{A \left(-36 a^2 c^2+35 a b^2 c+32 a b c^2 x-5 b^4-5 b^3 c x\right)+a B \left(-16 a b c-28 a c^2 x+b^3+b^2 c x\right)}{a \sqrt{x} \left(4 a c-b^2\right) (a+x (b+c x))}+\frac{\frac{3 \left(A \left(-60 a^2 c^2+37 a b^2 c-5 b^4\right)+a b B \left(b^2-8 a c\right)\right)}{\sqrt{x}}+\frac{3 \sqrt{c} \left(-\frac{\left(A \left(60 a^2 c^2 \sqrt{b^2-4 a c}+124 a^2 b c^2-47 a b^3 c-37 a b^2 c \sqrt{b^2-4 a c}+5 b^4 \sqrt{b^2-4 a c}+5 b^5\right)-a B \left(56 a^2 c^2-10 a b^2 c-8 a b c \sqrt{b^2-4 a c}+b^3 \sqrt{b^2-4 a c}+b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(A \left(60 a^2 c^2 \sqrt{b^2-4 a c}-124 a^2 b c^2+47 a b^3 c-37 a b^2 c \sqrt{b^2-4 a c}+5 b^4 \sqrt{b^2-4 a c}-5 b^5\right)+a B \left(56 a^2 c^2-10 a b^2 c+8 a b c \sqrt{b^2-4 a c}-b^3 \sqrt{b^2-4 a c}+b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{b^2-4 a c}}}{a^2 \left(b^2-4 a c\right)}+\frac{2 \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{\sqrt{x} (a+x (b+c x))^2}}{4 a \left(b^2-4 a c\right)}","-\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^2-10 a b^2 c-8 a b c \sqrt{b^2-4 a c}+b^3 \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^2-47 a b^3 c-37 a b^2 c \sqrt{b^2-4 a c}+5 b^4 \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^2-10 a b^2 c+8 a b c \sqrt{b^2-4 a c}-b^3 \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^2-47 a b^3 c+37 a b^2 c \sqrt{b^2-4 a c}-5 b^4 \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,"((2*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(Sqrt[x]*(a + x*(b + c*x))^2) + (a*B*(b^3 - 16*a*b*c + b^2*c*x - 28*a*c^2*x) + A*(-5*b^4 + 35*a*b^2*c - 36*a^2*c^2 - 5*b^3*c*x + 32*a*b*c^2*x))/(a*(-b^2 + 4*a*c)*Sqrt[x]*(a + x*(b + c*x))) + ((3*(a*b*B*(b^2 - 8*a*c) + A*(-5*b^4 + 37*a*b^2*c - 60*a^2*c^2)))/Sqrt[x] + (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]]])/Sqrt[b - Sqrt[b^2 - 4*a*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]]])/Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(Sqrt[2]*Sqrt[b^2 - 4*a*c]))/(a^2*(b^2 - 4*a*c)))/(4*a*(b^2 - 4*a*c))","A",1
1029,1,638,454,4.916839,"\int \sqrt{x} (A+B x) \sqrt{a+b x+c x^2} \, dx","Integrate[Sqrt[x]*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{x} \sqrt{a+x (b+c x)} \left(c (10 a B+3 c x (7 A+5 B x))+b c (7 A+3 B x)-4 b^2 B\right)}{105 c^2}-\frac{i x^{3/2} \left(\sqrt{b^2-4 a c}-b\right) \sqrt{\frac{2 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+1} \sqrt{\frac{-2 x \sqrt{b^2-4 a c}+4 a+2 b x}{b x-x \sqrt{b^2-4 a c}}} \left(42 a A c^2-29 a b B c-14 A b^2 c+8 b^3 B\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)-4 \sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}} (a+x (b+c x)) \left(42 a A c^2-29 a b B c-14 A b^2 c+8 b^3 B\right)+i x^{3/2} \sqrt{\frac{2 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+1} \sqrt{\frac{-2 x \sqrt{b^2-4 a c}+4 a+2 b x}{b x-x \sqrt{b^2-4 a c}}} \left(2 a c^2 \left(10 a B-21 A \sqrt{b^2-4 a c}\right)+b^2 \left(14 A c \sqrt{b^2-4 a c}-37 a B c\right)+a b c \left(29 B \sqrt{b^2-4 a c}+56 A c\right)-2 b^3 \left(4 B \sqrt{b^2-4 a c}+7 A c\right)+8 b^4 B\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)}{210 c^3 \sqrt{x} \sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}} \sqrt{a+x (b+c x)}}","-\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 \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 B \sqrt{x} \left(a+b x+c x^2\right)^{3/2}}{7 c}",1,"(2*Sqrt[x]*Sqrt[a + x*(b + c*x)]*(-4*b^2*B + b*c*(7*A + 3*B*x) + c*(10*a*B + 3*c*x*(7*A + 5*B*x))))/(105*c^2) - (-4*(8*b^3*B - 14*A*b^2*c - 29*a*b*B*c + 42*a*A*c^2)*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])]*(a + x*(b + c*x)) + I*(8*b^3*B - 14*A*b^2*c - 29*a*b*B*c + 42*a*A*c^2)*(-b + Sqrt[b^2 - 4*a*c])*Sqrt[1 + (2*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*x^(3/2)*Sqrt[(4*a + 2*b*x - 2*Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])] + I*(8*b^4*B + 2*a*c^2*(10*a*B - 21*A*Sqrt[b^2 - 4*a*c]) - 2*b^3*(7*A*c + 4*B*Sqrt[b^2 - 4*a*c]) + a*b*c*(56*A*c + 29*B*Sqrt[b^2 - 4*a*c]) + b^2*(-37*a*B*c + 14*A*c*Sqrt[b^2 - 4*a*c]))*Sqrt[1 + (2*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*x^(3/2)*Sqrt[(4*a + 2*b*x - 2*Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])])/(210*c^3*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])]*Sqrt[x]*Sqrt[a + x*(b + c*x)])","C",1
1030,1,550,373,3.9831894,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{\sqrt{x}} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/Sqrt[x],x]","\frac{\frac{4 \sqrt{x} (a+x (b+c x)) (5 A c+b B+3 B c x)}{c}+\frac{x \left(-\frac{4 (a+x (b+c x)) \left(-6 a B c-5 A b c+2 b^2 B\right)}{x^{3/2}}+\frac{i \left(\sqrt{b^2-4 a c}-b\right) \sqrt{\frac{4 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+2} \sqrt{\frac{-x \sqrt{b^2-4 a c}+2 a+b x}{b x-x \sqrt{b^2-4 a c}}} \left(-6 a B c-5 A b c+2 b^2 B\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}}}+\frac{i \sqrt{\frac{4 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+2} \sqrt{\frac{-x \sqrt{b^2-4 a c}+2 a+b x}{b x-x \sqrt{b^2-4 a c}}} \left(-b^2 \left(2 B \sqrt{b^2-4 a c}+5 A c\right)+b \left(5 A c \sqrt{b^2-4 a c}-8 a B c\right)+2 a c \left(3 B \sqrt{b^2-4 a c}+10 A c\right)+2 b^3 B\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}}}\right)}{c^2}}{30 \sqrt{a+x (b+c 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}",1,"((4*Sqrt[x]*(b*B + 5*A*c + 3*B*c*x)*(a + x*(b + c*x)))/c + (x*((-4*(2*b^2*B - 5*A*b*c - 6*a*B*c)*(a + x*(b + c*x)))/x^(3/2) + (I*(2*b^2*B - 5*A*b*c - 6*a*B*c)*(-b + Sqrt[b^2 - 4*a*c])*Sqrt[2 + (4*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*Sqrt[(2*a + b*x - Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])])/Sqrt[a/(b + Sqrt[b^2 - 4*a*c])] + (I*(2*b^3*B - b^2*(5*A*c + 2*B*Sqrt[b^2 - 4*a*c]) + 2*a*c*(10*A*c + 3*B*Sqrt[b^2 - 4*a*c]) + b*(-8*a*B*c + 5*A*c*Sqrt[b^2 - 4*a*c]))*Sqrt[2 + (4*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*Sqrt[(2*a + b*x - Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])])/Sqrt[a/(b + Sqrt[b^2 - 4*a*c])]))/c^2)/(30*Sqrt[a + x*(b + c*x)])","C",1
1031,1,491,341,2.3610129,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^(3/2),x]","\frac{\frac{i x \sqrt{\frac{4 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+2} \sqrt{\frac{-x \sqrt{b^2-4 a c}+2 a+b x}{b x-x \sqrt{b^2-4 a c}}} \left(6 A c \sqrt{b^2-4 a c}+b B \sqrt{b^2-4 a c}+4 a B c+b^2 (-B)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)}{c \sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}}}-\frac{i x \left(\sqrt{b^2-4 a c}-b\right) \sqrt{\frac{4 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+2} \sqrt{\frac{-x \sqrt{b^2-4 a c}+2 a+b x}{b x-x \sqrt{b^2-4 a c}}} (6 A c+b B) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)}{c \sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}}}+\frac{4 (B x-3 A) (a+x (b+c x))}{\sqrt{x}}+\frac{4 (a+x (b+c x)) (6 A c+b B)}{c \sqrt{x}}}{6 \sqrt{a+x (b+c 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,"((4*(b*B + 6*A*c)*(a + x*(b + c*x)))/(c*Sqrt[x]) + (4*(-3*A + B*x)*(a + x*(b + c*x)))/Sqrt[x] - (I*(b*B + 6*A*c)*(-b + Sqrt[b^2 - 4*a*c])*Sqrt[2 + (4*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*x*Sqrt[(2*a + b*x - Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])])/(c*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])]) + (I*(-(b^2*B) + 4*a*B*c + b*B*Sqrt[b^2 - 4*a*c] + 6*A*c*Sqrt[b^2 - 4*a*c])*Sqrt[2 + (4*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*x*Sqrt[(2*a + b*x - Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])])/(c*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])]))/(6*Sqrt[a + x*(b + c*x)])","C",1
1032,1,499,353,2.7982455,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^(5/2),x]","\frac{-4 (a+x (b+c x)) (a (A+3 B x)+A b x)+\frac{x \left(i x^{3/2} \sqrt{\frac{2 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+1} \sqrt{\frac{-2 x \sqrt{b^2-4 a c}+4 a+2 b x}{b x-x \sqrt{b^2-4 a c}}} \left(A \left(b \sqrt{b^2-4 a c}+4 a c-b^2\right)+6 a B \sqrt{b^2-4 a c}\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)+i x^{3/2} \left(b-\sqrt{b^2-4 a c}\right) (6 a B+A b) \sqrt{\frac{2 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+1} \sqrt{\frac{-2 x \sqrt{b^2-4 a c}+4 a+2 b x}{b x-x \sqrt{b^2-4 a c}}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)+4 \sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}} (6 a B+A b) (a+x (b+c x))\right)}{\sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}}}}{6 a x^{3/2} \sqrt{a+x (b+c 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}}",1,"(-4*(A*b*x + a*(A + 3*B*x))*(a + x*(b + c*x)) + (x*(4*(A*b + 6*a*B)*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])]*(a + x*(b + c*x)) + I*(A*b + 6*a*B)*(b - Sqrt[b^2 - 4*a*c])*Sqrt[1 + (2*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*x^(3/2)*Sqrt[(4*a + 2*b*x - 2*Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])] + I*(6*a*B*Sqrt[b^2 - 4*a*c] + A*(-b^2 + 4*a*c + b*Sqrt[b^2 - 4*a*c]))*Sqrt[1 + (2*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*x^(3/2)*Sqrt[(4*a + 2*b*x - 2*Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])]))/Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/(6*a*x^(3/2)*Sqrt[a + x*(b + c*x)])","C",1
1033,1,576,421,4.0498292,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^{7/2}} \, dx","Integrate[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^(7/2),x]","\frac{-4 (a+x (b+c x)) \left(a^2 (3 A+5 B x)+a x (A (b+6 c x)+5 b B x)-2 A b^2 x^2\right)+\frac{x^2 \left(i x^{3/2} \left(\sqrt{b^2-4 a c}-b\right) \sqrt{\frac{2 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+1} \sqrt{\frac{-2 x \sqrt{b^2-4 a c}+4 a+2 b x}{b x-x \sqrt{b^2-4 a c}}} \left(2 A \left(b^2-3 a c\right)-5 a b B\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)+4 \sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}} (a+x (b+c x)) \left(6 a A c+5 a b B-2 A b^2\right)-i x^{3/2} \sqrt{\frac{2 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+1} \sqrt{\frac{-2 x \sqrt{b^2-4 a c}+4 a+2 b x}{b x-x \sqrt{b^2-4 a c}}} \left(2 A \left(b^2 \sqrt{b^2-4 a c}-3 a c \sqrt{b^2-4 a c}+4 a b c-b^3\right)+5 a B \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)\right)}{\sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}}}}{30 a^2 x^{5/2} \sqrt{a+x (b+c x)}}","-\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} \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{a+b x+c x^2} (x (5 a B+A b)+3 a A)}{15 a x^{5/2}}",1,"(-4*(a + x*(b + c*x))*(-2*A*b^2*x^2 + a^2*(3*A + 5*B*x) + a*x*(5*b*B*x + A*(b + 6*c*x))) + (x^2*(4*(-2*A*b^2 + 5*a*b*B + 6*a*A*c)*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])]*(a + x*(b + c*x)) + I*(-b + Sqrt[b^2 - 4*a*c])*(-5*a*b*B + 2*A*(b^2 - 3*a*c))*Sqrt[1 + (2*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*x^(3/2)*Sqrt[(4*a + 2*b*x - 2*Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])] - I*(5*a*B*(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c]) + 2*A*(-b^3 + 4*a*b*c + b^2*Sqrt[b^2 - 4*a*c] - 3*a*c*Sqrt[b^2 - 4*a*c]))*Sqrt[1 + (2*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*x^(3/2)*Sqrt[(4*a + 2*b*x - 2*Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])]))/Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/(30*a^2*x^(5/2)*Sqrt[a + x*(b + c*x)])","C",1
1034,1,178,251,0.2152176,"\int (2-5 x) x^{7/2} \sqrt{2+5 x+3 x^2} \, dx","Integrate[(2 - 5*x)*x^(7/2)*Sqrt[2 + 5*x + 3*x^2],x]","\frac{-495928 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+1543648 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+2 \left(-7577955 x^8-10195794 x^7+671895 x^6+2892348 x^5+58374 x^4-141444 x^3+670548 x^2+2811400 x+1543648\right)}{6567561 \sqrt{x} \sqrt{3 x^2+5 x+2}}","\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}",1,"(2*(1543648 + 2811400*x + 670548*x^2 - 141444*x^3 + 58374*x^4 + 2892348*x^5 + 671895*x^6 - 10195794*x^7 - 7577955*x^8) + (1543648*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (495928*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(6567561*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1035,1,170,228,0.1701279,"\int (2-5 x) x^{5/2} \sqrt{2+5 x+3 x^2} \, dx","Integrate[(2 - 5*x)*x^(5/2)*Sqrt[2 + 5*x + 3*x^2],x]","\frac{66544 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-261784 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2296350 x^7-3129840 x^6+271350 x^5+947916 x^4+39780 x^3-198168 x^2-918440 x-523568}{841995 \sqrt{x} \sqrt{3 x^2+5 x+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}",1,"(-523568 - 918440*x - 198168*x^2 + 39780*x^3 + 947916*x^4 + 271350*x^5 - 3129840*x^6 - 2296350*x^7 - (261784*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (66544*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(841995*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1036,1,165,205,0.160441,"\int (2-5 x) x^{3/2} \sqrt{2+5 x+3 x^2} \, dx","Integrate[(2 - 5*x)*x^(3/2)*Sqrt[2 + 5*x + 3*x^2],x]","\frac{-356 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+2360 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-17010 x^6-23652 x^5+2970 x^4+7920 x^3+1380 x^2+7792 x+4720}{5103 \sqrt{x} \sqrt{3 x^2+5 x+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}",1,"(4720 + 7792*x + 1380*x^2 + 7920*x^3 + 2970*x^4 - 23652*x^5 - 17010*x^6 + (2360*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (356*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(5103*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1037,1,163,182,0.1680823,"\int (2-5 x) \sqrt{x} \sqrt{2+5 x+3 x^2} \, dx","Integrate[(2 - 5*x)*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2],x]","\frac{16 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2476 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(6075 x^5+8748 x^4-1935 x^3-3354 x^2+3730 x+2476\right)}{2835 \sqrt{x} \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,"(-2*(2476 + 3730*x - 3354*x^2 - 1935*x^3 + 8748*x^4 + 6075*x^5) - (2476*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (16*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(2835*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1038,1,158,159,0.1606486,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{\sqrt{x}} \, dx","Integrate[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/Sqrt[x],x]","\frac{14 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+88 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+2 \left(-81 x^4-126 x^3+93 x^2+226 x+88\right)}{27 \sqrt{x} \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,"(2*(88 + 226*x + 93*x^2 - 126*x^3 - 81*x^4) + (88*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (14*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(27*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1039,1,153,159,0.1731774,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{3/2}} \, dx","Integrate[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(3/2),x]","\frac{8 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+22 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(45 x^3+96 x^2+65 x+14\right)}{9 \sqrt{x} \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,"(-2*(14 + 65*x + 96*x^2 + 45*x^3) + (22*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (8*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(9*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1040,1,153,157,0.1679388,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{5/2}} \, dx","Integrate[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(5/2),x]","\frac{-13 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{5/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-50 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{5/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(45 x^3+81 x^2+40 x+4\right)}{3 x^{3/2} \sqrt{3 x^2+5 x+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}}",1,"(-2*(4 + 40*x + 81*x^2 + 45*x^3) - (50*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(5/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (13*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(5/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(3*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1041,1,153,180,0.1696738,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{7/2}} \, dx","Integrate[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(7/2),x]","\frac{-26 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{7/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-139 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{7/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+4 \left(30 x^3+41 x^2+5 x-6\right)}{15 x^{5/2} \sqrt{3 x^2+5 x+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}}",1,"(4*(-6 + 5*x + 41*x^2 + 30*x^3) - (139*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (26*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(15*x^(5/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1042,1,155,205,0.1627287,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{9/2}} \, dx","Integrate[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(9/2),x]","\frac{5 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{9/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+124 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{9/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+258 x^4+646 x^3+460 x^2+24 x-48}{42 x^{7/2} \sqrt{3 x^2+5 x+2}}","-\frac{62 \sqrt{3 x^2+5 x+2}}{21 \sqrt{x}}+\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{43 \sqrt{3 x^2+5 x+2}}{21 x^{3/2}}",1,"(-48 + 24*x + 460*x^2 + 646*x^3 + 258*x^4 + (124*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(9/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (5*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(9/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(42*x^(7/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1043,1,160,228,0.1698887,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{11/2}} \, dx","Integrate[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(11/2),x]","\frac{146 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{11/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-1331 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{11/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2370 x^5-2204 x^4+3730 x^3+4324 x^2+200 x-560}{630 x^{9/2} \sqrt{3 x^2+5 x+2}}","\frac{1331 \sqrt{3 x^2+5 x+2}}{630 \sqrt{x}}-\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{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}}",1,"(-560 + 200*x + 4324*x^2 + 3730*x^3 - 2204*x^4 - 2370*x^5 - (1331*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(11/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (146*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(11/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(630*x^(9/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1044,1,183,256,0.1978843,"\int (2-5 x) x^{5/2} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(2 - 5*x)*x^(5/2)*(2 + 5*x + 3*x^2)^(3/2),x]","\frac{-497824 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(214108 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+98513415 x^9+320800095 x^8+337486905 x^7+69664455 x^6-83323080 x^5-37601118 x^4+91620 x^3-273876 x^2+318520 x+497824\right)}{32837805 \sqrt{x} \sqrt{3 x^2+5 x+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}",1,"((-497824*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - 2*(497824 + 318520*x - 273876*x^2 + 91620*x^3 - 37601118*x^4 - 83323080*x^5 + 69664455*x^6 + 337486905*x^7 + 320800095*x^8 + 98513415*x^9 + (214108*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2]))/(32837805*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1045,1,178,233,0.1887557,"\int (2-5 x) x^{3/2} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(2 - 5*x)*x^(3/2)*(2 + 5*x + 3*x^2)^(3/2),x]","\frac{21232 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+55112 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(2525985 x^8+8374023 x^7+8989785 x^6+1830195 x^5-2497986 x^4-1171602 x^3+8508 x^2-61436 x-55112\right)}{729729 \sqrt{x} \sqrt{3 x^2+5 x+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}",1,"(-2*(-55112 - 61436*x + 8508*x^2 - 1171602*x^3 - 2497986*x^4 + 1830195*x^5 + 8989785*x^6 + 8374023*x^7 + 2525985*x^8) + (55112*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (21232*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(729729*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1046,1,173,210,0.1919073,"\int (2-5 x) \sqrt{x} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(2 - 5*x)*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2),x]","\frac{-424 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(58 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+4725 x^7+16065 x^6+17775 x^5+3497 x^4-6140 x^3-3106 x^2+520 x+424\right)}{1155 \sqrt{x} \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*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - 2*(424 + 520*x - 3106*x^2 - 6140*x^3 + 3497*x^4 + 17775*x^5 + 16065*x^6 + 4725*x^7 + (58*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2]))/(1155*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1047,1,165,187,0.1625922,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{\sqrt{x}} \, dx","Integrate[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/Sqrt[x],x]","\frac{208 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+860 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2430 x^6-8586 x^5-9990 x^4-1746 x^3+6420 x^2+6052 x+1720}{243 \sqrt{x} \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,"(1720 + 6052*x + 6420*x^2 - 1746*x^3 - 9990*x^4 - 8586*x^5 - 2430*x^6 + (860*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (208*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(243*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1048,1,163,187,0.1787368,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{3/2}} \, dx","Integrate[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(3/2),x]","\frac{1382 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+5848 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(2025 x^5+7641 x^4+9855 x^3+177 x^2-7390 x-3328\right)}{315 \sqrt{x} \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,"(-2*(-3328 - 7390*x + 177*x^2 + 9855*x^3 + 7641*x^4 + 2025*x^5) + (5848*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (1382*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(315*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1049,1,163,183,0.1953009,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{5/2}} \, dx","Integrate[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(5/2),x]","\frac{-34 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{5/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(4 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{5/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+27 x^5+117 x^4+219 x^3+195 x^2+74 x+8\right)}{3 x^{3/2} \sqrt{3 x^2+5 x+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}}",1,"((-34*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(5/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - 2*(8 + 74*x + 195*x^2 + 219*x^3 + 117*x^4 + 27*x^5 + (4*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(5/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2]))/(3*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1050,1,163,185,0.189085,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{7/2}} \, dx","Integrate[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(7/2),x]","\frac{-337 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{7/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-1418 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{7/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(225 x^5+1605 x^4+2230 x^3+906 x^2+80 x+24\right)}{15 x^{5/2} \sqrt{3 x^2+5 x+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}}",1,"(-2*(24 + 80*x + 906*x^2 + 2230*x^3 + 1605*x^4 + 225*x^5) - (1418*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (337*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(15*x^(5/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1051,1,163,187,0.1770823,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{9/2}} \, dx","Integrate[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(9/2),x]","\frac{-150 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{9/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-633 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{9/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(315 x^5+384 x^4-19 x^3-72 x^2+24 x+8\right)}{7 x^{7/2} \sqrt{3 x^2+5 x+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}}",1,"(-2*(8 + 24*x - 72*x^2 - 19*x^3 + 384*x^4 + 315*x^5) - (633*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(9/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (150*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(9/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(7*x^(7/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1052,1,160,210,0.1690814,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{11/2}} \, dx","Integrate[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(11/2),x]","\frac{-2609 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{11/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-10876 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{11/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+29730 x^5+64706 x^4+44480 x^3+7424 x^2-3200 x-1120}{630 x^{9/2} \sqrt{3 x^2+5 x+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}}",1,"(-1120 - 3200*x + 7424*x^2 + 44480*x^3 + 64706*x^4 + 29730*x^5 - (10876*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(11/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (2609*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(11/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(630*x^(9/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1053,1,165,233,0.1725469,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{13/2}} \, dx","Integrate[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(13/2),x]","\frac{842 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{13/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+3229 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{13/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+8142 x^6+48256 x^5+86914 x^4+61744 x^3+11360 x^2-5600 x-2016}{1386 x^{11/2} \sqrt{3 x^2+5 x+2}}","-\frac{3229 \sqrt{3 x^2+5 x+2}}{1386 \sqrt{x}}+\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{1357 \sqrt{3 x^2+5 x+2}}{693 x^{3/2}}",1,"(-2016 - 5600*x + 11360*x^2 + 61744*x^3 + 86914*x^4 + 48256*x^5 + 8142*x^6 + (3229*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(13/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (842*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(13/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(1386*x^(11/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1054,1,170,256,0.1821609,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{15/2}} \, dx","Integrate[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(15/2),x]","\frac{-4651 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{15/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-13814 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{15/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-36930 x^7-29726 x^6+361120 x^5+840316 x^4+654400 x^3+125440 x^2-67200 x-24640}{20020 x^{13/2} \sqrt{3 x^2+5 x+2}}","\frac{6907 \sqrt{3 x^2+5 x+2}}{10010 \sqrt{x}}-\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{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}}",1,"(-24640 - 67200*x + 125440*x^2 + 654400*x^3 + 840316*x^4 + 361120*x^5 - 29726*x^6 - 36930*x^7 - (13814*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(15/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (4651*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(15/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(20020*x^(13/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1055,1,444,300,1.6954658,"\int \frac{A+B x}{\sqrt{e x} \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/(Sqrt[e*x]*Sqrt[a + b*x + c*x^2]),x]","-\frac{x^2 \left(-\frac{i \sqrt{\frac{4 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+2} \sqrt{\frac{-x \sqrt{b^2-4 a c}+2 a+b x}{b x-x \sqrt{b^2-4 a c}}} \left(B \sqrt{b^2-4 a c}+2 A c-b B\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)}{\sqrt{x}}-\frac{4 B \sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}} (a+x (b+c x))}{x^2}+\frac{i B \left(\sqrt{b^2-4 a c}-b\right) \sqrt{\frac{4 a}{x \left(\sqrt{b^2-4 a c}+b\right)}+2} \sqrt{\frac{-x \sqrt{b^2-4 a c}+2 a+b x}{b x-x \sqrt{b^2-4 a c}}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{a}{b+\sqrt{b^2-4 a c}}}}{\sqrt{x}}\right)|\frac{b+\sqrt{b^2-4 a c}}{b-\sqrt{b^2-4 a c}}\right)}{\sqrt{x}}\right)}{2 c \sqrt{e x} \sqrt{\frac{a}{\sqrt{b^2-4 a c}+b}} \sqrt{a+x (b+c 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)}",1,"-1/2*(x^2*((-4*B*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])]*(a + x*(b + c*x)))/x^2 + (I*B*(-b + Sqrt[b^2 - 4*a*c])*Sqrt[2 + (4*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*Sqrt[(2*a + b*x - Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])])/Sqrt[x] - (I*(-(b*B) + 2*A*c + B*Sqrt[b^2 - 4*a*c])*Sqrt[2 + (4*a)/((b + Sqrt[b^2 - 4*a*c])*x)]*Sqrt[(2*a + b*x - Sqrt[b^2 - 4*a*c]*x)/(b*x - Sqrt[b^2 - 4*a*c]*x)]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[x]], (b + Sqrt[b^2 - 4*a*c])/(b - Sqrt[b^2 - 4*a*c])])/Sqrt[x]))/(c*Sqrt[a/(b + Sqrt[b^2 - 4*a*c])]*Sqrt[e*x]*Sqrt[a + x*(b + c*x)])","C",1
1056,1,168,223,0.1890925,"\int \frac{(2-5 x) x^{7/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((2 - 5*x)*x^(7/2))/Sqrt[2 + 5*x + 3*x^2],x]","\frac{34960 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-68920 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(8505 x^6-6399 x^5+4590 x^4-9306 x^3+40620 x^2+138340 x+68920\right)}{15309 \sqrt{x} \sqrt{3 x^2+5 x+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}",1,"(-2*(68920 + 138340*x + 40620*x^2 - 9306*x^3 + 4590*x^4 - 6399*x^5 + 8505*x^6) - (68920*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (34960*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(15309*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1057,1,160,200,0.1663469,"\int \frac{(2-5 x) x^{5/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((2 - 5*x)*x^(5/2))/Sqrt[2 + 5*x + 3*x^2],x]","\frac{-7508 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+13688 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-4050 x^5+3618 x^4-3960 x^3+17076 x^2+56080 x+27376}{2835 \sqrt{x} \sqrt{3 x^2+5 x+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}",1,"(27376 + 56080*x + 17076*x^2 - 3960*x^3 + 3618*x^4 - 4050*x^5 + (13688*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (7508*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(2835*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1058,1,158,177,0.1738936,"\int \frac{(2-5 x) x^{3/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((2 - 5*x)*x^(3/2))/Sqrt[2 + 5*x + 3*x^2],x]","\frac{256 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-412 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(81 x^4-99 x^3+282 x^2+874 x+412\right)}{81 \sqrt{x} \sqrt{3 x^2+5 x+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}",1,"(-2*(412 + 874*x + 282*x^2 - 99*x^3 + 81*x^4) - (412*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (256*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(81*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1059,1,150,154,0.1586719,"\int \frac{(2-5 x) \sqrt{x}}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((2 - 5*x)*Sqrt[x])/Sqrt[2 + 5*x + 3*x^2],x]","\frac{-106 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+136 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-90 x^3+258 x^2+620 x+272}{27 \sqrt{x} \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,"(272 + 620*x + 258*x^2 - 90*x^3 + (136*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (106*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(27*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1060,1,150,129,0.151374,"\int \frac{2-5 x}{\sqrt{x} \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(2 - 5*x)/(Sqrt[x]*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{2 x^{3/2} \left(5 \left(\frac{2}{x^2}+\frac{5}{x}+3\right)-\frac{8 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)}{\sqrt{x}}+\frac{5 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)}{\sqrt{x}}\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,"(-2*x^(3/2)*(5*(3 + 2/x^2 + 5/x) + ((5*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/Sqrt[x] - ((8*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/Sqrt[x]))/(3*Sqrt[2 + 5*x + 3*x^2])","C",1
1061,1,90,146,0.1418603,"\int \frac{2-5 x}{x^{3/2} \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(2 - 5*x)/(x^(3/2)*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} x \left(2 E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-7 F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)\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,"(I*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x*(2*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - 7*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2]))/Sqrt[2 + 5*x + 3*x^2]","C",1
1062,1,148,175,0.1569703,"\int \frac{2-5 x}{x^{5/2} \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(2 - 5*x)/(x^(5/2)*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{22 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{5/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-25 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{5/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(3 x^2+5 x+2\right)}{3 x^{3/2} \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{\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{2 \sqrt{3 x^2+5 x+2}}{3 x^{3/2}}",1,"(-2*(2 + 5*x + 3*x^2) - (25*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(5/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (22*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(5/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(3*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1063,1,150,196,0.1649683,"\int \frac{2-5 x}{x^{7/2} \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(2 - 5*x)/(x^(7/2)*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{-87 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{7/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+132 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{7/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+90 x^3+138 x^2+40 x-8}{10 x^{5/2} \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{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{3 \sqrt{3 x^2+5 x+2}}{x^{3/2}}-\frac{2 \sqrt{3 x^2+5 x+2}}{5 x^{5/2}}",1,"(-8 + 40*x + 138*x^2 + 90*x^3 + (132*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (87*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(10*x^(5/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1064,1,156,197,0.1764346,"\int \frac{(2-5 x) x^{7/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((2 - 5*x)*x^(7/2))/(2 + 5*x + 3*x^2)^(3/2),x]","\frac{12 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-72 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(x^4-4 x^3+22 x^2+120 x+72\right)}{3 \sqrt{x} \sqrt{3 x^2+5 x+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}",1,"(-2*(72 + 120*x + 22*x^2 - 4*x^3 + x^4) - (72*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (12*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(3*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1065,1,150,182,0.1733198,"\int \frac{(2-5 x) x^{5/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((2 - 5*x)*x^(5/2))/(2 + 5*x + 3*x^2)^(3/2),x]","\frac{-64 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+1804 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-90 x^3+708 x^2+5540 x+3608}{81 \sqrt{x} \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}}",1,"(3608 + 5540*x + 708*x^2 - 90*x^3 + (1804*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (64*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(81*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1066,1,145,159,0.1596011,"\int \frac{(2-5 x) x^{3/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((2 - 5*x)*x^(3/2))/(2 + 5*x + 3*x^2)^(3/2),x]","\frac{-22 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-200 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-30 x^2-556 x-400}{9 \sqrt{x} \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,"(-400 - 556*x - 30*x^2 - (200*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (22*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(9*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1067,1,140,155,0.1523078,"\int \frac{(2-5 x) \sqrt{x}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((2 - 5*x)*Sqrt[x])/(2 + 5*x + 3*x^2)^(3/2),x]","\frac{16 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+74 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+190 x+148}{3 \sqrt{x} \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,"(148 + 190*x + (74*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (16*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(3*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1068,1,137,151,0.1615165,"\int \frac{2-5 x}{\sqrt{x} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(2 - 5*x)/(Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{-7 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-30 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-74 x-60}{\sqrt{x} \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,"(-60 - 74*x - (30*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (7*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1069,1,137,172,0.1702749,"\int \frac{2-5 x}{x^{3/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(2 - 5*x)/(x^(3/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{6 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+39 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+90 x+76}{\sqrt{x} \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,"(76 + 90*x + (39*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (6*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])","C",1
1070,1,145,201,0.1656368,"\int \frac{2-5 x}{x^{5/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(2 - 5*x)/(x^(5/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{-5 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{5/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-340 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{5/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-690 x^2-610 x-4}{6 x^{3/2} \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 (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{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}}",1,"(-4 - 610*x - 690*x^2 - (340*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(5/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (5*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(5/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(6*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1071,1,150,224,0.1722586,"\int \frac{2-5 x}{x^{7/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(2 - 5*x)/(x^(7/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{-338 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{7/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+2693 i \sqrt{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{2}{x}+3} x^{7/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+4710 x^3+4412 x^2+110 x-12}{30 x^{5/2} \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 (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{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}}",1,"(-12 + 110*x + 4412*x^2 + 4710*x^3 + (2693*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (338*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(30*x^(5/2)*Sqrt[2 + 5*x + 3*x^2])","C",1
1072,1,187,256,0.2711934,"\int \frac{(2-5 x) x^{13/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((2 - 5*x)*x^(13/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{-1646104 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-1521056 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(18225 x^7-70956 x^6+262710 x^5-2106756 x^4-2967300 x^3+5504080 x^2+8876240 x+3042112\right)}{76545 \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}}","\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}",1,"(-2*(3042112 + 8876240*x + 5504080*x^2 - 2967300*x^3 - 2106756*x^4 + 262710*x^5 - 70956*x^6 + 18225*x^7) - (1521056*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (1646104*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(76545*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))","C",1
1073,1,179,233,0.2629239,"\int \frac{(2-5 x) x^{11/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((2 - 5*x)*x^(11/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{-486 x^6+2484 x^5-21276 x^4+161784 x^3+534680 x^2+14512 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+33608 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+479680 x+134432}{729 \sqrt{x} \left(3 x^2+5 x+2\right)^{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}",1,"(134432 + 479680*x + 534680*x^2 + 161784*x^3 - 21276*x^4 + 2484*x^5 - 486*x^6 + (33608*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (14512*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(729*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))","C",1
1074,1,177,210,0.2580308,"\int \frac{(2-5 x) x^{9/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((2 - 5*x)*x^(9/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{-5108 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-17512 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(135 x^5-1512 x^4+58590 x^3+155660 x^2+129880 x+35024\right)}{243 \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}}","\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}}",1,"(-2*(35024 + 129880*x + 155660*x^2 + 58590*x^3 - 1512*x^4 + 135*x^5) - (17512*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (5108*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(243*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))","C",1
1075,1,169,187,0.2518862,"\int \frac{(2-5 x) x^{7/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((2 - 5*x)*x^(7/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{-270 x^4+58212 x^3+147100 x^2+2000 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+8020 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+120320 x+32080}{81 \sqrt{x} \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}}",1,"(32080 + 120320*x + 147100*x^2 + 58212*x^3 - 270*x^4 + (8020*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (2000*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(81*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))","C",1
1076,1,167,187,0.2536316,"\int \frac{(2-5 x) x^{5/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((2 - 5*x)*x^(5/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{-826 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-3464 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(12825 x^3+32020 x^2+26060 x+6928\right)}{27 \sqrt{x} \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}}",1,"(-2*(6928 + 26060*x + 32020*x^2 + 12825*x^3) - (3464*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (826*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(27*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))","C",1
1077,1,164,187,0.2473427,"\int \frac{(2-5 x) x^{3/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((2 - 5*x)*x^(3/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{10764 x^3+26830 x^2+344 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+1450 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+21824 x+5800}{9 \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}}","\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,"(5800 + 21824*x + 26830*x^2 + 10764*x^3 + (1450*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (344*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(9*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))","C",1
1078,1,165,179,0.2992691,"\int \frac{(2-5 x) \sqrt{x}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((2 - 5*x)*Sqrt[x])/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{47 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} x F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{198 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} x E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{2 \left(2205 x^3+5494 x^2+4470 x+1188\right)}{3 \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}}","-\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*(1188 + 4470*x + 5494*x^2 + 2205*x^3))/(3*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2)) - ((198*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/Sqrt[2 + 5*x + 3*x^2] - ((47*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/Sqrt[2 + 5*x + 3*x^2]","C",1
1079,1,167,185,0.2445169,"\int \frac{2-5 x}{\sqrt{x} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(2 - 5*x)/(Sqrt[x]*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{170 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+715 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+2 \left(2655 x^3+6615 x^2+5383 x+1430\right)}{3 \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}}","\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*(1430 + 5383*x + 6615*x^2 + 2655*x^3) + (715*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (170*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(3*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))","C",1
1080,1,167,208,0.2497251,"\int \frac{2-5 x}{x^{3/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(2 - 5*x)/(x^(3/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{-409 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-1676 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(6255 x^3+15576 x^2+12665 x+3358\right)}{6 \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}}","-\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*(3358 + 12665*x + 15576*x^2 + 6255*x^3) - (1676*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (409*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(3/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(6*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))","C",1
1081,1,169,225,0.253432,"\int \frac{2-5 x}{x^{5/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(2 - 5*x)/(x^(5/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{14310 x^4+35550 x^3+28806 x^2+510 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{5/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+1875 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{5/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)+7590 x-4}{6 x^{3/2} \left(3 x^2+5 x+2\right)^{3/2}}","\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{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{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}}",1,"(-4 + 7590*x + 28806*x^2 + 35550*x^3 + 14310*x^4 + (1875*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(5/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] + (510*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(5/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(6*x^(3/2)*(2 + 5*x + 3*x^2)^(3/2))","C",1
1082,1,177,256,0.2606509,"\int \frac{2-5 x}{x^{7/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(2 - 5*x)/(x^(7/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{-6953 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{7/2} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-19042 i \sqrt{\frac{2}{x}+2} \sqrt{\frac{2}{x}+3} \left(3 x^2+5 x+2\right) x^{7/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{2}{3}}}{\sqrt{x}}\right)|\frac{3}{2}\right)-2 \left(77985 x^5+192342 x^4+154195 x^3+39836 x^2-130 x+12\right)}{60 x^{5/2} \left(3 x^2+5 x+2\right)^{3/2}}","-\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 (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{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}}",1,"(-2*(12 - 130*x + 39836*x^2 + 154195*x^3 + 192342*x^4 + 77985*x^5) - (19042*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(7/2)*(2 + 5*x + 3*x^2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2] - (6953*I)*Sqrt[2 + 2/x]*Sqrt[3 + 2/x]*x^(7/2)*(2 + 5*x + 3*x^2)*EllipticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(60*x^(5/2)*(2 + 5*x + 3*x^2)^(3/2))","C",1
1083,1,672,240,1.4181824,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{(e x)^m \left(\frac{3 \left(\frac{2 x \left(-\frac{2 a^2 c (m+4) \left(2 a c (m+6) (b B (m+1)-2 A c (m+8))-b (m+1) \left(-2 a B c (m+7)-A b c (m+8)+b^2 B (m+4)\right)\right)}{m+1}-\frac{a b c (m+4) x \left(2 a c (m+6) (b B (m+1)-2 A c (m+8))-b (m+1) \left(-2 a B c (m+7)-A b c (m+8)+b^2 B (m+4)\right)\right)}{m+2}+\frac{x \left(b^2 (m+2)-2 a c (m+3)\right) \left(a b c (m+6) (b B (m+1)-2 A c (m+8))-\left(b^2 (m+3)-2 a c (m+5)\right) \left(-2 a B c (m+7)-A b c (m+8)+b^2 B (m+4)\right)\right)}{m+2}+(a+x (b+c x)) \left(c (m+3) x \left(\left(b^2 (m+3)-2 a c (m+5)\right) \left(-2 a B c (m+7)-A b c (m+8)+b^2 B (m+4)\right)-a b c (m+6) (b B (m+1)-2 A c (m+8))\right)-a c (m+4) \left(2 a c (m+6) (b B (m+1)-2 A c (m+8))-b (m+1) \left(-2 a B c (m+7)-A b c (m+8)+b^2 B (m+4)\right)\right)+b \left(\left(b^2 (m+3)-2 a c (m+5)\right) \left(-2 a B c (m+7)-A b c (m+8)+b^2 B (m+4)\right)-a b c (m+6) (b B (m+1)-2 A c (m+8))\right)\right)+a b \left(a b c (m+6) (b B (m+1)-2 A c (m+8))-\left(b^2 (m+3)-2 a c (m+5)\right) \left(-2 a B c (m+7)-A b c (m+8)+b^2 B (m+4)\right)\right)\right)}{c (m+3) (m+4)}-x (a+x (b+c x))^2 \left(c (m+5) x \left(-2 a B c (m+7)-A b c (m+8)+b^2 B (m+4)\right)+2 b \left(-2 a B c (m+7)-A b c (m+8)+b^2 B (m+4)\right)+a c (m+6) (b B (m+1)-2 A c (m+8))\right)\right)}{c (m+5) (m+6)}+x (a+x (b+c x))^3 (A c (m+8)+3 b B+B c (m+7) x)\right)}{c (m+7) (m+8)}","\frac{a^3 A (e x)^{m+1}}{e (m+1)}+\frac{a^2 (e x)^{m+2} (a B+3 A b)}{e^2 (m+2)}+\frac{3 c (e x)^{m+6} \left(a B c+A b c+b^2 B\right)}{e^6 (m+6)}+\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+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{(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{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,"((e*x)^m*(x*(3*b*B + A*c*(8 + m) + B*c*(7 + m)*x)*(a + x*(b + c*x))^3 + (3*(-(x*(a*c*(6 + m)*(b*B*(1 + m) - 2*A*c*(8 + m)) + 2*b*(b^2*B*(4 + m) - 2*a*B*c*(7 + m) - A*b*c*(8 + m)) + c*(5 + m)*(b^2*B*(4 + m) - 2*a*B*c*(7 + m) - A*b*c*(8 + m))*x)*(a + x*(b + c*x))^2) + (2*x*((-2*a^2*c*(4 + m)*(2*a*c*(6 + m)*(b*B*(1 + m) - 2*A*c*(8 + m)) - b*(1 + m)*(b^2*B*(4 + m) - 2*a*B*c*(7 + m) - A*b*c*(8 + m))))/(1 + m) + a*b*(a*b*c*(6 + m)*(b*B*(1 + m) - 2*A*c*(8 + m)) - (b^2*(3 + m) - 2*a*c*(5 + m))*(b^2*B*(4 + m) - 2*a*B*c*(7 + m) - A*b*c*(8 + m))) - (a*b*c*(4 + m)*(2*a*c*(6 + m)*(b*B*(1 + m) - 2*A*c*(8 + m)) - b*(1 + m)*(b^2*B*(4 + m) - 2*a*B*c*(7 + m) - A*b*c*(8 + m)))*x)/(2 + m) + ((b^2*(2 + m) - 2*a*c*(3 + m))*(a*b*c*(6 + m)*(b*B*(1 + m) - 2*A*c*(8 + m)) - (b^2*(3 + m) - 2*a*c*(5 + m))*(b^2*B*(4 + m) - 2*a*B*c*(7 + m) - A*b*c*(8 + m)))*x)/(2 + m) + (-(a*c*(4 + m)*(2*a*c*(6 + m)*(b*B*(1 + m) - 2*A*c*(8 + m)) - b*(1 + m)*(b^2*B*(4 + m) - 2*a*B*c*(7 + m) - A*b*c*(8 + m)))) + b*(-(a*b*c*(6 + m)*(b*B*(1 + m) - 2*A*c*(8 + m))) + (b^2*(3 + m) - 2*a*c*(5 + m))*(b^2*B*(4 + m) - 2*a*B*c*(7 + m) - A*b*c*(8 + m))) + c*(3 + m)*(-(a*b*c*(6 + m)*(b*B*(1 + m) - 2*A*c*(8 + m))) + (b^2*(3 + m) - 2*a*c*(5 + m))*(b^2*B*(4 + m) - 2*a*B*c*(7 + m) - A*b*c*(8 + m)))*x)*(a + x*(b + c*x))))/(c*(3 + m)*(4 + m))))/(c*(5 + m)*(6 + m))))/(c*(7 + m)*(8 + m))","B",1
1084,1,289,155,0.4785315,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{(e x)^m \left(\frac{2 x \left(-\frac{2 a^2 c (m+4) (b B (m+1)-2 A c (m+6))}{m+1}+\frac{x \left(b^2 (m+2)-2 a c (m+3)\right) \left(-2 a B c (m+5)-A b c (m+6)+b^2 B (m+3)\right)}{m+2}-(a+x (b+c x)) \left(c (m+3) x \left(-2 a B c (m+5)-A b c (m+6)+b^2 B (m+3)\right)+b \left(-2 a B c (m+5)-A b c (m+6)+b^2 B (m+3)\right)+a c (m+4) (b B (m+1)-2 A c (m+6))\right)+a b \left(-2 a B c (m+5)-A b c (m+6)+b^2 B (m+3)\right)-\frac{a b c (m+4) x (b B (m+1)-2 A c (m+6))}{m+2}\right)}{c (m+3) (m+4)}+x (a+x (b+c x))^2 (A c (m+6)+2 b B+B c (m+5) x)\right)}{c (m+5) (m+6)}","\frac{a^2 A (e x)^{m+1}}{e (m+1)}+\frac{(e x)^{m+4} \left(2 a B c+2 A b c+b^2 B\right)}{e^4 (m+4)}+\frac{(e x)^{m+3} \left(A \left(2 a c+b^2\right)+2 a b B\right)}{e^3 (m+3)}+\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,"((e*x)^m*(x*(2*b*B + A*c*(6 + m) + B*c*(5 + m)*x)*(a + x*(b + c*x))^2 + (2*x*((-2*a^2*c*(4 + m)*(b*B*(1 + m) - 2*A*c*(6 + m)))/(1 + m) + a*b*(b^2*B*(3 + m) - 2*a*B*c*(5 + m) - A*b*c*(6 + m)) - (a*b*c*(4 + m)*(b*B*(1 + m) - 2*A*c*(6 + m))*x)/(2 + m) + ((b^2*(2 + m) - 2*a*c*(3 + m))*(b^2*B*(3 + m) - 2*a*B*c*(5 + m) - A*b*c*(6 + m))*x)/(2 + m) - (a*c*(4 + m)*(b*B*(1 + m) - 2*A*c*(6 + m)) + b*(b^2*B*(3 + m) - 2*a*B*c*(5 + m) - A*b*c*(6 + m)) + c*(3 + m)*(b^2*B*(3 + m) - 2*a*B*c*(5 + m) - A*b*c*(6 + m))*x)*(a + x*(b + c*x))))/(c*(3 + m)*(4 + m))))/(c*(5 + m)*(6 + m))","A",1
1085,1,91,83,0.1141527,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[(e*x)^m*(A + B*x)*(a + b*x + c*x^2),x]","\frac{x (e x)^m \left(a \left(m^2+7 m+12\right) (A (m+2)+B (m+1) x)+(m+1) x (A (m+4) (b (m+3)+c (m+2) x)+B (m+2) x (b (m+4)+c (m+3) x))\right)}{(m+1) (m+2) (m+3) (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,"(x*(e*x)^m*(a*(12 + 7*m + m^2)*(A*(2 + m) + B*(1 + m)*x) + (1 + m)*x*(A*(4 + m)*(b*(3 + m) + c*(2 + m)*x) + B*(2 + m)*x*(b*(4 + m) + c*(3 + m)*x))))/((1 + m)*(2 + m)*(3 + m)*(4 + m))","A",1
1086,1,135,172,0.2756147,"\int \frac{(e x)^m (A+B x)}{a+b x+c x^2} \, dx","Integrate[((e*x)^m*(A + B*x))/(a + b*x + c*x^2),x]","\frac{x (e x)^m \left(\left(A \left(\sqrt{b^2-4 a c}+b\right)-2 a B\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+\left(A \left(\sqrt{b^2-4 a c}-b\right)+2 a B\right) \, _2F_1\left(1,m+1;m+2;-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)\right)}{2 a (m+1) \sqrt{b^2-4 a c}}","\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,"(x*(e*x)^m*((-2*a*B + A*(b + Sqrt[b^2 - 4*a*c]))*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + (2*a*B + A*(-b + Sqrt[b^2 - 4*a*c]))*Hypergeometric2F1[1, 1 + m, 2 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])]))/(2*a*Sqrt[b^2 - 4*a*c]*(1 + m))","A",1
1087,1,253,318,1.0024125,"\int \frac{(e x)^m (A+B x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((e*x)^m*(A + B*x))/(a + b*x + c*x^2)^2,x]","\frac{(e x)^m \left(\frac{c x \left(-\frac{\left(\frac{A b^2 m-2 a (2 A c (m-1)+b B)}{\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}{\sqrt{b^2-4 a c}-b}\right)}{b-\sqrt{b^2-4 a c}}-\frac{\left(\frac{4 a A c (m-1)+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)}{\sqrt{b^2-4 a c}+b}\right)}{m+1}+\frac{x \left(A \left(-2 a c+b^2+b c x\right)-a B (b+2 c x)\right)}{a+x (b+c x)}\right)}{a \left(b^2-4 a c\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)^m*((x*(-(a*B*(b + 2*c*x)) + A*(b^2 - 2*a*c + b*c*x)))/(a + x*(b + c*x)) + (c*x*(-((((A*b - 2*a*B)*m + (-2*a*(b*B + 2*A*c*(-1 + m)) + A*b^2*m)/Sqrt[b^2 - 4*a*c])*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])])/(b - Sqrt[b^2 - 4*a*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])*Hypergeometric2F1[1, 1 + m, 2 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(b + Sqrt[b^2 - 4*a*c])))/(1 + m)))/(a*(b^2 - 4*a*c))","A",1
1088,1,618,281,1.3329514,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{x (e x)^m \sqrt{a+x (b+c x)} \left(a^2 A \left(m^5+20 m^4+155 m^3+580 m^2+1044 m+720\right) 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}{\sqrt{b^2-4 a c}-b}\right)+(m+1) x \left((m+2) x \left((m+3) x \left(\left(m^2+11 m+30\right) \left(2 a B c+2 A b c+b^2 B\right) F_1\left(m+4;-\frac{1}{2},-\frac{1}{2};m+5;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+c (m+4) x \left((m+6) (A c+2 b B) F_1\left(m+5;-\frac{1}{2},-\frac{1}{2};m+6;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+B c (m+5) x F_1\left(m+6;-\frac{1}{2},-\frac{1}{2};m+7;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)\right)\right)+\left(m^3+15 m^2+74 m+120\right) \left(A \left(2 a c+b^2\right)+2 a b B\right) F_1\left(m+3;-\frac{1}{2},-\frac{1}{2};m+4;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)\right)+a \left(m^4+18 m^3+119 m^2+342 m+360\right) (a B+2 A b) 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}{\sqrt{b^2-4 a c}-b}\right)\right)\right)}{(m+1) (m+2) (m+3) (m+4) (m+5) (m+6) \sqrt{\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}} \sqrt{\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}}}","\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,"(x*(e*x)^m*Sqrt[a + x*(b + c*x)]*(a^2*A*(720 + 1044*m + 580*m^2 + 155*m^3 + 20*m^4 + m^5)*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])] + (1 + m)*x*(a*(2*A*b + a*B)*(360 + 342*m + 119*m^2 + 18*m^3 + m^4)*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])] + (2 + m)*x*((2*a*b*B + A*(b^2 + 2*a*c))*(120 + 74*m + 15*m^2 + m^3)*AppellF1[3 + m, -1/2, -1/2, 4 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + (3 + m)*x*((b^2*B + 2*A*b*c + 2*a*B*c)*(30 + 11*m + m^2)*AppellF1[4 + m, -1/2, -1/2, 5 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + c*(4 + m)*x*((2*b*B + A*c)*(6 + m)*AppellF1[5 + m, -1/2, -1/2, 6 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + B*c*(5 + m)*x*AppellF1[6 + m, -1/2, -1/2, 7 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])]))))))/((1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*Sqrt[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])])","B",0
1089,1,405,281,0.4521435,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{x (e x)^m \sqrt{a+x (b+c x)} \left((m+1) x \left(\left(m^2+7 m+12\right) (a B+A b) 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}{\sqrt{b^2-4 a c}-b}\right)+(m+2) x \left((m+4) (A c+b B) F_1\left(m+3;-\frac{1}{2},-\frac{1}{2};m+4;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+B c (m+3) x F_1\left(m+4;-\frac{1}{2},-\frac{1}{2};m+5;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)\right)\right)+a A \left(m^3+9 m^2+26 m+24\right) 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}{\sqrt{b^2-4 a c}-b}\right)\right)}{(m+1) (m+2) (m+3) (m+4) \sqrt{\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}} \sqrt{\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}}}","\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,"(x*(e*x)^m*Sqrt[a + x*(b + c*x)]*(a*A*(24 + 26*m + 9*m^2 + m^3)*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])] + (1 + m)*x*((A*b + a*B)*(12 + 7*m + m^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])] + (2 + m)*x*((b*B + A*c)*(4 + m)*AppellF1[3 + m, -1/2, -1/2, 4 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + B*c*(3 + m)*x*AppellF1[4 + m, -1/2, -1/2, 5 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])]))))/((1 + m)*(2 + m)*(3 + m)*(4 + m)*Sqrt[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])])","A",0
1090,1,234,281,0.1786096,"\int (e x)^m (A+B x) \sqrt{a+b x+c x^2} \, dx","Integrate[(e*x)^m*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{x (e x)^m \sqrt{a+x (b+c x)} \left(A (m+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}{\sqrt{b^2-4 a c}-b}\right)+B (m+1) x 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}{\sqrt{b^2-4 a c}-b}\right)\right)}{(m+1) (m+2) \sqrt{\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}} \sqrt{\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}}}","\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,"(x*(e*x)^m*Sqrt[a + x*(b + c*x)]*(A*(2 + m)*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])] + B*(1 + m)*x*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])]))/((1 + m)*(2 + m)*Sqrt[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])])","A",0
1091,1,234,281,0.2085927,"\int \frac{(e x)^m (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((e*x)^m*(A + B*x))/Sqrt[a + b*x + c*x^2],x]","\frac{x (e x)^m \sqrt{\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}} \sqrt{\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}} \left(A (m+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}{\sqrt{b^2-4 a c}-b}\right)+B (m+1) x 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}{\sqrt{b^2-4 a c}-b}\right)\right)}{(m+1) (m+2) \sqrt{a+x (b+c 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}}",1,"(x*(e*x)^m*Sqrt[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])]*(A*(2 + m)*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])] + B*(1 + m)*x*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])]))/((1 + m)*(2 + m)*Sqrt[a + x*(b + c*x)])","A",0
1092,1,272,281,0.3452121,"\int \frac{(e x)^m (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((e*x)^m*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{x (e x)^m \left(\sqrt{b^2-4 a c}-b-2 c x\right) \sqrt{\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)^{3/2} \left(A (m+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}{\sqrt{b^2-4 a c}-b}\right)+B (m+1) x 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}{\sqrt{b^2-4 a c}-b}\right)\right)}{(m+1) (m+2) \left(\sqrt{b^2-4 a c}-b\right) (a+x (b+c x))^{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,"(x*(e*x)^m*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x)*Sqrt[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^(3/2)*(A*(2 + m)*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])] + B*(1 + m)*x*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])]))/((-b + Sqrt[b^2 - 4*a*c])*(1 + m)*(2 + m)*(a + x*(b + c*x))^(3/2))","A",0
1093,1,237,281,0.3296985,"\int \frac{(e x)^m (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((e*x)^m*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","\frac{x (e x)^m \sqrt{\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}} \sqrt{\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}} \left(A (m+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}{\sqrt{b^2-4 a c}-b}\right)+B (m+1) x 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}{\sqrt{b^2-4 a c}-b}\right)\right)}{a^2 (m+1) (m+2) \sqrt{a+x (b+c 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}}",1,"(x*(e*x)^m*Sqrt[(b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c])]*(A*(2 + m)*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])] + B*(1 + m)*x*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])]))/(a^2*(1 + m)*(2 + m)*Sqrt[a + x*(b + c*x)])","A",0
1094,1,232,277,0.3485393,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^p \, dx","Integrate[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^p,x]","\frac{x (e x)^m \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)^{-p} (a+x (b+c x))^p \left(A (m+2) F_1\left(m+1;-p,-p;m+2;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+B (m+1) x F_1\left(m+2;-p,-p;m+3;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)\right)}{(m+1) (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,"(x*(e*x)^m*(a + x*(b + c*x))^p*(A*(2 + m)*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])] + B*(1 + m)*x*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])]))/((1 + m)*(2 + m)*((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",0
1095,1,210,442,0.3953064,"\int x^3 (A+B x) \left(a+b x+c x^2\right)^p \, dx","Integrate[x^3*(A + B*x)*(a + b*x + c*x^2)^p,x]","\frac{1}{20} x^4 \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)^{-p} (a+x (b+c x))^p \left(5 A F_1\left(4;-p,-p;5;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+4 B x F_1\left(5;-p,-p;6;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)\right)","-\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,"(x^4*(a + x*(b + c*x))^p*(5*A*AppellF1[4, -p, -p, 5, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + 4*B*x*AppellF1[5, -p, -p, 6, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])]))/(20*((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^p)","C",0
1096,1,210,287,0.3081309,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^p \, dx","Integrate[x^2*(A + B*x)*(a + b*x + c*x^2)^p,x]","\frac{1}{12} x^3 \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)^{-p} (a+x (b+c x))^p \left(4 A F_1\left(3;-p,-p;4;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+3 B x F_1\left(4;-p,-p;5;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)\right)","-\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,"(x^3*(a + x*(b + c*x))^p*(4*A*AppellF1[3, -p, -p, 4, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + 3*B*x*AppellF1[4, -p, -p, 5, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])]))/(12*((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^p)","C",0
1097,1,210,211,0.2806976,"\int x (A+B x) \left(a+b x+c x^2\right)^p \, dx","Integrate[x*(A + B*x)*(a + b*x + c*x^2)^p,x]","\frac{1}{6} x^2 \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)^{-p} (a+x (b+c x))^p \left(3 A F_1\left(2;-p,-p;3;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)+2 B x F_1\left(3;-p,-p;4;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)\right)","\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,"(x^2*(a + x*(b + c*x))^p*(3*A*AppellF1[2, -p, -p, 3, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])] + 2*B*x*AppellF1[3, -p, -p, 4, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])]))/(6*((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^p)","C",0
1098,1,268,158,0.395857,"\int (A+B x) \left(a+b x+c x^2\right)^p \, dx","Integrate[(A + B*x)*(a + b*x + c*x^2)^p,x]","\frac{1}{2} (a+x (b+c x))^p \left(\frac{A 2^p \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p} \, _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)}+B x^2 \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{b-\sqrt{b^2-4 a c}}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}+b}\right)^{-p} F_1\left(2;-p,-p;3;-\frac{2 c x}{b+\sqrt{b^2-4 a c}},\frac{2 c x}{\sqrt{b^2-4 a c}-b}\right)\right)","\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,"((a + x*(b + c*x))^p*((B*x^2*AppellF1[2, -p, -p, 3, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c]), (2*c*x)/(-b + Sqrt[b^2 - 4*a*c])])/(((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^p) + (2^p*A*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*Hypergeometric2F1[-p, 1 + p, 2 + p, (-b + Sqrt[b^2 - 4*a*c] - 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c*(1 + p)*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c])^p)))/2","C",0
1099,1,263,273,0.381086,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^p}{x} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^p)/x,x]","\frac{1}{2} (a+x (b+c x))^p \left(\frac{A 4^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} F_1\left(-2 p;-p,-p;1-2 p;-\frac{b+\sqrt{b^2-4 a c}}{2 c x},\frac{\sqrt{b^2-4 a c}-b}{2 c x}\right)}{p}+\frac{B 2^p \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p} \, _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)}\right)","\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,"((a + x*(b + c*x))^p*((4^p*A*AppellF1[-2*p, -p, -p, 1 - 2*p, -1/2*(b + Sqrt[b^2 - 4*a*c])/(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^p*B*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*Hypergeometric2F1[-p, 1 + p, 2 + p, (-b + Sqrt[b^2 - 4*a*c] - 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c*(1 + p)*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c])^p)))/2","A",0
1100,1,289,315,0.2432429,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^p}{x^2} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^p)/x^2,x]","\frac{\left(\frac{b-\sqrt{b^2-4 a c}}{2 c x}+1\right)^{-p} \left(\frac{b-\sqrt{b^2-4 a c}}{2 c}+x\right)^{-p} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{c}\right)^p \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} (a+x (b+c x))^p \left(2 A p F_1\left(1-2 p;-p,-p;2-2 p;-\frac{b+\sqrt{b^2-4 a c}}{2 c x},\frac{\sqrt{b^2-4 a c}-b}{2 c x}\right)+B (2 p-1) x F_1\left(-2 p;-p,-p;1-2 p;-\frac{b+\sqrt{b^2-4 a c}}{2 c x},\frac{\sqrt{b^2-4 a c}-b}{2 c x}\right)\right)}{2 p (2 p-1) 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,"(((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/c)^p*(a + x*(b + c*x))^p*(2*A*p*AppellF1[1 - 2*p, -p, -p, 2 - 2*p, -1/2*(b + Sqrt[b^2 - 4*a*c])/(c*x), (-b + Sqrt[b^2 - 4*a*c])/(2*c*x)] + B*(-1 + 2*p)*x*AppellF1[-2*p, -p, -p, 1 - 2*p, -1/2*(b + Sqrt[b^2 - 4*a*c])/(c*x), (-b + Sqrt[b^2 - 4*a*c])/(2*c*x)]))/(2*p*(-1 + 2*p)*(1 + (b - Sqrt[b^2 - 4*a*c])/(2*c*x))^p*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)","A",0
1101,1,295,376,0.2975437,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^p}{x^3} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^p)/x^3,x]","\frac{\left(\frac{b-\sqrt{b^2-4 a c}}{2 c x}+1\right)^{-p} \left(\frac{b-\sqrt{b^2-4 a c}}{2 c}+x\right)^{-p} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{c}\right)^p \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} (a+x (b+c x))^p \left(A (2 p-1) F_1\left(2-2 p;-p,-p;3-2 p;-\frac{b+\sqrt{b^2-4 a c}}{2 c x},\frac{\sqrt{b^2-4 a c}-b}{2 c x}\right)+2 B (p-1) x F_1\left(1-2 p;-p,-p;2-2 p;-\frac{b+\sqrt{b^2-4 a c}}{2 c x},\frac{\sqrt{b^2-4 a c}-b}{2 c x}\right)\right)}{2 (p-1) (2 p-1) 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,"(((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/c)^p*(a + x*(b + c*x))^p*(2*B*(-1 + p)*x*AppellF1[1 - 2*p, -p, -p, 2 - 2*p, -1/2*(b + Sqrt[b^2 - 4*a*c])/(c*x), (-b + Sqrt[b^2 - 4*a*c])/(2*c*x)] + A*(-1 + 2*p)*AppellF1[2 - 2*p, -p, -p, 3 - 2*p, -1/2*(b + Sqrt[b^2 - 4*a*c])/(c*x), (-b + Sqrt[b^2 - 4*a*c])/(2*c*x)]))/(2*(-1 + p)*(-1 + 2*p)*(1 + (b - Sqrt[b^2 - 4*a*c])/(2*c*x))^p*x^2*((b - Sqrt[b^2 - 4*a*c])/(2*c) + x)^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(c*x))^p)","A",0
1102,1,118,136,0.1165432,"\int (A+B x) (d+e x)^m \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^m*(b*x + c*x^2),x]","\frac{(d+e x)^{m+1} \left(-\frac{(d+e x)^2 (-A c e-b B e+3 B c d)}{m+3}+\frac{(d+e x) (A e (b e-2 c d)+B d (3 c d-2 b e))}{m+2}-\frac{d (B d-A e) (c d-b e)}{m+1}+\frac{B c (d+e x)^3}{m+4}\right)}{e^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 + e*x)^(1 + m)*(-((d*(B*d - A*e)*(c*d - b*e))/(1 + m)) + ((B*d*(3*c*d - 2*b*e) + A*e*(-2*c*d + b*e))*(d + e*x))/(2 + m) - ((3*B*c*d - b*B*e - A*c*e)*(d + e*x)^2)/(3 + m) + (B*c*(d + e*x)^3)/(4 + m)))/e^4","A",1
1103,1,177,118,0.0603083,"\int (A+B x) (d+e x)^4 \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^4*(b*x + c*x^2),x]","\frac{1}{3} d^3 x^3 (4 A b e+A c d+b B d)+\frac{1}{4} d^2 x^4 (2 A e (3 b e+2 c d)+B d (4 b e+c d))+\frac{1}{7} e^3 x^7 (A c e+b B e+4 B c d)+\frac{1}{6} e^2 x^6 (A e (b e+4 c d)+2 B d (2 b e+3 c d))+\frac{2}{5} d e x^5 (A e (2 b e+3 c d)+B d (3 b e+2 c d))+\frac{1}{2} A b d^4 x^2+\frac{1}{8} B c e^4 x^8","-\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,"(A*b*d^4*x^2)/2 + (d^3*(b*B*d + A*c*d + 4*A*b*e)*x^3)/3 + (d^2*(2*A*e*(2*c*d + 3*b*e) + B*d*(c*d + 4*b*e))*x^4)/4 + (2*d*e*(A*e*(3*c*d + 2*b*e) + B*d*(2*c*d + 3*b*e))*x^5)/5 + (e^2*(A*e*(4*c*d + b*e) + 2*B*d*(3*c*d + 2*b*e))*x^6)/6 + (e^3*(4*B*c*d + b*B*e + A*c*e)*x^7)/7 + (B*c*e^4*x^8)/8","A",1
1104,1,135,118,0.0433278,"\int (A+B x) (d+e x)^3 \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^3*(b*x + c*x^2),x]","\frac{1}{3} d^2 x^3 (3 A b e+A c d+b B d)+\frac{1}{6} e^2 x^6 (A c e+b B e+3 B c d)+\frac{1}{5} e x^5 (A e (b e+3 c d)+3 B d (b e+c d))+\frac{1}{4} d x^4 (3 A e (b e+c d)+B d (3 b e+c d))+\frac{1}{2} A b d^3 x^2+\frac{1}{7} B c e^3 x^7","-\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,"(A*b*d^3*x^2)/2 + (d^2*(b*B*d + A*c*d + 3*A*b*e)*x^3)/3 + (d*(3*A*e*(c*d + b*e) + B*d*(c*d + 3*b*e))*x^4)/4 + (e*(3*B*d*(c*d + b*e) + A*e*(3*c*d + b*e))*x^5)/5 + (e^2*(3*B*c*d + b*B*e + A*c*e)*x^6)/6 + (B*c*e^3*x^7)/7","A",1
1105,1,91,99,0.0421258,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^2*(b*x + c*x^2),x]","\frac{1}{60} x^2 \left(12 e x^3 (A c e+b B e+2 B c d)+15 x^2 (A e (b e+2 c d)+B d (2 b e+c d))+20 d x (2 A b e+A c d+b B d)+30 A b d^2+10 B c e^2 x^4\right)","\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,"(x^2*(30*A*b*d^2 + 20*d*(b*B*d + A*c*d + 2*A*b*e)*x + 15*(A*e*(2*c*d + b*e) + B*d*(c*d + 2*b*e))*x^2 + 12*e*(2*B*c*d + b*B*e + A*c*e)*x^3 + 10*B*c*e^2*x^4))/60","A",1
1106,1,55,61,0.0215679,"\int (A+B x) (d+e x) \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)*(b*x + c*x^2),x]","\frac{1}{60} x^2 \left(15 x^2 (A c e+b B e+B c d)+20 x (A b e+A c d+b B d)+30 A b d+12 B c e x^3\right)","\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,"(x^2*(30*A*b*d + 20*(b*B*d + A*c*d + A*b*e)*x + 15*(B*c*d + b*B*e + A*c*e)*x^2 + 12*B*c*e*x^3))/60","A",1
1107,1,29,33,0.0047827,"\int (A+B x) \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(b*x + c*x^2),x]","\frac{1}{12} x^2 (A (6 b+4 c x)+B x (4 b+3 c x))","\frac{1}{3} x^3 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{4} B c x^4",1,"(x^2*(B*x*(4*b + 3*c*x) + A*(6*b + 4*c*x)))/12","A",1
1108,1,88,87,0.0438342,"\int \frac{(A+B x) \left(b x+c x^2\right)}{d+e x} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/(d + e*x),x]","\frac{e x \left(3 A e (2 b e-2 c d+c e x)+3 b B e (e x-2 d)+B c \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)-6 d (B d-A e) (c d-b e) \log (d+e x)}{6 e^4}","-\frac{d (B d-A e) (c d-b e) \log (d+e x)}{e^4}+\frac{x (B d-A e) (c d-b e)}{e^3}-\frac{x^2 (-A c e-b B e+B c d)}{2 e^2}+\frac{B c x^3}{3 e}",1,"(e*x*(3*b*B*e*(-2*d + e*x) + 3*A*e*(-2*c*d + 2*b*e + c*e*x) + B*c*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) - 6*d*(B*d - A*e)*(c*d - b*e)*Log[d + e*x])/(6*e^4)","A",1
1109,1,93,99,0.0777617,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/(d + e*x)^2,x]","\frac{2 e x (A c e+b B e-2 B c d)+\frac{2 d (B d-A e) (c d-b e)}{d+e x}+2 \log (d+e x) (A e (b e-2 c d)+B d (3 c d-2 b e))+B c e^2 x^2}{2 e^4}","\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{x (-A c e-b B e+2 B c d)}{e^3}+\frac{B c x^2}{2 e^2}",1,"(2*e*(-2*B*c*d + b*B*e + A*c*e)*x + B*c*e^2*x^2 + (2*d*(B*d - A*e)*(c*d - b*e))/(d + e*x) + 2*(B*d*(3*c*d - 2*b*e) + A*e*(-2*c*d + b*e))*Log[d + e*x])/(2*e^4)","A",1
1110,1,96,104,0.0816783,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/(d + e*x)^3,x]","\frac{\frac{-2 A b e^2+4 A c d e+4 b B d e-6 B c d^2}{d+e x}+\frac{d (B d-A e) (c d-b e)}{(d+e x)^2}+2 \log (d+e x) (A c e+b B e-3 B c d)+2 B c e x}{2 e^4}","\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,"(2*B*c*e*x + (d*(B*d - A*e)*(c*d - b*e))/(d + e*x)^2 + (-6*B*c*d^2 + 4*b*B*d*e + 4*A*c*d*e - 2*A*b*e^2)/(d + e*x) + 2*(-3*B*c*d + b*B*e + A*c*e)*Log[d + e*x])/(2*e^4)","A",1
1111,1,112,111,0.0529008,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/(d + e*x)^4,x]","\frac{-A e \left(b e (d+3 e x)+2 c \left(d^2+3 d e x+3 e^2 x^2\right)\right)+B \left(c d \left(11 d^2+27 d e x+18 e^2 x^2\right)-2 b e \left(d^2+3 d e x+3 e^2 x^2\right)\right)+6 B c (d+e x)^3 \log (d+e x)}{6 e^4 (d+e x)^3}","\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,"(-(A*e*(b*e*(d + 3*e*x) + 2*c*(d^2 + 3*d*e*x + 3*e^2*x^2))) + B*(-2*b*e*(d^2 + 3*d*e*x + 3*e^2*x^2) + c*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) + 6*B*c*(d + e*x)^3*Log[d + e*x])/(6*e^4*(d + e*x)^3)","A",1
1112,1,101,116,0.0435481,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/(d + e*x)^5,x]","-\frac{A e \left(b e (d+4 e x)+c \left(d^2+4 d e x+6 e^2 x^2\right)\right)+B \left(b e \left(d^2+4 d e x+6 e^2 x^2\right)+3 c \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)}{12 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 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,"-1/12*(A*e*(b*e*(d + 4*e*x) + c*(d^2 + 4*d*e*x + 6*e^2*x^2)) + B*(b*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*c*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)))/(e^4*(d + e*x)^4)","A",1
1113,1,104,118,0.0479121,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/(d + e*x)^6,x]","-\frac{A e \left(3 b e (d+5 e x)+2 c \left(d^2+5 d e x+10 e^2 x^2\right)\right)+B \left(2 b e \left(d^2+5 d e x+10 e^2 x^2\right)+3 c \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)}{60 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 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,"-1/60*(A*e*(3*b*e*(d + 5*e*x) + 2*c*(d^2 + 5*d*e*x + 10*e^2*x^2)) + B*(2*b*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*c*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)))/(e^4*(d + e*x)^5)","A",1
1114,1,309,282,0.4444503,"\int (A+B x) (d+e x)^m \left(b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^m*(b*x + c*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(A e \left(\frac{(d+e x)^2 \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{m+3}+\frac{d^2 (c d-b e)^2}{m+1}-\frac{2 c (d+e x)^3 (2 c d-b e)}{m+4}-\frac{2 d (d+e x) (c d-b e) (2 c d-b e)}{m+2}+\frac{c^2 (d+e x)^4}{m+5}\right)+B \left(\frac{(d+e x)^3 \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{m+4}-\frac{d (d+e x)^2 \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{m+3}-\frac{d^3 (c d-b e)^2}{m+1}+\frac{d^2 (d+e x) (5 c d-3 b e) (c d-b e)}{m+2}-\frac{c (d+e x)^4 (5 c d-2 b e)}{m+5}+\frac{c^2 (d+e x)^5}{m+6}\right)\right)}{e^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 + e*x)^(1 + m)*(A*e*((d^2*(c*d - b*e)^2)/(1 + m) - (2*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x))/(2 + m) + ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^2)/(3 + m) - (2*c*(2*c*d - b*e)*(d + e*x)^3)/(4 + m) + (c^2*(d + e*x)^4)/(5 + m)) + B*(-((d^3*(c*d - b*e)^2)/(1 + m)) + (d^2*(5*c*d - 3*b*e)*(c*d - b*e)*(d + e*x))/(2 + m) - (d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2)*(d + e*x)^2)/(3 + m) + ((10*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*(d + e*x)^3)/(4 + m) - (c*(5*c*d - 2*b*e)*(d + e*x)^4)/(5 + m) + (c^2*(d + e*x)^5)/(6 + m))))/e^6","A",1
1115,1,228,228,0.0813101,"\int (A+B x) (d+e x)^3 \left(b x+c x^2\right)^2 \, dx","Integrate[(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",1
1116,1,162,162,0.0547677,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right)^2 \, dx","Integrate[(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",1
1117,1,101,100,0.0299171,"\int (A+B x) (d+e x) \left(b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)*(b*x + c*x^2)^2,x]","\frac{1}{5} x^5 \left(2 A b c e+A c^2 d+b^2 B e+2 b B c d\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 + ((2*b*B*c*d + A*c^2*d + b^2*B*e + 2*A*b*c*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",1
1118,1,49,55,0.013142,"\int (A+B x) \left(b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(b*x + c*x^2)^2,x]","\frac{1}{60} x^3 \left(20 A b^2+12 c x^2 (A c+2 b B)+15 b x (2 A c+b B)+10 B c^2 x^3\right)","\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,"(x^3*(20*A*b^2 + 15*b*(b*B + 2*A*c)*x + 12*c*(2*b*B + A*c)*x^2 + 10*B*c^2*x^3))/60","A",1
1119,1,156,161,0.1412905,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{d+e x} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x),x]","\frac{-60 d^2 (B d-A e) (c d-b e)^2 \log (d+e x)+15 c e^4 x^4 (A c e+2 b B e-B c d)+20 e^3 x^3 \left(A c e (2 b e-c d)+B (c d-b e)^2\right)+30 e^2 x^2 (A e-B d) (c d-b e)^2+60 d e x (B d-A e) (c d-b e)^2+12 B c^2 e^5 x^5}{60 e^6}","-\frac{d^2 (B d-A e) (c d-b e)^2 \log (d+e x)}{e^6}+\frac{d x (B d-A e) (c d-b e)^2}{e^5}-\frac{x^2 (B d-A e) (c d-b e)^2}{2 e^4}-\frac{x^3 \left(A c e (c d-2 b e)-B (c d-b e)^2\right)}{3 e^3}-\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,"(60*d*e*(B*d - A*e)*(c*d - b*e)^2*x + 30*e^2*(-(B*d) + A*e)*(c*d - b*e)^2*x^2 + 20*e^3*(B*(c*d - b*e)^2 + A*c*e*(-(c*d) + 2*b*e))*x^3 + 15*c*e^4*(-(B*c*d) + 2*b*B*e + A*c*e)*x^4 + 12*B*c^2*e^5*x^5 - 60*d^2*(B*d - A*e)*(c*d - b*e)^2*Log[d + e*x])/(60*e^6)","A",1
1120,1,184,194,0.0765964,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^2,x]","\frac{\frac{12 d^2 (B d-A e) (c d-b e)^2}{d+e x}+4 c e^3 x^3 (A c e+2 b B e-2 B c d)+6 e^2 x^2 (b e-c d) (2 A c e+b B e-3 B c d)+12 e x (b e-c d) (A e (b e-3 c d)+2 B d (2 c d-b e))+12 d (c d-b e) \log (d+e x) (2 A e (b e-2 c d)+B d (5 c d-3 b e))+3 B c^2 e^4 x^4}{12 e^6}","\frac{d^2 (B d-A e) (c d-b e)^2}{e^6 (d+e x)}+\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{x (c d-b e) (2 B d (2 c d-b e)-A e (3 c d-b e))}{e^5}+\frac{x^2 (c d-b e) (-2 A c e-b B e+3 B c d)}{2 e^4}-\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,"(12*e*(-(c*d) + b*e)*(2*B*d*(2*c*d - b*e) + A*e*(-3*c*d + b*e))*x + 6*e^2*(-(c*d) + b*e)*(-3*B*c*d + b*B*e + 2*A*c*e)*x^2 + 4*c*e^3*(-2*B*c*d + 2*b*B*e + A*c*e)*x^3 + 3*B*c^2*e^4*x^4 + (12*d^2*(B*d - A*e)*(c*d - b*e)^2)/(d + e*x) + 12*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])/(12*e^6)","A",1
1121,1,219,232,0.1585558,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^3,x]","\frac{6 e x \left(A c e (2 b e-3 c d)+B \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)\right)+6 \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)+\frac{3 d^2 (B d-A e) (c d-b e)^2}{(d+e x)^2}+3 c e^2 x^2 (A c e+2 b B e-3 B c d)-\frac{6 d (c d-b e) (2 A e (b e-2 c d)+B d (5 c d-3 b e))}{d+e x}+2 B c^2 e^3 x^3}{6 e^6}","\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{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{d^2 (B d-A e) (c d-b e)^2}{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))}{e^6 (d+e x)}-\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,"(6*e*(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 + 3*c*e^2*(-3*B*c*d + 2*b*B*e + A*c*e)*x^2 + 2*B*c^2*e^3*x^3 + (3*d^2*(B*d - A*e)*(c*d - b*e)^2)/(d + e*x)^2 - (6*d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) + 2*A*e*(-2*c*d + b*e)))/(d + e*x) + 6*(B*d*(-10*c^2*d^2 + 12*b*c*d*e - 3*b^2*e^2) + A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2))*Log[d + e*x])/(6*e^6)","A",1
1122,1,220,238,0.161153,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^4,x]","\frac{-\frac{6 \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)}{d+e x}+6 \log (d+e x) \left(2 A c e (b e-2 c d)+B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)+\frac{2 d^2 (B d-A e) (c d-b e)^2}{(d+e x)^3}-\frac{3 d (c d-b e) (2 A e (b e-2 c d)+B d (5 c d-3 b e))}{(d+e x)^2}+6 c e x (A c e+2 b B e-4 B c d)+3 B c^2 e^2 x^2}{6 e^6}","-\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,"(6*c*e*(-4*B*c*d + 2*b*B*e + A*c*e)*x + 3*B*c^2*e^2*x^2 + (2*d^2*(B*d - A*e)*(c*d - b*e)^2)/(d + e*x)^3 - (3*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 - (6*(B*d*(-10*c^2*d^2 + 12*b*c*d*e - 3*b^2*e^2) + A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)))/(d + e*x) + 6*(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])/(6*e^6)","A",1
1123,1,275,240,0.1418416,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^5,x]","-\frac{A e \left(b^2 e^2 \left(d^2+4 d e x+6 e^2 x^2\right)+6 b c e \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)+c^2 (-d) \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)\right)+12 c (d+e x)^4 \log (d+e x) (-A c e-2 b B e+5 B c d)+B \left(3 b^2 e^2 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)-2 b c d e \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)+c^2 \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)\right)}{12 e^6 (d+e x)^4}","\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,"-1/12*(A*e*(b^2*e^2*(d^2 + 4*d*e*x + 6*e^2*x^2) + 6*b*c*e*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) - c^2*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) + B*(3*b^2*e^2*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) - 2*b*c*d*e*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3) + c^2*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5)) + 12*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^4*Log[d + e*x])/(e^6*(d + e*x)^4)","A",1
1124,1,269,248,0.1249892,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^6,x]","\frac{-2 A e \left(b^2 e^2 \left(d^2+5 d e x+10 e^2 x^2\right)+3 b c e \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+6 c^2 \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)+B \left(-3 b^2 e^2 \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)-24 b c e \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)+c^2 d \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)\right)+60 B c^2 (d+e x)^5 \log (d+e x)}{60 e^6 (d+e x)^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)}{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,"(-2*A*e*(b^2*e^2*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*b*c*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 6*c^2*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4)) + B*(-3*b^2*e^2*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) - 24*b*c*e*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4) + c^2*d*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4)) + 60*B*c^2*(d + e*x)^5*Log[d + e*x])/(60*e^6*(d + e*x)^5)","A",1
1125,1,257,253,0.1108189,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^7,x]","-\frac{A e \left(b^2 e^2 \left(d^2+6 d e x+15 e^2 x^2\right)+2 b c e \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+2 c^2 \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)+B \left(b^2 e^2 \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+4 b c e \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)+10 c^2 \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right)\right)}{60 e^6 (d+e x)^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)}{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,"-1/60*(A*e*(b^2*e^2*(d^2 + 6*d*e*x + 15*e^2*x^2) + 2*b*c*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 2*c^2*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)) + B*(b^2*e^2*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 4*b*c*e*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4) + 10*c^2*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5)))/(e^6*(d + e*x)^6)","A",1
1126,1,260,255,0.1103558,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^8,x]","-\frac{2 A e \left(2 b^2 e^2 \left(d^2+7 d e x+21 e^2 x^2\right)+3 b c e \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+2 c^2 \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)+B \left(3 b^2 e^2 \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+8 b c e \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)+10 c^2 \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)\right)}{420 e^6 (d+e x)^7}","\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,"-1/420*(2*A*e*(2*b^2*e^2*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*b*c*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 2*c^2*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)) + B*(3*b^2*e^2*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 8*b*c*e*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4) + 10*c^2*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5)))/(e^6*(d + e*x)^7)","A",1
1127,1,525,484,0.9798258,"\int (A+B x) (d+e x)^m \left(b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^m*(b*x + c*x^2)^3,x]","\frac{(d+e x)^{m+1} \left(A e \left(\frac{3 c (d+e x)^4 \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{m+5}-\frac{(d+e x)^3 (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{m+4}+\frac{3 d (d+e x)^2 (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{m+3}-\frac{3 c^2 (d+e x)^5 (2 c d-b e)}{m+6}+\frac{d^3 (c d-b e)^3}{m+1}-\frac{3 d^2 (d+e x) (c d-b e)^2 (2 c d-b e)}{m+2}+\frac{c^3 (d+e x)^6}{m+7}\right)+B \left(\frac{3 c (d+e x)^5 \left(b^2 e^2-6 b c d e+7 c^2 d^2\right)}{m+6}-\frac{3 d^2 (d+e x)^2 (c d-b e) \left(2 b^2 e^2-8 b c d e+7 c^2 d^2\right)}{m+3}-\frac{(d+e x)^4 \left(-b^3 e^3+15 b^2 c d e^2-45 b c^2 d^2 e+35 c^3 d^3\right)}{m+5}+\frac{d (d+e x)^3 \left(-4 b^3 e^3+30 b^2 c d e^2-60 b c^2 d^2 e+35 c^3 d^3\right)}{m+4}-\frac{c^2 (d+e x)^6 (7 c d-3 b e)}{m+7}-\frac{d^4 (c d-b e)^3}{m+1}+\frac{d^3 (d+e x) (7 c d-4 b e) (c d-b e)^2}{m+2}+\frac{c^3 (d+e x)^7}{m+8}\right)\right)}{e^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{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{(d+e x)^{m+4} \left(B d \left(-4 b^3 e^3+30 b^2 c d e^2-60 b c^2 d^2 e+35 c^3 d^3\right)-A e \left(-b^3 e^3+12 b^2 c d e^2-30 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(-b^3 e^3+15 b^2 c d e^2-45 b c^2 d^2 e+35 c^3 d^3\right)\right)}{e^8 (m+5)}-\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 + e*x)^(1 + m)*(A*e*((d^3*(c*d - b*e)^3)/(1 + m) - (3*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x))/(2 + m) + (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^2)/(3 + m) - ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^3)/(4 + m) + (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^4)/(5 + m) - (3*c^2*(2*c*d - b*e)*(d + e*x)^5)/(6 + m) + (c^3*(d + e*x)^6)/(7 + m)) + B*(-((d^4*(c*d - b*e)^3)/(1 + m)) + (d^3*(7*c*d - 4*b*e)*(c*d - b*e)^2*(d + e*x))/(2 + m) - (3*d^2*(c*d - b*e)*(7*c^2*d^2 - 8*b*c*d*e + 2*b^2*e^2)*(d + e*x)^2)/(3 + m) + (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)*(d + e*x)^3)/(4 + m) - ((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)^4)/(5 + m) + (3*c*(7*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^5)/(6 + m) - (c^2*(7*c*d - 3*b*e)*(d + e*x)^6)/(7 + m) + (c^3*(d + e*x)^7)/(8 + m))))/e^8","A",1
1128,1,412,412,0.1554755,"\int (A+B x) (d+e x)^4 \left(b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^4*(b*x + c*x^2)^3,x]","\frac{1}{4} A b^3 d^4 x^4+\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}{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}{7} d x^7 \left(2 b^3 e^2 (2 A e+3 B d)+6 b^2 c d e (3 A e+2 B d)+3 b c^2 d^2 (4 A e+B d)+A c^3 d^3\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(b^3 e^3+12 b^2 c d e^2+18 b c^2 d^2 e+4 c^3 d^3\right)\right)+\frac{1}{8} x^8 \left(A e \left(b^3 e^3+12 b^2 c d e^2+18 b c^2 d^2 e+4 c^3 d^3\right)+B d \left(4 b^3 e^3+18 b^2 c d e^2+12 b c^2 d^2 e+c^3 d^3\right)\right)+\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}{4} A b^3 d^4 x^4+\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}{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}{7} d x^7 \left(2 b^3 e^2 (2 A e+3 B d)+6 b^2 c d e (3 A e+2 B d)+3 b c^2 d^2 (4 A e+B d)+A c^3 d^3\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(b^3 e^3+12 b^2 c d e^2+18 b c^2 d^2 e+4 c^3 d^3\right)\right)+\frac{1}{8} x^8 \left(A e \left(b^3 e^3+12 b^2 c d e^2+18 b c^2 d^2 e+4 c^3 d^3\right)+B d \left(4 b^3 e^3+18 b^2 c d e^2+12 b c^2 d^2 e+c^3 d^3\right)\right)+\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",1
1129,1,305,305,0.1157061,"\int (A+B x) (d+e x)^3 \left(b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^3*(b*x + c*x^2)^3,x]","\frac{1}{4} A b^3 d^3 x^4+\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}{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}{7} x^7 \left(b^3 e^2 (A e+3 B d)+9 b^2 c d e (A e+B d)+3 b c^2 d^2 (3 A e+B d)+A c^3 d^3\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(b^3 e^3+9 b^2 c d e^2+9 b c^2 d^2 e+c^3 d^3\right)\right)+\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}{4} A b^3 d^3 x^4+\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}{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}{7} x^7 \left(b^3 e^2 (A e+3 B d)+9 b^2 c d e (A e+B d)+3 b c^2 d^2 (3 A e+B d)+A c^3 d^3\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(b^3 e^3+9 b^2 c d e^2+9 b c^2 d^2 e+c^3 d^3\right)\right)+\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",1
1130,1,225,225,0.0780427,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^2*(b*x + c*x^2)^3,x]","\frac{1}{4} A b^3 d^2 x^4+\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}{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}{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}{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}{4} A b^3 d^2 x^4+\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}{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}{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}{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",1
1131,1,141,139,0.0435877,"\int (A+B x) (d+e x) \left(b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)*(b*x + c*x^2)^3,x]","\frac{1}{4} A b^3 d x^4+\frac{1}{7} c x^7 \left(3 A b c e+A c^2 d+3 b^2 B e+3 b B c d\right)+\frac{1}{6} b x^6 \left(3 A b c e+3 A c^2 d+b^2 B e+3 b B c d\right)+\frac{1}{5} b^2 x^5 (A b e+3 A c d+b B d)+\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} A b^3 d x^4+\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}{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*b*B*c*d + 3*A*c^2*d + b^2*B*e + 3*A*b*c*e)*x^6)/6 + (c*(3*b*B*c*d + A*c^2*d + 3*b^2*B*e + 3*A*b*c*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",1
1132,1,75,75,0.011818,"\int (A+B x) \left(b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{4} A b^3 x^4+\frac{1}{5} b^2 x^5 (3 A c+b B)+\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}{4} A b^3 x^4+\frac{1}{5} b^2 x^5 (3 A c+b B)+\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",1
1133,1,248,257,0.1021185,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{d+e x} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/(d + e*x),x]","\frac{84 c e^5 x^5 \left(A c e (3 b e-c d)+B \left(3 b^2 e^2-3 b c d e+c^2 d^2\right)\right)+105 e^4 x^4 \left(A c e \left(3 b^2 e^2-3 b c d e+c^2 d^2\right)-B (c d-b e)^3\right)+70 c^2 e^6 x^6 (A c e+3 b B e-B c d)-420 d^3 (B d-A e) (c d-b e)^3 \log (d+e x)+420 d^2 e x (B d-A e) (c d-b e)^3+140 e^3 x^3 (A e-B d) (b e-c d)^3-210 d e^2 x^2 (B d-A e) (c d-b e)^3+60 B c^3 e^7 x^7}{420 e^8}","-\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 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{c^2 x^6 (-A c e-3 b B e+B c d)}{6 e^2}-\frac{d^3 (B d-A e) (c d-b e)^3 \log (d+e x)}{e^8}+\frac{d^2 x (B d-A e) (c d-b e)^3}{e^7}-\frac{d x^2 (B d-A e) (c d-b e)^3}{2 e^6}+\frac{x^3 (B d-A e) (c d-b e)^3}{3 e^5}+\frac{B c^3 x^7}{7 e}",1,"(420*d^2*e*(B*d - A*e)*(c*d - b*e)^3*x - 210*d*e^2*(B*d - A*e)*(c*d - b*e)^3*x^2 + 140*e^3*(-(B*d) + A*e)*(-(c*d) + b*e)^3*x^3 + 105*e^4*(-(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 + 84*c*e^5*(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 + 70*c^2*e^6*(-(B*c*d) + 3*b*B*e + A*c*e)*x^6 + 60*B*c^3*e^7*x^7 - 420*d^3*(B*d - A*e)*(c*d - b*e)^3*Log[d + e*x])/(420*e^8)","A",1
1134,1,274,287,0.1192048,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/(d + e*x)^2,x]","\frac{12 c^2 e^5 x^5 (A c e+3 b B e-2 B c d)+\frac{60 d^3 (B d-A e) (c d-b e)^3}{d+e x}+60 d^2 (c d-b e)^2 \log (d+e x) (3 A e (b e-2 c d)+B d (7 c d-4 b e))-15 c e^4 x^4 \left(A c e (2 c d-3 b e)-3 B (c d-b e)^2\right)+20 e^3 x^3 (c d-b e)^2 (3 A c e+b B e-4 B c d)+30 e^2 x^2 (c d-b e)^2 (A e (b e-4 c d)+B d (5 c d-2 b e))-60 d e x (c d-b e)^2 (A e (2 b e-5 c d)+3 B d (2 c d-b e))+10 B c^3 e^6 x^6}{60 e^8}","-\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{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{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{x^3 (c d-b e)^2 (-3 A c e-b B e+4 B c d)}{3 e^5}-\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{B c^3 x^6}{6 e^2}",1,"(-60*d*e*(c*d - b*e)^2*(3*B*d*(2*c*d - b*e) + A*e*(-5*c*d + 2*b*e))*x + 30*e^2*(c*d - b*e)^2*(B*d*(5*c*d - 2*b*e) + A*e*(-4*c*d + b*e))*x^2 + 20*e^3*(c*d - b*e)^2*(-4*B*c*d + b*B*e + 3*A*c*e)*x^3 - 15*c*e^4*(A*c*e*(2*c*d - 3*b*e) - 3*B*(c*d - b*e)^2)*x^4 + 12*c^2*e^5*(-2*B*c*d + 3*b*B*e + A*c*e)*x^5 + 10*B*c^3*e^6*x^6 + (60*d^3*(B*d - A*e)*(c*d - b*e)^3)/(d + e*x) + 60*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])/(60*e^8)","A",1
1135,1,342,359,0.1456651,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/(d + e*x)^3,x]","\frac{10 e^2 x^2 (b e-c d) \left(3 A c e (b e-2 c d)+B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)+20 e x (b e-c d) \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)-60 d (c d-b e) \log (d+e x) \left(B d \left(2 b^2 e^2-8 b c d e+7 c^2 d^2\right)-A e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)\right)+5 c^2 e^4 x^4 (A c e+3 b B e-3 B c d)+\frac{10 d^3 (B d-A e) (c d-b e)^3}{(d+e x)^2}-\frac{20 d^2 (c d-b e)^2 (3 A e (b e-2 c d)+B d (7 c d-4 b e))}{d+e x}-20 c e^3 x^3 (c d-b e) (A c e+b B e-2 B c d)+4 B c^3 e^5 x^5}{20 e^8}","\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{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{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{c^2 x^4 (-A c e-3 b B e+3 B c d)}{4 e^4}+\frac{d^3 (B d-A e) (c d-b e)^3}{2 e^8 (d+e x)^2}-\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{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,"(20*e*(-(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 + 10*e^2*(-(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 - 20*c*e^3*(c*d - b*e)*(-2*B*c*d + b*B*e + A*c*e)*x^3 + 5*c^2*e^4*(-3*B*c*d + 3*b*B*e + A*c*e)*x^4 + 4*B*c^3*e^5*x^5 + (10*d^3*(B*d - A*e)*(c*d - b*e)^3)/(d + e*x)^2 - (20*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) - 60*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])/(20*e^8)","A",1
1136,1,400,422,0.1604802,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^3)/(d + e*x)^4,x]","\frac{-6 c e^2 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)+\frac{36 d (c d-b e) \left(B d \left(2 b^2 e^2-8 b c d e+7 c^2 d^2\right)-A e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)\right)}{d+e x}+12 e x \left(A c e \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)+B \left(b^3 e^3-12 b^2 c d e^2+30 b c^2 d^2 e-20 c^3 d^3\right)\right)+12 \log (d+e x) \left(A e \left(b^3 e^3-12 b^2 c d e^2+30 b c^2 d^2 e-20 c^3 d^3\right)+B d \left(-4 b^3 e^3+30 b^2 c d e^2-60 b c^2 d^2 e+35 c^3 d^3\right)\right)+4 c^2 e^3 x^3 (A c e+3 b B e-4 B c d)+\frac{4 d^3 (B d-A e) (c d-b e)^3}{(d+e x)^3}-\frac{6 d^2 (c d-b e)^2 (3 A e (b e-2 c d)+B d (7 c d-4 b e))}{(d+e x)^2}+3 B c^3 e^4 x^4}{12 e^8}","-\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{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{\log (d+e x) \left(B d \left(-4 b^3 e^3+30 b^2 c d e^2-60 b c^2 d^2 e+35 c^3 d^3\right)-A e \left(-b^3 e^3+12 b^2 c d e^2-30 b c^2 d^2 e+20 c^3 d^3\right)\right)}{e^8}+\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(-b^3 e^3+12 b^2 c d e^2-30 b c^2 d^2 e+20 c^3 d^3\right)\right)}{e^7}-\frac{c^2 x^3 (-A c e-3 b B e+4 B c d)}{3 e^5}+\frac{d^3 (B d-A e) (c d-b e)^3}{3 e^8 (d+e x)^3}-\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{B c^3 x^4}{4 e^4}",1,"(12*e*(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 - 6*c*e^2*(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 + 4*c^2*e^3*(-4*B*c*d + 3*b*B*e + A*c*e)*x^3 + 3*B*c^3*e^4*x^4 + (4*d^3*(B*d - A*e)*(c*d - b*e)^3)/(d + e*x)^3 - (6*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 + (36*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) + 12*(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])/(12*e^8)","A",1
1137,1,187,207,0.1330781,"\int \frac{(A+B x) (d+e x)^4}{b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(b*x + c*x^2),x]","\frac{e x \left(2 A c e \left(6 b^2 e^2-3 b c e (8 d+e x)+2 c^2 \left(18 d^2+6 d e x+e^2 x^2\right)\right)+B \left(-12 b^3 e^3+6 b^2 c e^2 (8 d+e x)-4 b c^2 e \left(18 d^2+6 d e x+e^2 x^2\right)+c^3 \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)\right)\right)}{12 c^4}+\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{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(-b^3 e^3+4 b^2 c d e^2-6 b c^2 d^2 e+4 c^3 d^3\right)\right)}{c^4}+\frac{(b B-A c) (c d-b e)^4 \log (b+c x)}{b c^5}+\frac{e^3 x^3 (A c e-b B e+4 B c d)}{3 c^2}+\frac{A d^4 \log (x)}{b}+\frac{B e^4 x^4}{4 c}",1,"(e*x*(2*A*c*e*(6*b^2*e^2 - 3*b*c*e*(8*d + e*x) + 2*c^2*(18*d^2 + 6*d*e*x + e^2*x^2)) + B*(-12*b^3*e^3 + 6*b^2*c*e^2*(8*d + e*x) - 4*b*c^2*e*(18*d^2 + 6*d*e*x + e^2*x^2) + c^3*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3))))/(12*c^4) + (A*d^4*Log[x])/b + ((b*B - A*c)*(c*d - b*e)^4*Log[b + c*x])/(b*c^5)","A",1
1138,1,118,128,0.0775224,"\int \frac{(A+B x) (d+e x)^3}{b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2),x]","\frac{b c e x \left(3 A c e (-2 b e+6 c d+c e x)+B \left(6 b^2 e^2-3 b c e (6 d+e x)+c^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)\right)-6 (b B-A c) (b e-c d)^3 \log (b+c x)+6 A c^4 d^3 \log (x)}{6 b c^4}","\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{(b B-A c) (c d-b e)^3 \log (b+c x)}{b c^4}+\frac{e^2 x^2 (A c e-b B e+3 B c d)}{2 c^2}+\frac{A d^3 \log (x)}{b}+\frac{B e^3 x^3}{3 c}",1,"(b*c*e*x*(3*A*c*e*(6*c*d - 2*b*e + c*e*x) + B*(6*b^2*e^2 - 3*b*c*e*(6*d + e*x) + c^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2))) + 6*A*c^4*d^3*Log[x] - 6*(b*B - A*c)*(-(c*d) + b*e)^3*Log[b + c*x])/(6*b*c^4)","A",1
1139,1,74,77,0.044473,"\int \frac{(A+B x) (d+e x)^2}{b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2),x]","\frac{b c e x (2 A c e+B (-2 b e+4 c d+c e x))+2 (b B-A c) (c d-b e)^2 \log (b+c x)+2 A c^3 d^2 \log (x)}{2 b c^3}","\frac{(b B-A c) (c d-b e)^2 \log (b+c x)}{b c^3}+\frac{e x (A c e-b B e+2 B c d)}{c^2}+\frac{A d^2 \log (x)}{b}+\frac{B e^2 x^2}{2 c}",1,"(b*c*e*x*(2*A*c*e + B*(4*c*d - 2*b*e + c*e*x)) + 2*A*c^3*d^2*Log[x] + 2*(b*B - A*c)*(c*d - b*e)^2*Log[b + c*x])/(2*b*c^3)","A",1
1140,1,46,45,0.0227429,"\int \frac{(A+B x) (d+e x)}{b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x))/(b*x + c*x^2),x]","\frac{-(b B-A c) (b e-c d) \log (b+c x)+A c^2 d \log (x)+b B c e x}{b c^2}","\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*B*c*e*x + A*c^2*d*Log[x] - (b*B - A*c)*(-(c*d) + b*e)*Log[b + c*x])/(b*c^2)","A",1
1141,1,29,29,0.0098098,"\int \frac{A+B x}{b x+c x^2} \, dx","Integrate[(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",1
1142,1,63,68,0.0428328,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)*(b*x + c*x^2)),x]","\frac{\log (b+c x) (A c d-b B d)+b (B d-A e) \log (d+e x)+A \log (x) (b e-c d)}{b d (b e-c 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*(-(c*d) + b*e)*Log[x] + (-(b*B*d) + A*c*d)*Log[b + c*x] + b*(B*d - A*e)*Log[d + e*x])/(b*d*(-(c*d) + b*e))","A",1
1143,1,106,110,0.1362342,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)),x]","\frac{\frac{c d^2 (d+e x) (b B-A c) \log (b+c x)-b (d+e x) \log (d+e x) \left(A e (b e-2 c d)+B c d^2\right)+b d (B d-A e) (c d-b e)}{(d+e x) (c d-b e)^2}+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,"(A*Log[x] + (b*d*(B*d - A*e)*(c*d - b*e) + c*(b*B - A*c)*d^2*(d + e*x)*Log[b + c*x] - b*(B*c*d^2 + A*e*(-2*c*d + b*e))*(d + e*x)*Log[d + e*x])/((c*d - b*e)^2*(d + e*x)))/(b*d^2)","A",1
1144,1,169,171,0.2029724,"\int \frac{A+B x}{(d+e x)^3 \left(b x+c x^2\right)} \, dx","Integrate[(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 (A c-b B) \log (b+c x)}{b (b e-c d)^3}+\frac{A e (b e-2 c d)+B c d^2}{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",1
1145,1,241,245,0.3376199,"\int \frac{A+B x}{(d+e x)^4 \left(b x+c x^2\right)} \, dx","Integrate[(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(A e \left(b^3 e^3-4 b^2 c d e^2+6 b c^2 d^2 e-4 c^3 d^3\right)+B c^3 d^4\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{A e (b e-2 c d)+B c d^2}{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(-b^3 e^3+4 b^2 c d e^2-6 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",1
1146,1,155,156,0.0881792,"\int \frac{(A+B x) (d+e x)^4}{\left(b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(b*x + c*x^2)^2,x]","\frac{d^3 \log (x) (4 A b e-2 A c d+b B d)}{b^3}+\frac{(b B-A c) (c d-b e)^4}{b^2 c^4 (b+c x)}-\frac{A d^4}{b^2 x}+\frac{(b e-c d)^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{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{d^3 \log (x) (4 A b e-2 A c d+b B d)}{b^3}+\frac{(b B-A c) (c d-b e)^4}{b^2 c^4 (b+c x)}-\frac{A d^4}{b^2 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{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",1
1147,1,128,128,0.0697585,"\int \frac{(A+B x) (d+e x)^3}{\left(b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2)^2,x]","\frac{d^2 \log (x) (3 A b e-2 A c d+b B d)}{b^3}-\frac{(b B-A c) (b e-c d)^3}{b^2 c^3 (b+c x)}-\frac{A d^3}{b^2 x}+\frac{(c d-b e)^2 \log (b+c x) \left(A b c e+2 A c^2 d-2 b^2 B e-b B c d\right)}{b^3 c^3}+\frac{B e^3 x}{c^2}","\frac{d^2 \log (x) (3 A b e-2 A c d+b B d)}{b^3}+\frac{(b B-A c) (c d-b e)^3}{b^2 c^3 (b+c x)}-\frac{A d^3}{b^2 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{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*(-(b*B*c*d) + 2*A*c^2*d - 2*b^2*B*e + A*b*c*e)*Log[b + c*x])/(b^3*c^3)","A",1
1148,1,101,108,0.1120981,"\int \frac{(A+B x) (d+e x)^2}{\left(b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2)^2,x]","\frac{\frac{(b e-c d) \log (b+c x) \left(-2 A c^2 d+b^2 B e+b B c d\right)}{c^2}+\frac{b (b B-A c) (c d-b e)^2}{c^2 (b+c x)}+d \log (x) (2 A b e-2 A c d+b B d)-\frac{A b d^2}{x}}{b^3}","\frac{d \log (x) (2 A b e-2 A c d+b B d)}{b^3}+\frac{(b B-A c) (c d-b e)^2}{b^2 c^2 (b+c x)}-\frac{A d^2}{b^2 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}",1,"(-((A*b*d^2)/x) + (b*(b*B - A*c)*(c*d - b*e)^2)/(c^2*(b + c*x)) + d*(b*B*d - 2*A*c*d + 2*A*b*e)*Log[x] + ((-(c*d) + b*e)*(b*B*c*d - 2*A*c^2*d + b^2*B*e)*Log[b + c*x])/c^2)/b^3","A",1
1149,1,80,86,0.1010099,"\int \frac{(A+B x) (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x))/(b*x + c*x^2)^2,x]","-\frac{\frac{b (b B-A c) (b e-c d)}{c (b+c x)}-\log (x) (A b e-2 A c d+b B d)+\log (b+c x) (A b e-2 A c d+b B d)+\frac{A b d}{x}}{b^3}","\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{(b B-A c) (c d-b e)}{b^2 c (b+c x)}-\frac{A d}{b^2 x}",1,"-(((A*b*d)/x + (b*(b*B - A*c)*(-(c*d) + b*e))/(c*(b + c*x)) - (b*B*d - 2*A*c*d + A*b*e)*Log[x] + (b*B*d - 2*A*c*d + A*b*e)*Log[b + c*x])/b^3)","A",1
1150,1,56,62,0.0450382,"\int \frac{A+B x}{\left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(b*x + c*x^2)^2,x]","\frac{\frac{b (b B-A c)}{b+c x}+\log (x) (b B-2 A c)+(2 A c-b B) \log (b+c x)-\frac{A b}{x}}{b^3}","\frac{\log (x) (b B-2 A c)}{b^3}-\frac{(b B-2 A c) \log (b+c x)}{b^3}+\frac{b B-A c}{b^2 (b+c x)}-\frac{A}{b^2 x}",1,"(-((A*b)/x) + (b*(b*B - A*c))/(b + c*x) + (b*B - 2*A*c)*Log[x] + (-(b*B) + 2*A*c)*Log[b + c*x])/b^3","A",1
1151,1,146,147,0.1637353,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)*(b*x + c*x^2)^2),x]","\frac{\log (x) (-A b e-2 A c d+b B d)}{b^3 d^2}+\frac{c (A c-b B)}{b^2 (b+c x) (b e-c d)}-\frac{A}{b^2 d 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{e^2 (A e-B d) \log (d+e x)}{d^2 (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{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{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",1
1152,1,201,201,0.3150443,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)^2),x]","\frac{\log (x) (-2 A b e-2 A c d+b B d)}{b^3 d^3}+\frac{c^2 (b B-A c)}{b^2 (b+c x) (c d-b e)^2}-\frac{A}{b^2 d^2 x}-\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 (b e-c d)^3}-\frac{e^2 \log (d+e x) (2 A e (b e-2 c d)+B d (3 c d-b e))}{d^3 (c d-b e)^3}+\frac{e^2 (B d-A e)}{d^2 (d+e x) (c d-b e)^2}","\frac{\log (x) (-2 A b e-2 A c d+b B d)}{b^3 d^3}+\frac{c^2 (b B-A c)}{b^2 (b+c x) (c d-b e)^2}-\frac{A}{b^2 d^2 x}+\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{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{e^2 (B d-A e)}{d^2 (d+e x) (c d-b e)^2}",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*(B*d*(3*c*d - b*e) + 2*A*e*(-2*c*d + b*e))*Log[d + e*x])/(d^3*(c*d - b*e)^3)","A",1
1153,1,279,283,0.4877188,"\int \frac{A+B x}{(d+e x)^3 \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^3*(b*x + c*x^2)^2),x]","\frac{\log (x) (-3 A b e-2 A c d+b B d)}{b^3 d^4}+\frac{c^3 (A c-b B)}{b^2 (b+c x) (b e-c d)^3}+\frac{e^2 \log (d+e x) \left(A e \left(3 b^2 e^2-10 b c d e+10 c^2 d^2\right)-B d \left(b^2 e^2-4 b c d e+6 c^2 d^2\right)\right)}{d^4 (c d-b e)^4}-\frac{A}{b^2 d^3 x}+\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{e^2 (2 A e (b e-2 c d)+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{\log (x) (-3 A b e-2 A c d+b B d)}{b^3 d^4}+\frac{c^3 (b B-A c)}{b^2 (b+c x) (c d-b e)^3}-\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{A}{b^2 d^3 x}+\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{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*(B*d*(3*c*d - b*e) + 2*A*e*(-2*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",1
1154,1,254,257,0.1285273,"\int \frac{(A+B x) (d+e x)^5}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^5)/(b*x + c*x^2)^3,x]","-\frac{d^4 (5 A b e-3 A c d+b B d)}{b^4 x}+\frac{(b B-A c) (b e-c d)^5}{2 b^3 c^4 (b+c x)^2}-\frac{A d^5}{2 b^3 x^2}+\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{(c d-b e)^3 \log (b+c x) \left(b^2 c e (A e-4 B d)+3 b c^2 d (A e-B d)+6 A c^3 d^2-3 b^3 B e^2\right)}{b^5 c^4}+\frac{B e^5 x}{c^3}","-\frac{d^4 (5 A b e-3 A c d+b B d)}{b^4 x}-\frac{(b B-A c) (c d-b e)^5}{2 b^3 c^4 (b+c x)^2}-\frac{A d^5}{2 b^3 x^2}+\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{(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{B e^5 x}{c^3}",1,"-1/2*(A*d^5)/(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 + b^2*c*e*(-4*B*d + A*e) + 3*b*c^2*d*(-(B*d) + A*e))*Log[b + c*x])/(b^5*c^4)","A",1
1155,1,228,235,0.1584575,"\int \frac{(A+B x) (d+e x)^4}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(b*x + c*x^2)^3,x]","-\frac{\frac{b^2 (b B-A c) (c d-b e)^4}{c^3 (b+c x)^2}-2 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)-\frac{2 b (b e-c d)^3 \left(b c (2 B d-A e)-3 A c^2 d+2 b^2 B e\right)}{c^3 (b+c x)}+\frac{A b^2 d^4}{x^2}-\frac{2 (c d-b e)^2 \log (b+c x) \left(-6 A c^3 d^2+b^3 B e^2+2 b^2 B c d e+3 b B c^2 d^2\right)}{c^3}+\frac{2 b d^3 (4 A b e-3 A c d+b B d)}{x}}{2 b^5}","-\frac{d^3 (4 A b e-3 A c d+b B d)}{b^4 x}-\frac{(b B-A c) (c d-b e)^4}{2 b^3 c^3 (b+c x)^2}-\frac{A d^4}{2 b^3 x^2}+\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{(c d-b e)^2 \log (b+c x) \left(-6 A c^3 d^2+b^3 B e^2+2 b^2 B c d e+3 b B c^2 d^2\right)}{b^5 c^3}",1,"-1/2*((A*b^2*d^4)/x^2 + (2*b*d^3*(b*B*d - 3*A*c*d + 4*A*b*e))/x + (b^2*(b*B - A*c)*(c*d - b*e)^4)/(c^3*(b + c*x)^2) - (2*b*(-(c*d) + b*e)^3*(-3*A*c^2*d + 2*b^2*B*e + b*c*(2*B*d - A*e)))/(c^3*(b + c*x)) - 2*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] - (2*(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])/c^3)/b^5","A",1
1156,1,177,185,0.1225744,"\int \frac{(A+B x) (d+e x)^3}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2)^3,x]","-\frac{\frac{2 b (c d-b e)^2 \left(-3 A c^2 d+b^2 B e+2 b B c d\right)}{c^2 (b+c x)}-\frac{b^2 (b B-A c) (b e-c d)^3}{c^2 (b+c x)^2}+\frac{A b^2 d^3}{x^2}+\frac{2 b d^2 (3 A b e-3 A c d+b B d)}{x}-6 d \log (x) (b e-c d) (A b e-2 A c d+b B d)+6 d (b e-c d) \log (b+c x) (A b e-2 A c d+b B d)}{2 b^5}","-\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{d^2 (3 A b e-3 A c d+b B d)}{b^4 x}-\frac{(b B-A c) (c d-b e)^3}{2 b^3 c^2 (b+c x)^2}-\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)}",1,"-1/2*((A*b^2*d^3)/x^2 + (2*b*d^2*(b*B*d - 3*A*c*d + 3*A*b*e))/x - (b^2*(b*B - A*c)*(-(c*d) + b*e)^3)/(c^2*(b + c*x)^2) + (2*b*(c*d - b*e)^2*(2*b*B*c*d - 3*A*c^2*d + b^2*B*e))/(c^2*(b + c*x)) - 6*d*(-(c*d) + b*e)*(b*B*d - 2*A*c*d + A*b*e)*Log[x] + 6*d*(-(c*d) + b*e)*(b*B*d - 2*A*c*d + A*b*e)*Log[b + c*x])/b^5","A",1
1157,1,190,198,0.2670619,"\int \frac{(A+B x) (d+e x)^2}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2)^3,x]","-\frac{-2 \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)+2 \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)+\frac{b^2 (b B-A c) (c d-b e)^2}{c (b+c x)^2}+\frac{A b^2 d^2}{x^2}+\frac{2 b d (2 A b e-3 A c d+b B d)}{x}-\frac{2 b (b e-c d) (A b e-3 A c d+2 b B d)}{b+c x}}{2 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}",1,"-1/2*((A*b^2*d^2)/x^2 + (2*b*d*(b*B*d - 3*A*c*d + 2*A*b*e))/x + (b^2*(b*B - A*c)*(c*d - b*e)^2)/(c*(b + c*x)^2) - (2*b*(-(c*d) + b*e)*(2*b*B*d - 3*A*c*d + A*b*e))/(b + c*x) - 2*(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] + 2*(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",1
1158,1,162,168,0.1445912,"\int \frac{(A+B x) (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x))/(b*x + c*x^2)^3,x]","\frac{\frac{2 b \left(-2 b c (A e+B d)+3 A c^2 d+b^2 B e\right)}{b+c x}+2 \log (x) \left(-3 b c (A e+B d)+6 A c^2 d+b^2 B e\right)-2 \log (b+c x) \left(-3 b c (A e+B d)+6 A c^2 d+b^2 B e\right)+\frac{b^2 (b B-A c) (b e-c d)}{(b+c x)^2}-\frac{A b^2 d}{x^2}-\frac{2 b (A b e-3 A c d+b B d)}{x}}{2 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{\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{-2 b c (A e+B d)+3 A c^2 d+b^2 B e}{b^4 (b+c x)}",1,"(-((A*b^2*d)/x^2) - (2*b*(b*B*d - 3*A*c*d + A*b*e))/x + (b^2*(b*B - A*c)*(-(c*d) + b*e))/(b + c*x)^2 + (2*b*(3*A*c^2*d + b^2*B*e - 2*b*c*(B*d + A*e)))/(b + c*x) + 2*(6*A*c^2*d + b^2*B*e - 3*b*c*(B*d + A*e))*Log[x] - 2*(6*A*c^2*d + b^2*B*e - 3*b*c*(B*d + A*e))*Log[b + c*x])/(2*b^5)","A",1
1159,1,106,109,0.0781918,"\int \frac{A+B x}{\left(b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/(b*x + c*x^2)^3,x]","\frac{-\frac{b \left(A \left(b^3-4 b^2 c x-18 b c^2 x^2-12 c^3 x^3\right)+b B x \left(2 b^2+9 b c x+6 c^2 x^2\right)\right)}{x^2 (b+c x)^2}+6 c \log (x) (2 A c-b B)+6 c (b B-2 A c) \log (b+c x)}{2 b^5}","-\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{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{A}{2 b^3 x^2}",1,"(-((b*(b*B*x*(2*b^2 + 9*b*c*x + 6*c^2*x^2) + A*(b^3 - 4*b^2*c*x - 18*b*c^2*x^2 - 12*c^3*x^3)))/(x^2*(b + c*x)^2)) + 6*c*(-(b*B) + 2*A*c)*Log[x] + 6*c*(b*B - 2*A*c)*Log[b + c*x])/(2*b^5)","A",1
1160,1,276,279,1.0523232,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/((d + e*x)*(b*x + c*x^2)^3),x]","\frac{A b e+3 A c d-b B d}{b^4 d^2 x}+\frac{c^2 (b B-A c)}{2 b^3 (b+c x)^2 (b e-c d)}-\frac{A}{2 b^3 d x^2}-\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 \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 (b e-c d)^3}+\frac{e^4 (A e-B d) \log (d+e x)}{d^3 (c d-b e)^3}","-\frac{-A b e-3 A c d+b B d}{b^4 d^2 x}-\frac{c^2 (b B-A c)}{2 b^3 (b+c x)^2 (c d-b e)}-\frac{A}{2 b^3 d x^2}+\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 \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{e^4 (B d-A e) \log (d+e x)}{d^3 (c d-b e)^3}",1,"-1/2*A/(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",1
1161,1,328,331,0.5511862,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)^3),x]","\frac{2 A b e+3 A c d-b B d}{b^4 d^3 x}+\frac{c^3 (A c-b B)}{2 b^3 (b+c x)^2 (c d-b e)^2}-\frac{A}{2 b^3 d^2 x^2}-\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(b c (5 A e+2 B d)-3 A c^2 d-4 b^2 B e\right)}{b^4 (b+c x) (b e-c d)^3}+\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{e^4 \log (d+e x) (3 A e (b e-2 c d)+B d (5 c d-2 b e))}{d^4 (c d-b e)^4}+\frac{e^4 (B d-A e)}{d^3 (d+e x) (c d-b e)^3}","-\frac{-2 A b e-3 A c d+b B d}{b^4 d^3 x}-\frac{c^3 (b B-A c)}{2 b^3 (b+c x)^2 (c d-b e)^2}-\frac{A}{2 b^3 d^2 x^2}+\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 \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{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{e^4 (B d-A e)}{d^3 (d+e x) (c d-b e)^3}",1,"-1/2*A/(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*(-3*A*c^2*d - 4*b^2*B*e + b*c*(2*B*d + 5*A*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",1
1162,1,422,404,1.0762162,"\int (A+B x) (d+e x)^3 \sqrt{b x+c x^2} \, dx","Integrate[(A + B*x)*(d + e*x)^3*Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(-210 b^4 c e^2 (2 A e+6 B d+B e x)+8 b^3 c^2 e \left(5 A e (45 d+7 e x)+3 B \left(75 d^2+35 d e x+7 e^2 x^2\right)\right)-16 b^2 c^3 \left(A e \left(180 d^2+75 d e x+14 e^2 x^2\right)+B \left(60 d^3+75 d^2 e x+42 d e^2 x^2+9 e^3 x^3\right)\right)+64 b c^4 \left(3 A \left(10 d^3+10 d^2 e x+5 d e^2 x^2+e^3 x^3\right)+B x \left(10 d^3+15 d^2 e x+9 d e^2 x^2+2 e^3 x^3\right)\right)+128 c^5 x \left(3 A \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)+B x \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)\right)+315 b^5 B e^3\right)-\frac{15 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(-28 b^3 c e^2 (A e+3 B d)+120 b^2 c^2 d e (A e+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)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{7680 c^{11/2}}","\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(-105 b^3 e^3+420 b^2 c d e^2-456 b c^2 d^2 e+64 c^3 d^3\right)\right)}{960 c^4}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(-28 b^3 c e^2 (A e+3 B d)+120 b^2 c^2 d e (A e+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{(b+2 c x) \sqrt{b x+c x^2} \left(-28 b^3 c e^2 (A e+3 B d)+120 b^2 c^2 d e (A e+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{\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(315*b^5*B*e^3 - 210*b^4*c*e^2*(6*B*d + 2*A*e + B*e*x) + 8*b^3*c^2*e*(5*A*e*(45*d + 7*e*x) + 3*B*(75*d^2 + 35*d*e*x + 7*e^2*x^2)) + 64*b*c^4*(3*A*(10*d^3 + 10*d^2*e*x + 5*d*e^2*x^2 + e^3*x^3) + B*x*(10*d^3 + 15*d^2*e*x + 9*d*e^2*x^2 + 2*e^3*x^3)) - 16*b^2*c^3*(A*e*(180*d^2 + 75*d*e*x + 14*e^2*x^2) + B*(60*d^3 + 75*d^2*e*x + 42*d*e^2*x^2 + 9*e^3*x^3)) + 128*c^5*x*(3*A*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3) + B*x*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3))) - (15*b^(3/2)*(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))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(7680*c^(11/2))","A",1
1163,1,293,267,0.5848761,"\int (A+B x) (d+e x)^2 \sqrt{b x+c x^2} \, dx","Integrate[(A + B*x)*(d + e*x)^2*Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\frac{15 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\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)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(10 b^3 c e (15 A e+30 B d+7 B e x)-4 b^2 c^2 \left(5 A e (24 d+5 e x)+2 B \left(30 d^2+25 d e x+7 e^2 x^2\right)\right)+16 b c^3 \left(5 A \left(6 d^2+4 d e x+e^2 x^2\right)+B x \left(10 d^2+10 d e x+3 e^2 x^2\right)\right)+32 c^4 x \left(5 A \left(6 d^2+8 d e x+3 e^2 x^2\right)+2 B x \left(10 d^2+15 d e x+6 e^2 x^2\right)\right)-105 b^4 B e^2\right)\right)}{1920 c^{9/2}}","\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 \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+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 \left(b x+c x^2\right)^{3/2} (d+e x)^2}{5 c}",1,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-105*b^4*B*e^2 + 10*b^3*c*e*(30*B*d + 15*A*e + 7*B*e*x) + 16*b*c^3*(5*A*(6*d^2 + 4*d*e*x + e^2*x^2) + B*x*(10*d^2 + 10*d*e*x + 3*e^2*x^2)) + 32*c^4*x*(5*A*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + 2*B*x*(10*d^2 + 15*d*e*x + 6*e^2*x^2)) - 4*b^2*c^2*(5*A*e*(24*d + 5*e*x) + 2*B*(30*d^2 + 25*d*e*x + 7*e^2*x^2))) + (15*b^(3/2)*(-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))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(1920*c^(9/2))","A",1
1164,1,177,154,0.4311478,"\int (A+B x) (d+e x) \sqrt{b x+c x^2} \, dx","Integrate[(A + B*x)*(d + e*x)*Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(-2 b^2 c (12 A e+12 B d+5 B e x)+8 b c^2 (2 A (3 d+e x)+B x (2 d+e x))+16 c^3 x (A (6 d+4 e x)+B x (4 d+3 e x))+15 b^3 B e\right)-\frac{3 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(-8 b c (A e+B d)+16 A c^2 d+5 b^2 B e\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{192 c^{7/2}}","-\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{(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{\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(15*b^3*B*e - 2*b^2*c*(12*B*d + 12*A*e + 5*B*e*x) + 8*b*c^2*(B*x*(2*d + e*x) + 2*A*(3*d + e*x)) + 16*c^3*x*(B*x*(4*d + 3*e*x) + A*(6*d + 4*e*x))) - (3*b^(3/2)*(16*A*c^2*d + 5*b^2*B*e - 8*b*c*(B*d + A*e))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(192*c^(7/2))","A",1
1165,1,108,97,0.1830289,"\int (A+B x) \sqrt{b x+c x^2} \, dx","Integrate[(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\frac{3 b^{3/2} (b B-2 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(2 b c (3 A+B x)+4 c^2 x (3 A+2 B x)-3 b^2 B\right)\right)}{24 c^{5/2}}","\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-3*b^2*B + 2*b*c*(3*A + B*x) + 4*c^2*x*(3*A + 2*B*x)) + (3*b^(3/2)*(b*B - 2*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(24*c^(5/2))","A",1
1166,1,208,200,0.6945461,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{d+e x} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x),x]","\frac{\sqrt{x (b+c x)} \left(\frac{\sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(4 A c e (b e-2 c d)+B \left(-b^2 e^2-4 b c d e+8 c^2 d^2\right)\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(e \sqrt{x} (4 A c e+B (b e-4 c d+2 c e x))-\frac{8 c \sqrt{d} (B d-A e) \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{b+c x}}\right)\right)}{4 c^{3/2} e^3 \sqrt{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{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{\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}",1,"(Sqrt[x*(b + c*x)]*(((4*A*c*e*(-2*c*d + b*e) + B*(8*c^2*d^2 - 4*b*c*d*e - b^2*e^2))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b]) + Sqrt[c]*(e*Sqrt[x]*(4*A*c*e + B*(-4*c*d + b*e + 2*c*e*x)) - (8*c*Sqrt[d]*(B*d - A*e)*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/Sqrt[b + c*x])))/(4*c^(3/2)*e^3*Sqrt[x])","A",1
1167,1,252,185,1.2613857,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^2} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^2,x]","\frac{\sqrt{x (b+c x)} \left(\frac{e \sqrt{x} (B d (2 b e-2 c d+c e x)-A e (b e-c d+c e x))+\frac{d (b e-c d) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) (2 A c e+b B e-4 B c d)}{\sqrt{b} \sqrt{c} \sqrt{\frac{c x}{b}+1}}-\frac{\sqrt{d} \sqrt{c d-b e} (A e (b e-2 c d)+B d (4 c d-3 b e)) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{b+c x}}}{e^3}-\frac{x^{3/2} (b+c x) (B d-A e)}{d+e x}\right)}{d \sqrt{x} (b e-c d)}","-\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)}",1,"(Sqrt[x*(b + c*x)]*(-(((B*d - A*e)*x^(3/2)*(b + c*x))/(d + e*x)) + (e*Sqrt[x]*(-(A*e*(-(c*d) + b*e + c*e*x)) + B*d*(-2*c*d + 2*b*e + c*e*x)) + (d*(-(c*d) + b*e)*(-4*B*c*d + b*B*e + 2*A*c*e)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]) - (Sqrt[d]*Sqrt[c*d - b*e]*(B*d*(4*c*d - 3*b*e) + A*e*(-2*c*d + b*e))*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/Sqrt[b + c*x])/e^3))/(d*(-(c*d) + b*e)*Sqrt[x])","A",1
1168,1,690,235,3.6471658,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^3} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^3,x]","\frac{x \left(\frac{(d+e x) \left((d+e x) \left(b \sqrt{c} e \sqrt{x} \left(A \left(b^2 e^2+4 b c d e-8 c^2 d^2\right)+3 b^2 B d e\right) \left(e (b+c x) \left(b \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{3/2}+\sqrt{b} (b+c x) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)\right)-2 b \sqrt{c} \sqrt{d} \left(\frac{c x}{b}+1\right)^{3/2} \left(\sqrt{b} \sqrt{c} \sqrt{d} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)-\sqrt{b+c x} \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)\right)\right)-(A e (2 c d-b e)+B d (2 c d-3 b e)) \left(e^2 (b+c x)^2 \left(b c x (b+2 c x) \sqrt{\frac{c x}{b}+1}-b^{5/2} \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)\right)-4 b c^{3/2} d \sqrt{x} \left(e (b+c x) \left(b \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{3/2}+\sqrt{b} (b+c x) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)\right)-2 b \sqrt{c} \sqrt{d} \left(\frac{c x}{b}+1\right)^{3/2} \left(\sqrt{b} \sqrt{c} \sqrt{d} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)-\sqrt{b+c x} \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)\right)\right)\right)\right)-2 b c e^3 x^2 (b+c x)^3 \sqrt{\frac{c x}{b}+1} (A e (b e-2 c d)+B d (3 b e-2 c d))\right)}{b c d e^3 \sqrt{\frac{c x}{b}+1} (c d-b e)}-4 x^2 (b+c x)^3 (B d-A e)\right)}{8 d (x (b+c x))^{3/2} (d+e x)^2 (b e-c d)}","-\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,"(x*(-4*(B*d - A*e)*x^2*(b + c*x)^3 + ((d + e*x)*(-2*b*c*e^3*(A*e*(-2*c*d + b*e) + B*d*(-2*c*d + 3*b*e))*x^2*(b + c*x)^3*Sqrt[1 + (c*x)/b] + (d + e*x)*(b*Sqrt[c]*e*(3*b^2*B*d*e + A*(-8*c^2*d^2 + 4*b*c*d*e + b^2*e^2))*Sqrt[x]*(e*(b + c*x)*(b*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2) + Sqrt[b]*(b + c*x)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]) - 2*b*Sqrt[c]*Sqrt[d]*(1 + (c*x)/b)^(3/2)*(Sqrt[b]*Sqrt[c]*Sqrt[d]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]] - Sqrt[c*d - b*e]*Sqrt[b + c*x]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])) - (B*d*(2*c*d - 3*b*e) + A*e*(2*c*d - b*e))*(e^2*(b + c*x)^2*(b*c*x*(b + 2*c*x)*Sqrt[1 + (c*x)/b] - b^(5/2)*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]) - 4*b*c^(3/2)*d*Sqrt[x]*(e*(b + c*x)*(b*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2) + Sqrt[b]*(b + c*x)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]) - 2*b*Sqrt[c]*Sqrt[d]*(1 + (c*x)/b)^(3/2)*(Sqrt[b]*Sqrt[c]*Sqrt[d]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]] - Sqrt[c*d - b*e]*Sqrt[b + c*x]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])]))))))/(b*c*d*e^3*(c*d - b*e)*Sqrt[1 + (c*x)/b])))/(8*d*(-(c*d) + b*e)*(x*(b + c*x))^(3/2)*(d + e*x)^2)","B",1
1169,1,199,200,0.3862345,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^4} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^4,x]","\frac{\sqrt{x (b+c x)} \left(8 x^{3/2} (b+c x) (A e-B d)-\frac{3 (d+e x) (A b e-2 A c d+b B d) \left(b^2 (d+e x)^2 \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)+\sqrt{d} \sqrt{x} \sqrt{b+c x} \sqrt{c d-b e} (-b d+b e x-2 c d x)\right)}{d^{3/2} \sqrt{b+c x} (c d-b e)^{3/2}}\right)}{24 d \sqrt{x} (d+e x)^3 (b e-c d)}","\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,"(Sqrt[x*(b + c*x)]*(8*(-(B*d) + A*e)*x^(3/2)*(b + c*x) - (3*(b*B*d - 2*A*c*d + A*b*e)*(d + e*x)*(Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[x]*Sqrt[b + c*x]*(-(b*d) - 2*c*d*x + b*e*x) + b^2*(d + e*x)^2*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])]))/(d^(3/2)*(c*d - b*e)^(3/2)*Sqrt[b + c*x])))/(24*d*(-(c*d) + b*e)*Sqrt[x]*(d + e*x)^3)","A",1
1170,1,279,310,0.747409,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^5} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^5,x]","\frac{\sqrt{x (b+c x)} \left(\frac{3 (d+e x)^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) \left(b^2 (d+e x)^2 \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)+\sqrt{d} \sqrt{x} \sqrt{b+c x} \sqrt{c d-b e} (-b d+b e x-2 c d x)\right)}{d^{5/2} \sqrt{b+c x} (c d-b e)^{5/2}}-\frac{8 x^{3/2} (b+c x) (d+e x) (5 A e (b e-2 c d)+B d (3 b e+2 c d))}{d (c d-b e)}+48 x^{3/2} (b+c x) (A e-B d)\right)}{192 d \sqrt{x} (d+e x)^4 (b e-c d)}","-\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{\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{\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,"(Sqrt[x*(b + c*x)]*(48*(-(B*d) + A*e)*x^(3/2)*(b + c*x) - (8*(5*A*e*(-2*c*d + b*e) + B*d*(2*c*d + 3*b*e))*x^(3/2)*(b + c*x)*(d + e*x))/(d*(c*d - b*e)) + (3*(16*A*c^2*d^2 - 8*b*c*d*(B*d + 2*A*e) + b^2*e*(3*B*d + 5*A*e))*(d + e*x)^2*(Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[x]*Sqrt[b + c*x]*(-(b*d) - 2*c*d*x + b*e*x) + b^2*(d + e*x)^2*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])]))/(d^(5/2)*(c*d - b*e)^(5/2)*Sqrt[b + c*x])))/(192*d*(-(c*d) + b*e)*Sqrt[x]*(d + e*x)^4)","A",1
1171,1,387,449,2.7079352,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^6} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^6,x]","-\frac{\sqrt{x (b+c x)} \left(\frac{8 x^{3/2} (b+c x) (d+e x)^2 \left(A e \left(-35 b^2 e^2+108 b c d e-108 c^2 d^2\right)+B d \left(-15 b^2 e^2+42 b c d e+8 c^2 d^2\right)\right)}{d^2 (c d-b e)^2}+\frac{15 (d+e x)^3 \left(b^3 e^2 (7 A e+3 B d)-6 b^2 c d e (5 A e+2 B d)+16 b c^2 d^2 (3 A e+B d)-32 A c^3 d^3\right) \left(b^2 (d+e x)^2 \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)+\sqrt{d} \sqrt{x} \sqrt{b+c x} \sqrt{c d-b e} (-b d+b e x-2 c d x)\right)}{d^{7/2} \sqrt{b+c x} (c d-b e)^{7/2}}+\frac{48 x^{3/2} (b+c x) (d+e x) (7 A e (b e-2 c d)+B d (3 b e+4 c d))}{d (c d-b e)}+384 x^{3/2} (b+c x) (B d-A e)\right)}{1920 d \sqrt{x} (d+e x)^5 (b e-c d)}","\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{b^2 \left(b^3 \left(-e^2\right) (7 A e+3 B d)+6 b^2 c d e (5 A e+2 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{\sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(b^3 \left(-e^2\right) (7 A e+3 B d)+6 b^2 c d e (5 A e+2 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{\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,"-1/1920*(Sqrt[x*(b + c*x)]*(384*(B*d - A*e)*x^(3/2)*(b + c*x) + (48*(7*A*e*(-2*c*d + b*e) + B*d*(4*c*d + 3*b*e))*x^(3/2)*(b + c*x)*(d + e*x))/(d*(c*d - b*e)) + (8*(A*e*(-108*c^2*d^2 + 108*b*c*d*e - 35*b^2*e^2) + B*d*(8*c^2*d^2 + 42*b*c*d*e - 15*b^2*e^2))*x^(3/2)*(b + c*x)*(d + e*x)^2)/(d^2*(c*d - b*e)^2) + (15*(-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))*(d + e*x)^3*(Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[x]*Sqrt[b + c*x]*(-(b*d) - 2*c*d*x + b*e*x) + b^2*(d + e*x)^2*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])]))/(d^(7/2)*(c*d - b*e)^(7/2)*Sqrt[b + c*x])))/(d*(-(c*d) + b*e)*Sqrt[x]*(d + e*x)^5)","A",1
1172,1,415,345,1.5972519,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)^2*(b*x + c*x^2)^(3/2),x]","\frac{\sqrt{x (b+c x)} \left(14 A c \left(\frac{5}{4} \left(7 b^2 e^2-24 b c d e+24 c^2 d^2\right) \left(3 b^{9/2} \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)+b c x \sqrt{\frac{c x}{b}+1} \left(-3 b^3+2 b^2 c x+24 b c^2 x^2+16 c^3 x^3\right)\right)+320 b c^4 e x^3 (b+c x)^2 \sqrt{\frac{c x}{b}+1} (d+e x)-224 b c^3 e x^3 (b+c x)^2 \sqrt{\frac{c x}{b}+1} (b e-2 c d)\right)+B \left(\frac{7}{4} \left(9 b^2 e^2-28 b c d e+24 c^2 d^2\right) \left(b c x \sqrt{\frac{c x}{b}+1} \left(15 b^4-10 b^3 c x+8 b^2 c^2 x^2+176 b c^3 x^3+128 c^4 x^4\right)-15 b^{11/2} \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)\right)+3840 b c^5 e x^4 (b+c x)^2 \sqrt{\frac{c x}{b}+1} (d+e x)+320 b c^4 e x^4 (b+c x)^2 \sqrt{\frac{c x}{b}+1} (16 c d-9 b e)\right)\right)}{26880 b c^6 x \sqrt{\frac{c x}{b}+1}}","\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 (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{(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,"(Sqrt[x*(b + c*x)]*(14*A*c*(-224*b*c^3*e*(-2*c*d + b*e)*x^3*(b + c*x)^2*Sqrt[1 + (c*x)/b] + 320*b*c^4*e*x^3*(b + c*x)^2*Sqrt[1 + (c*x)/b]*(d + e*x) + (5*(24*c^2*d^2 - 24*b*c*d*e + 7*b^2*e^2)*(b*c*x*Sqrt[1 + (c*x)/b]*(-3*b^3 + 2*b^2*c*x + 24*b*c^2*x^2 + 16*c^3*x^3) + 3*b^(9/2)*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/4) + B*(320*b*c^4*e*(16*c*d - 9*b*e)*x^4*(b + c*x)^2*Sqrt[1 + (c*x)/b] + 3840*b*c^5*e*x^4*(b + c*x)^2*Sqrt[1 + (c*x)/b]*(d + e*x) + (7*(24*c^2*d^2 - 28*b*c*d*e + 9*b^2*e^2)*(b*c*x*Sqrt[1 + (c*x)/b]*(15*b^4 - 10*b^3*c*x + 8*b^2*c^2*x^2 + 176*b*c^3*x^3 + 128*c^4*x^4) - 15*b^(11/2)*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/4)))/(26880*b*c^6*x*Sqrt[1 + (c*x)/b])","A",1
1173,1,245,209,0.5899264,"\int (A+B x) (d+e x) \left(b x+c x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)*(b*x + c*x^2)^(3/2),x]","\frac{\sqrt{x (b+c x)} \left(\frac{15 b^{7/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(-12 b c (A e+B d)+24 A c^2 d+7 b^2 B e\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(10 b^4 c (18 A e+18 B d+7 B e x)-8 b^3 c^2 (15 A (3 d+e x)+B x (15 d+7 e x))+48 b^2 c^3 x (A (5 d+2 e x)+B x (2 d+e x))+64 b c^4 x^2 (A (45 d+33 e x)+B x (33 d+26 e x))+128 c^5 x^3 (3 A (5 d+4 e x)+2 B x (6 d+5 e x))-105 b^5 B e\right)\right)}{7680 c^{9/2}}","-\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-105*b^5*B*e + 10*b^4*c*(18*B*d + 18*A*e + 7*B*e*x) + 48*b^2*c^3*x*(B*x*(2*d + e*x) + A*(5*d + 2*e*x)) + 128*c^5*x^3*(3*A*(5*d + 4*e*x) + 2*B*x*(6*d + 5*e*x)) - 8*b^3*c^2*(15*A*(3*d + e*x) + B*x*(15*d + 7*e*x)) + 64*b*c^4*x^2*(B*x*(33*d + 26*e*x) + A*(45*d + 33*e*x))) + (15*b^(7/2)*(24*A*c^2*d + 7*b^2*B*e - 12*b*c*(B*d + A*e))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(7680*c^(9/2))","A",1
1174,1,146,134,0.2512161,"\int (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(-10 b^3 c (3 A+B x)+4 b^2 c^2 x (5 A+2 B x)+16 b c^3 x^2 (15 A+11 B x)+32 c^4 x^3 (5 A+4 B x)+15 b^4 B\right)-\frac{15 b^{7/2} (b B-2 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{640 c^{7/2}}","-\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{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{128 c^3}-\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(15*b^4*B - 10*b^3*c*(3*A + B*x) + 4*b^2*c^2*x*(5*A + 2*B*x) + 32*c^4*x^3*(5*A + 4*B*x) + 16*b*c^3*x^2*(15*A + 11*B*x)) - (15*b^(7/2)*(b*B - 2*A*c)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(640*c^(7/2))","A",1
1175,1,386,392,1.4094644,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{d+e x} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x),x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(e \sqrt{x} \left(8 A c e \left(3 b^2 e^2+2 b c e (7 e x-15 d)+4 c^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+B \left(-9 b^3 e^3+6 b^2 c e^2 (e x-4 d)+8 b c^2 e \left(30 d^2-14 d e x+9 e^2 x^2\right)-16 c^3 \left(12 d^3-6 d^2 e x+4 d e^2 x^2-3 e^3 x^3\right)\right)\right)-\frac{384 c^2 d^{3/2} (B d-A e) (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{b+c x}}\right)+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(B \left(3 b^4 e^4+8 b^3 c d e^3+48 b^2 c^2 d^2 e^2-192 b c^3 d^3 e+128 c^4 d^4\right)-8 A c e \left(b^3 e^3+6 b^2 c d e^2-24 b c^2 d^2 e+16 c^3 d^3\right)\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right)}{192 c^{5/2} e^5 \sqrt{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(3 b^3 e^3+8 b^2 c d e^2-80 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(b^3 e^3+6 b^2 c d e^2-24 b c^2 d^2 e+16 c^3 d^3\right)-B \left(3 b^4 e^4+8 b^3 c d e^3+48 b^2 c^2 d^2 e^2-192 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,"(Sqrt[x*(b + c*x)]*((3*(-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))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b]) + Sqrt[c]*(e*Sqrt[x]*(8*A*c*e*(3*b^2*e^2 + 2*b*c*e*(-15*d + 7*e*x) + 4*c^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + B*(-9*b^3*e^3 + 6*b^2*c*e^2*(-4*d + e*x) + 8*b*c^2*e*(30*d^2 - 14*d*e*x + 9*e^2*x^2) - 16*c^3*(12*d^3 - 6*d^2*e*x + 4*d*e^2*x^2 - 3*e^3*x^3))) - (384*c^2*d^(3/2)*(B*d - A*e)*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/Sqrt[b + c*x])))/(192*c^(5/2)*e^5*Sqrt[x])","A",1
1176,1,353,323,1.6406214,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^2,x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(\frac{e \sqrt{x} \left(6 A c e \left(b e (9 d+5 e x)-2 c \left(6 d^2+3 d e x-e^2 x^2\right)\right)+B \left(3 b^2 e^2 (d+e x)+2 b c e \left(-42 d^2-23 d e x+7 e^2 x^2\right)+8 c^2 \left(12 d^3+6 d^2 e x-2 d e^2 x^2+e^3 x^3\right)\right)\right)}{d+e x}+\frac{24 c \sqrt{d} \sqrt{c d-b e} (3 A e (b e-2 c d)+B d (8 c d-5 b e)) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{b+c x}}\right)-\frac{3 \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(B \left(b^3 e^3+12 b^2 c d e^2-72 b c^2 d^2 e+64 c^3 d^3\right)-6 A c e \left(b^2 e^2-8 b c d e+8 c^2 d^2\right)\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right)}{24 c^{3/2} e^5 \sqrt{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{\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{\left(b x+c x^2\right)^{3/2} (-3 A e+4 B d+B e x)}{3 e^2 (d+e x)}",1,"(Sqrt[x*(b + c*x)]*((-3*(-6*A*c*e*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2) + B*(64*c^3*d^3 - 72*b*c^2*d^2*e + 12*b^2*c*d*e^2 + b^3*e^3))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b]) + Sqrt[c]*((e*Sqrt[x]*(6*A*c*e*(b*e*(9*d + 5*e*x) - 2*c*(6*d^2 + 3*d*e*x - e^2*x^2)) + B*(3*b^2*e^2*(d + e*x) + 2*b*c*e*(-42*d^2 - 23*d*e*x + 7*e^2*x^2) + 8*c^2*(12*d^3 + 6*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3))))/(d + e*x) + (24*c*Sqrt[d]*Sqrt[c*d - b*e]*(B*d*(8*c*d - 5*b*e) + 3*A*e*(-2*c*d + b*e))*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/Sqrt[b + c*x])))/(24*c^(3/2)*e^5*Sqrt[x])","A",1
1177,1,1358,314,6.1247811,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^3,x]","\frac{\left(\frac{\left(\frac{1}{2} e (5 b B d-4 A c d-A b e)-3 c d (B d-A e)\right) x^{5/2} (b+c x)^{5/2}}{d (b e-c d) (d+e x)}+\frac{\frac{1}{4} \left(-3 e (5 B d-A e) b^2+4 c d (5 B d-4 A e) b+8 A c^2 d^2\right) \left(\frac{2 b x^{3/2} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{3 \left(\frac{2 c x}{b}-\frac{2 \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right) b^2}{32 c^2 x^2 \left(\frac{c x}{b}+1\right)^2}+\frac{1}{2} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{4 \left(\frac{c x}{b}+1\right)^2}\right)\right)}{3 e}-\frac{d \left(\frac{2 b \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{1}{4} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{2 \left(\frac{c x}{b}+1\right)^2}\right)+\frac{3 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{8 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{5/2}}\right)}{e}-\frac{d \left(\frac{2 c \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right) \left(\frac{\sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{2 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{3/2}}+\frac{1}{2 \left(\frac{c x}{b}+1\right)}\right)}{e}-\frac{(c d-b e) \left(\frac{2 \sqrt{b} \sqrt{c} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{e \sqrt{b+c x}}-\frac{2 \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c d-b e} \sqrt{x}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{d} e}\right)}{e}\right)}{e}\right)}{e}\right)+2 c (B d (6 c d-5 b e)-A e (2 c d-b e)) \left(\frac{2 b x^{5/2} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{5}{8} \left(\frac{1}{\frac{c x}{b}+1}+\frac{1}{2 \left(\frac{c x}{b}+1\right)^2}\right)-\frac{15 b^3 \left(-\frac{4 c^2 x^2}{3 b^2}+\frac{2 c x}{b}-\frac{2 \sqrt{c} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \sqrt{x}}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right)}{256 c^3 x^3 \left(\frac{c x}{b}+1\right)^2}\right)}{5 e}-\frac{d \left(\frac{2 b x^{3/2} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{3 \left(\frac{2 c x}{b}-\frac{2 \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right) b^2}{32 c^2 x^2 \left(\frac{c x}{b}+1\right)^2}+\frac{1}{2} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{4 \left(\frac{c x}{b}+1\right)^2}\right)\right)}{3 e}-\frac{d \left(\frac{2 b \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{1}{4} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{2 \left(\frac{c x}{b}+1\right)^2}\right)+\frac{3 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{8 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{5/2}}\right)}{e}-\frac{d \left(\frac{2 c \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right) \left(\frac{\sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{2 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{3/2}}+\frac{1}{2 \left(\frac{c x}{b}+1\right)}\right)}{e}-\frac{(c d-b e) \left(\frac{2 \sqrt{b} \sqrt{c} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{e \sqrt{b+c x}}-\frac{2 \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c d-b e} \sqrt{x}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{d} e}\right)}{e}\right)}{e}\right)}{e}\right)}{e}\right)}{d (b e-c d)}\right) (x (b+c x))^{3/2}}{2 d (b e-c d) x^{3/2} (b+c x)^{3/2}}+\frac{(A e-B d) x (b+c x) (x (b+c x))^{3/2}}{2 d (b e-c d) (d+e x)^2}","-\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{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{\left(b x+c x^2\right)^{3/2} (-A e+2 B d+B e x)}{2 e^2 (d+e x)^2}",1,"((-(B*d) + A*e)*x*(b + c*x)*(x*(b + c*x))^(3/2))/(2*d*(-(c*d) + b*e)*(d + e*x)^2) + ((x*(b + c*x))^(3/2)*(((-3*c*d*(B*d - A*e) + (e*(5*b*B*d - 4*A*c*d - A*b*e))/2)*x^(5/2)*(b + c*x)^(5/2))/(d*(-(c*d) + b*e)*(d + e*x)) + (((8*A*c^2*d^2 + 4*b*c*d*(5*B*d - 4*A*e) - 3*b^2*e*(5*B*d - A*e))*((2*b*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 + (3*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(32*c^2*x^2*(1 + (c*x)/b)^2)))/(3*e) - (d*((2*b*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - (d*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/4 + 2*c*(B*d*(6*c*d - 5*b*e) - A*e*(2*c*d - b*e))*((2*b*x^(5/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((5*(1/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/8 - (15*b^3*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(256*c^3*x^3*(1 + (c*x)/b)^2)))/(5*e) - (d*((2*b*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 + (3*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(32*c^2*x^2*(1 + (c*x)/b)^2)))/(3*e) - (d*((2*b*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - (d*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/e))/(d*(-(c*d) + b*e))))/(2*d*(-(c*d) + b*e)*x^(3/2)*(b + c*x)^(3/2))","B",1
1178,1,1533,426,6.1922763,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^4,x]","\frac{\left(\frac{\left(\frac{1}{2} e (5 b B d-6 A c d+A b e)-2 c d (B d-A e)\right) x^{5/2} (b+c x)^{5/2}}{2 d (b e-c d) (d+e x)^2}+\frac{\frac{\left(\frac{1}{4} e \left(A \left(24 c^2 d^2-18 b c e d-b^2 e^2\right)-5 b^2 B d e\right)-\frac{3}{2} c d (B d (4 c d-5 b e)+A e (2 c d-b e))\right) x^{5/2} (b+c x)^{5/2}}{d (b e-c d) (d+e x)}+\frac{\frac{1}{8} \left(3 e^2 (5 B d+A e) b^3-2 c d e (70 B d-13 A e) b^2+24 c^2 d^2 (5 B d+A e) b-48 A c^3 d^3\right) \left(\frac{2 b x^{3/2} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{3 \left(\frac{2 c x}{b}-\frac{2 \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right) b^2}{32 c^2 x^2 \left(\frac{c x}{b}+1\right)^2}+\frac{1}{2} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{4 \left(\frac{c x}{b}+1\right)^2}\right)\right)}{3 e}-\frac{d \left(\frac{2 b \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{1}{4} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{2 \left(\frac{c x}{b}+1\right)^2}\right)+\frac{3 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{8 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{5/2}}\right)}{e}-\frac{d \left(\frac{2 c \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right) \left(\frac{\sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{2 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{3/2}}+\frac{1}{2 \left(\frac{c x}{b}+1\right)}\right)}{e}-\frac{(c d-b e) \left(\frac{2 \sqrt{b} \sqrt{c} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{e \sqrt{b+c x}}-\frac{2 \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c d-b e} \sqrt{x}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{d} e}\right)}{e}\right)}{e}\right)}{e}\right)-c \left(A e \left(12 c^2 d^2-12 b c e d-b^2 e^2\right)-B d \left(24 c^2 d^2-30 b c e d+5 b^2 e^2\right)\right) \left(\frac{2 b x^{5/2} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{5}{8} \left(\frac{1}{\frac{c x}{b}+1}+\frac{1}{2 \left(\frac{c x}{b}+1\right)^2}\right)-\frac{15 b^3 \left(-\frac{4 c^2 x^2}{3 b^2}+\frac{2 c x}{b}-\frac{2 \sqrt{c} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \sqrt{x}}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right)}{256 c^3 x^3 \left(\frac{c x}{b}+1\right)^2}\right)}{5 e}-\frac{d \left(\frac{2 b x^{3/2} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{3 \left(\frac{2 c x}{b}-\frac{2 \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right) b^2}{32 c^2 x^2 \left(\frac{c x}{b}+1\right)^2}+\frac{1}{2} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{4 \left(\frac{c x}{b}+1\right)^2}\right)\right)}{3 e}-\frac{d \left(\frac{2 b \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{1}{4} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{2 \left(\frac{c x}{b}+1\right)^2}\right)+\frac{3 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{8 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{5/2}}\right)}{e}-\frac{d \left(\frac{2 c \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right) \left(\frac{\sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{2 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{3/2}}+\frac{1}{2 \left(\frac{c x}{b}+1\right)}\right)}{e}-\frac{(c d-b e) \left(\frac{2 \sqrt{b} \sqrt{c} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{e \sqrt{b+c x}}-\frac{2 \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c d-b e} \sqrt{x}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{d} e}\right)}{e}\right)}{e}\right)}{e}\right)}{e}\right)}{d (b e-c d)}}{2 d (b e-c d)}\right) (x (b+c x))^{3/2}}{3 d (b e-c d) x^{3/2} (b+c x)^{3/2}}+\frac{(A e-B d) x (b+c x) (x (b+c x))^{3/2}}{3 d (b e-c d) (d+e x)^3}","-\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(-5 b^3 e^3+60 b^2 c d e^2-120 b c^2 d^2 e+64 c^3 d^3\right)-A e \left(b^3 e^3+6 b^2 c d e^2-24 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{\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{\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)}",1,"((-(B*d) + A*e)*x*(b + c*x)*(x*(b + c*x))^(3/2))/(3*d*(-(c*d) + b*e)*(d + e*x)^3) + ((x*(b + c*x))^(3/2)*(((-2*c*d*(B*d - A*e) + (e*(5*b*B*d - 6*A*c*d + A*b*e))/2)*x^(5/2)*(b + c*x)^(5/2))/(2*d*(-(c*d) + b*e)*(d + e*x)^2) + ((((-3*c*d*(B*d*(4*c*d - 5*b*e) + A*e*(2*c*d - b*e)))/2 + (e*(-5*b^2*B*d*e + A*(24*c^2*d^2 - 18*b*c*d*e - b^2*e^2)))/4)*x^(5/2)*(b + c*x)^(5/2))/(d*(-(c*d) + b*e)*(d + e*x)) + (((-48*A*c^3*d^3 - 2*b^2*c*d*e*(70*B*d - 13*A*e) + 24*b*c^2*d^2*(5*B*d + A*e) + 3*b^3*e^2*(5*B*d + A*e))*((2*b*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 + (3*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(32*c^2*x^2*(1 + (c*x)/b)^2)))/(3*e) - (d*((2*b*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - (d*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/8 - c*(A*e*(12*c^2*d^2 - 12*b*c*d*e - b^2*e^2) - B*d*(24*c^2*d^2 - 30*b*c*d*e + 5*b^2*e^2))*((2*b*x^(5/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((5*(1/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/8 - (15*b^3*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(256*c^3*x^3*(1 + (c*x)/b)^2)))/(5*e) - (d*((2*b*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 + (3*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(32*c^2*x^2*(1 + (c*x)/b)^2)))/(3*e) - (d*((2*b*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - (d*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/e))/(d*(-(c*d) + b*e)))/(2*d*(-(c*d) + b*e))))/(3*d*(-(c*d) + b*e)*x^(3/2)*(b + c*x)^(3/2))","B",1
1179,1,1984,421,6.2059938,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^5,x]","\frac{\left(\frac{\left(\frac{1}{2} e (5 b B d-8 A c d+3 A b e)-c d (B d-A e)\right) x^{5/2} (b+c x)^{5/2}}{3 d (b e-c d) (d+e x)^3}+\frac{\frac{\left(\frac{1}{4} e \left(e (5 B d+3 A e) b^2-4 c d (5 B d+9 A e) b+48 A c^2 d^2\right)-c d (B d (2 c d-5 b e)+3 A e (2 c d-b e))\right) x^{5/2} (b+c x)^{5/2}}{2 d (b e-c d) (d+e x)^2}+\frac{\frac{\left(\frac{1}{8} e \left(-e^2 (5 B d+3 A e) b^3-4 c d e (25 B d+9 A e) b^2+24 c^2 d^2 (5 B d+9 A e) b-192 A c^3 d^3\right)+\frac{3}{4} c d \left(3 A e \left(8 c^2 d^2-8 b c e d+b^2 e^2\right)-B \left(8 c^2 d^3-5 b^2 d e^2\right)\right)\right) x^{5/2} (b+c x)^{5/2}}{d (b e-c d) (d+e x)}+\frac{\left(-\frac{1}{8} c d \left(-e^2 (5 B d+3 A e) b^3-4 c d e (25 B d+9 A e) b^2+24 c^2 d^2 (5 B d+9 A e) b-192 A c^3 d^3\right)+\frac{1}{8} b e \left(-e^2 (5 B d+3 A e) b^3-4 c d e (25 B d+9 A e) b^2+24 c^2 d^2 (5 B d+9 A e) b-192 A c^3 d^3\right)-\frac{5}{2} b \left(\frac{1}{8} e \left(-e^2 (5 B d+3 A e) b^3-4 c d e (25 B d+9 A e) b^2+24 c^2 d^2 (5 B d+9 A e) b-192 A c^3 d^3\right)+\frac{3}{4} c d \left(3 A e \left(8 c^2 d^2-8 b c e d+b^2 e^2\right)-B \left(8 c^2 d^3-5 b^2 d e^2\right)\right)\right)\right) \left(\frac{2 b x^{3/2} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{3 \left(\frac{2 c x}{b}-\frac{2 \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right) b^2}{32 c^2 x^2 \left(\frac{c x}{b}+1\right)^2}+\frac{1}{2} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{4 \left(\frac{c x}{b}+1\right)^2}\right)\right)}{3 e}-\frac{d \left(\frac{2 b \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{1}{4} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{2 \left(\frac{c x}{b}+1\right)^2}\right)+\frac{3 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{8 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{5/2}}\right)}{e}-\frac{d \left(\frac{2 c \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right) \left(\frac{\sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{2 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{3/2}}+\frac{1}{2 \left(\frac{c x}{b}+1\right)}\right)}{e}-\frac{(c d-b e) \left(\frac{2 \sqrt{b} \sqrt{c} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{e \sqrt{b+c x}}-\frac{2 \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c d-b e} \sqrt{x}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{d} e}\right)}{e}\right)}{e}\right)}{e}\right)-4 c \left(\frac{1}{8} e \left(-e^2 (5 B d+3 A e) b^3-4 c d e (25 B d+9 A e) b^2+24 c^2 d^2 (5 B d+9 A e) b-192 A c^3 d^3\right)+\frac{3}{4} c d \left(3 A e \left(8 c^2 d^2-8 b c e d+b^2 e^2\right)-B \left(8 c^2 d^3-5 b^2 d e^2\right)\right)\right) \left(\frac{2 b x^{5/2} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{5}{8} \left(\frac{1}{\frac{c x}{b}+1}+\frac{1}{2 \left(\frac{c x}{b}+1\right)^2}\right)-\frac{15 b^3 \left(-\frac{4 c^2 x^2}{3 b^2}+\frac{2 c x}{b}-\frac{2 \sqrt{c} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \sqrt{x}}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right)}{256 c^3 x^3 \left(\frac{c x}{b}+1\right)^2}\right)}{5 e}-\frac{d \left(\frac{2 b x^{3/2} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{3 \left(\frac{2 c x}{b}-\frac{2 \sqrt{c} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right) b^2}{32 c^2 x^2 \left(\frac{c x}{b}+1\right)^2}+\frac{1}{2} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{4 \left(\frac{c x}{b}+1\right)^2}\right)\right)}{3 e}-\frac{d \left(\frac{2 b \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right)^2 \left(\frac{1}{4} \left(\frac{1}{\frac{c x}{b}+1}+\frac{3}{2 \left(\frac{c x}{b}+1\right)^2}\right)+\frac{3 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{8 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{5/2}}\right)}{e}-\frac{d \left(\frac{2 c \sqrt{x} \sqrt{b+c x} \left(\frac{c x}{b}+1\right) \left(\frac{\sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{2 \sqrt{c} \sqrt{x} \left(\frac{c x}{b}+1\right)^{3/2}}+\frac{1}{2 \left(\frac{c x}{b}+1\right)}\right)}{e}-\frac{(c d-b e) \left(\frac{2 \sqrt{b} \sqrt{c} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{e \sqrt{b+c x}}-\frac{2 \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c d-b e} \sqrt{x}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{d} e}\right)}{e}\right)}{e}\right)}{e}\right)}{e}\right)}{d (b e-c d)}}{2 d (b e-c d)}}{3 d (b e-c d)}\right) (x (b+c x))^{3/2}}{4 d (b e-c d) x^{3/2} (b+c x)^{3/2}}+\frac{(A e-B d) x (b+c x) (x (b+c x))^{3/2}}{4 d (b e-c d) (d+e x)^4}","-\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(-5 b^3 e^3+98 b^2 c d e^2-192 b c^2 d^2 e+96 c^3 d^3\right)\right)+d \left(3 A b^3 e^4+B d \left(5 b^3 e^3+40 b^2 c d e^2-112 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(-5 b^4 e^4-40 b^3 c d e^3+240 b^2 c^2 d^2 e^2-320 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,"((-(B*d) + A*e)*x*(b + c*x)*(x*(b + c*x))^(3/2))/(4*d*(-(c*d) + b*e)*(d + e*x)^4) + ((x*(b + c*x))^(3/2)*(((-(c*d*(B*d - A*e)) + (e*(5*b*B*d - 8*A*c*d + 3*A*b*e))/2)*x^(5/2)*(b + c*x)^(5/2))/(3*d*(-(c*d) + b*e)*(d + e*x)^3) + ((((e*(48*A*c^2*d^2 + b^2*e*(5*B*d + 3*A*e) - 4*b*c*d*(5*B*d + 9*A*e)))/4 - c*d*(B*d*(2*c*d - 5*b*e) + 3*A*e*(2*c*d - b*e)))*x^(5/2)*(b + c*x)^(5/2))/(2*d*(-(c*d) + b*e)*(d + e*x)^2) + ((((e*(-192*A*c^3*d^3 - b^3*e^2*(5*B*d + 3*A*e) + 24*b*c^2*d^2*(5*B*d + 9*A*e) - 4*b^2*c*d*e*(25*B*d + 9*A*e)))/8 + (3*c*d*(3*A*e*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2) - B*(8*c^2*d^3 - 5*b^2*d*e^2)))/4)*x^(5/2)*(b + c*x)^(5/2))/(d*(-(c*d) + b*e)*(d + e*x)) + ((-1/8*(c*d*(-192*A*c^3*d^3 - b^3*e^2*(5*B*d + 3*A*e) + 24*b*c^2*d^2*(5*B*d + 9*A*e) - 4*b^2*c*d*e*(25*B*d + 9*A*e))) + (b*e*(-192*A*c^3*d^3 - b^3*e^2*(5*B*d + 3*A*e) + 24*b*c^2*d^2*(5*B*d + 9*A*e) - 4*b^2*c*d*e*(25*B*d + 9*A*e)))/8 - (5*b*((e*(-192*A*c^3*d^3 - b^3*e^2*(5*B*d + 3*A*e) + 24*b*c^2*d^2*(5*B*d + 9*A*e) - 4*b^2*c*d*e*(25*B*d + 9*A*e)))/8 + (3*c*d*(3*A*e*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2) - B*(8*c^2*d^3 - 5*b^2*d*e^2)))/4))/2)*((2*b*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 + (3*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(32*c^2*x^2*(1 + (c*x)/b)^2)))/(3*e) - (d*((2*b*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - (d*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e) - 4*c*((e*(-192*A*c^3*d^3 - b^3*e^2*(5*B*d + 3*A*e) + 24*b*c^2*d^2*(5*B*d + 9*A*e) - 4*b^2*c*d*e*(25*B*d + 9*A*e)))/8 + (3*c*d*(3*A*e*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2) - B*(8*c^2*d^3 - 5*b^2*d*e^2)))/4)*((2*b*x^(5/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((5*(1/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/8 - (15*b^3*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(256*c^3*x^3*(1 + (c*x)/b)^2)))/(5*e) - (d*((2*b*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 + (3*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(32*c^2*x^2*(1 + (c*x)/b)^2)))/(3*e) - (d*((2*b*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - (d*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/e))/(d*(-(c*d) + b*e)))/(2*d*(-(c*d) + b*e)))/(3*d*(-(c*d) + b*e))))/(4*d*(-(c*d) + b*e)*x^(3/2)*(b + c*x)^(3/2))","B",1
1180,1,268,269,1.0427008,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^6,x]","\frac{(x (b+c x))^{3/2} \left(\frac{5 (A b e-2 A c d+b B d) \left(-\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{8 d^{5/2} (c d-b e)^{3/2}}-\frac{b^2 \sqrt{x} \sqrt{b+c x} (5 b d+3 b e x+2 c d x)}{8 d^2 (d+e x)^2 (c d-b e)}-\frac{2 x^{3/2} (b+c x)^{5/2}}{(d+e x)^4}+\frac{b \sqrt{x} (b+c x)^{5/2}}{(d+e x)^3 (c d-b e)}\right)}{8 (b+c x)^{3/2} (b e-c d)}+\frac{2 x^{5/2} (b+c x) (A e-B d)}{(d+e x)^5}\right)}{10 d x^{3/2} (b e-c d)}","-\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{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{\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,"((x*(b + c*x))^(3/2)*((2*(-(B*d) + A*e)*x^(5/2)*(b + c*x))/(d + e*x)^5 + (5*(b*B*d - 2*A*c*d + A*b*e)*((-2*x^(3/2)*(b + c*x)^(5/2))/(d + e*x)^4 + (b*Sqrt[x]*(b + c*x)^(5/2))/((c*d - b*e)*(d + e*x)^3) - (b^2*Sqrt[x]*Sqrt[b + c*x]*(5*b*d + 2*c*d*x + 3*b*e*x))/(8*d^2*(c*d - b*e)*(d + e*x)^2) - (3*b^4*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(8*d^(5/2)*(c*d - b*e)^(3/2))))/(8*(-(c*d) + b*e)*(b + c*x)^(3/2))))/(10*d*(-(c*d) + b*e)*x^(3/2))","A",1
1181,1,352,402,1.3258025,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^7,x]","\frac{(x (b+c x))^{3/2} \left(\frac{\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) \left(-\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{8 d^{5/2} (c d-b e)^{3/2}}-\frac{b^2 \sqrt{x} \sqrt{b+c x} (5 b d+3 b e x+2 c d x)}{8 d^2 (d+e x)^2 (c d-b e)}-\frac{2 x^{3/2} (b+c x)^{5/2}}{(d+e x)^4}+\frac{b \sqrt{x} (b+c x)^{5/2}}{(d+e x)^3 (c d-b e)}\right)}{32 d (b+c x)^{3/2} (c d-b e)^2}-\frac{x^{5/2} (b+c x) (7 A e (b e-2 c d)+B d (5 b e+2 c d))}{10 d (d+e x)^5 (c d-b e)}+\frac{x^{5/2} (b+c x) (A e-B d)}{(d+e x)^6}\right)}{6 d x^{3/2} (b e-c d)}","-\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,"((x*(b + c*x))^(3/2)*(((-(B*d) + A*e)*x^(5/2)*(b + c*x))/(d + e*x)^6 - ((7*A*e*(-2*c*d + b*e) + B*d*(2*c*d + 5*b*e))*x^(5/2)*(b + c*x))/(10*d*(c*d - b*e)*(d + e*x)^5) + ((24*A*c^2*d^2 - 12*b*c*d*(B*d + 2*A*e) + b^2*e*(5*B*d + 7*A*e))*((-2*x^(3/2)*(b + c*x)^(5/2))/(d + e*x)^4 + (b*Sqrt[x]*(b + c*x)^(5/2))/((c*d - b*e)*(d + e*x)^3) - (b^2*Sqrt[x]*Sqrt[b + c*x]*(5*b*d + 2*c*d*x + 3*b*e*x))/(8*d^2*(c*d - b*e)*(d + e*x)^2) - (3*b^4*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(8*d^(5/2)*(c*d - b*e)^(3/2))))/(32*d*(c*d - b*e)^2*(b + c*x)^(3/2))))/(6*d*(-(c*d) + b*e)*x^(3/2))","A",1
1182,1,505,565,3.5053584,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^8,x]","\frac{(x (b+c x))^{3/2} \left(-\frac{x^{5/2} (b+c x) \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)}{120 d^2 (d+e x)^5 (c d-b e)^2}-\frac{7 \left(b^3 \left(-e^2\right) (9 A e+5 B d)+2 b^2 c d e (21 A e+10 B d)-24 b c^2 d^2 (3 A e+B d)+48 A c^3 d^3\right) \left(16 d^{5/2} x^{3/2} (b+c x)^{5/2} (c d-b e)^{3/2}-b (d+e x) \left(8 d^{5/2} \sqrt{x} (b+c x)^{5/2} \sqrt{c d-b e}-b (d+e x) \left(2 d^{3/2} \sqrt{x} (b+c x)^{3/2} \sqrt{c d-b e}+3 b (d+e x) \left(\sqrt{d} \sqrt{x} \sqrt{b+c x} \sqrt{c d-b e}+b (d+e x) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)\right)\right)\right)\right)}{3072 d^{9/2} (b+c x)^{3/2} (d+e x)^4 (c d-b e)^{9/2}}-\frac{x^{5/2} (b+c x) (9 A e (b e-2 c d)+B d (5 b e+4 c d))}{12 d (d+e x)^6 (c d-b e)}-\frac{x^{5/2} (b+c x) (B d-A e)}{(d+e x)^7}\right)}{7 d x^{3/2} (b e-c d)}","\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{b^2 \sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(b^3 \left(-e^2\right) (9 A e+5 B d)+2 b^2 c d e (21 A e+10 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)^{3/2} (x (2 c d-b e)+b d) \left(b^3 \left(-e^2\right) (9 A e+5 B d)+2 b^2 c d e (21 A e+10 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(b^3 \left(-e^2\right) (9 A e+5 B d)+2 b^2 c d e (21 A e+10 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,"((x*(b + c*x))^(3/2)*(-(((B*d - A*e)*x^(5/2)*(b + c*x))/(d + e*x)^7) - ((9*A*e*(-2*c*d + b*e) + B*d*(4*c*d + 5*b*e))*x^(5/2)*(b + c*x))/(12*d*(c*d - b*e)*(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))*x^(5/2)*(b + c*x))/(120*d^2*(c*d - b*e)^2*(d + e*x)^5) - (7*(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))*(16*d^(5/2)*(c*d - b*e)^(3/2)*x^(3/2)*(b + c*x)^(5/2) - b*(d + e*x)*(8*d^(5/2)*Sqrt[c*d - b*e]*Sqrt[x]*(b + c*x)^(5/2) - b*(d + e*x)*(2*d^(3/2)*Sqrt[c*d - b*e]*Sqrt[x]*(b + c*x)^(3/2) + 3*b*(d + e*x)*(Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[x]*Sqrt[b + c*x] + b*(d + e*x)*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])))))/(3072*d^(9/2)*(c*d - b*e)^(9/2)*(b + c*x)^(3/2)*(d + e*x)^4)))/(7*d*(-(c*d) + b*e)*x^(3/2))","A",1
1183,1,417,423,1.4496996,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^2*(b*x + c*x^2)^(5/2),x]","\frac{(x (b+c x))^{7/2} \left(\frac{1323 A \left(9 b^2 e^2-32 b c d e+32 c^2 d^2\right) \left(\sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \left(15 b^5-10 b^4 c x+8 b^3 c^2 x^2+432 b^2 c^3 x^3+640 b c^4 x^4+256 c^5 x^5\right)-15 b^{11/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)\right)}{1024 c^{9/2} x^{7/2} \sqrt{\frac{c x}{b}+1}}+\frac{5103 A e (b+c x)^3 (2 c d-b e)}{c}+7938 A e (b+c x)^3 (d+e x)+\frac{189 B \left(11 b^2 e^2-36 b c d e+32 c^2 d^2\right) \left(105 b^{13/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)+\sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \left(-105 b^6+70 b^5 c x-56 b^4 c^2 x^2+48 b^3 c^3 x^3+4736 b^2 c^4 x^4+7424 b c^5 x^5+3072 c^6 x^6\right)\right)}{2048 c^{11/2} x^{7/2} \sqrt{\frac{c x}{b}+1}}+\frac{441 B e x (b+c x)^3 (20 c d-11 b e)}{c}+7056 B e x (b+c x)^3 (d+e x)\right)}{63504 c (b+c x)^3}","\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{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{(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{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{B \left(b x+c x^2\right)^{7/2} (d+e x)^2}{9 c}",1,"((x*(b + c*x))^(7/2)*((5103*A*e*(2*c*d - b*e)*(b + c*x)^3)/c + (441*B*e*(20*c*d - 11*b*e)*x*(b + c*x)^3)/c + 7938*A*e*(b + c*x)^3*(d + e*x) + 7056*B*e*x*(b + c*x)^3*(d + e*x) + (1323*A*(32*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2)*(Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*(15*b^5 - 10*b^4*c*x + 8*b^3*c^2*x^2 + 432*b^2*c^3*x^3 + 640*b*c^4*x^4 + 256*c^5*x^5) - 15*b^(11/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(1024*c^(9/2)*x^(7/2)*Sqrt[1 + (c*x)/b]) + (189*B*(32*c^2*d^2 - 36*b*c*d*e + 11*b^2*e^2)*(Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*(-105*b^6 + 70*b^5*c*x - 56*b^4*c^2*x^2 + 48*b^3*c^3*x^3 + 4736*b^2*c^4*x^4 + 7424*b*c^5*x^5 + 3072*c^6*x^6) + 105*b^(13/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(2048*c^(11/2)*x^(7/2)*Sqrt[1 + (c*x)/b])))/(63504*c*(b + c*x)^3)","A",1
1184,1,315,264,0.7984786,"\int (A+B x) (d+e x) \left(b x+c x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)*(b*x + c*x^2)^(5/2),x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(-210 b^6 c (8 A e+8 B d+3 B e x)+56 b^5 c^2 (20 A (3 d+e x)+B x (20 d+9 e x))-16 b^4 c^3 x (28 A (5 d+2 e x)+B x (56 d+27 e x))+128 b^3 c^4 x^2 (2 A (7 d+3 e x)+3 B x (2 d+e x))+256 b^2 c^5 x^3 (A (378 d+296 e x)+B x (296 d+243 e x))+1024 b c^6 x^4 (4 A (35 d+29 e x)+B x (116 d+99 e x))+2048 c^7 x^5 (4 A (7 d+6 e x)+3 B x (8 d+7 e x))+945 b^7 B e\right)-\frac{105 b^{11/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{344064 c^{11/2}}","-\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{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{\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(945*b^7*B*e - 210*b^6*c*(8*B*d + 8*A*e + 3*B*e*x) + 128*b^3*c^4*x^2*(3*B*x*(2*d + e*x) + 2*A*(7*d + 3*e*x)) + 2048*c^7*x^5*(4*A*(7*d + 6*e*x) + 3*B*x*(8*d + 7*e*x)) + 56*b^5*c^2*(20*A*(3*d + e*x) + B*x*(20*d + 9*e*x)) - 16*b^4*c^3*x*(28*A*(5*d + 2*e*x) + B*x*(56*d + 27*e*x)) + 1024*b*c^6*x^4*(4*A*(35*d + 29*e*x) + B*x*(116*d + 99*e*x)) + 256*b^2*c^5*x^3*(B*x*(296*d + 243*e*x) + A*(378*d + 296*e*x))) - (105*b^(11/2)*(32*A*c^2*d + 9*b^2*B*e - 16*b*c*(B*d + A*e))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(344064*c^(11/2))","A",1
1185,1,171,171,0.3443788,"\int (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(b*x + c*x^2)^(5/2),x]","\frac{(x (b+c x))^{7/2} \left(\frac{49 (b B-2 A c) \left(15 b^{11/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)-\sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \left(15 b^5-10 b^4 c x+8 b^3 c^2 x^2+432 b^2 c^3 x^3+640 b c^4 x^4+256 c^5 x^5\right)\right)}{3072 c^{7/2} x^{7/2} \sqrt{\frac{c x}{b}+1}}+7 B (b+c x)^3\right)}{49 c (b+c x)^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{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{(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,"((x*(b + c*x))^(7/2)*(7*B*(b + c*x)^3 + (49*(b*B - 2*A*c)*(-(Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*(15*b^5 - 10*b^4*c*x + 8*b^3*c^2*x^2 + 432*b^2*c^3*x^3 + 640*b*c^4*x^4 + 256*c^5*x^5)) + 15*b^(11/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]]))/(3072*c^(7/2)*x^(7/2)*Sqrt[1 + (c*x)/b])))/(49*c*(b + c*x)^3)","A",1
1186,1,650,703,2.465867,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{d+e x} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x),x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(e \sqrt{x} \left(4 A c e \left(-45 b^4 e^4+30 b^3 c e^3 (e x-5 d)+4 b^2 c^2 e^2 \left(660 d^2-295 d e x+186 e^2 x^2\right)+16 b c^3 e \left(-270 d^3+130 d^2 e x-85 d e^2 x^2+63 e^3 x^3\right)+32 c^4 \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)+B \left(75 b^5 e^5+10 b^4 c e^4 (18 d-5 e x)+40 b^3 c^2 e^3 \left(15 d^2-3 d e x+e^2 x^2\right)+16 b^2 c^3 e^2 \left(-660 d^3+295 d^2 e x-186 d e^2 x^2+135 e^3 x^3\right)+64 b c^4 e \left(270 d^4-130 d^3 e x+85 d^2 e^2 x^2-63 d e^3 x^3+50 e^4 x^4\right)-128 c^5 \left(60 d^5-30 d^4 e x+20 d^3 e^2 x^2-15 d^2 e^3 x^3+12 d e^4 x^4-10 e^5 x^5\right)\right)\right)-\frac{15360 c^3 d^{5/2} (B d-A e) (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{b+c x}}\right)+\frac{15 \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(4 A c e \left(3 b^5 e^5+10 b^4 c d e^4+80 b^3 c^2 d^2 e^3-480 b^2 c^3 d^3 e^2+640 b c^4 d^4 e-256 c^5 d^5\right)+B \left(-5 b^6 e^6-12 b^5 c d e^5-40 b^4 c^2 d^2 e^4-320 b^3 c^3 d^3 e^3+1920 b^2 c^4 d^4 e^2-2560 b c^5 d^5 e+1024 c^6 d^6\right)\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right)}{7680 c^{7/2} e^7 \sqrt{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(5 b^3 e^3+12 b^2 c d e^2-88 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(-3 b^4 e^4-10 b^3 c d e^3+176 b^2 c^2 d^2 e^2-288 b c^3 d^3 e+128 c^4 d^4\right)-B \left(-5 b^5 e^5-12 b^4 c d e^4-40 b^3 c^2 d^2 e^3+704 b^2 c^3 d^3 e^2-1152 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(-3 b^5 e^5-10 b^4 c d e^4-80 b^3 c^2 d^2 e^3+480 b^2 c^3 d^3 e^2-640 b c^4 d^4 e+256 c^5 d^5\right)-B \left(-5 b^6 e^6-12 b^5 c d e^5-40 b^4 c^2 d^2 e^4-320 b^3 c^3 d^3 e^3+1920 b^2 c^4 d^4 e^2-2560 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,"(Sqrt[x*(b + c*x)]*((15*(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))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b]) + Sqrt[c]*(e*Sqrt[x]*(4*A*c*e*(-45*b^4*e^4 + 30*b^3*c*e^3*(-5*d + e*x) + 4*b^2*c^2*e^2*(660*d^2 - 295*d*e*x + 186*e^2*x^2) + 16*b*c^3*e*(-270*d^3 + 130*d^2*e*x - 85*d*e^2*x^2 + 63*e^3*x^3) + 32*c^4*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4)) + B*(75*b^5*e^5 + 10*b^4*c*e^4*(18*d - 5*e*x) + 40*b^3*c^2*e^3*(15*d^2 - 3*d*e*x + e^2*x^2) + 16*b^2*c^3*e^2*(-660*d^3 + 295*d^2*e*x - 186*d*e^2*x^2 + 135*e^3*x^3) + 64*b*c^4*e*(270*d^4 - 130*d^3*e*x + 85*d^2*e^2*x^2 - 63*d*e^3*x^3 + 50*e^4*x^4) - 128*c^5*(60*d^5 - 30*d^4*e*x + 20*d^3*e^2*x^2 - 15*d^2*e^3*x^3 + 12*d*e^4*x^4 - 10*e^5*x^5))) - (15360*c^3*d^(5/2)*(B*d - A*e)*(c*d - b*e)^(5/2)*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/Sqrt[b + c*x])))/(7680*c^(7/2)*e^7*Sqrt[x])","A",1
1187,1,618,574,3.1972965,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x)^2,x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(\frac{e \sqrt{x} \left(10 A c e \left(15 b^3 e^3 (d+e x)+2 b^2 c e^2 \left(-360 d^2-205 d e x+59 e^2 x^2\right)+8 b c^2 e \left(210 d^3+110 d^2 e x-35 d e^2 x^2+17 e^3 x^3\right)-16 c^3 \left(60 d^4+30 d^3 e x-10 d^2 e^2 x^2+5 d e^3 x^3-3 e^4 x^4\right)\right)+B \left(-45 b^4 e^4 (d+e x)+30 b^3 c e^3 \left(-10 d^2-9 d e x+e^2 x^2\right)+8 b^2 c^2 e^2 \left(1230 d^3+695 d^2 e x-202 d e^2 x^2+93 e^3 x^3\right)+16 b c^3 e \left(-1320 d^4-690 d^3 e x+220 d^2 e^2 x^2-107 d e^3 x^3+63 e^4 x^4\right)+192 c^4 \left(60 d^5+30 d^4 e x-10 d^3 e^2 x^2+5 d^2 e^3 x^3-3 d e^4 x^4+2 e^5 x^5\right)\right)\right)}{d+e x}+\frac{1920 c^2 d^{3/2} (c d-b e)^{3/2} (5 A e (b e-2 c d)+B d (12 c d-7 b e)) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{b+c x}}\right)+\frac{15 \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(B \left(3 b^5 e^5+20 b^4 c d e^4+240 b^3 c^2 d^2 e^3-1920 b^2 c^3 d^3 e^2+3200 b c^4 d^4 e-1536 c^5 d^5\right)-10 A c e \left(b^4 e^4+16 b^3 c d e^3-144 b^2 c^2 d^2 e^2+256 b c^3 d^3 e-128 c^4 d^4\right)\right)}{\sqrt{b} \sqrt{\frac{c x}{b}+1}}\right)}{1920 c^{5/2} e^7 \sqrt{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(-b^3 e^3+48 b^2 c d e^2-112 b c^2 d^2 e+64 c^3 d^3\right)-B \left(-3 b^4 e^4-20 b^3 c d e^3+656 b^2 c^2 d^2 e^2-1408 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(-b^4 e^4-16 b^3 c d e^3+144 b^2 c^2 d^2 e^2-256 b c^3 d^3 e+128 c^4 d^4\right)-B \left(-3 b^5 e^5-20 b^4 c d e^4-240 b^3 c^2 d^2 e^3+1920 b^2 c^3 d^3 e^2-3200 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,"(Sqrt[x*(b + c*x)]*((15*(-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))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b]) + Sqrt[c]*((e*Sqrt[x]*(10*A*c*e*(15*b^3*e^3*(d + e*x) + 2*b^2*c*e^2*(-360*d^2 - 205*d*e*x + 59*e^2*x^2) + 8*b*c^2*e*(210*d^3 + 110*d^2*e*x - 35*d*e^2*x^2 + 17*e^3*x^3) - 16*c^3*(60*d^4 + 30*d^3*e*x - 10*d^2*e^2*x^2 + 5*d*e^3*x^3 - 3*e^4*x^4)) + B*(-45*b^4*e^4*(d + e*x) + 30*b^3*c*e^3*(-10*d^2 - 9*d*e*x + e^2*x^2) + 8*b^2*c^2*e^2*(1230*d^3 + 695*d^2*e*x - 202*d*e^2*x^2 + 93*e^3*x^3) + 16*b*c^3*e*(-1320*d^4 - 690*d^3*e*x + 220*d^2*e^2*x^2 - 107*d*e^3*x^3 + 63*e^4*x^4) + 192*c^4*(60*d^5 + 30*d^4*e*x - 10*d^3*e^2*x^2 + 5*d^2*e^3*x^3 - 3*d*e^4*x^4 + 2*e^5*x^5))))/(d + e*x) + (1920*c^2*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[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/Sqrt[b + c*x])))/(1920*c^(5/2)*e^7*Sqrt[x])","A",1
1188,1,2047,508,6.174163,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x)^3,x]","\text{Result too large to show}","\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{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(-b^3 e^3+88 b^2 c d e^2-272 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(-b^3 e^3+18 b^2 c d e^2-48 b c^2 d^2 e+32 c^3 d^3\right)-B \left(-b^4 e^4-24 b^3 c d e^3+288 b^2 c^2 d^2 e^2-640 b c^3 d^3 e+384 c^4 d^4\right)\right)}{64 c^{3/2} e^7}-\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{\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}",1,"((-(B*d) + A*e)*x*(b + c*x)*(x*(b + c*x))^(5/2))/(2*d*(-(c*d) + b*e)*(d + e*x)^2) + ((x*(b + c*x))^(5/2)*(((-5*c*d*(B*d - A*e) + (e*(7*b*B*d - 4*A*c*d - 3*A*b*e))/2)*x^(7/2)*(b + c*x)^(7/2))/(d*(-(c*d) + b*e)*(d + e*x)) + (((8*A*c^2*d^2 + 4*b*c*d*(14*B*d - 11*A*e) - 5*b^2*e*(7*B*d - 3*A*e))*((2*b^2*x^(5/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((5/(16*(1 + (c*x)/b)^3) + 5/(8*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 - (15*b^3*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(512*c^3*x^3*(1 + (c*x)/b)^3)))/(5*e) - (d*((2*b^2*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((3*(5/(8*(1 + (c*x)/b)^3) + 5/(6*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/8 + (15*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(256*c^2*x^2*(1 + (c*x)/b)^3)))/(3*e) - (d*((2*b^2*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((15/(8*(1 + (c*x)/b)^3) + 5/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/6 + (5*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(16*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(7/2))))/e - (d*((2*b*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - ((c*d - b*e)*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/e))/e))/4 + 3*c*(B*d*(10*c*d - 7*b*e) - 3*A*e*(2*c*d - b*e))*((2*b^2*x^(7/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((7*(3/(16*(1 + (c*x)/b)^3) + 1/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/12 + (35*b^4*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) + (16*c^3*x^3)/(15*b^3) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(2048*c^4*x^4*(1 + (c*x)/b)^3)))/(7*e) - (d*((2*b^2*x^(5/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((5/(16*(1 + (c*x)/b)^3) + 5/(8*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 - (15*b^3*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(512*c^3*x^3*(1 + (c*x)/b)^3)))/(5*e) - (d*((2*b^2*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((3*(5/(8*(1 + (c*x)/b)^3) + 5/(6*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/8 + (15*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(256*c^2*x^2*(1 + (c*x)/b)^3)))/(3*e) - (d*((2*b^2*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((15/(8*(1 + (c*x)/b)^3) + 5/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/6 + (5*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(16*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(7/2))))/e - (d*((2*b*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - ((c*d - b*e)*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/e))/e))/e))/(d*(-(c*d) + b*e))))/(2*d*(-(c*d) + b*e)*x^(5/2)*(b + c*x)^(5/2))","B",1
1189,1,2233,495,6.2606316,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x)^4,x]","\text{Result too large to show}","-\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(-b^3 e^3+24 b^2 c d e^2-80 b c^2 d^2 e+64 c^3 d^3\right)\right)}{8 \sqrt{c} e^7}+\frac{5 \left(B d \left(-7 b^3 e^3+56 b^2 c d e^2-112 b c^2 d^2 e+64 c^3 d^3\right)-A e \left(-b^3 e^3+18 b^2 c d e^2-48 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{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{\left(b x+c x^2\right)^{5/2} (-A e+2 B d+B e x)}{3 e^2 (d+e x)^3}",1,"((-(B*d) + A*e)*x*(b + c*x)*(x*(b + c*x))^(5/2))/(3*d*(-(c*d) + b*e)*(d + e*x)^3) + ((x*(b + c*x))^(5/2)*(((-4*c*d*(B*d - A*e) + (e*(7*b*B*d - 6*A*c*d - A*b*e))/2)*x^(7/2)*(b + c*x)^(7/2))/(2*d*(-(c*d) + b*e)*(d + e*x)^2) + ((((e*(24*A*c^2*d^2 + 2*b*c*d*(14*B*d - 17*A*e) - 3*b^2*e*(7*B*d - A*e)))/4 - (5*c*d*(B*d*(8*c*d - 7*b*e) - A*e*(2*c*d - b*e)))/2)*x^(7/2)*(b + c*x)^(7/2))/(d*(-(c*d) + b*e)*(d + e*x)) + ((-3*(16*A*c^3*d^3 + 2*b^2*c*d*e*(98*B*d - 39*A*e) - 8*b*c^2*d^2*(21*B*d - 8*A*e) - 5*b^3*e^2*(7*B*d - A*e))*((2*b^2*x^(5/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((5/(16*(1 + (c*x)/b)^3) + 5/(8*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 - (15*b^3*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(512*c^3*x^3*(1 + (c*x)/b)^3)))/(5*e) - (d*((2*b^2*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((3*(5/(8*(1 + (c*x)/b)^3) + 5/(6*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/8 + (15*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(256*c^2*x^2*(1 + (c*x)/b)^3)))/(3*e) - (d*((2*b^2*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((15/(8*(1 + (c*x)/b)^3) + 5/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/6 + (5*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(16*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(7/2))))/e - (d*((2*b*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - ((c*d - b*e)*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/e))/e))/8 - (3*c*(A*e*(44*c^2*d^2 - 44*b*c*d*e + 3*b^2*e^2) - B*d*(80*c^2*d^2 - 98*b*c*d*e + 21*b^2*e^2))*((2*b^2*x^(7/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((7*(3/(16*(1 + (c*x)/b)^3) + 1/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/12 + (35*b^4*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) + (16*c^3*x^3)/(15*b^3) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(2048*c^4*x^4*(1 + (c*x)/b)^3)))/(7*e) - (d*((2*b^2*x^(5/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((5/(16*(1 + (c*x)/b)^3) + 5/(8*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 - (15*b^3*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(512*c^3*x^3*(1 + (c*x)/b)^3)))/(5*e) - (d*((2*b^2*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((3*(5/(8*(1 + (c*x)/b)^3) + 5/(6*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/8 + (15*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(256*c^2*x^2*(1 + (c*x)/b)^3)))/(3*e) - (d*((2*b^2*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((15/(8*(1 + (c*x)/b)^3) + 5/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/6 + (5*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(16*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(7/2))))/e - (d*((2*b*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - ((c*d - b*e)*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/e))/e))/e))/2)/(d*(-(c*d) + b*e)))/(2*d*(-(c*d) + b*e))))/(3*d*(-(c*d) + b*e)*x^(5/2)*(b + c*x)^(5/2))","B",1
1190,1,2680,633,6.2883384,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x)^5,x]","\text{Result too large to show}","-\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(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(b^3 e^3+16 b^2 c d e^2-80 b c^2 d^2 e+64 c^3 d^3\right)+B d \left(-7 b^3 e^3+120 b^2 c d e^2-304 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 \left(A e \left(-b^4 e^4-16 b^3 c d e^3+144 b^2 c^2 d^2 e^2-256 b c^3 d^3 e+128 c^4 d^4\right)-B d \left(7 b^4 e^4-168 b^3 c d e^3+672 b^2 c^2 d^2 e^2-896 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,"((-(B*d) + A*e)*x*(b + c*x)*(x*(b + c*x))^(5/2))/(4*d*(-(c*d) + b*e)*(d + e*x)^4) + ((x*(b + c*x))^(5/2)*(((-3*c*d*(B*d - A*e) + (e*(7*b*B*d - 8*A*c*d + A*b*e))/2)*x^(7/2)*(b + c*x)^(7/2))/(3*d*(-(c*d) + b*e)*(d + e*x)^3) + (((-2*c*d*(B*d*(6*c*d - 7*b*e) + A*e*(2*c*d - b*e)) + (e*(-7*b^2*B*d*e + A*(48*c^2*d^2 - 40*b*c*d*e - b^2*e^2)))/4)*x^(7/2)*(b + c*x)^(7/2))/(2*d*(-(c*d) + b*e)*(d + e*x)^2) + ((((e*(-192*A*c^3*d^3 - 4*b^2*c*d*e*(91*B*d - 17*A*e) + 3*b^3*e^2*(7*B*d + A*e) + 16*b*c^2*d^2*(21*B*d + 8*A*e)))/8 + (5*c*d*(A*e*(32*c^2*d^2 - 32*b*c*d*e - b^2*e^2) - B*d*(48*c^2*d^2 - 56*b*c*d*e + 7*b^2*e^2)))/4)*x^(7/2)*(b + c*x)^(7/2))/(d*(-(c*d) + b*e)*(d + e*x)) + ((-1/8*(c*d*(-192*A*c^3*d^3 - 4*b^2*c*d*e*(91*B*d - 17*A*e) + 3*b^3*e^2*(7*B*d + A*e) + 16*b*c^2*d^2*(21*B*d + 8*A*e))) + (b*e*(-192*A*c^3*d^3 - 4*b^2*c*d*e*(91*B*d - 17*A*e) + 3*b^3*e^2*(7*B*d + A*e) + 16*b*c^2*d^2*(21*B*d + 8*A*e)))/8 - (7*b*((e*(-192*A*c^3*d^3 - 4*b^2*c*d*e*(91*B*d - 17*A*e) + 3*b^3*e^2*(7*B*d + A*e) + 16*b*c^2*d^2*(21*B*d + 8*A*e)))/8 + (5*c*d*(A*e*(32*c^2*d^2 - 32*b*c*d*e - b^2*e^2) - B*d*(48*c^2*d^2 - 56*b*c*d*e + 7*b^2*e^2)))/4))/2)*((2*b^2*x^(5/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((5/(16*(1 + (c*x)/b)^3) + 5/(8*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 - (15*b^3*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(512*c^3*x^3*(1 + (c*x)/b)^3)))/(5*e) - (d*((2*b^2*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((3*(5/(8*(1 + (c*x)/b)^3) + 5/(6*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/8 + (15*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(256*c^2*x^2*(1 + (c*x)/b)^3)))/(3*e) - (d*((2*b^2*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((15/(8*(1 + (c*x)/b)^3) + 5/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/6 + (5*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(16*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(7/2))))/e - (d*((2*b*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - ((c*d - b*e)*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/e))/e) - 6*c*((e*(-192*A*c^3*d^3 - 4*b^2*c*d*e*(91*B*d - 17*A*e) + 3*b^3*e^2*(7*B*d + A*e) + 16*b*c^2*d^2*(21*B*d + 8*A*e)))/8 + (5*c*d*(A*e*(32*c^2*d^2 - 32*b*c*d*e - b^2*e^2) - B*d*(48*c^2*d^2 - 56*b*c*d*e + 7*b^2*e^2)))/4)*((2*b^2*x^(7/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((7*(3/(16*(1 + (c*x)/b)^3) + 1/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/12 + (35*b^4*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) + (16*c^3*x^3)/(15*b^3) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(2048*c^4*x^4*(1 + (c*x)/b)^3)))/(7*e) - (d*((2*b^2*x^(5/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((5/(16*(1 + (c*x)/b)^3) + 5/(8*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/2 - (15*b^3*((2*c*x)/b - (4*c^2*x^2)/(3*b^2) - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(512*c^3*x^3*(1 + (c*x)/b)^3)))/(5*e) - (d*((2*b^2*x^(3/2)*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((3*(5/(8*(1 + (c*x)/b)^3) + 5/(6*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1)))/8 + (15*b^2*((2*c*x)/b - (2*Sqrt[c]*Sqrt[x]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (c*x)/b])))/(256*c^2*x^2*(1 + (c*x)/b)^3)))/(3*e) - (d*((2*b^2*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^3*((15/(8*(1 + (c*x)/b)^3) + 5/(4*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/6 + (5*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(16*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(7/2))))/e - (d*((2*b*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)^2*((3/(2*(1 + (c*x)/b)^2) + (1 + (c*x)/b)^(-1))/4 + (3*Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(8*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(5/2))))/e - ((c*d - b*e)*((2*c*Sqrt[x]*Sqrt[b + c*x]*(1 + (c*x)/b)*(1/(2*(1 + (c*x)/b)) + (Sqrt[b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(2*Sqrt[c]*Sqrt[x]*(1 + (c*x)/b)^(3/2))))/e - ((c*d - b*e)*((2*Sqrt[b]*Sqrt[c]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(e*Sqrt[b + c*x]) - (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*e)))/e))/e))/e))/e))/e))/e))/(d*(-(c*d) + b*e)))/(2*d*(-(c*d) + b*e)))/(3*d*(-(c*d) + b*e))))/(4*d*(-(c*d) + b*e)*x^(5/2)*(b + c*x)^(5/2))","B",1
1191,1,278,305,0.789884,"\int \frac{(A+B x) (d+e x)^3}{\sqrt{b x+c x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\sqrt{c} \left(8 A c e \left(15 b^2 e^2-2 b c e (27 d+5 e x)+4 c^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+B \left(-105 b^3 e^3+10 b^2 c e^2 (36 d+7 e x)-8 b c^2 e \left(54 d^2+30 d e x+7 e^2 x^2\right)+48 c^3 \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)\right)\right)+\frac{3 \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(-40 b^3 c e^2 (A e+3 B d)+144 b^2 c^2 d e (A e+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)}{\sqrt{b} \sqrt{x} \sqrt{\frac{c x}{b}+1}}\right)}{192 c^{9/2}}","\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(-105 b^3 e^3+360 b^2 c d e^2-376 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(-40 b^3 c e^2 (A e+3 B d)+144 b^2 c^2 d e (A e+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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(8*A*c*e*(15*b^2*e^2 - 2*b*c*e*(27*d + 5*e*x) + 4*c^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2)) + B*(-105*b^3*e^3 + 10*b^2*c*e^2*(36*d + 7*e*x) - 8*b*c^2*e*(54*d^2 + 30*d*e*x + 7*e^2*x^2) + 48*c^3*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3))) + (3*(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))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[x]*Sqrt[1 + (c*x)/b])))/(192*c^(9/2))","A",1
1192,1,190,189,0.2242846,"\int \frac{(A+B x) (d+e x)^2}{\sqrt{b x+c x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{c} x (b+c x) \left(6 A c e (-3 b e+8 c d+2 c e x)+B \left(15 b^2 e^2-2 b c e (18 d+5 e x)+8 c^2 \left(3 d^2+3 d e x+e^2 x^2\right)\right)\right)-3 \sqrt{b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\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)}{24 c^{7/2} \sqrt{x (b+c 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}",1,"(Sqrt[c]*x*(b + c*x)*(6*A*c*e*(8*c*d - 3*b*e + 2*c*e*x) + B*(15*b^2*e^2 - 2*b*c*e*(18*d + 5*e*x) + 8*c^2*(3*d^2 + 3*d*e*x + e^2*x^2))) - 3*Sqrt[b]*(-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))*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(24*c^(7/2)*Sqrt[x*(b + c*x)])","A",1
1193,1,115,99,0.3266492,"\int \frac{(A+B x) (d+e x)}{\sqrt{b x+c x^2}} \, dx","Integrate[((A + B*x)*(d + e*x))/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{x (b+c x)} \left(\frac{\sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) \left(-4 b c (A e+B d)+8 A c^2 d+3 b^2 B e\right)}{\sqrt{b} \sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} (4 A c e+B (-3 b e+4 c d+2 c e x))\right)}{4 c^{5/2}}","\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,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(4*A*c*e + B*(4*c*d - 3*b*e + 2*c*e*x)) + ((8*A*c^2*d + 3*b^2*B*e - 4*b*c*(B*d + A*e))*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*Sqrt[x]*Sqrt[1 + (c*x)/b])))/(4*c^(5/2))","A",1
1194,1,80,55,0.0586999,"\int \frac{A+B x}{\sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/Sqrt[b*x + c*x^2],x]","\frac{B \sqrt{c} x (b+c x)-\sqrt{b} \sqrt{x} \sqrt{\frac{c x}{b}+1} (b B-2 A c) \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{3/2} \sqrt{x (b+c 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}}",1,"(B*Sqrt[c]*x*(b + c*x) - Sqrt[b]*(b*B - 2*A*c)*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(c^(3/2)*Sqrt[x*(b + c*x)])","A",1
1195,1,131,113,0.1657334,"\int \frac{A+B x}{(d+e x) \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)*Sqrt[b*x + c*x^2]),x]","\frac{2 \sqrt{x} \left(\frac{\sqrt{b+c x} (A e-B d) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{d} \sqrt{c d-b e}}+\frac{\sqrt{b} B \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{c}}\right)}{e \sqrt{x (b+c 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}}",1,"(2*Sqrt[x]*((Sqrt[b]*B*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/Sqrt[c] + ((-(B*d) + A*e)*Sqrt[b + c*x]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(Sqrt[d]*Sqrt[c*d - b*e])))/(e*Sqrt[x*(b + c*x)])","A",1
1196,1,133,128,0.070319,"\int \frac{A+B x}{(d+e x)^2 \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^2*Sqrt[b*x + c*x^2]),x]","\frac{\sqrt{x} \left(\frac{\sqrt{d} \sqrt{x} (b+c x) (A e-B d)}{d+e x}+\frac{\sqrt{b+c x} (A b e-2 A c d+b B d) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{\sqrt{c d-b e}}\right)}{d^{3/2} \sqrt{x (b+c x)} (b e-c d)}","\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,"(Sqrt[x]*((Sqrt[d]*(-(B*d) + A*e)*Sqrt[x]*(b + c*x))/(d + e*x) + ((b*B*d - 2*A*c*d + A*b*e)*Sqrt[b + c*x]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/Sqrt[c*d - b*e]))/(d^(3/2)*(-(c*d) + b*e)*Sqrt[x*(b + c*x)])","A",1
1197,1,217,216,0.3902681,"\int \frac{A+B x}{(d+e x)^3 \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^3*Sqrt[b*x + c*x^2]),x]","\frac{\sqrt{x} \left(-\frac{\sqrt{b+c x} \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{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{2 d^{3/2} (c d-b e)^{3/2}}-\frac{\sqrt{x} (b+c x) (3 A e (b e-2 c d)+B d (b e+2 c d))}{2 d (d+e x) (c d-b e)}+\frac{\sqrt{x} (b+c x) (A e-B d)}{(d+e x)^2}\right)}{2 d \sqrt{x (b+c x)} (b e-c d)}","\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,"(Sqrt[x]*(((-(B*d) + A*e)*Sqrt[x]*(b + c*x))/(d + e*x)^2 - ((3*A*e*(-2*c*d + b*e) + B*d*(2*c*d + b*e))*Sqrt[x]*(b + c*x))/(2*d*(c*d - b*e)*(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))*Sqrt[b + c*x]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(2*d^(3/2)*(c*d - b*e)^(3/2))))/(2*d*(-(c*d) + b*e)*Sqrt[x*(b + c*x)])","A",1
1198,1,345,331,1.715953,"\int \frac{A+B x}{(d+e x)^4 \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^4*Sqrt[b*x + c*x^2]),x]","-\frac{\sqrt{x} \left(\frac{\sqrt{b+c x} (d+e x) \left(2 d^{3/2} \sqrt{x} \sqrt{b+c x} (c d-b e)^{3/2} (5 A e (b e-2 c d)+B d (b e+4 c d))-(d+e x) \left(-\sqrt{d} \sqrt{x} \sqrt{b+c x} \sqrt{c d-b e} \left(A e \left(-15 b^2 e^2+44 b c d e-44 c^2 d^2\right)+B d \left(-3 b^2 e^2+10 b c d e+8 c^2 d^2\right)\right)-3 (d+e x) \left(b^3 \left(-e^2\right) (5 A e+B d)+2 b^2 c d e (9 A e+2 B d)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)\right)\right)}{d^{5/2} (c d-b e)^{5/2}}+8 \sqrt{x} (b+c x) (B d-A e)\right)}{24 d \sqrt{x (b+c x)} (d+e x)^3 (b e-c d)}","\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(b^3 \left(-e^2\right) (5 A e+B d)+2 b^2 c d e (9 A e+2 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,"-1/24*(Sqrt[x]*(8*(B*d - A*e)*Sqrt[x]*(b + c*x) + (Sqrt[b + c*x]*(d + e*x)*(2*d^(3/2)*(c*d - b*e)^(3/2)*(5*A*e*(-2*c*d + b*e) + B*d*(4*c*d + b*e))*Sqrt[x]*Sqrt[b + c*x] - (d + e*x)*(-(Sqrt[d]*Sqrt[c*d - b*e]*(A*e*(-44*c^2*d^2 + 44*b*c*d*e - 15*b^2*e^2) + B*d*(8*c^2*d^2 + 10*b*c*d*e - 3*b^2*e^2))*Sqrt[x]*Sqrt[b + c*x]) - 3*(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))*(d + e*x)*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])))/(d^(5/2)*(c*d - b*e)^(5/2))))/(d*(-(c*d) + b*e)*Sqrt[x*(b + c*x)]*(d + e*x)^3)","A",1
1199,1,229,238,0.2344198,"\int \frac{(A+B x) (d+e x)^3}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2)^(3/2),x]","\frac{3 b^{5/2} e \sqrt{x} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\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)+\sqrt{c} \left(4 A c \left(3 b^3 e^3 x+b^2 c e^2 x (e x-6 d)-2 b c^2 d^2 (d-3 e x)-4 c^3 d^3 x\right)+b B x \left(-15 b^3 e^3+b^2 c e^2 (36 d-5 e x)+2 b c^2 e \left(-12 d^2+6 d e x+e^2 x^2\right)+8 c^3 d^3\right)\right)}{4 b^2 c^{7/2} \sqrt{x (b+c x)}}","-\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{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{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}",1,"(Sqrt[c]*(4*A*c*(-4*c^3*d^3*x + 3*b^3*e^3*x - 2*b*c^2*d^2*(d - 3*e*x) + b^2*c*e^2*x*(-6*d + e*x)) + b*B*x*(8*c^3*d^3 - 15*b^3*e^3 + b^2*c*e^2*(36*d - 5*e*x) + 2*b*c^2*e*(-12*d^2 + 6*d*e*x + e^2*x^2))) + 3*b^(5/2)*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))*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*b^2*c^(7/2)*Sqrt[x*(b + c*x)])","A",1
1200,1,150,151,0.1994673,"\int \frac{(A+B x) (d+e x)^2}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2)^(3/2),x]","\frac{\sqrt{c} \left(b B x \left(3 b^2 e^2+b c e (e x-4 d)+2 c^2 d^2\right)-2 A c \left(b^2 e^2 x+b c d (d-2 e x)+2 c^2 d^2 x\right)\right)-b^{5/2} e \sqrt{x} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right) (-2 A c e+3 b B e-4 B c d)}{b^2 c^{5/2} \sqrt{x (b+c 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}}",1,"(Sqrt[c]*(-2*A*c*(2*c^2*d^2*x + b^2*e^2*x + b*c*d*(d - 2*e*x)) + b*B*x*(2*c^2*d^2 + 3*b^2*e^2 + b*c*e*(-4*d + e*x))) - b^(5/2)*e*(-4*B*c*d + 3*b*B*e - 2*A*c*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(b^2*c^(5/2)*Sqrt[x*(b + c*x)])","A",1
1201,1,101,85,0.0669863,"\int \frac{(A+B x) (d+e x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 b^{5/2} B e \sqrt{x} \sqrt{\frac{c x}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)-2 \sqrt{c} (A c (b d-b e x+2 c d x)+b B x (b e-c d))}{b^2 c^{3/2} \sqrt{x (b+c 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}}",1,"(-2*Sqrt[c]*(b*B*(-(c*d) + b*e)*x + A*c*(b*d + 2*c*d*x - b*e*x)) + 2*b^(5/2)*B*e*Sqrt[x]*Sqrt[1 + (c*x)/b]*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(b^2*c^(3/2)*Sqrt[x*(b + c*x)])","A",1
1202,1,30,33,0.0115646,"\int \frac{A+B x}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(b*x + c*x^2)^(3/2),x]","\frac{2 b B x-2 A (b+2 c x)}{b^2 \sqrt{x (b+c x)}}","-\frac{2 (A b-x (b B-2 A c))}{b^2 \sqrt{b x+c x^2}}",1,"(2*b*B*x - 2*A*(b + 2*c*x))/(b^2*Sqrt[x*(b + c*x)])","A",1
1203,1,144,141,0.1589214,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)*(b*x + c*x^2)^(3/2)),x]","\frac{2 \left(\sqrt{d} \sqrt{c d-b e} \left(A \left(b^2 e-b c d+b c e x-2 c^2 d x\right)+b B c d x\right)+b^2 e \sqrt{x} \sqrt{b+c x} (A e-B d) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)\right)}{b^2 d^{3/2} \sqrt{x (b+c x)} (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*(Sqrt[d]*Sqrt[c*d - b*e]*(b*B*c*d*x + A*(-(b*c*d) + b^2*e - 2*c^2*d*x + b*c*e*x)) + b^2*e*(-(B*d) + A*e)*Sqrt[x]*Sqrt[b + c*x]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])]))/(b^2*d^(3/2)*(c*d - b*e)^(3/2)*Sqrt[x*(b + c*x)])","A",1
1204,1,226,245,0.5932027,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)^(3/2)),x]","\frac{x \left(\frac{c x (b+c x) \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 (b e-c d)}+\frac{e \sqrt{x} (b+c x)^{3/2} (3 A e (b e-2 c d)+B d (4 c d-b e)) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)}{d^{3/2} (c d-b e)^{3/2}}+\frac{(b+c x) (-3 A b e+2 A c d+b B d)}{b d}+\frac{(b+c x) (A e-B d)}{d+e x}\right)}{d (x (b+c x))^{3/2} (b e-c d)}","-\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,"(x*(((b*B*d + 2*A*c*d - 3*A*b*e)*(b + c*x))/(b*d) + (c*(-4*A*c^2*d^2 + b^2*e*(B*d - 3*A*e) + 2*b*c*d*(B*d + 2*A*e))*x*(b + c*x))/(b^2*d*(-(c*d) + b*e)) + ((-(B*d) + A*e)*(b + c*x))/(d + e*x) + (e*(B*d*(4*c*d - b*e) + 3*A*e*(-2*c*d + b*e))*Sqrt[x]*(b + c*x)^(3/2)*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(d^(3/2)*(c*d - b*e)^(3/2))))/(d*(-(c*d) + b*e)*(x*(b + c*x))^(3/2))","A",1
1205,1,377,374,1.5028433,"\int \frac{A+B x}{(d+e x)^3 \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^3*(b*x + c*x^2)^(3/2)),x]","\frac{2 b^2 d^{5/2} (B d-A e) (c d-b e)^{5/2}+(d+e x) \left(b^2 d^{3/2} (c d-b e)^{3/2} (5 A e (b e-2 c d)+B d (6 c d-b e))-(d+e x) \left(3 b^2 e \sqrt{x} \sqrt{b+c x} \left(A e \left(-5 b^2 e^2+16 b c d e-16 c^2 d^2\right)+B d \left(b^2 e^2-4 b c d e+8 c^2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)+b \sqrt{d} (c d-b e)^{3/2} \left(3 b^2 e (5 A e-B d)+4 b c d (2 B d-7 A e)+8 A c^2 d^2\right)+c \sqrt{d} x \sqrt{c d-b e} \left(3 b^3 e^2 (B d-5 A e)+2 b^2 c d e (19 A e-5 B d)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)\right)\right)}{4 b^2 d^{7/2} \sqrt{x (b+c x)} (d+e x)^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{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{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(3 b^3 e^2 (B d-5 A e)-2 b^2 c d e (5 B d-19 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}",1,"(2*b^2*d^(5/2)*(B*d - A*e)*(c*d - b*e)^(5/2) + (d + e*x)*(b^2*d^(3/2)*(c*d - b*e)^(3/2)*(B*d*(6*c*d - b*e) + 5*A*e*(-2*c*d + b*e)) - (d + e*x)*(b*Sqrt[d]*(c*d - b*e)^(3/2)*(8*A*c^2*d^2 + 4*b*c*d*(2*B*d - 7*A*e) + 3*b^2*e*(-(B*d) + 5*A*e)) + c*Sqrt[d]*Sqrt[c*d - b*e]*(16*A*c^3*d^3 + 3*b^3*e^2*(B*d - 5*A*e) - 8*b*c^2*d^2*(B*d + 3*A*e) + 2*b^2*c*d*e*(-5*B*d + 19*A*e))*x + 3*b^2*e*(A*e*(-16*c^2*d^2 + 16*b*c*d*e - 5*b^2*e^2) + B*d*(8*c^2*d^2 - 4*b*c*d*e + b^2*e^2))*Sqrt[x]*Sqrt[b + c*x]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])))/(4*b^2*d^(7/2)*(c*d - b*e)^(7/2)*Sqrt[x*(b + c*x)]*(d + e*x)^2)","A",1
1206,1,237,341,5.3718819,"\int \frac{(A+B x) (d+e x)^4}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(b*x + c*x^2)^(5/2),x]","\frac{x^{5/2} \left(\frac{e^3 (b+c x)^{5/2} \log \left(\sqrt{c} \sqrt{b+c x}+c \sqrt{x}\right) (2 A c e-5 b B e+8 B c d)}{c^{7/2}}-\frac{(b+c x) \left(2 x^2 (b+c x) (c d-b e)^3 \left(b c (5 B d-4 A e)-8 A c^2 d+7 b^2 B e\right)+2 c^3 d^3 x (b+c x)^2 (3 b (4 A e+B d)-8 A c d)+2 b x^2 (b B-A c) (c d-b e)^4+2 A b c^3 d^4 (b+c x)^2-3 b^4 B e^4 x^2 (b+c x)^2\right)}{3 b^4 c^3 x^{3/2}}\right)}{(x (b+c x))^{5/2}}","-\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 \sqrt{b x+c x^2} \left(2 b^3 c e^2 (3 A e+7 B d)+4 b^2 c^2 d e (A e+2 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(2 b^3 c e^2 (A e+3 B d)+4 b^2 c^2 d e (A e+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{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,"(x^(5/2)*(-1/3*((b + c*x)*(2*b*(b*B - A*c)*(c*d - b*e)^4*x^2 + 2*(c*d - b*e)^3*(-8*A*c^2*d + 7*b^2*B*e + b*c*(5*B*d - 4*A*e))*x^2*(b + c*x) + 2*A*b*c^3*d^4*(b + c*x)^2 + 2*c^3*d^3*(-8*A*c*d + 3*b*(B*d + 4*A*e))*x*(b + c*x)^2 - 3*b^4*B*e^4*x^2*(b + c*x)^2))/(b^4*c^3*x^(3/2)) + (e^3*(8*B*c*d - 5*b*B*e + 2*A*c*e)*(b + c*x)^(5/2)*Log[c*Sqrt[x] + Sqrt[c]*Sqrt[b + c*x]])/c^(7/2)))/(x*(b + c*x))^(5/2)","A",1
1207,1,199,220,5.4815313,"\int \frac{(A+B x) (d+e x)^3}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2)^(5/2),x]","\frac{x^{5/2} \left(\frac{2 B e^3 (b+c x)^{5/2} \log \left(\sqrt{c} \sqrt{b+c x}+c \sqrt{x}\right)}{c^{5/2}}-\frac{2 (b+c x) \left(x^2 (b+c x) (c d-b e)^2 \left(b c (5 B d-A e)-8 A c^2 d+4 b^2 B e\right)+c^2 d^2 x (b+c x)^2 (9 A b e-8 A c d+3 b B d)+b x^2 (b B-A c) (c d-b e)^3+A b c^2 d^3 (b+c x)^2\right)}{3 b^4 c^2 x^{3/2}}\right)}{(x (b+c x))^{5/2}}","-\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 \left(b c d^2 \left(-4 b c (2 A e+B d)+8 A c^2 d+b^2 B e\right)+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^3-3 b^4 B e^3+2 b^3 B c d e^2\right)\right)}{3 b^4 c^2 \sqrt{b x+c x^2}}+\frac{2 B e^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}",1,"(x^(5/2)*((-2*(b + c*x)*(b*(b*B - A*c)*(c*d - b*e)^3*x^2 + (c*d - b*e)^2*(-8*A*c^2*d + 4*b^2*B*e + b*c*(5*B*d - A*e))*x^2*(b + c*x) + A*b*c^2*d^3*(b + c*x)^2 + c^2*d^2*(3*b*B*d - 8*A*c*d + 9*A*b*e)*x*(b + c*x)^2))/(3*b^4*c^2*x^(3/2)) + (2*B*e^3*(b + c*x)^(5/2)*Log[c*Sqrt[x] + Sqrt[c]*Sqrt[b + c*x]])/c^(5/2)))/(x*(b + c*x))^(5/2)","A",1
1208,1,149,92,0.0745571,"\int \frac{(A+B x) (d+e x)^2}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2)^(5/2),x]","\frac{2 \left(A \left(-\left(b^3 \left(d^2+6 d e x-3 e^2 x^2\right)\right)+2 b^2 c x \left(3 d^2-12 d e x+e^2 x^2\right)+8 b c^2 d x^2 (3 d-2 e x)+16 c^3 d^2 x^3\right)+b B x \left(b^2 \left(-3 d^2+6 d e x+e^2 x^2\right)+4 b c d x (e x-3 d)-8 c^2 d^2 x^2\right)\right)}{3 b^4 (x (b+c x))^{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}}",1,"(2*(A*(16*c^3*d^2*x^3 + 8*b*c^2*d*x^2*(3*d - 2*e*x) - b^3*(d^2 + 6*d*e*x - 3*e^2*x^2) + 2*b^2*c*x*(3*d^2 - 12*d*e*x + e^2*x^2)) + b*B*x*(-8*c^2*d^2*x^2 + 4*b*c*d*x*(-3*d + e*x) + b^2*(-3*d^2 + 6*d*e*x + e^2*x^2))))/(3*b^4*(x*(b + c*x))^(3/2))","A",1
1209,1,107,111,0.0477735,"\int \frac{(A+B x) (d+e x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x))/(b*x + c*x^2)^(5/2),x]","-\frac{2 \left(A \left(b^3 (d+3 e x)-6 b^2 c x (d-2 e x)+8 b c^2 x^2 (e x-3 d)-16 c^3 d x^3\right)+b B x \left(3 b^2 (d-e x)-2 b c x (e x-6 d)+8 c^2 d x^2\right)\right)}{3 b^4 (x (b+c x))^{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*(b*B*x*(8*c^2*d*x^2 + 3*b^2*(d - e*x) - 2*b*c*x*(-6*d + e*x)) + A*(-16*c^3*d*x^3 - 6*b^2*c*x*(d - 2*e*x) + 8*b*c^2*x^2*(-3*d + e*x) + b^3*(d + 3*e*x))))/(3*b^4*(x*(b + c*x))^(3/2))","A",1
1210,1,72,70,0.0231053,"\int \frac{A+B x}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(b*x + c*x^2)^(5/2),x]","-\frac{2 \left(A \left(b^3-6 b^2 c x-24 b c^2 x^2-16 c^3 x^3\right)+b B x \left(3 b^2+12 b c x+8 c^2 x^2\right)\right)}{3 b^4 (x (b+c x))^{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*(b*B*x*(3*b^2 + 12*b*c*x + 8*c^2*x^2) + A*(b^3 - 6*b^2*c*x - 24*b*c^2*x^2 - 16*c^3*x^3)))/(3*b^4*(x*(b + c*x))^(3/2))","A",1
1211,1,277,287,0.7669725,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((d + e*x)*(b*x + c*x^2)^(5/2)),x]","\frac{2 \left(-\frac{3 c x^2 \left(3 b^2 e (B d-A e)-4 b c d (A e+B d)+8 A c^2 d^2\right)}{b^2 d (b e-c d)}+\frac{3 x^{3/2} (b+c x) \left(3 b^4 e^3 \sqrt{b+c x} (A e-B d) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)+c \sqrt{d} \sqrt{x} \sqrt{c d-b e} \left(3 b^3 e^2 (A e-B d)+2 b^2 c d e (A e+7 B d)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)\right)}{b^3 d^{3/2} (c d-b e)^{5/2}}+9 x \left(\frac{2 A c}{b}+\frac{A e}{d}-B\right)-3 A\right)}{9 b d (x (b+c x))^{3/2}}","-\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{2 \left(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)+c x \left(-3 b^3 e^2 (B d-A e)+2 b^2 c d e (A e+7 B d)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}-\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*(-3*A + 9*(-B + (2*A*c)/b + (A*e)/d)*x - (3*c*(8*A*c^2*d^2 + 3*b^2*e*(B*d - A*e) - 4*b*c*d*(B*d + A*e))*x^2)/(b^2*d*(-(c*d) + b*e)) + (3*x^(3/2)*(b + c*x)*(c*Sqrt[d]*Sqrt[c*d - b*e]*(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))*Sqrt[x] + 3*b^4*e^3*(-(B*d) + A*e)*Sqrt[b + c*x]*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])]))/(b^3*d^(3/2)*(c*d - b*e)^(5/2))))/(9*b*d*(x*(b + c*x))^(3/2))","A",1
1212,1,557,449,0.8277833,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)^(5/2)),x]","\frac{3 b^4 e^3 x^{3/2} (b+c x)^{3/2} (d+e x) (B d (3 b e-8 c d)-5 A e (b e-2 c d)) \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt{c d-b e}}{\sqrt{d} \sqrt{b+c x}}\right)+\sqrt{d} \sqrt{c d-b e} \left(A \left(b^6 e^3 \left(2 d^2-10 d e x-15 e^2 x^2\right)-6 b^5 c e^2 \left(d^3-3 d^2 e x+5 e^3 x^3\right)+3 b^4 c^2 e \left(2 d^4+2 d^3 e x+14 d^2 e^2 x^2+10 d e^3 x^3-5 e^4 x^4\right)-2 b^3 c^3 d \left(d^4+13 d^3 e x+3 d^2 e^2 x^2-19 d e^3 x^3-10 e^4 x^4\right)+12 b^2 c^4 d^2 x \left(d^3-7 d^2 e x-7 d e^2 x^2+e^3 x^3\right)-16 b c^5 d^3 x^2 \left(-3 d^2+d e x+4 e^2 x^2\right)+32 c^6 d^4 x^3 (d+e x)\right)+b B d x \left(3 b^5 e^3 (2 d+3 e x)-6 b^4 c e^2 \left(3 d^2+d e x-3 e^2 x^2\right)+3 b^3 c^2 e \left(6 d^3-6 d^2 e x-10 d e^2 x^2+3 e^3 x^3\right)-6 b^2 c^3 d \left(d^3-9 d^2 e x-7 d e^2 x^2+3 e^3 x^3\right)+8 b c^4 d^2 x \left(-3 d^2+2 d e x+5 e^2 x^2\right)-16 c^5 d^3 x^2 (d+e x)\right)\right)}{3 b^4 d^{7/2} (x (b+c x))^{3/2} (d+e x) (c d-b e)^{7/2}}","-\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{2 \left(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)+c x \left(b^3 \left(-e^2\right) (3 B d-5 A e)+2 b^2 c d e (8 B d-A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (d+e x) (c d-b e)^2}+\frac{e \sqrt{b x+c x^2} \left(3 b^4 e^3 (3 B d-5 A e)-2 b^3 c d e^2 (9 B d-10 A e)+4 b^2 c^2 d^2 e (3 A e+10 B d)-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{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,"(Sqrt[d]*Sqrt[c*d - b*e]*(b*B*d*x*(-16*c^5*d^3*x^2*(d + e*x) + 3*b^5*e^3*(2*d + 3*e*x) - 6*b^4*c*e^2*(3*d^2 + d*e*x - 3*e^2*x^2) + 8*b*c^4*d^2*x*(-3*d^2 + 2*d*e*x + 5*e^2*x^2) + 3*b^3*c^2*e*(6*d^3 - 6*d^2*e*x - 10*d*e^2*x^2 + 3*e^3*x^3) - 6*b^2*c^3*d*(d^3 - 9*d^2*e*x - 7*d*e^2*x^2 + 3*e^3*x^3)) + A*(32*c^6*d^4*x^3*(d + e*x) + b^6*e^3*(2*d^2 - 10*d*e*x - 15*e^2*x^2) - 16*b*c^5*d^3*x^2*(-3*d^2 + d*e*x + 4*e^2*x^2) + 12*b^2*c^4*d^2*x*(d^3 - 7*d^2*e*x - 7*d*e^2*x^2 + e^3*x^3) - 6*b^5*c*e^2*(d^3 - 3*d^2*e*x + 5*e^3*x^3) - 2*b^3*c^3*d*(d^4 + 13*d^3*e*x + 3*d^2*e^2*x^2 - 19*d*e^3*x^3 - 10*e^4*x^4) + 3*b^4*c^2*e*(2*d^4 + 2*d^3*e*x + 14*d^2*e^2*x^2 + 10*d*e^3*x^3 - 5*e^4*x^4))) + 3*b^4*e^3*(-5*A*e*(-2*c*d + b*e) + B*d*(-8*c*d + 3*b*e))*x^(3/2)*(b + c*x)^(3/2)*(d + e*x)*ArcTanh[(Sqrt[c*d - b*e]*Sqrt[x])/(Sqrt[d]*Sqrt[b + c*x])])/(3*b^4*d^(7/2)*(c*d - b*e)^(7/2)*(x*(b + c*x))^(3/2)*(d + e*x))","A",1
1213,1,113,126,0.1406278,"\int (A+B x) (d+e x)^{7/2} \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^(7/2)*(b*x + c*x^2),x]","\frac{2 (d+e x)^{9/2} \left(5 A e \left(13 b e (9 e x-2 d)+c \left(8 d^2-36 d e x+99 e^2 x^2\right)\right)+B \left(5 b e \left(8 d^2-36 d e x+99 e^2 x^2\right)+c \left(-16 d^3+72 d^2 e x-198 d e^2 x^2+429 e^3 x^3\right)\right)\right)}{6435 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 + e*x)^(9/2)*(5*A*e*(13*b*e*(-2*d + 9*e*x) + c*(8*d^2 - 36*d*e*x + 99*e^2*x^2)) + B*(5*b*e*(8*d^2 - 36*d*e*x + 99*e^2*x^2) + c*(-16*d^3 + 72*d^2*e*x - 198*d*e^2*x^2 + 429*e^3*x^3))))/(6435*e^4)","A",1
1214,1,113,126,0.1230611,"\int (A+B x) (d+e x)^{5/2} \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^(5/2)*(b*x + c*x^2),x]","\frac{2 (d+e x)^{7/2} \left(13 A e \left(11 b e (7 e x-2 d)+c \left(8 d^2-28 d e x+63 e^2 x^2\right)\right)+B \left(13 b e \left(8 d^2-28 d e x+63 e^2 x^2\right)+c \left(-48 d^3+168 d^2 e x-378 d e^2 x^2+693 e^3 x^3\right)\right)\right)}{9009 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 + e*x)^(7/2)*(13*A*e*(11*b*e*(-2*d + 7*e*x) + c*(8*d^2 - 28*d*e*x + 63*e^2*x^2)) + B*(13*b*e*(8*d^2 - 28*d*e*x + 63*e^2*x^2) + c*(-48*d^3 + 168*d^2*e*x - 378*d*e^2*x^2 + 693*e^3*x^3))))/(9009*e^4)","A",1
1215,1,114,126,0.1119431,"\int (A+B x) (d+e x)^{3/2} \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^(3/2)*(b*x + c*x^2),x]","\frac{2 (d+e x)^{5/2} \left(11 A e \left(9 b e (5 e x-2 d)+c \left(8 d^2-20 d e x+35 e^2 x^2\right)\right)+B \left(11 b e \left(8 d^2-20 d e x+35 e^2 x^2\right)-3 c \left(16 d^3-40 d^2 e x+70 d e^2 x^2-105 e^3 x^3\right)\right)\right)}{3465 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 + e*x)^(5/2)*(11*A*e*(9*b*e*(-2*d + 5*e*x) + c*(8*d^2 - 20*d*e*x + 35*e^2*x^2)) + B*(11*b*e*(8*d^2 - 20*d*e*x + 35*e^2*x^2) - 3*c*(16*d^3 - 40*d^2*e*x + 70*d*e^2*x^2 - 105*e^3*x^3))))/(3465*e^4)","A",1
1216,1,113,126,0.0987748,"\int (A+B x) \sqrt{d+e x} \left(b x+c x^2\right) \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*(b*x + c*x^2),x]","\frac{2 (d+e x)^{3/2} \left(3 A e \left(7 b e (3 e x-2 d)+c \left(8 d^2-12 d e x+15 e^2 x^2\right)\right)+B \left(3 b e \left(8 d^2-12 d e x+15 e^2 x^2\right)+c \left(-16 d^3+24 d^2 e x-30 d e^2 x^2+35 e^3 x^3\right)\right)\right)}{315 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 + e*x)^(3/2)*(3*A*e*(7*b*e*(-2*d + 3*e*x) + c*(8*d^2 - 12*d*e*x + 15*e^2*x^2)) + B*(3*b*e*(8*d^2 - 12*d*e*x + 15*e^2*x^2) + c*(-16*d^3 + 24*d^2*e*x - 30*d*e^2*x^2 + 35*e^3*x^3))))/(315*e^4)","A",1
1217,1,113,124,0.0862377,"\int \frac{(A+B x) \left(b x+c x^2\right)}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(7 A e \left(5 b e (e x-2 d)+c \left(8 d^2-4 d e x+3 e^2 x^2\right)\right)+B \left(7 b e \left(8 d^2-4 d e x+3 e^2 x^2\right)-3 c \left(16 d^3-8 d^2 e x+6 d e^2 x^2-5 e^3 x^3\right)\right)\right)}{105 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*Sqrt[d + e*x]*(7*A*e*(5*b*e*(-2*d + e*x) + c*(8*d^2 - 4*d*e*x + 3*e^2*x^2)) + B*(7*b*e*(8*d^2 - 4*d*e*x + 3*e^2*x^2) - 3*c*(16*d^3 - 8*d^2*e*x + 6*d*e^2*x^2 - 5*e^3*x^3))))/(105*e^4)","A",1
1218,1,110,122,0.0457249,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/(d + e*x)^(3/2),x]","\frac{2 \left(5 A e \left(3 b e (2 d+e x)+c \left(-8 d^2-4 d e x+e^2 x^2\right)\right)+B \left(5 b e \left(-8 d^2-4 d e x+e^2 x^2\right)+3 c \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)\right)\right)}{15 e^4 \sqrt{d+e 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}",1,"(2*(5*A*e*(3*b*e*(2*d + e*x) + c*(-8*d^2 - 4*d*e*x + e^2*x^2)) + B*(5*b*e*(-8*d^2 - 4*d*e*x + e^2*x^2) + 3*c*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3))))/(15*e^4*Sqrt[d + e*x])","A",1
1219,1,110,122,0.0463494,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/(d + e*x)^(5/2),x]","\frac{2 \left(A e \left(c \left(8 d^2+12 d e x+3 e^2 x^2\right)-b e (2 d+3 e x)\right)+B \left(b e \left(8 d^2+12 d e x+3 e^2 x^2\right)+c \left(-16 d^3-24 d^2 e x-6 d e^2 x^2+e^3 x^3\right)\right)\right)}{3 e^4 (d+e x)^{3/2}}","-\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*(A*e*(-(b*e*(2*d + 3*e*x)) + c*(8*d^2 + 12*d*e*x + 3*e^2*x^2)) + B*(b*e*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + c*(-16*d^3 - 24*d^2*e*x - 6*d*e^2*x^2 + e^3*x^3))))/(3*e^4*(d + e*x)^(3/2))","A",1
1220,1,111,122,0.0468365,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2))/(d + e*x)^(7/2),x]","-\frac{2 \left(A e \left(b e (2 d+5 e x)+c \left(8 d^2+20 d e x+15 e^2 x^2\right)\right)+B \left(b e \left(8 d^2+20 d e x+15 e^2 x^2\right)-3 c \left(16 d^3+40 d^2 e x+30 d e^2 x^2+5 e^3 x^3\right)\right)\right)}{15 e^4 (d+e x)^{5/2}}","\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*(A*e*(b*e*(2*d + 5*e*x) + c*(8*d^2 + 20*d*e*x + 15*e^2*x^2)) + B*(b*e*(8*d^2 + 20*d*e*x + 15*e^2*x^2) - 3*c*(16*d^3 + 40*d^2*e*x + 30*d*e^2*x^2 + 5*e^3*x^3))))/(15*e^4*(d + e*x)^(5/2))","A",1
1221,1,273,267,0.2318338,"\int (A+B x) (d+e x)^{7/2} \left(b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^(7/2)*(b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{9/2} \left(19 A e \left(85 b^2 e^2 \left(8 d^2-36 d e x+99 e^2 x^2\right)+34 b c e \left(-16 d^3+72 d^2 e x-198 d e^2 x^2+429 e^3 x^3\right)+c^2 \left(128 d^4-576 d^3 e x+1584 d^2 e^2 x^2-3432 d e^3 x^3+6435 e^4 x^4\right)\right)+B \left(323 b^2 e^2 \left(-16 d^3+72 d^2 e x-198 d e^2 x^2+429 e^3 x^3\right)+38 b c e \left(128 d^4-576 d^3 e x+1584 d^2 e^2 x^2-3432 d e^3 x^3+6435 e^4 x^4\right)-5 c^2 \left(256 d^5-1152 d^4 e x+3168 d^3 e^2 x^2-6864 d^2 e^3 x^3+12870 d e^4 x^4-21879 e^5 x^5\right)\right)\right)}{2078505 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 + e*x)^(9/2)*(19*A*e*(85*b^2*e^2*(8*d^2 - 36*d*e*x + 99*e^2*x^2) + 34*b*c*e*(-16*d^3 + 72*d^2*e*x - 198*d*e^2*x^2 + 429*e^3*x^3) + c^2*(128*d^4 - 576*d^3*e*x + 1584*d^2*e^2*x^2 - 3432*d*e^3*x^3 + 6435*e^4*x^4)) + B*(323*b^2*e^2*(-16*d^3 + 72*d^2*e*x - 198*d*e^2*x^2 + 429*e^3*x^3) + 38*b*c*e*(128*d^4 - 576*d^3*e*x + 1584*d^2*e^2*x^2 - 3432*d*e^3*x^3 + 6435*e^4*x^4) - 5*c^2*(256*d^5 - 1152*d^4*e*x + 3168*d^3*e^2*x^2 - 6864*d^2*e^3*x^3 + 12870*d*e^4*x^4 - 21879*e^5*x^5))))/(2078505*e^6)","A",1
1222,1,273,267,0.2039649,"\int (A+B x) (d+e x)^{5/2} \left(b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^(5/2)*(b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{7/2} \left(17 A e \left(65 b^2 e^2 \left(8 d^2-28 d e x+63 e^2 x^2\right)+30 b c e \left(-16 d^3+56 d^2 e x-126 d e^2 x^2+231 e^3 x^3\right)+c^2 \left(128 d^4-448 d^3 e x+1008 d^2 e^2 x^2-1848 d e^3 x^3+3003 e^4 x^4\right)\right)+B \left(255 b^2 e^2 \left(-16 d^3+56 d^2 e x-126 d e^2 x^2+231 e^3 x^3\right)+34 b c e \left(128 d^4-448 d^3 e x+1008 d^2 e^2 x^2-1848 d e^3 x^3+3003 e^4 x^4\right)-5 c^2 \left(256 d^5-896 d^4 e x+2016 d^3 e^2 x^2-3696 d^2 e^3 x^3+6006 d e^4 x^4-9009 e^5 x^5\right)\right)\right)}{765765 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 + e*x)^(7/2)*(17*A*e*(65*b^2*e^2*(8*d^2 - 28*d*e*x + 63*e^2*x^2) + 30*b*c*e*(-16*d^3 + 56*d^2*e*x - 126*d*e^2*x^2 + 231*e^3*x^3) + c^2*(128*d^4 - 448*d^3*e*x + 1008*d^2*e^2*x^2 - 1848*d*e^3*x^3 + 3003*e^4*x^4)) + B*(255*b^2*e^2*(-16*d^3 + 56*d^2*e*x - 126*d*e^2*x^2 + 231*e^3*x^3) + 34*b*c*e*(128*d^4 - 448*d^3*e*x + 1008*d^2*e^2*x^2 - 1848*d*e^3*x^3 + 3003*e^4*x^4) - 5*c^2*(256*d^5 - 896*d^4*e*x + 2016*d^3*e^2*x^2 - 3696*d^2*e^3*x^3 + 6006*d*e^4*x^4 - 9009*e^5*x^5))))/(765765*e^6)","A",1
1223,1,272,267,0.1947835,"\int (A+B x) (d+e x)^{3/2} \left(b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^(3/2)*(b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{5/2} \left(A e \left(143 b^2 e^2 \left(8 d^2-20 d e x+35 e^2 x^2\right)+78 b c e \left(-16 d^3+40 d^2 e x-70 d e^2 x^2+105 e^3 x^3\right)+3 c^2 \left(128 d^4-320 d^3 e x+560 d^2 e^2 x^2-840 d e^3 x^3+1155 e^4 x^4\right)\right)+B \left(39 b^2 e^2 \left(-16 d^3+40 d^2 e x-70 d e^2 x^2+105 e^3 x^3\right)+6 b c e \left(128 d^4-320 d^3 e x+560 d^2 e^2 x^2-840 d e^3 x^3+1155 e^4 x^4\right)+c^2 \left(-256 d^5+640 d^4 e x-1120 d^3 e^2 x^2+1680 d^2 e^3 x^3-2310 d e^4 x^4+3003 e^5 x^5\right)\right)\right)}{45045 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 + e*x)^(5/2)*(A*e*(143*b^2*e^2*(8*d^2 - 20*d*e*x + 35*e^2*x^2) + 78*b*c*e*(-16*d^3 + 40*d^2*e*x - 70*d*e^2*x^2 + 105*e^3*x^3) + 3*c^2*(128*d^4 - 320*d^3*e*x + 560*d^2*e^2*x^2 - 840*d*e^3*x^3 + 1155*e^4*x^4)) + B*(39*b^2*e^2*(-16*d^3 + 40*d^2*e*x - 70*d*e^2*x^2 + 105*e^3*x^3) + 6*b*c*e*(128*d^4 - 320*d^3*e*x + 560*d^2*e^2*x^2 - 840*d*e^3*x^3 + 1155*e^4*x^4) + c^2*(-256*d^5 + 640*d^4*e*x - 1120*d^3*e^2*x^2 + 1680*d^2*e^3*x^3 - 2310*d*e^4*x^4 + 3003*e^5*x^5))))/(45045*e^6)","A",1
1224,1,273,267,0.1827322,"\int (A+B x) \sqrt{d+e x} \left(b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*(b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{3/2} \left(13 A e \left(33 b^2 e^2 \left(8 d^2-12 d e x+15 e^2 x^2\right)+22 b c e \left(-16 d^3+24 d^2 e x-30 d e^2 x^2+35 e^3 x^3\right)+c^2 \left(128 d^4-192 d^3 e x+240 d^2 e^2 x^2-280 d e^3 x^3+315 e^4 x^4\right)\right)+B \left(143 b^2 e^2 \left(-16 d^3+24 d^2 e x-30 d e^2 x^2+35 e^3 x^3\right)+26 b c e \left(128 d^4-192 d^3 e x+240 d^2 e^2 x^2-280 d e^3 x^3+315 e^4 x^4\right)-5 c^2 \left(256 d^5-384 d^4 e x+480 d^3 e^2 x^2-560 d^2 e^3 x^3+630 d e^4 x^4-693 e^5 x^5\right)\right)\right)}{45045 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 + e*x)^(3/2)*(13*A*e*(33*b^2*e^2*(8*d^2 - 12*d*e*x + 15*e^2*x^2) + 22*b*c*e*(-16*d^3 + 24*d^2*e*x - 30*d*e^2*x^2 + 35*e^3*x^3) + c^2*(128*d^4 - 192*d^3*e*x + 240*d^2*e^2*x^2 - 280*d*e^3*x^3 + 315*e^4*x^4)) + B*(143*b^2*e^2*(-16*d^3 + 24*d^2*e*x - 30*d*e^2*x^2 + 35*e^3*x^3) + 26*b*c*e*(128*d^4 - 192*d^3*e*x + 240*d^2*e^2*x^2 - 280*d*e^3*x^3 + 315*e^4*x^4) - 5*c^2*(256*d^5 - 384*d^4*e*x + 480*d^3*e^2*x^2 - 560*d^2*e^3*x^3 + 630*d*e^4*x^4 - 693*e^5*x^5))))/(45045*e^6)","A",1
1225,1,273,265,0.202955,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(11 A e \left(21 b^2 e^2 \left(8 d^2-4 d e x+3 e^2 x^2\right)+18 b c e \left(-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right)+c^2 \left(128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right)\right)+B \left(99 b^2 e^2 \left(-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right)+22 b c e \left(128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right)-5 c^2 \left(256 d^5-128 d^4 e x+96 d^3 e^2 x^2-80 d^2 e^3 x^3+70 d e^4 x^4-63 e^5 x^5\right)\right)\right)}{3465 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*Sqrt[d + e*x]*(11*A*e*(21*b^2*e^2*(8*d^2 - 4*d*e*x + 3*e^2*x^2) + 18*b*c*e*(-16*d^3 + 8*d^2*e*x - 6*d*e^2*x^2 + 5*e^3*x^3) + c^2*(128*d^4 - 64*d^3*e*x + 48*d^2*e^2*x^2 - 40*d*e^3*x^3 + 35*e^4*x^4)) + B*(99*b^2*e^2*(-16*d^3 + 8*d^2*e*x - 6*d*e^2*x^2 + 5*e^3*x^3) + 22*b*c*e*(128*d^4 - 64*d^3*e*x + 48*d^2*e^2*x^2 - 40*d*e^3*x^3 + 35*e^4*x^4) - 5*c^2*(256*d^5 - 128*d^4*e*x + 96*d^3*e^2*x^2 - 80*d^2*e^3*x^3 + 70*d*e^4*x^4 - 63*e^5*x^5))))/(3465*e^6)","A",1
1226,1,273,263,0.1726727,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^(3/2),x]","\frac{2 B \left(63 b^2 e^2 \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)+18 b c e \left(-128 d^4-64 d^3 e x+16 d^2 e^2 x^2-8 d e^3 x^3+5 e^4 x^4\right)+5 c^2 \left(256 d^5+128 d^4 e x-32 d^3 e^2 x^2+16 d^2 e^3 x^3-10 d e^4 x^4+7 e^5 x^5\right)\right)-6 A e \left(35 b^2 e^2 \left(8 d^2+4 d e x-e^2 x^2\right)-42 b c e \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)+3 c^2 \left(128 d^4+64 d^3 e x-16 d^2 e^2 x^2+8 d e^3 x^3-5 e^4 x^4\right)\right)}{315 e^6 \sqrt{d+e 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}",1,"(-6*A*e*(35*b^2*e^2*(8*d^2 + 4*d*e*x - e^2*x^2) - 42*b*c*e*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) + 3*c^2*(128*d^4 + 64*d^3*e*x - 16*d^2*e^2*x^2 + 8*d*e^3*x^3 - 5*e^4*x^4)) + 2*B*(63*b^2*e^2*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) + 18*b*c*e*(-128*d^4 - 64*d^3*e*x + 16*d^2*e^2*x^2 - 8*d*e^3*x^3 + 5*e^4*x^4) + 5*c^2*(256*d^5 + 128*d^4*e*x - 32*d^3*e^2*x^2 + 16*d^2*e^3*x^3 - 10*d*e^4*x^4 + 7*e^5*x^5)))/(315*e^6*Sqrt[d + e*x])","A",1
1227,1,271,263,0.1607414,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^(5/2),x]","\frac{2 \left(7 A e \left(5 b^2 e^2 \left(8 d^2+12 d e x+3 e^2 x^2\right)+10 b c e \left(-16 d^3-24 d^2 e x-6 d e^2 x^2+e^3 x^3\right)+c^2 \left(128 d^4+192 d^3 e x+48 d^2 e^2 x^2-8 d e^3 x^3+3 e^4 x^4\right)\right)+B \left(35 b^2 e^2 \left(-16 d^3-24 d^2 e x-6 d e^2 x^2+e^3 x^3\right)+14 b c e \left(128 d^4+192 d^3 e x+48 d^2 e^2 x^2-8 d e^3 x^3+3 e^4 x^4\right)-5 c^2 \left(256 d^5+384 d^4 e x+96 d^3 e^2 x^2-16 d^2 e^3 x^3+6 d e^4 x^4-3 e^5 x^5\right)\right)\right)}{105 e^6 (d+e x)^{3/2}}","-\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*(7*A*e*(5*b^2*e^2*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + 10*b*c*e*(-16*d^3 - 24*d^2*e*x - 6*d*e^2*x^2 + e^3*x^3) + c^2*(128*d^4 + 192*d^3*e*x + 48*d^2*e^2*x^2 - 8*d*e^3*x^3 + 3*e^4*x^4)) + B*(35*b^2*e^2*(-16*d^3 - 24*d^2*e*x - 6*d*e^2*x^2 + e^3*x^3) + 14*b*c*e*(128*d^4 + 192*d^3*e*x + 48*d^2*e^2*x^2 - 8*d*e^3*x^3 + 3*e^4*x^4) - 5*c^2*(256*d^5 + 384*d^4*e*x + 96*d^3*e^2*x^2 - 16*d^2*e^3*x^3 + 6*d*e^4*x^4 - 3*e^5*x^5))))/(105*e^6*(d + e*x)^(3/2))","A",1
1228,1,272,263,0.1539074,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^(7/2),x]","\frac{2 \left(A e \left(-b^2 e^2 \left(8 d^2+20 d e x+15 e^2 x^2\right)+6 b c e \left(16 d^3+40 d^2 e x+30 d e^2 x^2+5 e^3 x^3\right)-\left(c^2 \left(128 d^4+320 d^3 e x+240 d^2 e^2 x^2+40 d e^3 x^3-5 e^4 x^4\right)\right)\right)+B \left(3 b^2 e^2 \left(16 d^3+40 d^2 e x+30 d e^2 x^2+5 e^3 x^3\right)-2 b c e \left(128 d^4+320 d^3 e x+240 d^2 e^2 x^2+40 d e^3 x^3-5 e^4 x^4\right)+c^2 \left(256 d^5+640 d^4 e x+480 d^3 e^2 x^2+80 d^2 e^3 x^3-10 d e^4 x^4+3 e^5 x^5\right)\right)\right)}{15 e^6 (d+e x)^{5/2}}","-\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*(A*e*(-(b^2*e^2*(8*d^2 + 20*d*e*x + 15*e^2*x^2)) + 6*b*c*e*(16*d^3 + 40*d^2*e*x + 30*d*e^2*x^2 + 5*e^3*x^3) - c^2*(128*d^4 + 320*d^3*e*x + 240*d^2*e^2*x^2 + 40*d*e^3*x^3 - 5*e^4*x^4)) + B*(3*b^2*e^2*(16*d^3 + 40*d^2*e*x + 30*d*e^2*x^2 + 5*e^3*x^3) - 2*b*c*e*(128*d^4 + 320*d^3*e*x + 240*d^2*e^2*x^2 + 40*d*e^3*x^3 - 5*e^4*x^4) + c^2*(256*d^5 + 640*d^4*e*x + 480*d^3*e^2*x^2 + 80*d^2*e^3*x^3 - 10*d*e^4*x^4 + 3*e^5*x^5))))/(15*e^6*(d + e*x)^(5/2))","A",1
1229,1,212,228,0.5008314,"\int \frac{(A+B x) (d+e x)^{7/2}}{b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2),x]","\frac{2 \left(\frac{(b B-A c) \left(7 (c d-b e) \left(5 (c d-b e) \left(\sqrt{c} \sqrt{d+e x} (-3 b e+4 c d+c e x)-3 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)+3 c^{5/2} (d+e x)^{5/2}\right)+15 c^{7/2} (d+e x)^{7/2}\right)}{c^{9/2}}-105 A d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)+A \sqrt{d+e x} \left(176 d^3+122 d^2 e x+66 d e^2 x^2+15 e^3 x^3\right)\right)}{105 b}","\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 (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 (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 (d+e x)^{5/2} (A c e-b B e+B c d)}{5 c^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*(A*Sqrt[d + e*x]*(176*d^3 + 122*d^2*e*x + 66*d*e^2*x^2 + 15*e^3*x^3) - 105*A*d^(7/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + ((b*B - A*c)*(15*c^(7/2)*(d + e*x)^(7/2) + 7*(c*d - b*e)*(3*c^(5/2)*(d + e*x)^(5/2) + 5*(c*d - b*e)*(Sqrt[c]*Sqrt[d + e*x]*(4*c*d - 3*b*e + c*e*x) - 3*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]]))))/c^(9/2)))/(105*b)","A",1
1230,1,174,173,0.2274415,"\int \frac{(A+B x) (d+e x)^{5/2}}{b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2),x]","\frac{2 \left(\frac{(b B-A c) \left(5 (c d-b e) \left(\sqrt{c} \sqrt{d+e x} (-3 b e+4 c d+c e x)-3 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)+3 c^{5/2} (d+e x)^{5/2}\right)}{c^{7/2}}-15 A d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)+A \sqrt{d+e x} \left(23 d^2+11 d e x+3 e^2 x^2\right)\right)}{15 b}","-\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 \sqrt{d+e x} \left(A c e (2 c d-b e)+B (c d-b e)^2\right)}{c^3}+\frac{2 (d+e x)^{3/2} (A c e-b B e+B c d)}{3 c^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*(A*Sqrt[d + e*x]*(23*d^2 + 11*d*e*x + 3*e^2*x^2) - 15*A*d^(5/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + ((b*B - A*c)*(3*c^(5/2)*(d + e*x)^(5/2) + 5*(c*d - b*e)*(Sqrt[c]*Sqrt[d + e*x]*(4*c*d - 3*b*e + c*e*x) - 3*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])))/c^(7/2)))/(15*b)","A",1
1231,1,123,131,0.1468933,"\int \frac{(A+B x) (d+e x)^{3/2}}{b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2),x]","\frac{2 (A c-b B) (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 \sqrt{d+e x} (3 A c e+B (-3 b e+4 c d+c e x))}{3 c^2}-\frac{2 A d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}","-\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 \sqrt{d+e x} (A c e-b B e+B c d)}{c^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*Sqrt[d + e*x]*(3*A*c*e + B*(4*c*d - 3*b*e + c*e*x)))/(3*c^2) - (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",1
1232,1,101,101,0.1139192,"\int \frac{(A+B x) \sqrt{d+e x}}{b x+c x^2} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2),x]","\frac{2 (A c-b B) \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",1
1233,1,84,86,0.150145,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)),x]","\frac{2 \left(\frac{(A c-b B) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{\sqrt{c} \sqrt{c d-b e}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{\sqrt{d}}\right)}{b}","-\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]])/Sqrt[d]) + ((-(b*B) + A*c)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(Sqrt[c]*Sqrt[c*d - b*e])))/b","A",1
1234,1,89,118,0.029651,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)),x]","\frac{2 \left(d (b B-A c) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{c (d+e x)}{c d-b e}\right)+A (c d-b e) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{e x}{d}+1\right)\right)}{b d \sqrt{d+e x} (c d-b e)}","\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*B - A*c)*d*Hypergeometric2F1[-1/2, 1, 1/2, (c*(d + e*x))/(c*d - b*e)] + A*(c*d - b*e)*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (e*x)/d]))/(b*d*(c*d - b*e)*Sqrt[d + e*x])","C",1
1235,1,91,164,0.0308163,"\int \frac{A+B x}{(d+e x)^{5/2} \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*(b*x + c*x^2)),x]","\frac{2 \left(d (b B-A c) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{c (d+e x)}{c d-b e}\right)+A (c d-b e) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{e x}{d}+1\right)\right)}{3 b d (d+e x)^{3/2} (c d-b e)}","-\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*B - A*c)*d*Hypergeometric2F1[-3/2, 1, -1/2, (c*(d + e*x))/(c*d - b*e)] + A*(c*d - b*e)*Hypergeometric2F1[-3/2, 1, -1/2, 1 + (e*x)/d]))/(3*b*d*(c*d - b*e)*(d + e*x)^(3/2))","C",1
1236,1,91,225,0.0340981,"\int \frac{A+B x}{(d+e x)^{7/2} \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^(7/2)*(b*x + c*x^2)),x]","\frac{2 \left(d (b B-A c) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{c (d+e x)}{c d-b e}\right)+A (c d-b e) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{e x}{d}+1\right)\right)}{5 b d (d+e x)^{5/2} (c d-b e)}","\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*B - A*c)*d*Hypergeometric2F1[-5/2, 1, -3/2, (c*(d + e*x))/(c*d - b*e)] + A*(c*d - b*e)*Hypergeometric2F1[-5/2, 1, -3/2, 1 + (e*x)/d]))/(5*b*d*(c*d - b*e)*(d + e*x)^(5/2))","C",1
1237,1,91,301,0.03869,"\int \frac{A+B x}{(d+e x)^{9/2} \left(b x+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^(9/2)*(b*x + c*x^2)),x]","\frac{2 \left(d (b B-A c) \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};\frac{c (d+e x)}{c d-b e}\right)+A (c d-b e) \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};\frac{e x}{d}+1\right)\right)}{7 b d (d+e x)^{7/2} (c d-b e)}","\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 \left(B c^3 d^4-A e \left(-b^3 e^3+4 b^2 c d e^2-6 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 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*B - A*c)*d*Hypergeometric2F1[-7/2, 1, -5/2, (c*(d + e*x))/(c*d - b*e)] + A*(c*d - b*e)*Hypergeometric2F1[-7/2, 1, -5/2, 1 + (e*x)/d]))/(7*b*d*(c*d - b*e)*(d + e*x)^(7/2))","C",1
1238,1,376,386,2.3627006,"\int \frac{(A+B x) (d+e x)^{9/2}}{\left(b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(9/2))/(b*x + c*x^2)^2,x]","-\frac{-\frac{315 \left(\frac{2}{315} \sqrt{d+e x} \left(563 d^4+506 d^3 e x+408 d^2 e^2 x^2+185 d e^3 x^3+35 e^4 x^4\right)-2 d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\right) (9 A b e-4 A c d+2 b B d)-\frac{2 d \left(b c (2 B d-5 A e)-4 A c^2 d+7 b^2 B e\right) \left(3 (c d-b e) \left(7 (c d-b e) \left(5 (c d-b e) \left(\sqrt{c} \sqrt{d+e x} (-3 b e+4 c d+c e x)-3 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)+3 c^{5/2} (d+e x)^{5/2}\right)+15 c^{7/2} (d+e x)^{7/2}\right)+35 c^{9/2} (d+e x)^{9/2}\right)}{c^{9/2} (c d-b e)}}{630 b^2}+\frac{c (d+e x)^{11/2} (A b e-2 A c d+b B d)}{b (b+c x) (b e-c d)}+\frac{A (d+e x)^{11/2}}{x (b+c x)}}{b d}","-\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{(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{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^3 c e^2 (5 A e+19 B d)+b^2 c^2 d e (11 A e+15 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}",1,"-(((c*(b*B*d - 2*A*c*d + A*b*e)*(d + e*x)^(11/2))/(b*(-(c*d) + b*e)*(b + c*x)) + (A*(d + e*x)^(11/2))/(x*(b + c*x)) - (315*(2*b*B*d - 4*A*c*d + 9*A*b*e)*((2*Sqrt[d + e*x]*(563*d^4 + 506*d^3*e*x + 408*d^2*e^2*x^2 + 185*d*e^3*x^3 + 35*e^4*x^4))/315 - 2*d^(9/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) - (2*d*(-4*A*c^2*d + 7*b^2*B*e + b*c*(2*B*d - 5*A*e))*(35*c^(9/2)*(d + e*x)^(9/2) + 3*(c*d - b*e)*(15*c^(7/2)*(d + e*x)^(7/2) + 7*(c*d - b*e)*(3*c^(5/2)*(d + e*x)^(5/2) + 5*(c*d - b*e)*(Sqrt[c]*Sqrt[d + e*x]*(4*c*d - 3*b*e + c*e*x) - 3*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])))))/(c^(9/2)*(c*d - b*e)))/(630*b^2))/(b*d))","A",1
1239,1,341,292,1.5467244,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2)^2,x]","-\frac{-\frac{105 \left(-2 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)+\frac{2}{15} d \sqrt{d+e x} \left(23 d^2+11 d e x+3 e^2 x^2\right)+\frac{2}{7} (d+e x)^{7/2}\right) (7 A b e-4 A c d+2 b B d)-\frac{2 d \left(b c (2 B d-3 A e)-4 A c^2 d+5 b^2 B e\right) \left(7 (c d-b e) \left(5 (c d-b e) \left(\sqrt{c} \sqrt{d+e x} (-3 b e+4 c d+c e x)-3 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)+3 c^{5/2} (d+e x)^{5/2}\right)+15 c^{7/2} (d+e x)^{7/2}\right)}{c^{7/2} (c d-b e)}}{210 b^2}+\frac{c (d+e x)^{9/2} (A b e-2 A c d+b B d)}{b (b+c x) (b e-c d)}+\frac{A (d+e x)^{9/2}}{x (b+c x)}}{b d}","-\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{(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{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}",1,"-(((c*(b*B*d - 2*A*c*d + A*b*e)*(d + e*x)^(9/2))/(b*(-(c*d) + b*e)*(b + c*x)) + (A*(d + e*x)^(9/2))/(x*(b + c*x)) - (105*(2*b*B*d - 4*A*c*d + 7*A*b*e)*((2*(d + e*x)^(7/2))/7 + (2*d*Sqrt[d + e*x]*(23*d^2 + 11*d*e*x + 3*e^2*x^2))/15 - 2*d^(7/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) - (2*d*(-4*A*c^2*d + 5*b^2*B*e + b*c*(2*B*d - 3*A*e))*(15*c^(7/2)*(d + e*x)^(7/2) + 7*(c*d - b*e)*(3*c^(5/2)*(d + e*x)^(5/2) + 5*(c*d - b*e)*(Sqrt[c]*Sqrt[d + e*x]*(4*c*d - 3*b*e + c*e*x) - 3*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]]))))/(c^(7/2)*(c*d - b*e)))/(210*b^2))/(b*d))","A",1
1240,1,302,225,1.2258473,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2)^2,x]","-\frac{\frac{\frac{2 d \left(b c (2 B d-A e)-4 A c^2 d+3 b^2 B e\right) \left(\sqrt{c} \sqrt{d+e x} \left(15 b^2 e^2-5 b c e (7 d+e x)+c^2 \left(23 d^2+11 d e x+3 e^2 x^2\right)\right)-15 (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)}{c^{5/2} (c d-b e)}+2 \left(15 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)-\sqrt{d+e x} \left(23 d^2+11 d e x+3 e^2 x^2\right)\right) (5 A b e-4 A c d+2 b B d)}{30 b^2}+\frac{c (d+e x)^{7/2} (A b e-2 A c d+b B d)}{b (b+c x) (b e-c d)}+\frac{A (d+e x)^{7/2}}{x (b+c x)}}{b d}","-\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}}",1,"-(((c*(b*B*d - 2*A*c*d + A*b*e)*(d + e*x)^(7/2))/(b*(-(c*d) + b*e)*(b + c*x)) + (A*(d + e*x)^(7/2))/(x*(b + c*x)) + (2*(2*b*B*d - 4*A*c*d + 5*A*b*e)*(-(Sqrt[d + e*x]*(23*d^2 + 11*d*e*x + 3*e^2*x^2)) + 15*d^(5/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) + (2*d*(-4*A*c^2*d + 3*b^2*B*e + b*c*(2*B*d - A*e))*(Sqrt[c]*Sqrt[d + e*x]*(15*b^2*e^2 - 5*b*c*e*(7*d + e*x) + c^2*(23*d^2 + 11*d*e*x + 3*e^2*x^2)) - 15*(c*d - b*e)^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]]))/(c^(5/2)*(c*d - b*e)))/(30*b^2))/(b*d))","A",1
1241,1,171,181,0.3308375,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2)^2,x]","\frac{-\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)}{c^{3/2}}+\frac{b \sqrt{d+e x} (A c (-b d+b e x-2 c d x)+b B x (c d-b e))}{c x (b+c x)}+\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} \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}}",1,"((b*Sqrt[d + e*x]*(b*B*(c*d - b*e)*x + A*c*(-(b*d) - 2*c*d*x + b*e*x)))/(c*x*(b + c*x)) + Sqrt[d]*(-2*b*B*d + 4*A*c*d - 3*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] - (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]])/c^(3/2))/b^3","A",1
1242,1,232,158,0.5480596,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2)^2,x]","\frac{\frac{\frac{d \left(-b c (3 A e+2 B d)+4 A c^2 d+b^2 B e\right) \left(\sqrt{c} \sqrt{d+e x}-\sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)}{\sqrt{c} (c d-b e)}+\left(\sqrt{d+e x}-\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\right) (A b e-4 A c d+2 b B d)}{b^2}-\frac{c (d+e x)^{3/2} (A b e-2 A c d+b B d)}{b (b+c x) (b e-c d)}-\frac{A (d+e x)^{3/2}}{x (b+c x)}}{b d}","-\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{\sqrt{d+e x} (A b-x (b B-2 A c))}{b^2 \left(b x+c x^2\right)}+\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}}",1,"(-((c*(b*B*d - 2*A*c*d + A*b*e)*(d + e*x)^(3/2))/(b*(-(c*d) + b*e)*(b + c*x))) - (A*(d + e*x)^(3/2))/(x*(b + c*x)) + ((2*b*B*d - 4*A*c*d + A*b*e)*(Sqrt[d + e*x] - Sqrt[d]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) + (d*(4*A*c^2*d + b^2*B*e - b*c*(2*B*d + 3*A*e))*(Sqrt[c]*Sqrt[d + e*x] - Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]]))/(Sqrt[c]*(c*d - b*e)))/b^2)/(b*d)","A",1
1243,1,231,188,0.4298335,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)^2),x]","\frac{-\frac{2 \sqrt{c} d \left(-b c (5 A e+2 B d)+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^2 (c d-b e)^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (-A b e-4 A c d+2 b B d)}{b^2 \sqrt{d}}+\frac{c \sqrt{d+e x} (A b e+4 A c d-2 b B d)}{b (b+c x) (b e-c d)}+\frac{3 A c e \sqrt{d+e x}}{(b+c x) (c d-b e)}-\frac{2 A \sqrt{d+e x}}{x (b+c x)}}{2 b d}","-\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}}",1,"((3*A*c*e*Sqrt[d + e*x])/((c*d - b*e)*(b + c*x)) + (c*(-2*b*B*d + 4*A*c*d + A*b*e)*Sqrt[d + e*x])/(b*(-(c*d) + b*e)*(b + c*x)) - (2*A*Sqrt[d + e*x])/(x*(b + c*x)) - (2*(2*b*B*d - 4*A*c*d - A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^2*Sqrt[d]) - (2*Sqrt[c]*d*(4*A*c^2*d + 3*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^2*(c*d - b*e)^(3/2)))/(2*b*d)","A",1
1244,1,191,254,0.1756571,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)^2),x]","\frac{-x (b+c x) \left(c d^2 \left(b c (7 A e+2 B d)-4 A c^2 d-5 b^2 B e\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{c (d+e x)}{c d-b e}\right)+(c d-b e)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{e x}{d}+1\right) (3 A b e+4 A c d-2 b B d)\right)-A b^2 d (c d-b e)^2-b c d x (b e-c d) (A b e-2 A c d+b B d)}{b^3 d^2 x (b+c x) \sqrt{d+e x} (c d-b e)^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{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 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{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}}",1,"(-(A*b^2*d*(c*d - b*e)^2) - b*c*d*(-(c*d) + b*e)*(b*B*d - 2*A*c*d + A*b*e)*x - x*(b + c*x)*(c*d^2*(-4*A*c^2*d - 5*b^2*B*e + b*c*(2*B*d + 7*A*e))*Hypergeometric2F1[-1/2, 1, 1/2, (c*(d + e*x))/(c*d - b*e)] + (c*d - b*e)^2*(-2*b*B*d + 4*A*c*d + 3*A*b*e)*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (e*x)/d]))/(b^3*d^2*(c*d - b*e)^2*x*(b + c*x)*Sqrt[d + e*x])","C",1
1245,1,194,344,0.1929807,"\int \frac{A+B x}{(d+e x)^{5/2} \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*(b*x + c*x^2)^2),x]","\frac{-x (b+c x) \left(c d^2 \left(b c (9 A e+2 B d)-4 A c^2 d-7 b^2 B e\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{c (d+e x)}{c d-b e}\right)+(c d-b e)^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{e x}{d}+1\right) (5 A b e+4 A c d-2 b B d)\right)-3 A b^2 d (c d-b e)^2-3 b c d x (b e-c d) (A b e-2 A c d+b B d)}{3 b^3 d^2 x (b+c x) (d+e x)^{3/2} (c d-b e)^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{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 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{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{e \left(b^3 e^2 (2 B d-5 A e)-b^2 c d e (6 B d-11 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}",1,"(-3*A*b^2*d*(c*d - b*e)^2 - 3*b*c*d*(-(c*d) + b*e)*(b*B*d - 2*A*c*d + A*b*e)*x - x*(b + c*x)*(c*d^2*(-4*A*c^2*d - 7*b^2*B*e + b*c*(2*B*d + 9*A*e))*Hypergeometric2F1[-3/2, 1, -1/2, (c*(d + e*x))/(c*d - b*e)] + (c*d - b*e)^2*(-2*b*B*d + 4*A*c*d + 5*A*b*e)*Hypergeometric2F1[-3/2, 1, -1/2, 1 + (e*x)/d]))/(3*b^3*d^2*(c*d - b*e)^2*x*(b + c*x)*(d + e*x)^(3/2))","C",1
1246,1,194,457,0.1983712,"\int \frac{A+B x}{(d+e x)^{7/2} \left(b x+c x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^(7/2)*(b*x + c*x^2)^2),x]","\frac{-x (b+c x) \left(c d^2 \left(b c (11 A e+2 B d)-4 A c^2 d-9 b^2 B e\right) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{c (d+e x)}{c d-b e}\right)+(c d-b e)^2 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{e x}{d}+1\right) (7 A b e+4 A c d-2 b B d)\right)-5 A b^2 d (c d-b e)^2-5 b c d x (b e-c d) (A b e-2 A c d+b B d)}{5 b^3 d^2 x (b+c x) (d+e x)^{5/2} (c d-b e)^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{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 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{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{e \left(b^3 e^2 (2 B d-7 A e)-b^2 c d e (6 B d-17 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^4 \left(-e^3\right) (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-2 b^2 c^2 d^2 e (6 B d-13 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}",1,"(-5*A*b^2*d*(c*d - b*e)^2 - 5*b*c*d*(-(c*d) + b*e)*(b*B*d - 2*A*c*d + A*b*e)*x - x*(b + c*x)*(c*d^2*(-4*A*c^2*d - 9*b^2*B*e + b*c*(2*B*d + 11*A*e))*Hypergeometric2F1[-5/2, 1, -3/2, (c*(d + e*x))/(c*d - b*e)] + (c*d - b*e)^2*(-2*b*B*d + 4*A*c*d + 7*A*b*e)*Hypergeometric2F1[-5/2, 1, -3/2, 1 + (e*x)/d]))/(5*b^3*d^2*(c*d - b*e)^2*x*(b + c*x)*(d + e*x)^(5/2))","C",1
1247,1,589,461,5.2227327,"\int \frac{(A+B x) (d+e x)^{9/2}}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(9/2))/(b*x + c*x^2)^3,x]","\frac{\frac{630 c (d+e x)^{11/2} \left(b^2 (-e) (7 A e+4 B d)+b c d (17 A e+6 B d)-12 A c^2 d^2\right)}{b^2 d (b e-c d)}+\frac{(b+c x) \left((b+c x) \left(945 c^{11/2} (c d-b e)^2 \left(\frac{2}{315} \sqrt{d+e x} \left(563 d^4+506 d^3 e x+408 d^2 e^2 x^2+185 d e^3 x^3+35 e^4 x^4\right)-2 d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\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)-6 c^2 d^2 \left(b^2 c e (A e-8 B d)+4 b c^2 d (A e-2 B d)+16 A c^3 d^2-5 b^3 B e^2\right) \left(3 (c d-b e) \left(7 (c d-b e) \left(5 (c d-b e) \left(\sqrt{c} \sqrt{d+e x} (-3 b e+4 c d+c e x)-3 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)+3 c^{5/2} (d+e x)^{5/2}\right)+15 c^{7/2} (d+e x)^{7/2}\right)+35 c^{9/2} (d+e x)^{9/2}\right)\right)-630 b c^{13/2} (d+e x)^{11/2} \left(b^3 e^2 (7 A e+4 B d)-b^2 c d e (26 A e+9 B d)+12 b c^2 d^2 (3 A e+B d)-24 A c^3 d^3\right)\right)}{b^4 c^{11/2} d (c d-b e)^2}-\frac{630 (d+e x)^{11/2} (7 A b e-8 A c d+4 b B d)}{b d x}-\frac{1260 A (d+e x)^{11/2}}{x^2}}{2520 b d (b+c x)^2}","-\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{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{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{(d+e x)^{3/2} \left(b c d^2 \left(-b c (13 A e+6 B d)+12 A c^2 d+2 b^2 B e\right)+x \left(b^3 c e^2 (A e+4 B d)+b^2 c^2 d e (10 A e+9 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)\right)}{4 b^4 c^2 \left(b x+c x^2\right)}-\frac{3 e \sqrt{d+e x} \left(b^3 c e^2 (A e+2 B d)+b^2 c^2 d e (2 A e+3 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}",1,"((630*c*(-12*A*c^2*d^2 - b^2*e*(4*B*d + 7*A*e) + b*c*d*(6*B*d + 17*A*e))*(d + e*x)^(11/2))/(b^2*d*(-(c*d) + b*e)) - (1260*A*(d + e*x)^(11/2))/x^2 - (630*(4*b*B*d - 8*A*c*d + 7*A*b*e)*(d + e*x)^(11/2))/(b*d*x) + ((b + c*x)*(-630*b*c^(13/2)*(-24*A*c^3*d^3 + 12*b*c^2*d^2*(B*d + 3*A*e) + b^3*e^2*(4*B*d + 7*A*e) - b^2*c*d*e*(9*B*d + 26*A*e))*(d + e*x)^(11/2) + (b + c*x)*(945*c^(11/2)*(c*d - b*e)^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))*((2*Sqrt[d + e*x]*(563*d^4 + 506*d^3*e*x + 408*d^2*e^2*x^2 + 185*d*e^3*x^3 + 35*e^4*x^4))/315 - 2*d^(9/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) - 6*c^2*d^2*(16*A*c^3*d^2 - 5*b^3*B*e^2 + b^2*c*e*(-8*B*d + A*e) + 4*b*c^2*d*(-2*B*d + A*e))*(35*c^(9/2)*(d + e*x)^(9/2) + 3*(c*d - b*e)*(15*c^(7/2)*(d + e*x)^(7/2) + 7*(c*d - b*e)*(3*c^(5/2)*(d + e*x)^(5/2) + 5*(c*d - b*e)*(Sqrt[c]*Sqrt[d + e*x]*(4*c*d - 3*b*e + c*e*x) - 3*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])))))))/(b^4*c^(11/2)*d*(c*d - b*e)^2))/(2520*b*d*(b + c*x)^2)","A",1
1248,1,554,363,4.0509442,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2)^3,x]","\frac{-\frac{210 c (d+e x)^{9/2} \left(b^2 e (5 A e+4 B d)-3 b c d (5 A e+2 B d)+12 A c^2 d^2\right)}{b^2 d (b e-c d)}+\frac{(b+c x) \left((b+c x) \left(105 c^{9/2} (c d-b e)^2 \left(-2 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)+\frac{2}{15} d \sqrt{d+e x} \left(23 d^2+11 d e x+3 e^2 x^2\right)+\frac{2}{7} (d+e x)^{7/2}\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)-2 c^2 d^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) \left(7 (c d-b e) \left(5 (c d-b e) \left(\sqrt{c} \sqrt{d+e x} (-3 b e+4 c d+c e x)-3 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)+3 c^{5/2} (d+e x)^{5/2}\right)+15 c^{7/2} (d+e x)^{7/2}\right)\right)-210 b c^{11/2} (d+e x)^{9/2} \left(b^3 e^2 (5 A e+4 B d)-11 b^2 c d e (2 A e+B d)+12 b c^2 d^2 (3 A e+B d)-24 A c^3 d^3\right)\right)}{b^4 c^{9/2} d (c d-b e)^2}-\frac{210 (d+e x)^{9/2} (5 A b e-8 A c d+4 b B d)}{b d x}-\frac{420 A (d+e x)^{9/2}}{x^2}}{840 b d (b+c x)^2}","-\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{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{(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{\sqrt{d+e x} \left(b c d^2 \left(-b c (11 A e+6 B d)+12 A c^2 d+2 b^2 B e\right)+x \left(-A b^3 c e^3+b^2 c^2 d e (14 A e+11 B d)-12 b c^3 d^2 (3 A e+B d)+24 A c^4 d^3-3 b^4 B e^3\right)\right)}{4 b^4 c^2 \left(b x+c x^2\right)}",1,"((-210*c*(12*A*c^2*d^2 - 3*b*c*d*(2*B*d + 5*A*e) + b^2*e*(4*B*d + 5*A*e))*(d + e*x)^(9/2))/(b^2*d*(-(c*d) + b*e)) - (420*A*(d + e*x)^(9/2))/x^2 - (210*(4*b*B*d - 8*A*c*d + 5*A*b*e)*(d + e*x)^(9/2))/(b*d*x) + ((b + c*x)*(-210*b*c^(11/2)*(-24*A*c^3*d^3 - 11*b^2*c*d*e*(B*d + 2*A*e) + 12*b*c^2*d^2*(B*d + 3*A*e) + b^3*e^2*(4*B*d + 5*A*e))*(d + e*x)^(9/2) + (b + c*x)*(105*c^(9/2)*(c*d - b*e)^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))*((2*(d + e*x)^(7/2))/7 + (2*d*Sqrt[d + e*x]*(23*d^2 + 11*d*e*x + 3*e^2*x^2))/15 - 2*d^(7/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) - 2*c^2*d^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))*(15*c^(7/2)*(d + e*x)^(7/2) + 7*(c*d - b*e)*(3*c^(5/2)*(d + e*x)^(5/2) + 5*(c*d - b*e)*(Sqrt[c]*Sqrt[d + e*x]*(4*c*d - 3*b*e + c*e*x) - 3*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]]))))))/(b^4*c^(9/2)*d*(c*d - b*e)^2))/(840*b*d*(b + c*x)^2)","A",1
1249,1,516,344,3.0445857,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2)^3,x]","\frac{\frac{30 c (d+e x)^{7/2} \left(b^2 (-e) (3 A e+4 B d)+b c d (13 A e+6 B d)-12 A c^2 d^2\right)}{b^2 d (b e-c d)}+\frac{(b+c x) \left((b+c x) \left(15 c^{7/2} (c d-b e)^2 \left(-2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)+\frac{2}{3} d \sqrt{d+e x} (4 d+e x)+\frac{2}{5} (d+e x)^{5/2}\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)-2 c^2 d^2 \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) \left(5 (c d-b e) \left(\sqrt{c} \sqrt{d+e x} (-3 b e+4 c d+c e x)-3 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)+3 c^{5/2} (d+e x)^{5/2}\right)\right)-30 b c^{9/2} (d+e x)^{7/2} \left(b^3 e^2 (3 A e+4 B d)-b^2 c d e (18 A e+13 B d)+12 b c^2 d^2 (3 A e+B d)-24 A c^3 d^3\right)\right)}{b^4 c^{7/2} d (c d-b e)^2}-\frac{30 (d+e x)^{7/2} (3 A b e-8 A c d+4 b B d)}{b d x}-\frac{60 A (d+e x)^{7/2}}{x^2}}{120 b d (b+c x)^2}","-\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} \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{\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+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)}",1,"((30*c*(-12*A*c^2*d^2 - b^2*e*(4*B*d + 3*A*e) + b*c*d*(6*B*d + 13*A*e))*(d + e*x)^(7/2))/(b^2*d*(-(c*d) + b*e)) - (60*A*(d + e*x)^(7/2))/x^2 - (30*(4*b*B*d - 8*A*c*d + 3*A*b*e)*(d + e*x)^(7/2))/(b*d*x) + ((b + c*x)*(-30*b*c^(9/2)*(-24*A*c^3*d^3 + 12*b*c^2*d^2*(B*d + 3*A*e) + b^3*e^2*(4*B*d + 3*A*e) - b^2*c*d*e*(13*B*d + 18*A*e))*(d + e*x)^(7/2) + (b + c*x)*(15*c^(7/2)*(c*d - b*e)^2*(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))*((2*(d + e*x)^(5/2))/5 + (2*d*Sqrt[d + e*x]*(4*d + e*x))/3 - 2*d^(5/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) - 2*c^2*d^2*(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))*(3*c^(5/2)*(d + e*x)^(5/2) + 5*(c*d - b*e)*(Sqrt[c]*Sqrt[d + e*x]*(4*c*d - 3*b*e + c*e*x) - 3*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])))))/(b^4*c^(7/2)*d*(c*d - b*e)^2))/(120*b*d*(b + c*x)^2)","A",1
1250,1,472,346,2.852766,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2)^3,x]","\frac{\frac{6 b^2 c^{7/2} (d+e x)^{5/2} (c d-b e) \left(b^2 e (A e+4 B d)-b c d (11 A e+6 B d)+12 A c^2 d^2\right)+(b+c x) \left((b+c x) \left(9 c^{5/2} (c d-b e)^2 \left(\frac{2}{3} \sqrt{d+e x} (4 d+e x)-2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\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)-6 c^2 d^2 \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) \left(\sqrt{c} \sqrt{d+e x} (-3 b e+4 c d+c e x)-3 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)\right)-6 b c^{7/2} (d+e x)^{5/2} \left(b^3 e^2 (A e+4 B d)-b^2 c d e (14 A e+15 B d)+12 b c^2 d^2 (3 A e+B d)-24 A c^3 d^3\right)\right)}{b^4 c^{5/2} d (c d-b e)^2}-\frac{6 (d+e x)^{5/2} (A b e-8 A c d+4 b B d)}{b d x}-\frac{12 A (d+e x)^{5/2}}{x^2}}{24 b d (b+c x)^2}","-\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 \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{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}}",1,"((-12*A*(d + e*x)^(5/2))/x^2 - (6*(4*b*B*d - 8*A*c*d + A*b*e)*(d + e*x)^(5/2))/(b*d*x) + (6*b^2*c^(7/2)*(c*d - b*e)*(12*A*c^2*d^2 + b^2*e*(4*B*d + A*e) - b*c*d*(6*B*d + 11*A*e))*(d + e*x)^(5/2) + (b + c*x)*(-6*b*c^(7/2)*(-24*A*c^3*d^3 + b^3*e^2*(4*B*d + A*e) + 12*b*c^2*d^2*(B*d + 3*A*e) - b^2*c*d*e*(15*B*d + 14*A*e))*(d + e*x)^(5/2) + (b + c*x)*(9*c^(5/2)*(c*d - b*e)^2*(16*A*c^2*d^2 + b^2*e*(4*B*d + A*e) - 4*b*c*d*(2*B*d + 3*A*e))*((2*Sqrt[d + e*x]*(4*d + e*x))/3 - 2*d^(3/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) - 6*c^2*d^2*(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))*(Sqrt[c]*Sqrt[d + e*x]*(4*c*d - 3*b*e + c*e*x) - 3*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]]))))/(b^4*c^(5/2)*d*(c*d - b*e)^2))/(24*b*d*(b + c*x)^2)","A",1
1251,1,449,317,2.2161822,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(b x+c x^2\right)^3} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2)^3,x]","\frac{\frac{(b+c x) \left((b+c x) \left(2 c^{3/2} (c d-b e)^2 \left(\sqrt{d+e x}-\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)\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)+2 c^2 d^2 \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) \left(\sqrt{c} \sqrt{d+e x}-\sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)\right)\right)+2 b c^{5/2} (d+e x)^{3/2} \left(b^3 e^2 (A e-4 B d)+b^2 c d e (10 A e+17 B d)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\right)\right)-2 b^2 c^{5/2} (d+e x)^{3/2} (c d-b e) \left(b^2 e (A e-4 B d)+3 b c d (3 A e+2 B d)-12 A c^2 d^2\right)}{b^4 c^{3/2} d (c d-b e)^2}-\frac{2 (d+e x)^{3/2} (-A b e-8 A c d+4 b B d)}{b d x}-\frac{4 A (d+e x)^{3/2}}{x^2}}{8 b d (b+c x)^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{\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} \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{\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}}",1,"((-4*A*(d + e*x)^(3/2))/x^2 - (2*(4*b*B*d - 8*A*c*d - A*b*e)*(d + e*x)^(3/2))/(b*d*x) + (-2*b^2*c^(5/2)*(c*d - b*e)*(-12*A*c^2*d^2 + b^2*e*(-4*B*d + A*e) + 3*b*c*d*(2*B*d + 3*A*e))*(d + e*x)^(3/2) + (b + c*x)*(2*b*c^(5/2)*(24*A*c^3*d^3 + b^3*e^2*(-4*B*d + A*e) - 12*b*c^2*d^2*(B*d + 3*A*e) + b^2*c*d*e*(17*B*d + 10*A*e))*(d + e*x)^(3/2) + (b + c*x)*(2*c^(3/2)*(c*d - b*e)^2*(48*A*c^2*d^2 + b^2*e*(4*B*d - A*e) - 12*b*c*d*(2*B*d + A*e))*(Sqrt[d + e*x] - Sqrt[d]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]]) + 2*c^2*d^2*(-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))*(Sqrt[c]*Sqrt[d + e*x] - Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]]))))/(b^4*c^(3/2)*d*(c*d - b*e)^2))/(8*b*d*(b + c*x)^2)","A",1
1252,1,408,394,1.4800816,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)^3),x]","\frac{\frac{c \sqrt{d+e x} \left(b^2 e (3 A e-4 B d)+b c d (7 A e+6 B d)-12 A c^2 d^2\right)}{b^2 d (b+c x)^2 (b e-c d)}+\frac{-\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(b^2 e (3 A e-4 B d)+12 b c d (A e-2 B d)+48 A c^2 d^2\right)-\frac{b c \sqrt{d} \sqrt{d+e x} \left(b^3 e^2 (4 B d-3 A e)-b^2 c d e (6 A e+19 B d)+12 b c^2 d^2 (3 A e+B d)-24 A c^3 d^3\right)}{(b+c x) (c d-b e)^2}+\frac{c^{3/2} d^{5/2} \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)}{(c d-b e)^{5/2}}}{b^4 d^{3/2}}+\frac{\sqrt{d+e x} (3 A b e+8 A c d-4 b B d)}{b d x (b+c x)^2}-\frac{2 A \sqrt{d+e x}}{x^2 (b+c x)^2}}{4 b d}","-\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{\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{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{\sqrt{d+e x} \left(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)+c x \left(b^3 \left(-e^2\right) (4 B d-3 A e)+b^2 c d e (6 A e+19 B d)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\right)\right)}{4 b^4 d^2 \left(b x+c x^2\right) (c d-b e)^2}",1,"((c*(-12*A*c^2*d^2 + b^2*e*(-4*B*d + 3*A*e) + b*c*d*(6*B*d + 7*A*e))*Sqrt[d + e*x])/(b^2*d*(-(c*d) + b*e)*(b + c*x)^2) - (2*A*Sqrt[d + e*x])/(x^2*(b + c*x)^2) + ((-4*b*B*d + 8*A*c*d + 3*A*b*e)*Sqrt[d + e*x])/(b*d*x*(b + c*x)^2) + (-((b*c*Sqrt[d]*(-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))*Sqrt[d + e*x])/((c*d - b*e)^2*(b + c*x))) - (48*A*c^2*d^2 + 12*b*c*d*(-2*B*d + A*e) + b^2*e*(-4*B*d + 3*A*e))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]] + (c^(3/2)*d^(5/2)*(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]])/(c*d - b*e)^(5/2))/(b^4*d^(3/2)))/(4*b*d)","A",1
1253,1,387,506,0.5493754,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)^3),x]","\frac{2 A b^4 d^2 (b e-c d)^3+b^3 d x (b e-c d)^3 (-5 A b e-8 A c d+4 b B d)+x^2 \left(b^2 c d (c d-b e)^2 \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)+(b+c x) \left(b c d (b e-c d) \left(b^3 e^2 (4 B d-5 A e)-b^2 c d e (2 A e+21 B d)+12 b c^2 d^2 (3 A e+B d)-24 A c^3 d^3\right)-(b+c x) \left(3 c^2 d^3 \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) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{c (d+e x)}{c d-b e}\right)-3 (c d-b e)^3 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{e x}{d}+1\right) \left(b^2 e (5 A e-4 B d)+4 b c d (3 A e-2 B d)+16 A c^2 d^2\right)\right)\right)\right)}{4 b^5 d^3 x^2 (b+c x)^2 \sqrt{d+e x} (c d-b e)^3}","-\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{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{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{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)+c x \left(b^3 \left(-e^2\right) (4 B d-5 A e)+b^2 c d e (2 A e+21 B d)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\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^4 e^3 (4 B d-5 A e)-b^3 c d e^2 (4 B d-3 A e)+b^2 c^2 d^2 e (5 A e+9 B d)-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}",1,"(2*A*b^4*d^2*(-(c*d) + b*e)^3 + b^3*d*(-(c*d) + b*e)^3*(4*b*B*d - 8*A*c*d - 5*A*b*e)*x + x^2*(b^2*c*d*(c*d - b*e)^2*(12*A*c^2*d^2 + b^2*e*(4*B*d - 5*A*e) - b*c*d*(6*B*d + 5*A*e)) + (b + c*x)*(b*c*d*(-(c*d) + b*e)*(-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)) - (b + c*x)*(3*c^2*d^3*(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))*Hypergeometric2F1[-1/2, 1, 1/2, (c*(d + e*x))/(c*d - b*e)] - 3*(c*d - b*e)^3*(16*A*c^2*d^2 + 4*b*c*d*(-2*B*d + 3*A*e) + b^2*e*(-4*B*d + 5*A*e))*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (e*x)/d]))))/(4*b^5*d^3*(c*d - b*e)^3*x^2*(b + c*x)^2*Sqrt[d + e*x])","C",1
1254,1,388,644,0.5725874,"\int \frac{A+B x}{(d+e x)^{5/2} \left(b x+c x^2\right)^3} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*(b*x + c*x^2)^3),x]","\frac{6 A b^4 d^2 (b e-c d)^3+3 b^3 d x (b e-c d)^3 (-7 A b e-8 A c d+4 b B d)+x^2 \left(3 b^2 c d (c d-b e)^2 \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)+(b+c x) \left(3 b c d (b e-c d) \left(b^3 e^2 (4 B d-7 A e)+b^2 c d e (2 A e-23 B d)+12 b c^2 d^2 (3 A e+B d)-24 A c^3 d^3\right)-(b+c x) \left(c^2 d^3 \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) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{c (d+e x)}{c d-b e}\right)-(c d-b e)^3 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{e x}{d}+1\right) \left(5 b^2 e (7 A e-4 B d)+12 b c d (5 A e-2 B d)+48 A c^2 d^2\right)\right)\right)\right)}{12 b^5 d^3 x^2 (b+c x)^2 (d+e x)^{3/2} (c d-b e)^3}","-\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{\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^{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{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)+c x \left(b^3 \left(-e^2\right) (4 B d-7 A e)+b^2 c d e (23 B d-2 A e)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\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(5 b^4 e^3 (4 B d-7 A e)-9 b^3 c d e^2 (4 B d-5 A e)+3 b^2 c^2 d^2 e (9 A e+29 B d)-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{e \left(-5 b^5 e^4 (4 B d-7 A e)+8 b^4 c d e^3 (7 B d-10 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 (4 A e+5 B d)-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}",1,"(6*A*b^4*d^2*(-(c*d) + b*e)^3 + 3*b^3*d*(-(c*d) + b*e)^3*(4*b*B*d - 8*A*c*d - 7*A*b*e)*x + x^2*(3*b^2*c*d*(c*d - b*e)^2*(12*A*c^2*d^2 + b^2*e*(4*B*d - 7*A*e) - 3*b*c*d*(2*B*d + A*e)) + (b + c*x)*(3*b*c*d*(-(c*d) + b*e)*(-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)) - (b + c*x)*(c^2*d^3*(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))*Hypergeometric2F1[-3/2, 1, -1/2, (c*(d + e*x))/(c*d - b*e)] - (c*d - b*e)^3*(48*A*c^2*d^2 + 12*b*c*d*(-2*B*d + 5*A*e) + 5*b^2*e*(-4*B*d + 7*A*e))*Hypergeometric2F1[-3/2, 1, -1/2, 1 + (e*x)/d]))))/(12*b^5*d^3*(c*d - b*e)^3*x^2*(b + c*x)^2*(d + e*x)^(3/2))","C",1
1255,1,461,433,3.3732322,"\int (A+B x) \sqrt{d+e x} \sqrt{b x+c x^2} \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2],x]","-\frac{2 \left(b e x (b+c x) (d+e x) \left(B \left(4 b^2 e^2-b c e (2 d+3 e x)+c^2 \left(4 d^2-3 d e x-15 e^2 x^2\right)\right)-7 A c e (b e+c (d+3 e x))\right)+\sqrt{\frac{b}{c}} \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(7 A c e (c d-2 b e)-B \left(-8 b^2 e^2+b c d e+4 c^2 d^2\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(14 A c e \left(b^2 e^2-b c d e+c^2 d^2\right)+B \left(-8 b^3 e^3+5 b^2 c d e^2+5 b c^2 d^2 e-8 c^3 d^3\right)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(14 A c e \left(b^2 e^2-b c d e+c^2 d^2\right)+B \left(-8 b^3 e^3+5 b^2 c d e^2+5 b c^2 d^2 e-8 c^3 d^3\right)\right)\right)\right)}{105 b c^2 e^3 \sqrt{x (b+c x)} \sqrt{d+e 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}",1,"(-2*(b*e*x*(b + c*x)*(d + e*x)*(-7*A*c*e*(b*e + c*(d + 3*e*x)) + B*(4*b^2*e^2 - b*c*e*(2*d + 3*e*x) + c^2*(4*d^2 - 3*d*e*x - 15*e^2*x^2))) + Sqrt[b/c]*(Sqrt[b/c]*(14*A*c*e*(c^2*d^2 - b*c*d*e + b^2*e^2) + B*(-8*c^3*d^3 + 5*b*c^2*d^2*e + 5*b^2*c*d*e^2 - 8*b^3*e^3))*(b + c*x)*(d + e*x) + I*b*e*(14*A*c*e*(c^2*d^2 - b*c*d*e + b^2*e^2) + B*(-8*c^3*d^3 + 5*b*c^2*d^2*e + 5*b^2*c*d*e^2 - 8*b^3*e^3))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(7*A*c*e*(c*d - 2*b*e) - B*(4*c^2*d^2 + b*c*d*e - 8*b^2*e^2))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(105*b*c^2*e^3*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1256,1,344,318,1.5271772,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/Sqrt[d + e*x],x]","-\frac{2 \left(-b e x (b+c x) (d+e x) (5 A c e+B (b e-4 c d+3 c e x))-\sqrt{\frac{b}{c}} \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(5 A c e (b e-2 c d)+B \left(-2 b^2 e^2-3 b c d e+8 c^2 d^2\right)\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) (5 A c e-2 B (b e+2 c d)) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)\right)\right)}{15 b c e^3 \sqrt{x (b+c x)} \sqrt{d+e 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}",1,"(-2*(-(b*e*x*(b + c*x)*(d + e*x)*(5*A*c*e + B*(-4*c*d + b*e + 3*c*e*x))) - Sqrt[b/c]*(Sqrt[b/c]*(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))*(b + c*x)*(d + e*x) - I*b*e*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] + I*b*e*(c*d - b*e)*(5*A*c*e - 2*B*(2*c*d + b*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(15*b*c*e^3*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1257,1,269,283,1.2623532,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^(3/2),x]","\frac{2 \left(b e x (b+c x) (-3 A e+4 B d+B e x)+\sqrt{\frac{b}{c}} \left(i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (-3 A c e-b B e+4 B c d) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (-6 A c e-b B e+8 B c d) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) (6 A c e+b B e-8 B c d)\right)\right)}{3 b e^3 \sqrt{x (b+c x)} \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}}",1,"(2*(b*e*x*(b + c*x)*(4*B*d - 3*A*e + B*e*x) + Sqrt[b/c]*(Sqrt[b/c]*(-8*B*c*d + b*B*e + 6*A*c*e)*(b + c*x)*(d + e*x) - I*b*e*(8*B*c*d - b*B*e - 6*A*c*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] + I*b*e*(4*B*c*d - b*B*e - 3*A*c*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b*e^3*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1258,1,346,346,1.7142674,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^(5/2),x]","\frac{2 \left(e x \sqrt{\frac{b}{c}} (b+c x) \left(A e \left(c d (d+2 e x)-b e^2 x\right)+B d (b e (3 d+4 e x)-c d (4 d+5 e x))\right)+(d+e x) \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (4 B d-A e) (c d-b e) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (A e (2 c d-b e)+B d (7 b e-8 c d)) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) (A e (b e-2 c d)+B d (8 c d-7 b e))\right)\right)}{3 d e^3 \sqrt{\frac{b}{c}} \sqrt{x (b+c x)} (d+e x)^{3/2} (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*(Sqrt[b/c]*e*x*(b + c*x)*(A*e*(-(b*e^2*x) + c*d*(d + 2*e*x)) + B*d*(b*e*(3*d + 4*e*x) - c*d*(4*d + 5*e*x))) + (d + e*x)*(Sqrt[b/c]*(B*d*(8*c*d - 7*b*e) + A*e*(-2*c*d + b*e))*(b + c*x)*(d + e*x) - I*b*e*(A*e*(2*c*d - b*e) + B*d*(-8*c*d + 7*b*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(4*B*d - A*e)*(c*d - b*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*Sqrt[b/c]*d*e^3*(c*d - b*e)*Sqrt[x*(b + c*x)]*(d + e*x)^(3/2))","C",1
1259,1,491,494,2.4540681,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^(7/2),x]","\frac{2 \left(b e x (b+c x) \left((d+e 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)+3 d^2 (B d-A e) (c d-b e)^2-d (d+e x) (c d-b e) (A e (b e-2 c d)+B d (7 c d-6 b e))\right)-c \sqrt{\frac{b}{c}} (d+e x)^2 \left(i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (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)-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) (A e (c d-2 b e)+B d (4 c d-3 b e)) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)\right)\right)}{15 b d^2 e^3 \sqrt{x (b+c x)} (d+e x)^{5/2} (c d-b e)^2}","\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} \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} (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)}",1,"(2*(b*e*x*(b + c*x)*(3*d^2*(B*d - A*e)*(c*d - b*e)^2 - d*(c*d - b*e)*(B*d*(7*c*d - 6*b*e) + A*e*(-2*c*d + b*e))*(d + e*x) + (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))*(d + e*x)^2) - Sqrt[b/c]*c*(d + e*x)^2*(Sqrt[b/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))*(b + c*x)*(d + e*x) + I*b*e*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(B*d*(4*c*d - 3*b*e) + A*e*(c*d - 2*b*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(15*b*d^2*e^3*(c*d - b*e)^2*Sqrt[x*(b + c*x)]*(d + e*x)^(5/2))","C",1
1260,1,630,574,4.5516225,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/Sqrt[d + e*x],x]","-\frac{2 (x (b+c x))^{3/2} \left(b e x (b+c x) (d+e x) \left(B \left(4 b^3 e^3-3 b^2 c e^2 (e x-2 d)+b c^2 e \left(-84 d^2+61 d e x-50 e^2 x^2\right)+c^3 \left(64 d^3-48 d^2 e x+40 d e^2 x^2-35 e^3 x^3\right)\right)-9 A c e \left(b^2 e^2+b c e (8 e x-11 d)+c^2 \left(8 d^2-6 d e x+5 e^2 x^2\right)\right)\right)+\sqrt{\frac{b}{c}} \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(9 A c e \left(-2 b^2 e^2-5 b c d e+8 c^2 d^2\right)+B \left(8 b^3 e^3+15 b^2 c d e^2+36 b c^2 d^2 e-64 c^3 d^3\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(18 A c e \left(b^3 e^3+2 b^2 c d e^2-12 b c^2 d^2 e+8 c^3 d^3\right)-B \left(8 b^4 e^4+11 b^3 c d e^3+27 b^2 c^2 d^2 e^2-184 b c^3 d^3 e+128 c^4 d^4\right)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(18 A c e \left(b^3 e^3+2 b^2 c d e^2-12 b c^2 d^2 e+8 c^3 d^3\right)-B \left(8 b^4 e^4+11 b^3 c d e^3+27 b^2 c^2 d^2 e^2-184 b c^3 d^3 e+128 c^4 d^4\right)\right)\right)\right)}{315 b c^2 e^5 x^2 (b+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 \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(2 b^3 e^3+3 b^2 c d e^2-42 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(-4 b^3 e^3-9 b^2 c d e^2-120 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 \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*(x*(b + c*x))^(3/2)*(b*e*x*(b + c*x)*(d + e*x)*(-9*A*c*e*(b^2*e^2 + b*c*e*(-11*d + 8*e*x) + c^2*(8*d^2 - 6*d*e*x + 5*e^2*x^2)) + B*(4*b^3*e^3 - 3*b^2*c*e^2*(-2*d + e*x) + b*c^2*e*(-84*d^2 + 61*d*e*x - 50*e^2*x^2) + c^3*(64*d^3 - 48*d^2*e*x + 40*d*e^2*x^2 - 35*e^3*x^3))) + Sqrt[b/c]*(Sqrt[b/c]*(18*A*c*e*(8*c^3*d^3 - 12*b*c^2*d^2*e + 2*b^2*c*d*e^2 + b^3*e^3) - B*(128*c^4*d^4 - 184*b*c^3*d^3*e + 27*b^2*c^2*d^2*e^2 + 11*b^3*c*d*e^3 + 8*b^4*e^4))*(b + c*x)*(d + e*x) + I*b*e*(18*A*c*e*(8*c^3*d^3 - 12*b*c^2*d^2*e + 2*b^2*c*d*e^2 + b^3*e^3) - B*(128*c^4*d^4 - 184*b*c^3*d^3*e + 27*b^2*c^2*d^2*e^2 + 11*b^3*c*d*e^3 + 8*b^4*e^4))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(9*A*c*e*(8*c^2*d^2 - 5*b*c*d*e - 2*b^2*e^2) + B*(-64*c^3*d^3 + 36*b*c^2*d^2*e + 15*b^2*c*d*e^2 + 8*b^3*e^3))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(315*b*c^2*e^5*x^2*(b + c*x)^2*Sqrt[d + e*x])","C",1
1261,1,514,449,3.5165917,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{2 (x (b+c x))^{3/2} \left(b e x (b+c x) \left((d+e x) \left(7 A c e (2 b e-3 c d)+B \left(b^2 e^2-25 b c d e+29 c^2 d^2\right)\right)+c e x (d+e x) (7 A c e+8 b B e-13 B c d)+35 c d (B d-A e) (c d-b e)+5 B c^2 e^2 x^2 (d+e x)\right)+\sqrt{\frac{b}{c}} \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(7 A c e (8 c d-b e)+2 B \left(b^2 e^2+6 b c d e-32 c^2 d^2\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(7 A c e \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)-B \left(2 b^3 e^3+11 b^2 c d e^2-136 b c^2 d^2 e+128 c^3 d^3\right)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(7 A c e \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)-B \left(2 b^3 e^3+11 b^2 c d e^2-136 b c^2 d^2 e+128 c^3 d^3\right)\right)\right)\right)}{35 b c e^5 x^2 (b+c x)^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*(x*(b + c*x))^(3/2)*(b*e*x*(b + c*x)*(35*c*d*(B*d - A*e)*(c*d - b*e) + (7*A*c*e*(-3*c*d + 2*b*e) + B*(29*c^2*d^2 - 25*b*c*d*e + b^2*e^2))*(d + e*x) + c*e*(-13*B*c*d + 8*b*B*e + 7*A*c*e)*x*(d + e*x) + 5*B*c^2*e^2*x^2*(d + e*x)) + Sqrt[b/c]*(Sqrt[b/c]*(7*A*c*e*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2) - B*(128*c^3*d^3 - 136*b*c^2*d^2*e + 11*b^2*c*d*e^2 + 2*b^3*e^3))*(b + c*x)*(d + e*x) + I*b*e*(7*A*c*e*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2) - B*(128*c^3*d^3 - 136*b*c^2*d^2*e + 11*b^2*c*d*e^2 + 2*b^3*e^3))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(7*A*c*e*(8*c*d - b*e) + 2*B*(-32*c^2*d^2 + 6*b*c*d*e + b^2*e^2))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(35*b*c*e^5*x^2*(b + c*x)^2*Sqrt[d + e*x])","C",1
1262,1,436,413,2.1282563,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^(5/2),x]","\frac{2 (x (b+c x))^{3/2} \left(i e x^{3/2} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(5 A c e (8 c d-5 b e)+B \left(-3 b^2 e^2+52 b c d e-64 c^2 d^2\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)-i e x^{3/2} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\frac{(b+c x) (d+e x) \left(40 A c e (b e-2 c d)+B \left(3 b^2 e^2-88 b c d e+128 c^2 d^2\right)\right)}{c}+\frac{e x (b+c x) \left(5 A e \left(c \left(8 d^2+10 d e x+e^2 x^2\right)-b e (3 d+4 e x)\right)+B \left(b e \left(36 d^2+47 d e x+6 e^2 x^2\right)-c \left(64 d^3+80 d^2 e x+8 d e^2 x^2-3 e^3 x^3\right)\right)\right)}{d+e x}\right)}{15 e^5 x^2 (b+c x)^2 \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 \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 \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}}",1,"(2*(x*(b + c*x))^(3/2)*(((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))*(b + c*x)*(d + e*x))/c + (e*x*(b + c*x)*(5*A*e*(-(b*e*(3*d + 4*e*x)) + c*(8*d^2 + 10*d*e*x + e^2*x^2)) + B*(b*e*(36*d^2 + 47*d*e*x + 6*e^2*x^2) - c*(64*d^3 + 80*d^2*e*x + 8*d*e^2*x^2 - 3*e^3*x^3))))/(d + e*x) - I*Sqrt[b/c]*e*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] + I*Sqrt[b/c]*e*(5*A*c*e*(8*c*d - 5*b*e) + B*(-64*c^2*d^2 + 52*b*c*d*e - 3*b^2*e^2))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)]))/(15*e^5*x^2*(b + c*x)^2*Sqrt[d + e*x])","C",1
1263,1,530,516,2.9786781,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^(7/2),x]","\frac{2 (x (b+c x))^{3/2} \left(e x \sqrt{\frac{b}{c}} (b+c x) \left((d+e x)^2 \left(B d \left(23 b^2 e^2-93 b c d e+73 c^2 d^2\right)-3 A e \left(b^2 e^2-11 b c d e+11 c^2 d^2\right)\right)+3 d^2 (B d-A e) (c d-b e)^2-d (d+e x) (c d-b e) (6 A e (b e-2 c d)+B d (17 c d-11 b e))+5 B c d (d+e x)^3 (c d-b e)\right)+(d+e x)^2 \left(i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (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)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) (3 A e (b e-8 c d)+4 B d (16 c d-7 b e)) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)\right)\right)}{15 d e^5 x^2 \sqrt{\frac{b}{c}} (b+c x)^2 (d+e x)^{5/2} (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 \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 \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*(x*(b + c*x))^(3/2)*(Sqrt[b/c]*e*x*(b + c*x)*(3*d^2*(B*d - A*e)*(c*d - b*e)^2 - d*(c*d - b*e)*(B*d*(17*c*d - 11*b*e) + 6*A*e*(-2*c*d + b*e))*(d + e*x) + (-3*A*e*(11*c^2*d^2 - 11*b*c*d*e + b^2*e^2) + B*d*(73*c^2*d^2 - 93*b*c*d*e + 23*b^2*e^2))*(d + e*x)^2 + 5*B*c*d*(c*d - b*e)*(d + e*x)^3) + (d + e*x)^2*(Sqrt[b/c]*(B*d*(-128*c^2*d^2 + 168*b*c*d*e - 43*b^2*e^2) + 3*A*e*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2))*(b + c*x)*(d + e*x) + I*b*e*(B*d*(-128*c^2*d^2 + 168*b*c*d*e - 43*b^2*e^2) + 3*A*e*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] + I*b*e*(c*d - b*e)*(4*B*d*(16*c*d - 7*b*e) + 3*A*e*(-8*c*d + b*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(15*Sqrt[b/c]*d*e^5*(c*d - b*e)*x^2*(b + c*x)^2*(d + e*x)^(5/2))","C",1
1264,1,479,460,4.124399,"\int \frac{(A+B x) (d+e x)^{5/2}}{\sqrt{b x+c x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{x} \left(\sqrt{x} (b+c x) (d+e x) \left(7 A c e (-4 b e+11 c d+3 c e x)+B \left(24 b^2 e^2-b c e (61 d+18 e x)+15 c^2 \left(3 d^2+3 d e x+e^2 x^2\right)\right)\right)+\frac{i x \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (b e-c d) \left(-8 b^2 c e (7 A e+13 B d)+b c^2 d (133 A e+60 B d)-105 A c^3 d^2+48 b^3 B e^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)}{b}+\frac{(b+c x) (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(-48 b^3 e^3+128 b^2 c d e^2-103 b c^2 d^2 e+15 c^3 d^3\right)\right)}{c e \sqrt{x}}+i x \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(7 A c e \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)+B \left(-48 b^3 e^3+128 b^2 c d e^2-103 b c^2 d^2 e+15 c^3 d^3\right)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)\right)}{105 c^3 \sqrt{x (b+c x)} \sqrt{d+e x}}","-\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 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} \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(-48 b^3 e^3+128 b^2 c d e^2-103 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*Sqrt[x]*(((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))*(b + c*x)*(d + e*x))/(c*e*Sqrt[x]) + Sqrt[x]*(b + c*x)*(d + e*x)*(7*A*c*e*(11*c*d - 4*b*e + 3*c*e*x) + B*(24*b^2*e^2 - b*c*e*(61*d + 18*e*x) + 15*c^2*(3*d^2 + 3*d*e*x + e^2*x^2))) + I*Sqrt[b/c]*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] + (I*Sqrt[b/c]*(-(c*d) + b*e)*(-105*A*c^3*d^2 + 48*b^3*B*e^2 - 8*b^2*c*e*(13*B*d + 7*A*e) + b*c^2*d*(60*B*d + 133*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])/b))/(105*c^3*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1265,1,356,339,1.8366783,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{b x+c x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{x} \left(\frac{(b+c x) (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)}{c e \sqrt{x}}+i x \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)-\frac{i x \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (b e-c d) \left(-b c (10 A e+9 B d)+15 A c^2 d+8 b^2 B e\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)}{b}+\sqrt{x} (b+c x) (d+e x) (5 A c e+B (-4 b e+6 c d+3 c e x))\right)}{15 c^2 \sqrt{x (b+c x)} \sqrt{d+e 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} 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 \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 B \sqrt{b x+c x^2} (d+e x)^{3/2}}{5 c}",1,"(2*Sqrt[x]*(((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))*(b + c*x)*(d + e*x))/(c*e*Sqrt[x]) + Sqrt[x]*(b + c*x)*(d + e*x)*(5*A*c*e + B*(6*c*d - 4*b*e + 3*c*e*x)) + I*Sqrt[b/c]*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - (I*Sqrt[b/c]*(-(c*d) + b*e)*(15*A*c^2*d + 8*b^2*B*e - b*c*(9*B*d + 10*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])/b))/(15*c^2*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1266,1,263,254,1.1216299,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{b x+c x^2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/Sqrt[b*x + c*x^2],x]","\frac{2 x \left(\frac{(b+c x) (d+e x) (3 A c e-2 b B e+B c d)}{c e x}+\frac{i \sqrt{x} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (2 b B-3 A c) (b e-c d) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)}{b}+i \sqrt{x} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (3 A c e-2 b B e+B c d) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+B (b+c x) (d+e x)\right)}{3 c \sqrt{x (b+c x)} \sqrt{d+e 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}",1,"(2*x*(B*(b + c*x)*(d + e*x) + ((B*c*d - 2*b*B*e + 3*A*c*e)*(b + c*x)*(d + e*x))/(c*e*x) + I*Sqrt[b/c]*(B*c*d - 2*b*B*e + 3*A*c*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*Sqrt[x]*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] + (I*Sqrt[b/c]*(2*b*B - 3*A*c)*(-(c*d) + b*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*Sqrt[x]*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])/b))/(3*c*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1267,1,209,204,1.0578236,"\int \frac{A+B x}{\sqrt{d+e x} \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*Sqrt[b*x + c*x^2]),x]","\frac{-2 i e x^{3/2} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (b B-A c) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+2 i b B e x^{3/2} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\frac{2 b B (b+c x) (d+e x)}{c}}{b e \sqrt{x (b+c x)} \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*b*B*(b + c*x)*(d + e*x))/c + (2*I)*b*B*Sqrt[b/c]*e*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - (2*I)*Sqrt[b/c]*(b*B - A*c)*e*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])/(b*e*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1268,1,226,262,0.9955332,"\int \frac{A+B x}{(d+e x)^{3/2} \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*Sqrt[b*x + c*x^2]),x]","\frac{2 i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (A e-B d) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)-2 d \sqrt{\frac{b}{c}} (b+c x) (B d-A e)+2 i A e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)}{d e \sqrt{\frac{b}{c}} \sqrt{x (b+c x)} \sqrt{d+e x} (c d-b e)}","\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*Sqrt[b/c]*d*(B*d - A*e)*(b + c*x) + (2*I)*b*e*(-(B*d) + A*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] + (2*I)*A*e*(c*d - b*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])/(Sqrt[b/c]*d*e*(c*d - b*e)*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1269,1,347,369,2.0404883,"\int \frac{A+B x}{(d+e x)^{5/2} \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*Sqrt[b*x + c*x^2]),x]","\frac{2 \left(b e x (b+c x) \left(A e (b e (3 d+2 e x)-c d (5 d+4 e x))+B d \left(b e^2 x+c d (2 d+e x)\right)\right)-c \sqrt{\frac{b}{c}} (d+e x) \left(-i e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) (3 A c d-b (2 A e+B d)) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (2 A e (b e-2 c d)+B d (b e+c d)) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) (2 A e (b e-2 c d)+B d (b e+c d))\right)\right)}{3 b d^2 e \sqrt{x (b+c x)} (d+e x)^{3/2} (c d-b e)^2}","-\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*e*x*(b + c*x)*(B*d*(b*e^2*x + c*d*(2*d + e*x)) + A*e*(b*e*(3*d + 2*e*x) - c*d*(5*d + 4*e*x))) - Sqrt[b/c]*c*(d + e*x)*(Sqrt[b/c]*(2*A*e*(-2*c*d + b*e) + B*d*(c*d + b*e))*(b + c*x)*(d + e*x) + I*b*e*(2*A*e*(-2*c*d + b*e) + B*d*(c*d + b*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*e*(c*d - b*e)*(3*A*c*d - b*(B*d + 2*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b*d^2*e*(c*d - b*e)^2*Sqrt[x*(b + c*x)]*(d + e*x)^(3/2))","C",1
1270,1,506,510,3.0309251,"\int \frac{A+B x}{(d+e x)^{7/2} \sqrt{b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(7/2)*Sqrt[b*x + c*x^2]),x]","\frac{2 \left(b e x (b+c x) \left((d+e x)^2 \left(A e \left(-8 b^2 e^2+23 b c d e-23 c^2 d^2\right)+B d \left(-2 b^2 e^2+7 b c d e+3 c^2 d^2\right)\right)+3 d^2 (B d-A e) (c d-b e)^2+d (d+e x) (c d-b e) (4 A e (b e-2 c d)+B d (b e+3 c d))\right)-c \sqrt{\frac{b}{c}} (d+e x)^2 \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(A e \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)+B d \left(2 b^2 e^2-7 b c d e-3 c^2 d^2\right)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(A e \left(-8 b^2 e^2+23 b c d e-23 c^2 d^2\right)+B d \left(-2 b^2 e^2+7 b c d e+3 c^2 d^2\right)\right)-i e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(2 b^2 e (4 A e+B d)-b c d (19 A e+6 B d)+15 A c^2 d^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)\right)\right)}{15 b d^3 e \sqrt{x (b+c x)} (d+e x)^{5/2} (c d-b e)^3}","\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*e*x*(b + c*x)*(3*d^2*(B*d - A*e)*(c*d - b*e)^2 + d*(c*d - b*e)*(4*A*e*(-2*c*d + b*e) + B*d*(3*c*d + b*e))*(d + e*x) + (A*e*(-23*c^2*d^2 + 23*b*c*d*e - 8*b^2*e^2) + B*d*(3*c^2*d^2 + 7*b*c*d*e - 2*b^2*e^2))*(d + e*x)^2) - Sqrt[b/c]*c*(d + e*x)^2*(Sqrt[b/c]*(A*e*(-23*c^2*d^2 + 23*b*c*d*e - 8*b^2*e^2) + B*d*(3*c^2*d^2 + 7*b*c*d*e - 2*b^2*e^2))*(b + c*x)*(d + e*x) - I*b*e*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*e*(c*d - b*e)*(15*A*c^2*d^2 + 2*b^2*e*(B*d + 4*A*e) - b*c*d*(6*B*d + 19*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(15*b*d^3*e*(c*d - b*e)^3*Sqrt[x*(b + c*x)]*(d + e*x)^(5/2))","C",1
1271,1,493,527,4.0616295,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2)^(3/2),x]","\frac{2 \left(b (d+e x) \left(b^2 e^2 x (b+c x) (5 A c e-9 b B e+16 B c d)+15 x (b B-A c) (c d-b e)^3-15 A c^3 d^3 (b+c x)+3 b^2 B c e^3 x^2 (b+c x)\right)+\sqrt{\frac{b}{c}} \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(8 b^2 c e (5 A e+13 B d)-15 b c^2 d (5 A e+4 B d)+15 A c^3 d^2-48 b^3 B e^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(-8 b^3 c e^2 (5 A e+16 B d)+b^2 c^2 d e (95 A e+103 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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(-8 b^3 c e^2 (5 A e+16 B d)+b^2 c^2 d e (95 A e+103 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)\right)\right)}{15 b^3 c^3 \sqrt{x (b+c x)} \sqrt{d+e x}}","-\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(-8 b^3 c e^2 (5 A e+16 B d)+b^2 c^2 d e (95 A e+103 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}}",1,"(2*(b*(d + e*x)*(15*(b*B - A*c)*(c*d - b*e)^3*x - 15*A*c^3*d^3*(b + c*x) + b^2*e^2*(16*B*c*d - 9*b*B*e + 5*A*c*e)*x*(b + c*x) + 3*b^2*B*c*e^3*x^2*(b + c*x)) + Sqrt[b/c]*(Sqrt[b/c]*(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))*(b + c*x)*(d + e*x) + I*b*e*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(15*A*c^3*d^2 - 48*b^3*B*e^2 - 15*b*c^2*d*(4*B*d + 5*A*e) + 8*b^2*c*e*(13*B*d + 5*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(15*b^3*c^3*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1272,1,391,399,3.1729769,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2)^(3/2),x]","\frac{2 \left(b (d+e x) \left(3 x (b B-A c) (c d-b e)^2-3 A c^2 d^2 (b+c x)+b^2 B e^2 x (b+c x)\right)+\sqrt{\frac{b}{c}} \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(-3 b c (2 A e+3 B d)+3 A c^2 d+8 b^2 B e\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (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)\right)\right)}{3 b^3 c^2 \sqrt{x (b+c x)} \sqrt{d+e x}}","-\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}}",1,"(2*(b*(d + e*x)*(3*(b*B - A*c)*(c*d - b*e)^2*x - 3*A*c^2*d^2*(b + c*x) + b^2*B*e^2*x*(b + c*x)) + Sqrt[b/c]*(Sqrt[b/c]*(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))*(b + c*x)*(d + e*x) + I*b*e*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(3*A*c^2*d + 8*b^2*B*e - 3*b*c*(3*B*d + 2*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b^3*c^2*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1273,1,302,295,1.6687201,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2)^(3/2),x]","\frac{2 \left(b (d+e x) (x (b B-A c) (c d-b e)-A c d (b+c x))+\sqrt{\frac{b}{c}} \left(i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(-b c (A e+B d)+2 A c^2 d+2 b^2 B e\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(-b c (A e+B d)+2 A c^2 d+2 b^2 B e\right)-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (A c-2 b B) (c d-b e) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)\right)\right)}{b^3 c \sqrt{x (b+c x)} \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*(b*(d + e*x)*((b*B - A*c)*(c*d - b*e)*x - A*c*d*(b + c*x)) + Sqrt[b/c]*(Sqrt[b/c]*(2*A*c^2*d + 2*b^2*B*e - b*c*(B*d + A*e))*(b + c*x)*(d + e*x) + I*b*e*(2*A*c^2*d + 2*b^2*B*e - b*c*(B*d + A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*(-2*b*B + A*c)*e*(c*d - b*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(b^3*c*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1274,1,210,253,0.8391168,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2)^(3/2),x]","\frac{-2 (b B-A c) \left(b (d+e x)-i c e x^{3/2} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)\right)-2 i c e x^{3/2} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (b B-2 A c) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)}{b^2 c \sqrt{x (b+c x)} \sqrt{d+e 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}}",1,"((-2*I)*Sqrt[b/c]*c*(b*B - 2*A*c)*e*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - 2*(b*B - A*c)*(b*(d + e*x) - I*Sqrt[b/c]*c*e*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)]))/(b^2*c*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1275,1,233,295,1.0772264,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)^(3/2)),x]","\frac{-2 i e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (2 A c d-b (A e+B d)) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+2 d \sqrt{\frac{b}{c}} (d+e x) (b B-A c)+2 i A e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)}{b d \sqrt{\frac{b}{c}} \sqrt{x (b+c x)} \sqrt{d+e x} (b e-c d)}","-\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[b/c]*(b*B - A*c)*d*(d + e*x) - (2*I)*e*(2*A*c*d - b*(B*d + A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] + (2*I)*A*e*(c*d - b*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])/(b*Sqrt[b/c]*d*(-(c*d) + b*e)*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1276,1,367,415,1.8054877,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)^(3/2)),x]","\frac{2 \left(i c e x^{3/2} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(b^2 e (2 A e-B d)-b c d (2 A e+B d)+2 A c^2 d^2\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+(b+c x) (d+e x) \left(b^2 e (2 A e-B d)-b c d (2 A e+B d)+2 A c^2 d^2\right)+b^2 e^2 x (b+c x) (B d-A e)+c^2 d^2 x (d+e x) (b B-A c)-i c e x^{3/2} \sqrt{\frac{b}{c}} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) (-2 A b e+A c d+b B d) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)-A (b+c x) (d+e x) (c d-b e)^2\right)}{b^2 d^2 \sqrt{x (b+c x)} \sqrt{d+e x} (c d-b e)^2}","-\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*(b^2*e^2*(B*d - A*e)*x*(b + c*x) + c^2*(b*B - A*c)*d^2*x*(d + e*x) - A*(c*d - b*e)^2*(b + c*x)*(d + e*x) + (2*A*c^2*d^2 + b^2*e*(-(B*d) + 2*A*e) - b*c*d*(B*d + 2*A*e))*(b + c*x)*(d + e*x) + I*Sqrt[b/c]*c*e*(2*A*c^2*d^2 + b^2*e*(-(B*d) + 2*A*e) - b*c*d*(B*d + 2*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*Sqrt[b/c]*c*e*(c*d - b*e)*(b*B*d + A*c*d - 2*A*b*e)*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)]))/(b^2*d^2*(c*d - b*e)^2*Sqrt[x*(b + c*x)]*Sqrt[d + e*x])","C",1
1277,1,506,570,4.7969662,"\int \frac{A+B x}{(d+e x)^{5/2} \left(b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*(b*x + c*x^2)^(3/2)),x]","\frac{2 \left(b \left(b^2 d e^2 x (b+c x) (B d-A e) (c d-b e)+b^2 e^2 x (b+c x) (d+e x) (5 A e (b e-2 c d)+B d (7 c d-2 b e))+3 c^3 d^3 x (d+e x)^2 (b B-A c)-3 A (b+c x) (d+e x)^2 (c d-b e)^3\right)+c \sqrt{\frac{b}{c}} (d+e x) \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(2 b^2 e (4 A e-B d)+3 b c d (2 B d-5 A e)+3 A c^2 d^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(2 b^3 e^2 (B d-4 A e)+b^2 c d e (19 A e-7 B d)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(2 b^3 e^2 (B d-4 A e)+b^2 c d e (19 A e-7 B d)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right)\right)\right)}{3 b^3 d^3 \sqrt{x (b+c x)} (d+e x)^{3/2} (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(2 b^3 e^2 (B d-4 A e)-b^2 c d e (7 B d-19 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(2 b^3 e^2 (B d-4 A e)-b^2 c d e (7 B d-19 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}",1,"(2*(b*(b^2*d*e^2*(B*d - A*e)*(c*d - b*e)*x*(b + c*x) + b^2*e^2*(B*d*(7*c*d - 2*b*e) + 5*A*e*(-2*c*d + b*e))*x*(b + c*x)*(d + e*x) + 3*c^3*(b*B - A*c)*d^3*x*(d + e*x)^2 - 3*A*(c*d - b*e)^3*(b + c*x)*(d + e*x)^2) + Sqrt[b/c]*c*(d + e*x)*(Sqrt[b/c]*(6*A*c^3*d^3 + 2*b^3*e^2*(B*d - 4*A*e) - 3*b*c^2*d^2*(B*d + 3*A*e) + b^2*c*d*e*(-7*B*d + 19*A*e))*(b + c*x)*(d + e*x) + I*b*e*(6*A*c^3*d^3 + 2*b^3*e^2*(B*d - 4*A*e) - 3*b*c^2*d^2*(B*d + 3*A*e) + b^2*c*d*e*(-7*B*d + 19*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(3*A*c^2*d^2 + 3*b*c*d*(2*B*d - 5*A*e) + 2*b^2*e*(-(B*d) + 4*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b^3*d^3*(c*d - b*e)^3*Sqrt[x*(b + c*x)]*(d + e*x)^(3/2))","C",1
1278,1,530,524,4.7747582,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2)^(5/2),x]","-\frac{2 \left(b (d+e x) \left(x^2 (b+c x) (c d-b e)^2 \left(b c (5 B d-2 A e)-8 A c^2 d+5 b^2 B e\right)+c^2 d^2 x (b+c x)^2 (10 A b e-8 A c d+3 b B d)+b x^2 (b B-A c) (c d-b e)^3+A b c^2 d^3 (b+c x)^2\right)+x \sqrt{\frac{b}{c}} (b+c x) \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(-b^2 c e (2 A e+B d)-b c^2 d (5 A e+4 B d)+8 A c^3 d^2+8 b^3 B e^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(b^3 c e^2 (2 A e+5 B d)+b^2 c^2 d e (4 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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(b^3 c e^2 (2 A e+5 B d)+b^2 c^2 d e (4 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)\right)\right)}{3 b^5 c^2 (x (b+c x))^{3/2} \sqrt{d+e x}}","-\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 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{d+e x} \left(b c d^2 \left(-b c (9 A e+4 B d)+8 A c^2 d+b^2 B e\right)+x \left(b^3 c e^2 (A e+4 B d)+b^2 c^2 d e (6 A e+5 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)\right)}{3 b^4 c^2 \sqrt{b x+c x^2}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^3 c e^2 (2 A e+5 B d)+b^2 c^2 d e (4 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}}",1,"(-2*(b*(d + e*x)*(b*(b*B - A*c)*(c*d - b*e)^3*x^2 + (c*d - b*e)^2*(-8*A*c^2*d + 5*b^2*B*e + b*c*(5*B*d - 2*A*e))*x^2*(b + c*x) + A*b*c^2*d^3*(b + c*x)^2 + c^2*d^2*(3*b*B*d - 8*A*c*d + 10*A*b*e)*x*(b + c*x)^2) + Sqrt[b/c]*x*(b + c*x)*(Sqrt[b/c]*(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))*(b + c*x)*(d + e*x) + I*b*e*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(8*A*c^3*d^2 + 8*b^3*B*e^2 - b^2*c*e*(B*d + 2*A*e) - b*c^2*d*(4*B*d + 5*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b^5*c^2*(x*(b + c*x))^(3/2)*Sqrt[d + e*x])","C",1
1279,1,452,454,3.6300478,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2)^(5/2),x]","-\frac{2 \left(b (d+e x) \left(x^2 (b+c x) (c d-b e) \left(b c (A e+5 B d)-8 A c^2 d+2 b^2 B e\right)+b x^2 (b B-A c) (c d-b e)^2+c d x (b+c x)^2 (7 A b e-8 A c d+3 b B d)+A b c d^2 (b+c x)^2\right)+x \sqrt{\frac{b}{c}} (b+c x) \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(-b c (A e+4 B d)+8 A c^2 d-2 b^2 B e\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (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)\right)\right)}{3 b^5 c (x (b+c x))^{3/2} \sqrt{d+e x}}","-\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{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 \sqrt{d+e x} \left(b d \left(-b c (7 A e+4 B d)+8 A c^2 d+b^2 B e\right)+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)\right)}{3 b^4 c \sqrt{b x+c x^2}}",1,"(-2*(b*(d + e*x)*(b*(b*B - A*c)*(c*d - b*e)^2*x^2 + (c*d - b*e)*(-8*A*c^2*d + 2*b^2*B*e + b*c*(5*B*d + A*e))*x^2*(b + c*x) + A*b*c*d^2*(b + c*x)^2 + c*d*(3*b*B*d - 8*A*c*d + 7*A*b*e)*x*(b + c*x)^2) + Sqrt[b/c]*x*(b + c*x)*(Sqrt[b/c]*(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))*(b + c*x)*(d + e*x) + I*b*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))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(8*A*c^2*d - 2*b^2*B*e - b*c*(4*B*d + A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b^5*c*(x*(b + c*x))^(3/2)*Sqrt[d + e*x])","C",1
1280,1,378,410,2.1905315,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2)^(5/2),x]","-\frac{2 \left(b (d+e x) \left(A \left(b^3 (d+4 e x)+b^2 c x (13 e x-6 d)+8 b c^2 x^2 (e x-3 d)-16 c^3 d x^3\right)+b B x \left(b^2 (3 d-2 e x)+b c x (12 d-e x)+8 c^2 d x^2\right)\right)+x \sqrt{\frac{b}{c}} (b+c x) \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(-b c (5 A e+4 B d)+8 A c^2 d+b^2 B e\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(-8 b c (A e+B d)+16 A c^2 d+b^2 B e\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(-8 b c (A e+B d)+16 A c^2 d+b^2 B e\right)\right)\right)}{3 b^5 (x (b+c x))^{3/2} \sqrt{d+e 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(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{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}}",1,"(-2*(b*(d + e*x)*(b*B*x*(8*c^2*d*x^2 + b^2*(3*d - 2*e*x) + b*c*x*(12*d - e*x)) + A*(-16*c^3*d*x^3 + 8*b*c^2*x^2*(-3*d + e*x) + b^3*(d + 4*e*x) + b^2*c*x*(-6*d + 13*e*x))) + Sqrt[b/c]*x*(b + c*x)*(Sqrt[b/c]*(16*A*c^2*d + b^2*B*e - 8*b*c*(B*d + A*e))*(b + c*x)*(d + e*x) + I*b*e*(16*A*c^2*d + b^2*B*e - 8*b*c*(B*d + A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(8*A*c^2*d + b^2*B*e - b*c*(4*B*d + 5*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b^5*(x*(b + c*x))^(3/2)*Sqrt[d + e*x])","C",1
1281,1,441,420,2.2709875,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2)^(5/2),x]","-\frac{2 \left(\sqrt{\frac{b}{c}} (d+e x) \left(c d x^2 (b+c x) \left(b c (7 A e+5 B d)-8 A c^2 d-4 b^2 B e\right)+b c d x^2 (b B-A c) (c d-b e)+x (b+c x)^2 (c d-b e) (A b e-8 A c d+3 b B d)+A b d (b+c x)^2 (c d-b e)\right)+x (b+c x) \left(i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \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(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (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)-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) (8 A c d-b (A e+4 B d)) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)\right)\right)}{3 b^4 d \sqrt{\frac{b}{c}} (x (b+c x))^{3/2} \sqrt{d+e x} (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)}",1,"(-2*(Sqrt[b/c]*(d + e*x)*(b*c*(b*B - A*c)*d*(c*d - b*e)*x^2 + c*d*(-8*A*c^2*d - 4*b^2*B*e + b*c*(5*B*d + 7*A*e))*x^2*(b + c*x) + A*b*d*(c*d - b*e)*(b + c*x)^2 + (c*d - b*e)*(3*b*B*d - 8*A*c*d + A*b*e)*x*(b + c*x)^2) + x*(b + c*x)*(Sqrt[b/c]*(16*A*c^2*d^2 + b^2*e*(7*B*d + A*e) - 8*b*c*d*(B*d + 2*A*e))*(b + c*x)*(d + e*x) + I*b*e*(16*A*c^2*d^2 + b^2*e*(7*B*d + A*e) - 8*b*c*d*(B*d + 2*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(8*A*c*d - b*(4*B*d + A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b^4*Sqrt[b/c]*d*(c*d - b*e)*(x*(b + c*x))^(3/2)*Sqrt[d + e*x])","C",1
1282,1,514,543,4.1360908,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)^(5/2)),x]","-\frac{2 \left(b (d+e x) \left(c^2 d^2 x^2 (b+c x) \left(5 b c (2 A e+B d)-8 A c^2 d-7 b^2 B e\right)+b c^2 d^2 x^2 (b B-A c) (c d-b e)+x (b+c x)^2 (c d-b e)^2 (-2 A b e-8 A c d+3 b B d)+A b d (b+c x)^2 (c d-b e)^2\right)+c x \sqrt{\frac{b}{c}} (b+c x) \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (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) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(b^3 e^2 (2 A e-3 B d)+b^2 c d e (4 A e+13 B d)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(b^3 e^2 (2 A e-3 B d)+b^2 c d e (4 A e+13 B d)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)\right)\right)}{3 b^5 d^2 (x (b+c x))^{3/2} \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^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{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^3 \left(-e^2\right) (3 B d-2 A e)+b^2 c d e (4 A e+13 B d)-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{d+e x} \left(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)+c x \left(b^3 \left(-e^2\right) (3 B d-2 A e)+b^2 c d e (4 A e+13 B d)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}",1,"(-2*(b*(d + e*x)*(b*c^2*(b*B - A*c)*d^2*(c*d - b*e)*x^2 + c^2*d^2*(-8*A*c^2*d - 7*b^2*B*e + 5*b*c*(B*d + 2*A*e))*x^2*(b + c*x) + A*b*d*(c*d - b*e)^2*(b + c*x)^2 + (c*d - b*e)^2*(3*b*B*d - 8*A*c*d - 2*A*b*e)*x*(b + c*x)^2) + Sqrt[b/c]*c*x*(b + c*x)*(Sqrt[b/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))*(b + c*x)*(d + e*x) + I*b*e*(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[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(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))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b^5*d^2*(c*d - b*e)^2*(x*(b + c*x))^(3/2)*Sqrt[d + e*x])","C",1
1283,1,628,706,5.4673368,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)^(5/2)),x]","\frac{2 \left(b \left(3 b^4 e^4 x^2 (b+c x)^2 (B d-A e)+c^3 d^3 x^2 (b+c x) (d+e x) \left(-b c (13 A e+5 B d)+8 A c^2 d+10 b^2 B e\right)+b c^3 d^3 x^2 (d+e x) (b B-A c) (b e-c d)+x (b+c x)^2 (d+e x) (c d-b e)^3 (5 A b e+8 A c d-3 b B d)+A b d (b+c x)^2 (d+e x) (b e-c d)^3\right)-c x \sqrt{\frac{b}{c}} (b+c x) \left(-i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} (c d-b e) \left(b^3 \left(8 A e^3-6 B d e^2\right)+3 b^2 c d e (2 B d-A e)-b c^2 d^2 (9 A e+4 B d)+8 A c^3 d^3\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+i b e x^{3/2} \sqrt{\frac{b}{c x}+1} \sqrt{\frac{d}{e x}+1} \left(2 b^4 e^3 (3 B d-4 A e)+b^3 c d e^2 (7 A e-9 B d)+b^2 c^2 d^2 e (9 A e+19 B d)-8 b c^3 d^3 (4 A e+B d)+16 A c^4 d^4\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b}{c}}}{\sqrt{x}}\right)|\frac{c d}{b e}\right)+\sqrt{\frac{b}{c}} (b+c x) (d+e x) \left(2 b^4 e^3 (3 B d-4 A e)+b^3 c d e^2 (7 A e-9 B d)+b^2 c^2 d^2 e (9 A e+19 B d)-8 b c^3 d^3 (4 A e+B d)+16 A c^4 d^4\right)\right)\right)}{3 b^5 d^3 (x (b+c x))^{3/2} \sqrt{d+e x} (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 \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 \left(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)+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)\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{d+e x} \left(2 b^4 e^3 (3 B d-4 A e)-b^3 c d e^2 (9 B d-7 A e)+b^2 c^2 d^2 e (9 A e+19 B d)-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 e \sqrt{b x+c x^2} \left(b^4 \left(6 B d e^3-8 A e^4\right)-b^3 c d e^2 (9 B d-7 A e)+b^2 c^2 d^2 e (9 A e+19 B d)-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}",1,"(2*(b*(3*b^4*e^4*(B*d - A*e)*x^2*(b + c*x)^2 + b*c^3*(b*B - A*c)*d^3*(-(c*d) + b*e)*x^2*(d + e*x) + c^3*d^3*(8*A*c^2*d + 10*b^2*B*e - b*c*(5*B*d + 13*A*e))*x^2*(b + c*x)*(d + e*x) + A*b*d*(-(c*d) + b*e)^3*(b + c*x)^2*(d + e*x) + (c*d - b*e)^3*(-3*b*B*d + 8*A*c*d + 5*A*b*e)*x*(b + c*x)^2*(d + e*x)) - Sqrt[b/c]*c*x*(b + c*x)*(Sqrt[b/c]*(16*A*c^4*d^4 + 2*b^4*e^3*(3*B*d - 4*A*e) - 8*b*c^3*d^3*(B*d + 4*A*e) + b^3*c*d*e^2*(-9*B*d + 7*A*e) + b^2*c^2*d^2*e*(19*B*d + 9*A*e))*(b + c*x)*(d + e*x) + I*b*e*(16*A*c^4*d^4 + 2*b^4*e^3*(3*B*d - 4*A*e) - 8*b*c^3*d^3*(B*d + 4*A*e) + b^3*c*d*e^2*(-9*B*d + 7*A*e) + b^2*c^2*d^2*e*(19*B*d + 9*A*e))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticE[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)] - I*b*e*(c*d - b*e)*(8*A*c^3*d^3 + 3*b^2*c*d*e*(2*B*d - A*e) - b*c^2*d^2*(4*B*d + 9*A*e) + b^3*(-6*B*d*e^2 + 8*A*e^3))*Sqrt[1 + b/(c*x)]*Sqrt[1 + d/(e*x)]*x^(3/2)*EllipticF[I*ArcSinh[Sqrt[b/c]/Sqrt[x]], (c*d)/(b*e)])))/(3*b^5*d^3*(c*d - b*e)^3*(x*(b + c*x))^(3/2)*Sqrt[d + e*x])","C",1
1284,1,233,108,0.058187,"\int (A+B x) (d+e x)^5 \left(a+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^5*(a + c*x^2),x]","\frac{1}{7} e^3 x^7 \left(a B e^2+5 A c d e+10 B c d^2\right)+\frac{1}{3} d^3 x^3 \left(10 a A e^2+5 a B d e+A c d^2\right)+\frac{1}{6} e^2 x^6 \left(a A e^3+5 a B d e^2+10 A c d^2 e+10 B c d^3\right)+d e x^5 \left(a A e^3+2 a B d e^2+2 A c d^2 e+B c d^3\right)+\frac{1}{4} d^2 x^4 \left(10 a A e^3+10 a B d e^2+5 A c d^2 e+B c d^3\right)+\frac{1}{2} a d^4 x^2 (5 A e+B d)+a A d^5 x+\frac{1}{8} c e^4 x^8 (A e+5 B d)+\frac{1}{9} B c e^5 x^9","\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,"a*A*d^5*x + (a*d^4*(B*d + 5*A*e)*x^2)/2 + (d^3*(A*c*d^2 + 5*a*B*d*e + 10*a*A*e^2)*x^3)/3 + (d^2*(B*c*d^3 + 5*A*c*d^2*e + 10*a*B*d*e^2 + 10*a*A*e^3)*x^4)/4 + d*e*(B*c*d^3 + 2*A*c*d^2*e + 2*a*B*d*e^2 + a*A*e^3)*x^5 + (e^2*(10*B*c*d^3 + 10*A*c*d^2*e + 5*a*B*d*e^2 + a*A*e^3)*x^6)/6 + (e^3*(10*B*c*d^2 + 5*A*c*d*e + a*B*e^2)*x^7)/7 + (c*e^4*(5*B*d + A*e)*x^8)/8 + (B*c*e^5*x^9)/9","B",1
1285,1,194,108,0.0483335,"\int (A+B x) (d+e x)^4 \left(a+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a + c*x^2),x]","\frac{1}{6} e^2 x^6 \left(a B e^2+4 A c d e+6 B c d^2\right)+\frac{1}{3} d^2 x^3 \left(6 a A e^2+4 a B d e+A c d^2\right)+\frac{1}{5} e x^5 \left(a A e^3+4 a B d e^2+6 A c d^2 e+4 B c d^3\right)+\frac{1}{4} d x^4 \left(4 a A e^3+6 a B d e^2+4 A c d^2 e+B c d^3\right)+\frac{1}{2} a d^3 x^2 (4 A e+B d)+a A d^4 x+\frac{1}{7} c e^3 x^7 (A e+4 B d)+\frac{1}{8} B c e^4 x^8","\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,"a*A*d^4*x + (a*d^3*(B*d + 4*A*e)*x^2)/2 + (d^2*(A*c*d^2 + 4*a*B*d*e + 6*a*A*e^2)*x^3)/3 + (d*(B*c*d^3 + 4*A*c*d^2*e + 6*a*B*d*e^2 + 4*a*A*e^3)*x^4)/4 + (e*(4*B*c*d^3 + 6*A*c*d^2*e + 4*a*B*d*e^2 + a*A*e^3)*x^5)/5 + (e^2*(6*B*c*d^2 + 4*A*c*d*e + a*B*e^2)*x^6)/6 + (c*e^3*(4*B*d + A*e)*x^7)/7 + (B*c*e^4*x^8)/8","A",1
1286,1,150,108,0.0379375,"\int (A+B x) (d+e x)^3 \left(a+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a + c*x^2),x]","\frac{1}{5} e x^5 \left(a B e^2+3 A c d e+3 B c d^2\right)+\frac{1}{3} d x^3 \left(3 a A e^2+3 a B d e+A c d^2\right)+\frac{1}{4} x^4 \left(a A e^3+3 a B d e^2+3 A c d^2 e+B c d^3\right)+\frac{1}{2} a d^2 x^2 (3 A e+B d)+a A d^3 x+\frac{1}{6} c e^2 x^6 (A e+3 B d)+\frac{1}{7} B c e^3 x^7","\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,"a*A*d^3*x + (a*d^2*(B*d + 3*A*e)*x^2)/2 + (d*(A*c*d^2 + 3*a*B*d*e + 3*a*A*e^2)*x^3)/3 + ((B*c*d^3 + 3*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3)*x^4)/4 + (e*(3*B*c*d^2 + 3*A*c*d*e + a*B*e^2)*x^5)/5 + (c*e^2*(3*B*d + A*e)*x^6)/6 + (B*c*e^3*x^7)/7","A",1
1287,1,106,108,0.0274585,"\int (A+B x) (d+e x)^2 \left(a+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a + c*x^2),x]","\frac{1}{4} x^4 \left(a B e^2+2 A c d e+B c d^2\right)+\frac{1}{3} x^3 \left(a A e^2+2 a B d e+A c d^2\right)+\frac{1}{2} a d x^2 (2 A e+B d)+a A d^2 x+\frac{1}{5} c e x^5 (A e+2 B d)+\frac{1}{6} B c e^2 x^6","\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,"a*A*d^2*x + (a*d*(B*d + 2*A*e)*x^2)/2 + ((A*c*d^2 + 2*a*B*d*e + a*A*e^2)*x^3)/3 + ((B*c*d^2 + 2*A*c*d*e + a*B*e^2)*x^4)/4 + (c*e*(2*B*d + A*e)*x^5)/5 + (B*c*e^2*x^6)/6","A",1
1288,1,62,62,0.0211682,"\int (A+B x) (d+e x) \left(a+c x^2\right) \, dx","Integrate[(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",1
1289,1,32,31,0.0014245,"\int (A+B x) \left(a+c x^2\right) \, dx","Integrate[(A + B*x)*(a + c*x^2),x]","a A x+\frac{1}{2} a B x^2+\frac{1}{3} A c x^3+\frac{1}{4} B c x^4","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*B*x^2)/2 + (A*c*x^3)/3 + (B*c*x^4)/4","A",1
1290,1,80,86,0.040203,"\int \frac{(A+B x) \left(a+c x^2\right)}{d+e x} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x),x]","\frac{e x \left(6 a B e^2+3 A c e (e x-2 d)+B c \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)-6 \left(a e^2+c d^2\right) (B d-A e) \log (d+e x)}{6 e^4}","-\frac{\left(a e^2+c d^2\right) (B d-A e) \log (d+e x)}{e^4}+\frac{x \left(a B e^2-A c d e+B c d^2\right)}{e^3}-\frac{c x^2 (B d-A e)}{2 e^2}+\frac{B c x^3}{3 e}",1,"(e*x*(6*a*B*e^2 + 3*A*c*e*(-2*d + e*x) + B*c*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) - 6*(B*d - A*e)*(c*d^2 + a*e^2)*Log[d + e*x])/(6*e^4)","A",1
1291,1,86,89,0.0610779,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x)^2,x]","\frac{\frac{2 \left(a e^2+c d^2\right) (B d-A e)}{d+e x}+2 \log (d+e x) \left(a B e^2-2 A c d e+3 B c d^2\right)+2 c e x (A e-2 B d)+B c e^2 x^2}{2 e^4}","\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,"(2*c*e*(-2*B*d + A*e)*x + B*c*e^2*x^2 + (2*(B*d - A*e)*(c*d^2 + a*e^2))/(d + e*x) + 2*(3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*Log[d + e*x])/(2*e^4)","A",1
1292,1,88,94,0.0751905,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x)^3,x]","\frac{\frac{\left(a e^2+c d^2\right) (B d-A e)}{(d+e x)^2}-\frac{2 \left(a B e^2-2 A c d e+3 B c d^2\right)}{d+e x}+2 \log (d+e x) (A c e-3 B c d)+2 B c e x}{2 e^4}","\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,"(2*B*c*e*x + ((B*d - A*e)*(c*d^2 + a*e^2))/(d + e*x)^2 - (2*(3*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(d + e*x) + 2*(-3*B*c*d + A*c*e)*Log[d + e*x])/(2*e^4)","A",1
1293,1,98,101,0.0488827,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x)^4,x]","\frac{-2 A e \left(a e^2+c \left(d^2+3 d e x+3 e^2 x^2\right)\right)+B \left(c d \left(11 d^2+27 d e x+18 e^2 x^2\right)-a e^2 (d+3 e x)\right)+6 B c (d+e x)^3 \log (d+e x)}{6 e^4 (d+e x)^3}","-\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,"(-2*A*e*(a*e^2 + c*(d^2 + 3*d*e*x + 3*e^2*x^2)) + B*(-(a*e^2*(d + 3*e*x)) + c*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) + 6*B*c*(d + e*x)^3*Log[d + e*x])/(6*e^4*(d + e*x)^3)","A",1
1294,1,87,106,0.0443865,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x)^5,x]","-\frac{3 a A e^3+a B e^2 (d+4 e x)+A c e \left(d^2+4 d e x+6 e^2 x^2\right)+3 B c \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)}{12 e^4 (d+e x)^4}","-\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,"-1/12*(3*a*A*e^3 + a*B*e^2*(d + 4*e*x) + A*c*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*B*c*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3))/(e^4*(d + e*x)^4)","A",1
1295,1,90,108,0.0416455,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x)^6,x]","-\frac{2 A e \left(6 a e^2+c \left(d^2+5 d e x+10 e^2 x^2\right)\right)+3 B \left(a e^2 (d+5 e x)+c \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)}{60 e^4 (d+e x)^5}","-\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,"-1/60*(2*A*e*(6*a*e^2 + c*(d^2 + 5*d*e*x + 10*e^2*x^2)) + 3*B*(a*e^2*(d + 5*e*x) + c*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)))/(e^4*(d + e*x)^5)","A",1
1296,1,87,108,0.0424834,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x)^7,x]","-\frac{10 a A e^3+2 a B e^2 (d+6 e x)+A c e \left(d^2+6 d e x+15 e^2 x^2\right)+B c \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)}{60 e^4 (d+e x)^6}","-\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,"-1/60*(10*a*A*e^3 + 2*a*B*e^2*(d + 6*e*x) + A*c*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + B*c*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3))/(e^4*(d + e*x)^6)","A",1
1297,1,390,206,0.0970874,"\int (A+B x) (d+e x)^5 \left(a+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^5*(a + c*x^2)^2,x]","\frac{1}{7} e x^7 \left(a^2 B e^4+10 a A c d e^3+20 a B c d^2 e^2+10 A c^2 d^3 e+5 B c^2 d^4\right)+\frac{1}{5} d x^5 \left(5 a^2 A e^4+10 a^2 B d e^3+20 a A c d^2 e^2+10 a B c d^3 e+A c^2 d^4\right)+\frac{1}{6} x^6 \left(a^2 A e^5+5 a^2 B d e^4+20 a A c d^2 e^3+20 a B c d^3 e^2+5 A c^2 d^4 e+B c^2 d^5\right)+\frac{1}{2} a^2 d^4 x^2 (5 A e+B d)+a^2 A d^5 x+\frac{1}{9} c e^3 x^9 \left(2 a B e^2+5 A c d e+10 B c d^2\right)+\frac{1}{3} a d^3 x^3 \left(10 a A e^2+5 a B d e+2 A c d^2\right)+\frac{1}{4} c e^2 x^8 \left(a A e^3+5 a B d e^2+5 A c d^2 e+5 B c d^3\right)+\frac{1}{2} a d^2 x^4 \left(5 a A e^3+5 a B d e^2+5 A c d^2 e+B c d^3\right)+\frac{1}{10} c^2 e^4 x^{10} (A e+5 B d)+\frac{1}{11} B c^2 e^5 x^{11}","\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{(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 (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{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,"a^2*A*d^5*x + (a^2*d^4*(B*d + 5*A*e)*x^2)/2 + (a*d^3*(2*A*c*d^2 + 5*a*B*d*e + 10*a*A*e^2)*x^3)/3 + (a*d^2*(B*c*d^3 + 5*A*c*d^2*e + 5*a*B*d*e^2 + 5*a*A*e^3)*x^4)/2 + (d*(A*c^2*d^4 + 10*a*B*c*d^3*e + 20*a*A*c*d^2*e^2 + 10*a^2*B*d*e^3 + 5*a^2*A*e^4)*x^5)/5 + ((B*c^2*d^5 + 5*A*c^2*d^4*e + 20*a*B*c*d^3*e^2 + 20*a*A*c*d^2*e^3 + 5*a^2*B*d*e^4 + a^2*A*e^5)*x^6)/6 + (e*(5*B*c^2*d^4 + 10*A*c^2*d^3*e + 20*a*B*c*d^2*e^2 + 10*a*A*c*d*e^3 + a^2*B*e^4)*x^7)/7 + (c*e^2*(5*B*c*d^3 + 5*A*c*d^2*e + 5*a*B*d*e^2 + a*A*e^3)*x^8)/4 + (c*e^3*(10*B*c*d^2 + 5*A*c*d*e + 2*a*B*e^2)*x^9)/9 + (c^2*e^4*(5*B*d + A*e)*x^10)/10 + (B*c^2*e^5*x^11)/11","A",1
1298,1,314,206,0.0776957,"\int (A+B x) (d+e x)^4 \left(a+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a + c*x^2)^2,x]","\frac{1}{6} x^6 \left(a^2 B e^4+8 a A c d e^3+12 a B c d^2 e^2+4 A c^2 d^3 e+B c^2 d^4\right)+\frac{1}{5} x^5 \left(a^2 A e^4+4 a^2 B d e^3+12 a A c d^2 e^2+8 a B c d^3 e+A c^2 d^4\right)+\frac{1}{2} a^2 d^3 x^2 (4 A e+B d)+a^2 A d^4 x+\frac{1}{4} c e^2 x^8 \left(a B e^2+2 A c d e+3 B c d^2\right)+\frac{2}{3} a d^2 x^3 \left(3 a A e^2+2 a B d e+A c d^2\right)+\frac{2}{7} c e x^7 \left(a A e^3+4 a B d e^2+3 A c d^2 e+2 B c d^3\right)+\frac{1}{2} a d x^4 \left(2 a A e^3+3 a B d e^2+4 A c d^2 e+B c d^3\right)+\frac{1}{9} c^2 e^3 x^9 (A e+4 B d)+\frac{1}{10} B c^2 e^4 x^{10}","\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{(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{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{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,"a^2*A*d^4*x + (a^2*d^3*(B*d + 4*A*e)*x^2)/2 + (2*a*d^2*(A*c*d^2 + 2*a*B*d*e + 3*a*A*e^2)*x^3)/3 + (a*d*(B*c*d^3 + 4*A*c*d^2*e + 3*a*B*d*e^2 + 2*a*A*e^3)*x^4)/2 + ((A*c^2*d^4 + 8*a*B*c*d^3*e + 12*a*A*c*d^2*e^2 + 4*a^2*B*d*e^3 + a^2*A*e^4)*x^5)/5 + ((B*c^2*d^4 + 4*A*c^2*d^3*e + 12*a*B*c*d^2*e^2 + 8*a*A*c*d*e^3 + a^2*B*e^4)*x^6)/6 + (2*c*e*(2*B*c*d^3 + 3*A*c*d^2*e + 4*a*B*d*e^2 + a*A*e^3)*x^7)/7 + (c*e^2*(3*B*c*d^2 + 2*A*c*d*e + a*B*e^2)*x^8)/4 + (c^2*e^3*(4*B*d + A*e)*x^9)/9 + (B*c^2*e^4*x^10)/10","A",1
1299,1,244,206,0.065792,"\int (A+B x) (d+e x)^3 \left(a+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a + c*x^2)^2,x]","\frac{1}{5} x^5 \left(a^2 B e^3+6 a A c d e^2+6 a B c d^2 e+A c^2 d^3\right)+\frac{1}{2} a^2 d^2 x^2 (3 A e+B d)+a^2 A d^3 x+\frac{1}{7} c e x^7 \left(2 a B e^2+3 A c d e+3 B c d^2\right)+\frac{1}{3} a d x^3 \left(3 a A e^2+3 a B d e+2 A c d^2\right)+\frac{1}{6} c x^6 \left(2 a A e^3+6 a B d e^2+3 A c d^2 e+B c d^3\right)+\frac{1}{4} a x^4 \left(a A e^3+3 a B d e^2+6 A c d^2 e+2 B c d^3\right)+\frac{1}{8} c^2 e^2 x^8 (A e+3 B d)+\frac{1}{9} B c^2 e^3 x^9","\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{(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 (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{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,"a^2*A*d^3*x + (a^2*d^2*(B*d + 3*A*e)*x^2)/2 + (a*d*(2*A*c*d^2 + 3*a*B*d*e + 3*a*A*e^2)*x^3)/3 + (a*(2*B*c*d^3 + 6*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3)*x^4)/4 + ((A*c^2*d^3 + 6*a*B*c*d^2*e + 6*a*A*c*d*e^2 + a^2*B*e^3)*x^5)/5 + (c*(B*c*d^3 + 3*A*c*d^2*e + 6*a*B*d*e^2 + 2*a*A*e^3)*x^6)/6 + (c*e*(3*B*c*d^2 + 3*A*c*d*e + 2*a*B*e^2)*x^7)/7 + (c^2*e^2*(3*B*d + A*e)*x^8)/8 + (B*c^2*e^3*x^9)/9","A",1
1300,1,174,206,0.0443604,"\int (A+B x) (d+e x)^2 \left(a+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a + c*x^2)^2,x]","\frac{1}{2} a^2 d x^2 (2 A e+B d)+a^2 A d^2 x+\frac{1}{6} c x^6 \left(2 a B e^2+2 A c d e+B c d^2\right)+\frac{1}{5} c x^5 \left(2 a A e^2+4 a B d e+A c d^2\right)+\frac{1}{4} a x^4 \left(a B e^2+4 A c d e+2 B c d^2\right)+\frac{1}{3} a x^3 \left(a A e^2+2 a B d e+2 A c d^2\right)+\frac{1}{7} c^2 e x^7 (A e+2 B d)+\frac{1}{8} B c^2 e^2 x^8","\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{(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{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{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,"a^2*A*d^2*x + (a^2*d*(B*d + 2*A*e)*x^2)/2 + (a*(2*A*c*d^2 + 2*a*B*d*e + a*A*e^2)*x^3)/3 + (a*(2*B*c*d^2 + 4*A*c*d*e + a*B*e^2)*x^4)/4 + (c*(A*c*d^2 + 4*a*B*d*e + 2*a*A*e^2)*x^5)/5 + (c*(B*c*d^2 + 2*A*c*d*e + 2*a*B*e^2)*x^6)/6 + (c^2*e*(2*B*d + A*e)*x^7)/7 + (B*c^2*e^2*x^8)/8","A",1
1301,1,95,106,0.0442837,"\int (A+B x) (d+e x) \left(a+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)*(a + c*x^2)^2,x]","\frac{1}{210} x \left(35 a^2 (3 A (2 d+e x)+B x (3 d+2 e x))+7 a c x^2 (5 A (4 d+3 e x)+3 B x (5 d+4 e x))+c^2 x^4 (7 A (6 d+5 e x)+5 B x (7 d+6 e x))\right)","\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,"(x*(35*a^2*(3*A*(2*d + e*x) + B*x*(3*d + 2*e*x)) + 7*a*c*x^2*(5*A*(4*d + 3*e*x) + 3*B*x*(5*d + 4*e*x)) + c^2*x^4*(7*A*(6*d + 5*e*x) + 5*B*x*(7*d + 6*e*x))))/210","A",1
1302,1,60,45,0.0021629,"\int (A+B x) \left(a+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(a + c*x^2)^2,x]","a^2 A x+\frac{1}{2} a^2 B x^2+\frac{2}{3} a A c x^3+\frac{1}{2} a B c x^4+\frac{1}{5} A c^2 x^5+\frac{1}{6} B c^2 x^6","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 + (a^2*B*x^2)/2 + (2*a*A*c*x^3)/3 + (a*B*c*x^4)/2 + (A*c^2*x^5)/5 + (B*c^2*x^6)/6","A",1
1303,1,174,169,0.0977883,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{d+e x} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x),x]","\frac{e x \left(B \left(60 a^2 e^4+20 a c e^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)+c^2 \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)+5 A c e \left(12 a e^2 (e x-2 d)+c \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)\right)-60 \left(a e^2+c d^2\right)^2 (B d-A e) \log (d+e x)}{60 e^6}","-\frac{\left(a e^2+c d^2\right)^2 (B d-A e) \log (d+e x)}{e^6}+\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{c x^2 \left(2 a e^2+c d^2\right) (B d-A e)}{2 e^4}+\frac{c x^3 \left(2 a B e^2-A c d e+B c d^2\right)}{3 e^3}-\frac{c^2 x^4 (B d-A e)}{4 e^2}+\frac{B c^2 x^5}{5 e}",1,"(e*x*(5*A*c*e*(12*a*e^2*(-2*d + e*x) + c*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)) + B*(60*a^2*e^4 + 20*a*c*e^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + c^2*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4))) - 60*(B*d - A*e)*(c*d^2 + a*e^2)^2*Log[d + e*x])/(60*e^6)","A",1
1304,1,175,180,0.1377683,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^2,x]","\frac{6 c e^2 x^2 \left(2 a B e^2-2 A c d e+3 B c d^2\right)+\frac{12 \left(a e^2+c d^2\right)^2 (B d-A e)}{d+e x}+12 \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)+12 c e x \left(A e \left(2 a e^2+3 c d^2\right)-4 B \left(a d e^2+c d^3\right)\right)+4 c^2 e^3 x^3 (A e-2 B d)+3 B c^2 e^4 x^4}{12 e^6}","\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 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{c^2 x^3 (2 B d-A e)}{3 e^3}+\frac{B c^2 x^4}{4 e^2}",1,"(12*c*e*(A*e*(3*c*d^2 + 2*a*e^2) - 4*B*(c*d^3 + a*d*e^2))*x + 6*c*e^2*(3*B*c*d^2 - 2*A*c*d*e + 2*a*B*e^2)*x^2 + 4*c^2*e^3*(-2*B*d + A*e)*x^3 + 3*B*c^2*e^4*x^4 + (12*(B*d - A*e)*(c*d^2 + a*e^2)^2)/(d + e*x) + 12*(c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*Log[d + e*x])/(12*e^6)","A",1
1305,1,174,185,0.1616496,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^3,x]","\frac{6 c e x \left(2 a B e^2-3 A c d e+6 B c d^2\right)-\frac{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)}{d+e x}+\frac{3 \left(a e^2+c d^2\right)^2 (B d-A e)}{(d+e x)^2}+12 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)+3 c^2 e^2 x^2 (A e-3 B d)+2 B c^2 e^3 x^3}{6 e^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)}{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{c x \left(2 a B e^2-3 A c d e+6 B c d^2\right)}{e^5}-\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,"(6*c*e*(6*B*c*d^2 - 3*A*c*d*e + 2*a*B*e^2)*x + 3*c^2*e^2*(-3*B*d + A*e)*x^2 + 2*B*c^2*e^3*x^3 + (3*(B*d - A*e)*(c*d^2 + a*e^2)^2)/(d + e*x)^2 - (6*(c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(d + e*x) + 12*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])/(6*e^6)","A",1
1306,1,232,189,0.1126256,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^4,x]","\frac{-2 A e \left(a^2 e^4+2 a c e^2 \left(d^2+3 d e x+3 e^2 x^2\right)+c^2 \left(13 d^4+27 d^3 e x+9 d^2 e^2 x^2-9 d e^3 x^3-3 e^4 x^4\right)\right)+B \left(-a^2 e^4 (d+3 e x)+2 a c d e^2 \left(11 d^2+27 d e x+18 e^2 x^2\right)+c^2 \left(47 d^5+81 d^4 e x-9 d^3 e^2 x^2-63 d^2 e^3 x^3-15 d e^4 x^4+3 e^5 x^5\right)\right)+12 c (d+e x)^3 \log (d+e x) \left(a B e^2-2 A c d e+5 B c d^2\right)}{6 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)}{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{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{c^2 x (4 B d-A e)}{e^5}+\frac{B c^2 x^2}{2 e^4}",1,"(-2*A*e*(a^2*e^4 + 2*a*c*e^2*(d^2 + 3*d*e*x + 3*e^2*x^2) + c^2*(13*d^4 + 27*d^3*e*x + 9*d^2*e^2*x^2 - 9*d*e^3*x^3 - 3*e^4*x^4)) + B*(-(a^2*e^4*(d + 3*e*x)) + 2*a*c*d*e^2*(11*d^2 + 27*d*e*x + 18*e^2*x^2) + c^2*(47*d^5 + 81*d^4*e*x - 9*d^3*e^2*x^2 - 63*d^2*e^3*x^3 - 15*d*e^4*x^4 + 3*e^5*x^5)) + 12*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^3*Log[d + e*x])/(6*e^6*(d + e*x)^3)","A",1
1307,1,221,189,0.1059313,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^5,x]","\frac{A e \left(-3 a^2 e^4-2 a c e^2 \left(d^2+4 d e x+6 e^2 x^2\right)+c^2 d \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)\right)-B \left(a^2 e^4 (d+4 e x)+6 a c e^2 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)+c^2 \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)\right)-12 c^2 (d+e x)^4 (5 B d-A e) \log (d+e x)}{12 e^6 (d+e x)^4}","-\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{\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 \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{c^2 (5 B d-A e) \log (d+e x)}{e^6}+\frac{B c^2 x}{e^5}",1,"(A*e*(-3*a^2*e^4 - 2*a*c*e^2*(d^2 + 4*d*e*x + 6*e^2*x^2) + c^2*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) - B*(a^2*e^4*(d + 4*e*x) + 6*a*c*e^2*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) + c^2*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5)) - 12*c^2*(5*B*d - A*e)*(d + e*x)^4*Log[d + e*x])/(12*e^6*(d + e*x)^4)","A",1
1308,1,212,197,0.1058564,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^6,x]","\frac{-4 A e \left(3 a^2 e^4+a c e^2 \left(d^2+5 d e x+10 e^2 x^2\right)+3 c^2 \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)+B \left(-3 a^2 e^4 (d+5 e x)-6 a c e^2 \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+c^2 d \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)\right)+60 B c^2 (d+e x)^5 \log (d+e x)}{60 e^6 (d+e x)^5}","-\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{\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{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{c^2 (5 B d-A e)}{e^6 (d+e x)}+\frac{B c^2 \log (d+e x)}{e^6}",1,"(-4*A*e*(3*a^2*e^4 + a*c*e^2*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*c^2*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4)) + B*(-3*a^2*e^4*(d + 5*e*x) - 6*a*c*e^2*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + c^2*d*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4)) + 60*B*c^2*(d + e*x)^5*Log[d + e*x])/(60*e^6*(d + e*x)^5)","A",1
1309,1,198,204,0.0952577,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^7,x]","-\frac{A e \left(5 a^2 e^4+a c e^2 \left(d^2+6 d e x+15 e^2 x^2\right)+c^2 \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)+B \left(a^2 e^4 (d+6 e x)+a c e^2 \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+5 c^2 \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right)\right)}{30 e^6 (d+e x)^6}","-\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{\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 \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{c^2 (5 B d-A e)}{2 e^6 (d+e x)^2}-\frac{B c^2}{e^6 (d+e x)}",1,"-1/30*(A*e*(5*a^2*e^4 + a*c*e^2*(d^2 + 6*d*e*x + 15*e^2*x^2) + c^2*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)) + B*(a^2*e^4*(d + 6*e*x) + a*c*e^2*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 5*c^2*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5)))/(e^6*(d + e*x)^6)","A",1
1310,1,202,206,0.0930112,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^8,x]","-\frac{2 A e \left(15 a^2 e^4+2 a c e^2 \left(d^2+7 d e x+21 e^2 x^2\right)+c^2 \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)+B \left(5 a^2 e^4 (d+7 e x)+3 a c e^2 \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+5 c^2 \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)\right)}{210 e^6 (d+e x)^7}","-\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{\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{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{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,"-1/210*(2*A*e*(15*a^2*e^4 + 2*a*c*e^2*(d^2 + 7*d*e*x + 21*e^2*x^2) + c^2*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)) + B*(5*a^2*e^4*(d + 7*e*x) + 3*a*c*e^2*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 5*c^2*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5)))/(e^6*(d + e*x)^7)","A",1
1311,1,202,206,0.0943965,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^9} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^9,x]","-\frac{A e \left(105 a^2 e^4+10 a c e^2 \left(d^2+8 d e x+28 e^2 x^2\right)+3 c^2 \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)\right)+B \left(15 a^2 e^4 (d+8 e x)+6 a c e^2 \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+5 c^2 \left(d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right)\right)}{840 e^6 (d+e x)^8}","-\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{\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 \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{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,"-1/840*(A*e*(105*a^2*e^4 + 10*a*c*e^2*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*c^2*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4)) + B*(15*a^2*e^4*(d + 8*e*x) + 6*a*c*e^2*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + 5*c^2*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5)))/(e^6*(d + e*x)^8)","A",1
1312,1,202,206,0.0946064,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{10}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^10,x]","-\frac{4 A e \left(70 a^2 e^4+5 a c e^2 \left(d^2+9 d e x+36 e^2 x^2\right)+c^2 \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)\right)+5 B \left(7 a^2 e^4 (d+9 e x)+2 a c e^2 \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)+c^2 \left(d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right)\right)}{2520 e^6 (d+e x)^9}","-\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{\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{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{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,"-1/2520*(4*A*e*(70*a^2*e^4 + 5*a*c*e^2*(d^2 + 9*d*e*x + 36*e^2*x^2) + c^2*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4)) + 5*B*(7*a^2*e^4*(d + 9*e*x) + 2*a*c*e^2*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + c^2*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5)))/(e^6*(d + e*x)^9)","A",1
1313,1,542,334,0.1451073,"\int (A+B x) (d+e x)^5 \left(a+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^5*(a + c*x^2)^3,x]","\frac{1}{2} a^3 d^4 x^2 (5 A e+B d)+a^3 A d^5 x+\frac{1}{9} c e x^9 \left(B \left(3 a^2 e^4+30 a c d^2 e^2+5 c^2 d^4\right)+5 A c d e \left(3 a e^2+2 c d^2\right)\right)+\frac{1}{7} x^7 \left(A c d \left(15 a^2 e^4+30 a c d^2 e^2+c^2 d^4\right)+a B e \left(a^2 e^4+30 a c d^2 e^2+15 c^2 d^4\right)\right)+\frac{1}{5} a d x^5 \left(A \left(5 a^2 e^4+30 a c d^2 e^2+3 c^2 d^4\right)+5 a B d e \left(2 a e^2+3 c d^2\right)\right)+\frac{1}{8} c x^8 \left(A e \left(3 a^2 e^4+30 a c d^2 e^2+5 c^2 d^4\right)+B \left(15 a^2 d e^4+30 a c d^3 e^2+c^2 d^5\right)\right)+\frac{1}{6} a x^6 \left(A e \left(a^2 e^4+30 a c d^2 e^2+15 c^2 d^4\right)+B \left(5 a^2 d e^4+30 a c d^3 e^2+3 c^2 d^5\right)\right)+\frac{1}{3} a^2 d^3 x^3 \left(10 a A e^2+5 a B d e+3 A c d^2\right)+\frac{1}{4} a^2 d^2 x^4 \left(10 a A e^3+10 a B d e^2+15 A c d^2 e+3 B c d^3\right)+\frac{1}{11} c^2 e^3 x^{11} \left(3 a B e^2+5 A c d e+10 B c d^2\right)+\frac{1}{10} c^2 e^2 x^{10} \left(3 a A e^3+15 a B d e^2+10 A c d^2 e+10 B c d^3\right)+\frac{1}{12} c^3 e^4 x^{12} (A e+5 B d)+\frac{1}{13} B c^3 e^5 x^{13}","-\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{(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{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{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,"a^3*A*d^5*x + (a^3*d^4*(B*d + 5*A*e)*x^2)/2 + (a^2*d^3*(3*A*c*d^2 + 5*a*B*d*e + 10*a*A*e^2)*x^3)/3 + (a^2*d^2*(3*B*c*d^3 + 15*A*c*d^2*e + 10*a*B*d*e^2 + 10*a*A*e^3)*x^4)/4 + (a*d*(5*a*B*d*e*(3*c*d^2 + 2*a*e^2) + A*(3*c^2*d^4 + 30*a*c*d^2*e^2 + 5*a^2*e^4))*x^5)/5 + (a*(A*e*(15*c^2*d^4 + 30*a*c*d^2*e^2 + a^2*e^4) + B*(3*c^2*d^5 + 30*a*c*d^3*e^2 + 5*a^2*d*e^4))*x^6)/6 + ((a*B*e*(15*c^2*d^4 + 30*a*c*d^2*e^2 + a^2*e^4) + A*c*d*(c^2*d^4 + 30*a*c*d^2*e^2 + 15*a^2*e^4))*x^7)/7 + (c*(A*e*(5*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4) + B*(c^2*d^5 + 30*a*c*d^3*e^2 + 15*a^2*d*e^4))*x^8)/8 + (c*e*(5*A*c*d*e*(2*c*d^2 + 3*a*e^2) + B*(5*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*x^9)/9 + (c^2*e^2*(10*B*c*d^3 + 10*A*c*d^2*e + 15*a*B*d*e^2 + 3*a*A*e^3)*x^10)/10 + (c^2*e^3*(10*B*c*d^2 + 5*A*c*d*e + 3*a*B*e^2)*x^11)/11 + (c^3*e^4*(5*B*d + A*e)*x^12)/12 + (B*c^3*e^5*x^13)/13","A",1
1314,1,436,334,0.1210234,"\int (A+B x) (d+e x)^4 \left(a+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a + c*x^2)^3,x]","\frac{1}{2} a^3 d^3 x^2 (4 A e+B d)+a^3 A d^4 x+\frac{1}{8} c x^8 \left(B \left(3 a^2 e^4+18 a c d^2 e^2+c^2 d^4\right)+4 A c d e \left(3 a e^2+c d^2\right)\right)+\frac{1}{7} c x^7 \left(A \left(3 a^2 e^4+18 a c d^2 e^2+c^2 d^4\right)+12 a B d e \left(a e^2+c d^2\right)\right)+\frac{1}{6} a x^6 \left(B \left(a^2 e^4+18 a c d^2 e^2+3 c^2 d^4\right)+12 A c d e \left(a e^2+c d^2\right)\right)+\frac{1}{5} a x^5 \left(A \left(a^2 e^4+18 a c d^2 e^2+3 c^2 d^4\right)+4 a B d e \left(a e^2+3 c d^2\right)\right)+\frac{1}{3} a^2 d^2 x^3 \left(6 a A e^2+4 a B d e+3 A c d^2\right)+\frac{1}{4} a^2 d x^4 \left(4 a A e^3+6 a B d e^2+12 A c d^2 e+3 B c d^3\right)+\frac{1}{10} c^2 e^2 x^{10} \left(3 a B e^2+4 A c d e+6 B c d^2\right)+\frac{1}{9} c^2 e x^9 \left(3 a A e^3+12 a B d e^2+6 A c d^2 e+4 B c d^3\right)+\frac{1}{11} c^3 e^3 x^{11} (A e+4 B d)+\frac{1}{12} B c^3 e^4 x^{12}","-\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{(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{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{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,"a^3*A*d^4*x + (a^3*d^3*(B*d + 4*A*e)*x^2)/2 + (a^2*d^2*(3*A*c*d^2 + 4*a*B*d*e + 6*a*A*e^2)*x^3)/3 + (a^2*d*(3*B*c*d^3 + 12*A*c*d^2*e + 6*a*B*d*e^2 + 4*a*A*e^3)*x^4)/4 + (a*(4*a*B*d*e*(3*c*d^2 + a*e^2) + A*(3*c^2*d^4 + 18*a*c*d^2*e^2 + a^2*e^4))*x^5)/5 + (a*(12*A*c*d*e*(c*d^2 + a*e^2) + B*(3*c^2*d^4 + 18*a*c*d^2*e^2 + a^2*e^4))*x^6)/6 + (c*(12*a*B*d*e*(c*d^2 + a*e^2) + A*(c^2*d^4 + 18*a*c*d^2*e^2 + 3*a^2*e^4))*x^7)/7 + (c*(4*A*c*d*e*(c*d^2 + 3*a*e^2) + B*(c^2*d^4 + 18*a*c*d^2*e^2 + 3*a^2*e^4))*x^8)/8 + (c^2*e*(4*B*c*d^3 + 6*A*c*d^2*e + 12*a*B*d*e^2 + 3*a*A*e^3)*x^9)/9 + (c^2*e^2*(6*B*c*d^2 + 4*A*c*d*e + 3*a*B*e^2)*x^10)/10 + (c^3*e^3*(4*B*d + A*e)*x^11)/11 + (B*c^3*e^4*x^12)/12","A",1
1315,1,323,334,0.0931473,"\int (A+B x) (d+e x)^3 \left(a+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a + c*x^2)^3,x]","\frac{1}{2} a^3 d^2 x^2 (3 A e+B d)+a^3 A d^3 x+a^2 d x^3 \left(a A e^2+a B d e+A c d^2\right)+\frac{1}{4} a^2 x^4 \left(a A e^3+3 a B d e^2+9 A c d^2 e+3 B c d^3\right)+\frac{1}{3} c^2 e x^9 \left(a B e^2+A c d e+B c d^2\right)+\frac{1}{8} c^2 x^8 \left(3 a A e^3+9 a B d e^2+3 A c d^2 e+B c d^3\right)+\frac{1}{7} c x^7 \left(A c d \left(9 a e^2+c d^2\right)+3 a B e \left(a e^2+3 c d^2\right)\right)+\frac{1}{5} a x^5 \left(3 A c d \left(3 a e^2+c d^2\right)+a B e \left(a e^2+9 c d^2\right)\right)+\frac{1}{2} a c x^6 \left(a A e^3+3 a B d e^2+3 A c d^2 e+B c d^3\right)+\frac{1}{10} c^3 e^2 x^{10} (A e+3 B d)+\frac{1}{11} B c^3 e^3 x^{11}","-\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{(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 (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{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,"a^3*A*d^3*x + (a^3*d^2*(B*d + 3*A*e)*x^2)/2 + a^2*d*(A*c*d^2 + a*B*d*e + a*A*e^2)*x^3 + (a^2*(3*B*c*d^3 + 9*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3)*x^4)/4 + (a*(a*B*e*(9*c*d^2 + a*e^2) + 3*A*c*d*(c*d^2 + 3*a*e^2))*x^5)/5 + (a*c*(B*c*d^3 + 3*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3)*x^6)/2 + (c*(3*a*B*e*(3*c*d^2 + a*e^2) + A*c*d*(c*d^2 + 9*a*e^2))*x^7)/7 + (c^2*(B*c*d^3 + 3*A*c*d^2*e + 9*a*B*d*e^2 + 3*a*A*e^3)*x^8)/8 + (c^2*e*(B*c*d^2 + A*c*d*e + a*B*e^2)*x^9)/3 + (c^3*e^2*(3*B*d + A*e)*x^10)/10 + (B*c^3*e^3*x^11)/11","A",1
1316,1,238,334,0.0571364,"\int (A+B x) (d+e x)^2 \left(a+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a + c*x^2)^3,x]","\frac{1}{2} a^3 d x^2 (2 A e+B d)+a^3 A d^2 x+\frac{1}{4} a^2 x^4 \left(a B e^2+6 A c d e+3 B c d^2\right)+\frac{1}{3} a^2 x^3 \left(a A e^2+2 a B d e+3 A c d^2\right)+\frac{1}{8} c^2 x^8 \left(3 a B e^2+2 A c d e+B c d^2\right)+\frac{1}{7} c^2 x^7 \left(3 a A e^2+6 a B d e+A c d^2\right)+\frac{1}{2} a c x^6 \left(a B e^2+2 A c d e+B c d^2\right)+\frac{3}{5} a c x^5 \left(a A e^2+2 a B d e+A c d^2\right)+\frac{1}{9} c^3 e x^9 (A e+2 B d)+\frac{1}{10} B c^3 e^2 x^{10}","-\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{(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{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{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,"a^3*A*d^2*x + (a^3*d*(B*d + 2*A*e)*x^2)/2 + (a^2*(3*A*c*d^2 + 2*a*B*d*e + a*A*e^2)*x^3)/3 + (a^2*(3*B*c*d^2 + 6*A*c*d*e + a*B*e^2)*x^4)/4 + (3*a*c*(A*c*d^2 + 2*a*B*d*e + a*A*e^2)*x^5)/5 + (a*c*(B*c*d^2 + 2*A*c*d*e + a*B*e^2)*x^6)/2 + (c^2*(A*c*d^2 + 6*a*B*d*e + 3*a*A*e^2)*x^7)/7 + (c^2*(B*c*d^2 + 2*A*c*d*e + 3*a*B*e^2)*x^8)/8 + (c^3*e*(2*B*d + A*e)*x^9)/9 + (B*c^3*e^2*x^10)/10","A",1
1317,1,135,148,0.0475894,"\int (A+B x) (d+e x) \left(a+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)*(a + c*x^2)^3,x]","\frac{1}{6} a^3 x (3 A (2 d+e x)+B x (3 d+2 e x))+\frac{1}{20} a^2 c x^3 (5 A (4 d+3 e x)+3 B x (5 d+4 e x))+\frac{1}{70} a c^2 x^5 (7 A (6 d+5 e x)+5 B x (7 d+6 e x))+\frac{1}{504} c^3 x^7 (9 A (8 d+7 e x)+7 B x (9 d+8 e x))","\frac{1}{2} a^3 x^2 (A e+B d)+a^3 A d 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}{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*x*(3*A*(2*d + e*x) + B*x*(3*d + 2*e*x)))/6 + (a^2*c*x^3*(5*A*(4*d + 3*e*x) + 3*B*x*(5*d + 4*e*x)))/20 + (a*c^2*x^5*(7*A*(6*d + 5*e*x) + 5*B*x*(7*d + 6*e*x)))/70 + (c^3*x^7*(9*A*(8*d + 7*e*x) + 7*B*x*(9*d + 8*e*x)))/504","A",1
1318,1,85,56,0.002517,"\int (A+B x) \left(a+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(a + c*x^2)^3,x]","a^3 A x+\frac{1}{2} a^3 B x^2+a^2 A c x^3+\frac{3}{4} a^2 B c x^4+\frac{3}{5} a A c^2 x^5+\frac{1}{2} a B c^2 x^6+\frac{1}{7} A c^3 x^7+\frac{1}{8} B c^3 x^8","a^3 A x+a^2 A c x^3+\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^3*B*x^2)/2 + a^2*A*c*x^3 + (3*a^2*B*c*x^4)/4 + (3*a*A*c^2*x^5)/5 + (a*B*c^2*x^6)/2 + (A*c^3*x^7)/7 + (B*c^3*x^8)/8","A",1
1319,1,311,290,0.1778149,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{d+e x} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x),x]","\frac{e x \left(7 A c e \left(90 a^2 e^4 (e x-2 d)+15 a c e^2 \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+c^2 \left(-60 d^5+30 d^4 e x-20 d^3 e^2 x^2+15 d^2 e^3 x^3-12 d e^4 x^4+10 e^5 x^5\right)\right)+B \left(420 a^3 e^6+210 a^2 c e^4 \left(6 d^2-3 d e x+2 e^2 x^2\right)+21 a c^2 e^2 \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)+c^3 \left(420 d^6-210 d^5 e x+140 d^4 e^2 x^2-105 d^3 e^3 x^3+84 d^2 e^4 x^4-70 d e^5 x^5+60 e^6 x^6\right)\right)\right)-420 \left(a e^2+c d^2\right)^3 (B d-A e) \log (d+e x)}{420 e^8}","\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 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{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^2 x^4 \left(3 a e^2+c d^2\right) (B d-A e)}{4 e^4}+\frac{c^2 x^5 \left(3 a B e^2-A c d e+B c d^2\right)}{5 e^3}-\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,"(e*x*(7*A*c*e*(90*a^2*e^4*(-2*d + e*x) + 15*a*c*e^2*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + c^2*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5)) + B*(420*a^3*e^6 + 210*a^2*c*e^4*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + 21*a*c^2*e^2*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + c^3*(420*d^6 - 210*d^5*e*x + 140*d^4*e^2*x^2 - 105*d^3*e^3*x^3 + 84*d^2*e^4*x^4 - 70*d*e^5*x^5 + 60*e^6*x^6))) - 420*(B*d - A*e)*(c*d^2 + a*e^2)^3*Log[d + e*x])/(420*e^8)","A",1
1320,1,405,309,0.1750726,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^2,x]","\frac{6 A e \left(-10 a^3 e^6+30 a^2 c e^4 \left(-d^2+d e x+e^2 x^2\right)+10 a c^2 e^2 \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)+c^3 \left(-10 d^6+50 d^5 e x+30 d^4 e^2 x^2-10 d^3 e^3 x^3+5 d^2 e^4 x^4-3 d e^5 x^5+2 e^6 x^6\right)\right)+B \left(60 a^3 d e^6+90 a^2 c e^4 \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+15 a c^2 e^2 \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)+c^3 \left(60 d^7-360 d^6 e x-210 d^5 e^2 x^2+70 d^4 e^3 x^3-35 d^3 e^4 x^4+21 d^2 e^5 x^5-14 d e^6 x^6+10 e^7 x^7\right)\right)+60 (d+e x) \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)}{60 e^8 (d+e x)}","-\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 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^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,"(6*A*e*(-10*a^3*e^6 + 30*a^2*c*e^4*(-d^2 + d*e*x + e^2*x^2) + 10*a*c^2*e^2*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + c^3*(-10*d^6 + 50*d^5*e*x + 30*d^4*e^2*x^2 - 10*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 3*d*e^5*x^5 + 2*e^6*x^6)) + B*(60*a^3*d*e^6 + 90*a^2*c*e^4*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 15*a*c^2*e^2*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5) + c^3*(60*d^7 - 360*d^6*e*x - 210*d^5*e^2*x^2 + 70*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 - 14*d*e^6*x^6 + 10*e^7*x^7)) + 60*(c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2)*(d + e*x)*Log[d + e*x])/(60*e^8*(d + e*x))","A",1
1321,1,414,300,0.1948686,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^3,x]","\frac{5 A e \left(-2 a^3 e^6+6 a^2 c d e^4 (3 d+4 e x)+6 a c^2 e^2 \left(7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right)+c^3 \left(22 d^6-16 d^5 e x-68 d^4 e^2 x^2-20 d^3 e^3 x^3+5 d^2 e^4 x^4-2 d e^5 x^5+e^6 x^6\right)\right)+B \left(-10 a^3 e^6 (d+2 e x)+30 a^2 c e^4 \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)+10 a c^2 e^2 \left(-27 d^5+6 d^4 e x+63 d^3 e^2 x^2+20 d^2 e^3 x^3-5 d e^4 x^4+2 e^5 x^5\right)+c^3 \left(-130 d^7+160 d^6 e x+500 d^5 e^2 x^2+140 d^4 e^3 x^3-35 d^3 e^4 x^4+14 d^2 e^5 x^5-7 d e^6 x^6+4 e^7 x^7\right)\right)-60 c (d+e x)^2 \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)}{20 e^8 (d+e x)^2}","-\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,"(5*A*e*(-2*a^3*e^6 + 6*a^2*c*d*e^4*(3*d + 4*e*x) + 6*a*c^2*e^2*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4) + c^3*(22*d^6 - 16*d^5*e*x - 68*d^4*e^2*x^2 - 20*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 2*d*e^5*x^5 + e^6*x^6)) + B*(-10*a^3*e^6*(d + 2*e*x) + 30*a^2*c*e^4*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + 10*a*c^2*e^2*(-27*d^5 + 6*d^4*e*x + 63*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5) + c^3*(-130*d^7 + 160*d^6*e*x + 500*d^5*e^2*x^2 + 140*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 14*d^2*e^5*x^5 - 7*d*e^6*x^6 + 4*e^7*x^7)) - 60*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)^2*Log[d + e*x])/(20*e^8*(d + e*x)^2)","A",1
1322,1,294,310,0.1336802,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^4,x]","\frac{12 c \log (d+e x) \left(B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)-4 A c d e \left(3 a e^2+5 c d^2\right)\right)+6 c^2 e^2 x^2 \left(3 a B e^2-4 A c d e+10 B c d^2\right)+12 c^2 e x \left(A e \left(3 a e^2+10 c d^2\right)-4 B \left(3 a d e^2+5 c d^3\right)\right)-\frac{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)}{(d+e x)^2}+\frac{4 \left(a e^2+c d^2\right)^3 (B d-A e)}{(d+e x)^3}+\frac{36 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)}{d+e x}+4 c^3 e^3 x^3 (A e-4 B d)+3 B c^3 e^4 x^4}{12 e^8}","-\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{\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{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{c^3 x^3 (4 B d-A e)}{3 e^5}+\frac{B c^3 x^4}{4 e^4}",1,"(12*c^2*e*(A*e*(10*c*d^2 + 3*a*e^2) - 4*B*(5*c*d^3 + 3*a*d*e^2))*x + 6*c^2*e^2*(10*B*c*d^2 - 4*A*c*d*e + 3*a*B*e^2)*x^2 + 4*c^3*e^3*(-4*B*d + A*e)*x^3 + 3*B*c^3*e^4*x^4 + (4*(B*d - A*e)*(c*d^2 + a*e^2)^3)/(d + e*x)^3 - (6*(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 + (36*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) + 12*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])/(12*e^8)","A",1
1323,1,405,314,0.2099575,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^5,x]","\frac{3 A e \left(-a^3 e^6-a^2 c e^4 \left(d^2+4 d e x+6 e^2 x^2\right)+a c^2 d e^2 \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)+c^3 \left(57 d^6+168 d^5 e x+132 d^4 e^2 x^2-32 d^3 e^3 x^3-68 d^2 e^4 x^4-12 d e^5 x^5+2 e^6 x^6\right)\right)-B \left(a^3 e^6 (d+4 e x)+9 a^2 c e^4 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)+3 a c^2 e^2 \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)+c^3 \left(319 d^7+856 d^6 e x+444 d^5 e^2 x^2-544 d^4 e^3 x^3-556 d^3 e^4 x^4-84 d^2 e^5 x^5+14 d e^6 x^6-4 e^7 x^7\right)\right)+12 c^2 (d+e x)^4 \log (d+e x) \left(3 A e \left(a e^2+5 c d^2\right)-5 B \left(3 a d e^2+7 c d^3\right)\right)}{12 e^8 (d+e x)^4}","\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{\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{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{c^3 x^2 (5 B d-A e)}{2 e^6}+\frac{B c^3 x^3}{3 e^5}",1,"(3*A*e*(-(a^3*e^6) - a^2*c*e^4*(d^2 + 4*d*e*x + 6*e^2*x^2) + a*c^2*d*e^2*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3) + c^3*(57*d^6 + 168*d^5*e*x + 132*d^4*e^2*x^2 - 32*d^3*e^3*x^3 - 68*d^2*e^4*x^4 - 12*d*e^5*x^5 + 2*e^6*x^6)) - B*(a^3*e^6*(d + 4*e*x) + 9*a^2*c*e^4*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) + 3*a*c^2*e^2*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5) + c^3*(319*d^7 + 856*d^6*e*x + 444*d^5*e^2*x^2 - 544*d^4*e^3*x^3 - 556*d^3*e^4*x^4 - 84*d^2*e^5*x^5 + 14*d*e^6*x^6 - 4*e^7*x^7)) + 12*c^2*(3*A*e*(5*c*d^2 + a*e^2) - 5*B*(7*c*d^3 + 3*a*d*e^2))*(d + e*x)^4*Log[d + e*x])/(12*e^8*(d + e*x)^4)","A",1
1324,1,388,313,0.2003383,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^6,x]","\frac{-2 A e \left(2 a^3 e^6+a^2 c e^4 \left(d^2+5 d e x+10 e^2 x^2\right)+6 a c^2 e^2 \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)+c^3 \left(87 d^6+375 d^5 e x+600 d^4 e^2 x^2+400 d^3 e^3 x^3+50 d^2 e^4 x^4-50 d e^5 x^5-10 e^6 x^6\right)\right)+B \left(-a^3 e^6 (d+5 e x)-3 a^2 c e^4 \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+a c^2 d e^2 \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)+c^3 \left(459 d^7+1875 d^6 e x+2700 d^5 e^2 x^2+1300 d^4 e^3 x^3-400 d^3 e^4 x^4-500 d^2 e^5 x^5-70 d e^6 x^6+10 e^7 x^7\right)\right)+60 c^2 (d+e x)^5 \log (d+e x) \left(a B e^2-2 A c d e+7 B c d^2\right)}{20 e^8 (d+e x)^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)}{2 e^8 (d+e x)^2}+\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^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{\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 \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{c^3 x (6 B d-A e)}{e^7}+\frac{B c^3 x^2}{2 e^6}",1,"(-2*A*e*(2*a^3*e^6 + a^2*c*e^4*(d^2 + 5*d*e*x + 10*e^2*x^2) + 6*a*c^2*e^2*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4) + c^3*(87*d^6 + 375*d^5*e*x + 600*d^4*e^2*x^2 + 400*d^3*e^3*x^3 + 50*d^2*e^4*x^4 - 50*d*e^5*x^5 - 10*e^6*x^6)) + B*(-(a^3*e^6*(d + 5*e*x)) - 3*a^2*c*e^4*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + a*c^2*d*e^2*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4) + c^3*(459*d^7 + 1875*d^6*e*x + 2700*d^5*e^2*x^2 + 1300*d^4*e^3*x^3 - 400*d^3*e^4*x^4 - 500*d^2*e^5*x^5 - 70*d*e^6*x^6 + 10*e^7*x^7)) + 60*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^5*Log[d + e*x])/(20*e^8*(d + e*x)^5)","A",1
1325,1,377,320,0.2125393,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^7,x]","-\frac{A e \left(10 a^3 e^6+3 a^2 c e^4 \left(d^2+6 d e x+15 e^2 x^2\right)+6 a c^2 e^2 \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)-c^3 d \left(147 d^5+822 d^4 e x+1875 d^3 e^2 x^2+2200 d^2 e^3 x^3+1350 d e^4 x^4+360 e^5 x^5\right)\right)+B \left(2 a^3 e^6 (d+6 e x)+3 a^2 c e^4 \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+30 a c^2 e^2 \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right)+c^3 \left(669 d^7+3594 d^6 e x+7725 d^5 e^2 x^2+8200 d^4 e^3 x^3+4050 d^3 e^4 x^4+360 d^2 e^5 x^5-360 d e^6 x^6-60 e^7 x^7\right)\right)+60 c^3 (d+e x)^6 (7 B d-A e) \log (d+e x)}{60 e^8 (d+e x)^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)}{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{\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{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{c^3 (7 B d-A e) \log (d+e x)}{e^8}+\frac{B c^3 x}{e^7}",1,"-1/60*(A*e*(10*a^3*e^6 + 3*a^2*c*e^4*(d^2 + 6*d*e*x + 15*e^2*x^2) + 6*a*c^2*e^2*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4) - c^3*d*(147*d^5 + 822*d^4*e*x + 1875*d^3*e^2*x^2 + 2200*d^2*e^3*x^3 + 1350*d*e^4*x^4 + 360*e^5*x^5)) + B*(2*a^3*e^6*(d + 6*e*x) + 3*a^2*c*e^4*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 30*a*c^2*e^2*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5) + c^3*(669*d^7 + 3594*d^6*e*x + 7725*d^5*e^2*x^2 + 8200*d^4*e^3*x^3 + 4050*d^3*e^4*x^4 + 360*d^2*e^5*x^5 - 360*d*e^6*x^6 - 60*e^7*x^7)) + 60*c^3*(7*B*d - A*e)*(d + e*x)^6*Log[d + e*x])/(e^8*(d + e*x)^6)","A",1
1326,1,366,327,0.1956722,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^8,x]","\frac{-12 A e \left(5 a^3 e^6+a^2 c e^4 \left(d^2+7 d e x+21 e^2 x^2\right)+a c^2 e^2 \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)+5 c^3 \left(d^6+7 d^5 e x+21 d^4 e^2 x^2+35 d^3 e^3 x^3+35 d^2 e^4 x^4+21 d e^5 x^5+7 e^6 x^6\right)\right)+B \left(-10 a^3 e^6 (d+7 e x)-9 a^2 c e^4 \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)-30 a c^2 e^2 \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)+c^3 d \left(1089 d^6+7203 d^5 e x+20139 d^4 e^2 x^2+30625 d^3 e^3 x^3+26950 d^2 e^4 x^4+13230 d e^5 x^5+2940 e^6 x^6\right)\right)+420 B c^3 (d+e x)^7 \log (d+e x)}{420 e^8 (d+e x)^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)}{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{\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{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{c^3 (7 B d-A e)}{e^8 (d+e x)}+\frac{B c^3 \log (d+e x)}{e^8}",1,"(-12*A*e*(5*a^3*e^6 + a^2*c*e^4*(d^2 + 7*d*e*x + 21*e^2*x^2) + a*c^2*e^2*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4) + 5*c^3*(d^6 + 7*d^5*e*x + 21*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 35*d^2*e^4*x^4 + 21*d*e^5*x^5 + 7*e^6*x^6)) + B*(-10*a^3*e^6*(d + 7*e*x) - 9*a^2*c*e^4*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) - 30*a*c^2*e^2*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5) + c^3*d*(1089*d^6 + 7203*d^5*e*x + 20139*d^4*e^2*x^2 + 30625*d^3*e^3*x^3 + 26950*d^2*e^4*x^4 + 13230*d*e^5*x^5 + 2940*e^6*x^6)) + 420*B*c^3*(d + e*x)^7*Log[d + e*x])/(420*e^8*(d + e*x)^7)","A",1
1327,1,357,330,0.1724284,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^9} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^9,x]","-\frac{A e \left(35 a^3 e^6+5 a^2 c e^4 \left(d^2+8 d e x+28 e^2 x^2\right)+3 a c^2 e^2 \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)+5 c^3 \left(d^6+8 d^5 e x+28 d^4 e^2 x^2+56 d^3 e^3 x^3+70 d^2 e^4 x^4+56 d e^5 x^5+28 e^6 x^6\right)\right)+B \left(5 a^3 e^6 (d+8 e x)+3 a^2 c e^4 \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+5 a c^2 e^2 \left(d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right)+35 c^3 \left(d^7+8 d^6 e x+28 d^5 e^2 x^2+56 d^4 e^3 x^3+70 d^3 e^4 x^4+56 d^2 e^5 x^5+28 d e^6 x^6+8 e^7 x^7\right)\right)}{280 e^8 (d+e x)^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)}{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{\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 \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{c^3 (7 B d-A e)}{2 e^8 (d+e x)^2}-\frac{B c^3}{e^8 (d+e x)}",1,"-1/280*(A*e*(35*a^3*e^6 + 5*a^2*c*e^4*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*a*c^2*e^2*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4) + 5*c^3*(d^6 + 8*d^5*e*x + 28*d^4*e^2*x^2 + 56*d^3*e^3*x^3 + 70*d^2*e^4*x^4 + 56*d*e^5*x^5 + 28*e^6*x^6)) + B*(5*a^3*e^6*(d + 8*e*x) + 3*a^2*c*e^4*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + 5*a*c^2*e^2*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5) + 35*c^3*(d^7 + 8*d^6*e*x + 28*d^5*e^2*x^2 + 56*d^4*e^3*x^3 + 70*d^3*e^4*x^4 + 56*d^2*e^5*x^5 + 28*d*e^6*x^6 + 8*e^7*x^7)))/(e^8*(d + e*x)^8)","A",1
1328,1,359,334,0.1810396,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{10}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^10,x]","-\frac{2 A e \left(140 a^3 e^6+15 a^2 c e^4 \left(d^2+9 d e x+36 e^2 x^2\right)+6 a c^2 e^2 \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)+5 c^3 \left(d^6+9 d^5 e x+36 d^4 e^2 x^2+84 d^3 e^3 x^3+126 d^2 e^4 x^4+126 d e^5 x^5+84 e^6 x^6\right)\right)+5 B \left(7 a^3 e^6 (d+9 e x)+3 a^2 c e^4 \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)+3 a c^2 e^2 \left(d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right)+7 c^3 \left(d^7+9 d^6 e x+36 d^5 e^2 x^2+84 d^4 e^3 x^3+126 d^3 e^4 x^4+126 d^2 e^5 x^5+84 d e^6 x^6+36 e^7 x^7\right)\right)}{2520 e^8 (d+e x)^9}","\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{\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{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{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,"-1/2520*(2*A*e*(140*a^3*e^6 + 15*a^2*c*e^4*(d^2 + 9*d*e*x + 36*e^2*x^2) + 6*a*c^2*e^2*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4) + 5*c^3*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6)) + 5*B*(7*a^3*e^6*(d + 9*e*x) + 3*a^2*c*e^4*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 3*a*c^2*e^2*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5) + 7*c^3*(d^7 + 9*d^6*e*x + 36*d^5*e^2*x^2 + 84*d^4*e^3*x^3 + 126*d^3*e^4*x^4 + 126*d^2*e^5*x^5 + 84*d*e^6*x^6 + 36*e^7*x^7)))/(e^8*(d + e*x)^9)","A",1
1329,1,357,334,0.1722339,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{11}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^11,x]","-\frac{3 A e \left(84 a^3 e^6+7 a^2 c e^4 \left(d^2+10 d e x+45 e^2 x^2\right)+2 a c^2 e^2 \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)+c^3 \left(d^6+10 d^5 e x+45 d^4 e^2 x^2+120 d^3 e^3 x^3+210 d^2 e^4 x^4+252 d e^5 x^5+210 e^6 x^6\right)\right)+B \left(28 a^3 e^6 (d+10 e x)+9 a^2 c e^4 \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)+6 a c^2 e^2 \left(d^5+10 d^4 e x+45 d^3 e^2 x^2+120 d^2 e^3 x^3+210 d e^4 x^4+252 e^5 x^5\right)+7 c^3 \left(d^7+10 d^6 e x+45 d^5 e^2 x^2+120 d^4 e^3 x^3+210 d^3 e^4 x^4+252 d^2 e^5 x^5+210 d e^6 x^6+120 e^7 x^7\right)\right)}{2520 e^8 (d+e x)^{10}}","\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{\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{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{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,"-1/2520*(3*A*e*(84*a^3*e^6 + 7*a^2*c*e^4*(d^2 + 10*d*e*x + 45*e^2*x^2) + 2*a*c^2*e^2*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4) + c^3*(d^6 + 10*d^5*e*x + 45*d^4*e^2*x^2 + 120*d^3*e^3*x^3 + 210*d^2*e^4*x^4 + 252*d*e^5*x^5 + 210*e^6*x^6)) + B*(28*a^3*e^6*(d + 10*e*x) + 9*a^2*c*e^4*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 6*a*c^2*e^2*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5) + 7*c^3*(d^7 + 10*d^6*e*x + 45*d^5*e^2*x^2 + 120*d^4*e^3*x^3 + 210*d^3*e^4*x^4 + 252*d^2*e^5*x^5 + 210*d*e^6*x^6 + 120*e^7*x^7)))/(e^8*(d + e*x)^10)","A",1
1330,1,217,240,0.1782096,"\int \frac{(A+B x) (d+e x)^4}{a+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a + c*x^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A \left(a^2 e^4-6 a c d^2 e^2+c^2 d^4\right)+4 a B d e \left(a e^2-c d^2\right)\right)}{\sqrt{a} c^{5/2}}+\frac{6 \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)+c e x \left(-12 a A e^3-6 a B e^2 (8 d+e x)+4 A c e \left(18 d^2+6 d e x+e^2 x^2\right)+B c \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)\right)}{12 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{\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{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,"((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)) + (c*e*x*(-12*a*A*e^3 - 6*a*B*e^2*(8*d + e*x) + 4*A*c*e*(18*d^2 + 6*d*e*x + e^2*x^2) + B*c*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3)) + 6*(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])/(12*c^3)","A",1
1331,1,151,167,0.1461603,"\int \frac{(A+B x) (d+e x)^3}{a+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a + c*x^2),x]","\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(a e^2-3 c d^2\right)\right)}{\sqrt{a} c^{5/2}}+\frac{e x \left(-6 a B e^2+3 A c e (6 d+e x)+B c \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+3 \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)}{6 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 x \left(-a B e^2+3 A c d e+3 B c d^2\right)}{c^2}+\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^2 x^2 (A e+3 B d)}{2 c}+\frac{B e^3 x^3}{3 c}",1,"((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)) + (e*x*(-6*a*B*e^2 + 3*A*c*e*(6*d + e*x) + B*c*(18*d^2 + 9*d*e*x + 2*e^2*x^2)) + 3*(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])/(6*c^2)","A",1
1332,1,99,108,0.0890913,"\int \frac{(A+B x) (d+e x)^2}{a+c x^2} \, dx","Integrate[((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)-\frac{2 \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}}+c e x (2 A e+4 B d+B e x)}{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{\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{e x (A e+2 B d)}{c}+\frac{B e^2 x^2}{2 c}",1,"(c*e*x*(4*B*d + 2*A*e + B*e*x) - (2*Sqrt[c]*(-(A*c*d^2) + 2*a*B*d*e + a*A*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[a] + (B*c*d^2 + 2*A*c*d*e - a*B*e^2)*Log[a + c*x^2])/(2*c^2)","A",1
1333,1,65,64,0.0506371,"\int \frac{(A+B x) (d+e x)}{a+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x))/(a + c*x^2),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e-A c d)}{\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",1
1334,1,42,42,0.0133614,"\int \frac{A+B x}{a+c x^2} \, dx","Integrate[(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",1
1335,1,91,109,0.0609867,"\int \frac{A+B x}{(d+e x) \left(a+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)*(a + c*x^2)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+A c d)-\sqrt{a} \sqrt{c} (B d-A e) \left(2 \log (d+e x)-\log \left(a+c x^2\right)\right)}{2 \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,"(2*(A*c*d + a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]] - Sqrt[a]*Sqrt[c]*(B*d - A*e)*(2*Log[d + e*x] - Log[a + c*x^2]))/(2*Sqrt[a]*Sqrt[c]*(c*d^2 + a*e^2))","A",1
1336,1,148,173,0.1811328,"\int \frac{A+B x}{(d+e x)^2 \left(a+c x^2\right)} \, dx","Integrate[(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)+\frac{2 \left(a e^2+c d^2\right) (B d-A e)}{d+e x}+\log (d+e x) \left(2 a B e^2+4 A c d e-2 B c d^2\right)+\frac{2 \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}}}{2 \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,"((2*(B*d - A*e)*(c*d^2 + a*e^2))/(d + e*x) + (2*Sqrt[c]*(A*c*d^2 + 2*a*B*d*e - a*A*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/Sqrt[a] + (-2*B*c*d^2 + 4*A*c*d*e + 2*a*B*e^2)*Log[d + e*x] + (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",1
1337,1,223,251,0.3565113,"\int \frac{A+B x}{(d+e x)^3 \left(a+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^3*(a + c*x^2)),x]","\frac{\frac{\left(a e^2+c d^2\right) \left(B \left(c d^2 (3 d+2 e x)-a e^2 (d+2 e x)\right)-A e \left(a e^2+c d (5 d+4 e x)\right)\right)}{(d+e x)^2}+\frac{2 \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}}+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 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)}{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{\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{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}",1,"(((c*d^2 + a*e^2)*(B*(-(a*e^2*(d + 2*e*x)) + c*d^2*(3*d + 2*e*x)) - A*e*(a*e^2 + c*d*(5*d + 4*e*x))))/(d + e*x)^2 + (2*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] - 2*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*(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",1
1338,1,307,297,0.1750606,"\int \frac{(A+B x) (d+e x)^5}{\left(a+c x^2\right)^2} \, dx","Integrate[((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{-a^3 e^4 (A e+5 B d+B e x)+5 a^2 c d e^2 (A e (2 d+e x)+2 B d (d+e x))-a c^2 d^3 (5 A e (d+2 e x)+B d (d+5 e x))+A c^3 d^5 x}{2 a c^3 \left(a+c x^2\right)}+\frac{e^3 x \left(-2 a B e^2+5 A c d e+10 B c d^2\right)}{c^3}+\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^4 x^2 (A e+5 B d)}{2 c^2}+\frac{B e^5 x^3}{3 c^2}","\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^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^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^3 x^2 \left(-a A e^2-5 a B d e+2 A c d^2\right)}{a c^2}-\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^3*(10*B*c*d^2 + 5*A*c*d*e - 2*a*B*e^2)*x)/c^3 + (e^4*(5*B*d + A*e)*x^2)/(2*c^2) + (B*e^5*x^3)/(3*c^2) + (A*c^3*d^5*x - a^3*e^4*(5*B*d + A*e + B*e*x) + 5*a^2*c*d*e^2*(2*B*d*(d + e*x) + A*e*(2*d + e*x)) - a*c^2*d^3*(5*A*e*(d + 2*e*x) + B*d*(d + 5*e*x)))/(2*a*c^3*(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",1
1339,1,231,220,0.2016624,"\int \frac{(A+B x) (d+e x)^4}{\left(a+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a + c*x^2)^2,x]","\frac{\frac{\sqrt{c} \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)}{a^{3/2}}+\frac{-a^3 B e^4+a^2 c e^2 (A e (4 d+e x)+2 B d (3 d+2 e x))-a c^2 d^2 (2 A e (2 d+3 e x)+B d (d+4 e x))+A c^3 d^4 x}{a \left(a+c x^2\right)}+2 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)+2 c e^3 x (A e+4 B d)+B c e^4 x^2}{2 c^3}","\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,"(2*c*e^3*(4*B*d + A*e)*x + B*c*e^4*x^2 + (-(a^3*B*e^4) + A*c^3*d^4*x + a^2*c*e^2*(A*e*(4*d + e*x) + 2*B*d*(3*d + 2*e*x)) - a*c^2*d^2*(2*A*e*(2*d + 3*e*x) + B*d*(d + 4*e*x)))/(a*(a + c*x^2)) + (Sqrt[c]*(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]])/a^(3/2) + 2*e^2*(3*B*c*d^2 + 2*A*c*d*e - a*B*e^2)*Log[a + c*x^2])/(2*c^3)","A",1
1340,1,171,161,0.1204305,"\int \frac{(A+B x) (d+e x)^3}{\left(a+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a + c*x^2)^2,x]","\frac{\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)}{a^{3/2}}+\frac{\sqrt{c} \left(a^2 e^2 (A e+3 B d+B e x)-a c d (3 A e (d+e x)+B d (d+3 e x))+A c^2 d^3 x\right)}{a \left(a+c x^2\right)}+\sqrt{c} e^2 \log \left(a+c x^2\right) (A e+3 B d)+2 B \sqrt{c} e^3 x}{2 c^{5/2}}","\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,"(2*B*Sqrt[c]*e^3*x + (Sqrt[c]*(A*c^2*d^3*x + a^2*e^2*(3*B*d + A*e + B*e*x) - a*c*d*(3*A*e*(d + e*x) + B*d*(d + 3*e*x))))/(a*(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]])/a^(3/2) + Sqrt[c]*e^2*(3*B*d + A*e)*Log[a + c*x^2])/(2*c^(5/2))","A",1
1341,1,119,112,0.099452,"\int \frac{(A+B x) (d+e x)^2}{\left(a+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a + c*x^2)^2,x]","\frac{\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)}{a^{3/2}}+\frac{a^2 B e^2-a c (A e (2 d+e x)+B d (d+2 e x))+A c^2 d^2 x}{a \left(a+c x^2\right)}+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,"((a^2*B*e^2 + A*c^2*d^2*x - a*c*(A*e*(2*d + e*x) + B*d*(d + 2*e*x)))/(a*(a + c*x^2)) + (Sqrt[c]*(A*c*d^2 + 2*a*B*d*e + a*A*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/a^(3/2) + B*e^2*Log[a + c*x^2])/(2*c^2)","A",1
1342,1,78,79,0.0707493,"\int \frac{(A+B x) (d+e x)}{\left(a+c x^2\right)^2} \, dx","Integrate[((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-a B d-a B e x+A c d x}{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*A*e + A*c*d*x - 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",1
1343,1,57,57,0.0259364,"\int \frac{A+B x}{\left(a+c x^2\right)^2} \, dx","Integrate[(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 c x-a B}{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 c x-a B}{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",1
1344,1,158,195,0.1587161,"\int \frac{A+B x}{(d+e x) \left(a+c x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)*(a + c*x^2)^2),x]","\frac{\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(3 a e^2+c d^2\right)+a B e \left(a e^2-c d^2\right)\right)}{a^{3/2} \sqrt{c}}+\frac{\left(a e^2+c d^2\right) (a (A e-B d+B e x)+A c d x)}{a \left(a+c x^2\right)}+e^2 \log \left(a+c x^2\right) (B d-A e)+2 e^2 (A e-B d) \log (d+e x)}{2 \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,"(((c*d^2 + a*e^2)*(A*c*d*x + a*(-(B*d) + A*e + B*e*x)))/(a*(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]])/(a^(3/2)*Sqrt[c]) + 2*e^2*(-(B*d) + A*e)*Log[d + e*x] + e^2*(B*d - A*e)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^2)","A",1
1345,1,251,290,0.3592995,"\int \frac{A+B x}{(d+e x)^2 \left(a+c x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(a + c*x^2)^2),x]","\frac{\frac{\left(a e^2+c d^2\right) \left(a^2 B e^2-a c (A e (e x-2 d)+B d (d-2 e x))+A c^2 d^2 x\right)}{a \left(a+c x^2\right)}+\frac{\sqrt{c} \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)+2 a B d e \left(3 a e^2-c d^2\right)\right)}{a^{3/2}}-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)-\frac{2 e^2 \left(a e^2+c d^2\right) (A e-B d)}{d+e x}+2 e^2 \log (d+e x) \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{\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,"((-2*e^2*(-(B*d) + A*e)*(c*d^2 + a*e^2))/(d + e*x) + ((c*d^2 + a*e^2)*(a^2*B*e^2 + A*c^2*d^2*x - a*c*(B*d*(d - 2*e*x) + A*e*(-2*d + e*x))))/(a*(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]])/a^(3/2) + 2*e^2*(-3*B*c*d^2 + 4*A*c*d*e + a*B*e^2)*Log[d + e*x] - 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",1
1346,1,341,304,0.2455615,"\int \frac{(A+B x) (d+e x)^5}{\left(a+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^5)/(a + c*x^2)^3,x]","\frac{\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)}{a^{5/2}}+\frac{2 \sqrt{c} \left(-a^3 e^4 (A e+5 B d+B e x)+5 a^2 c d e^2 (A e (2 d+e x)+2 B d (d+e x))-a c^2 d^3 (5 A e (d+2 e x)+B d (d+5 e x))+A c^3 d^5 x\right)}{a \left(a+c x^2\right)^2}+\frac{\sqrt{c} \left(a^3 e^4 (8 A e+40 B d+9 B e x)-5 a^2 c d e^2 (A e (8 d+5 e x)+2 B d (4 d+5 e x))+5 a c^2 d^3 e x (2 A e+B d)+3 A c^3 d^5 x\right)}{a^2 \left(a+c x^2\right)}+4 \sqrt{c} e^4 \log \left(a+c x^2\right) (A e+5 B d)+8 B \sqrt{c} e^5 x}{8 c^{7/2}}","-\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{(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{\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,"(8*B*Sqrt[c]*e^5*x + (2*Sqrt[c]*(A*c^3*d^5*x - a^3*e^4*(5*B*d + A*e + B*e*x) + 5*a^2*c*d*e^2*(2*B*d*(d + e*x) + A*e*(2*d + e*x)) - a*c^2*d^3*(5*A*e*(d + 2*e*x) + B*d*(d + 5*e*x))))/(a*(a + c*x^2)^2) + (Sqrt[c]*(3*A*c^3*d^5*x + 5*a*c^2*d^3*e*(B*d + 2*A*e)*x + a^3*e^4*(40*B*d + 8*A*e + 9*B*e*x) - 5*a^2*c*d*e^2*(2*B*d*(4*d + 5*e*x) + A*e*(8*d + 5*e*x))))/(a^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]])/a^(5/2) + 4*Sqrt[c]*e^4*(5*B*d + A*e)*Log[a + c*x^2])/(8*c^(7/2))","A",1
1347,1,263,216,0.2111753,"\int \frac{(A+B x) (d+e x)^4}{\left(a+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a + c*x^2)^3,x]","\frac{\frac{\sqrt{c} \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)}{a^{5/2}}+\frac{-2 a^3 B e^4+2 a^2 c e^2 (A e (4 d+e x)+2 B d (3 d+2 e x))-2 a c^2 d^2 (2 A e (2 d+3 e x)+B d (d+4 e x))+2 A c^3 d^4 x}{a \left(a+c x^2\right)^2}+\frac{8 a^3 B e^4-a^2 c e^2 (A e (16 d+5 e x)+4 B d (6 d+5 e x))+2 a c^2 d^2 e x (3 A e+2 B d)+3 A c^3 d^4 x}{a^2 \left(a+c x^2\right)}+4 B e^4 \log \left(a+c x^2\right)}{8 c^3}","\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) \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{(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,"((-2*a^3*B*e^4 + 2*A*c^3*d^4*x + 2*a^2*c*e^2*(A*e*(4*d + e*x) + 2*B*d*(3*d + 2*e*x)) - 2*a*c^2*d^2*(2*A*e*(2*d + 3*e*x) + B*d*(d + 4*e*x)))/(a*(a + c*x^2)^2) + (8*a^3*B*e^4 + 3*A*c^3*d^4*x + 2*a*c^2*d^2*e*(2*B*d + 3*A*e)*x - a^2*c*e^2*(4*B*d*(6*d + 5*e*x) + A*e*(16*d + 5*e*x)))/(a^2*(a + c*x^2)) + (Sqrt[c]*(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]])/a^(5/2) + 4*B*e^4*Log[a + c*x^2])/(8*c^3)","A",1
1348,1,186,125,0.0969955,"\int \frac{(A+B x) (d+e x)^3}{\left(a+c x^2\right)^3} \, dx","Integrate[((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{-a^2 e^2 (4 A e+12 B d+5 B e x)+3 a c d e x (A e+B d)+3 A c^2 d^3 x}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{a^2 e^2 (A e+3 B d+B e x)-a c d (3 A e (d+e x)+B d (d+3 e x))+A c^2 d^3 x}{4 a c^2 \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,"(3*A*c^2*d^3*x + 3*a*c*d*e*(B*d + A*e)*x - a^2*e^2*(12*B*d + 4*A*e + 5*B*e*x))/(8*a^2*c^2*(a + c*x^2)) + (A*c^2*d^3*x + a^2*e^2*(3*B*d + A*e + B*e*x) - a*c*d*(3*A*e*(d + e*x) + B*d*(d + 3*e*x)))/(4*a*c^2*(a + c*x^2)^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",1
1349,1,158,142,0.107602,"\int \frac{(A+B x) (d+e x)^2}{\left(a+c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a + c*x^2)^3,x]","\frac{\frac{\sqrt{a} \left(-4 a^2 B e^2+a c e x (A e+2 B d)+3 A c^2 d^2 x\right)}{a+c x^2}+\frac{2 a^{3/2} \left(a^2 B e^2-a c (A e (2 d+e x)+B d (d+2 e x))+A c^2 d^2 x\right)}{\left(a+c x^2\right)^2}+\sqrt{c} \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^2}","\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{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{(d+e x)^2 (a B-A c x)}{4 a c \left(a+c x^2\right)^2}",1,"((Sqrt[a]*(-4*a^2*B*e^2 + 3*A*c^2*d^2*x + a*c*e*(2*B*d + A*e)*x))/(a + c*x^2) + (2*a^(3/2)*(a^2*B*e^2 + A*c^2*d^2*x - a*c*(A*e*(2*d + e*x) + B*d*(d + 2*e*x))))/(a + c*x^2)^2 + Sqrt[c]*(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^2)","A",1
1350,1,101,110,0.0828051,"\int \frac{(A+B x) (d+e x)}{\left(a+c x^2\right)^3} \, dx","Integrate[((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{-a^2 (2 A e+2 B d+B e x)+a c x \left(5 A d+B e x^2\right)+3 A c^2 d x^3}{8 a^2 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,"(3*A*c^2*d*x^3 - a^2*(2*B*d + 2*A*e + B*e*x) + a*c*x*(5*A*d + B*e*x^2))/(8*a^2*c*(a + c*x^2)^2) + ((3*A*c*d + a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(3/2))","A",1
1351,1,71,75,0.0470544,"\int \frac{A+B x}{\left(a+c x^2\right)^3} \, dx","Integrate[(A + B*x)/(a + c*x^2)^3,x]","\frac{\frac{\sqrt{a} \left(-2 a^2 B+5 a A c x+3 A c^2 x^3\right)}{\left(a+c x^2\right)^2}+3 A \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c}","\frac{3 A \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}+\frac{3 A x}{8 a^2 \left(a+c x^2\right)}+\frac{A c x-a B}{4 a c \left(a+c x^2\right)^2}",1,"((Sqrt[a]*(-2*a^2*B + 5*a*A*c*x + 3*A*c^2*x^3))/(a + c*x^2)^2 + 3*A*Sqrt[c]*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c)","A",1
1352,1,263,307,0.2830116,"\int \frac{A+B x}{(d+e x) \left(a+c x^2\right)^3} \, dx","Integrate[(A + B*x)/((d + e*x)*(a + c*x^2)^3),x]","\frac{\frac{\left(a e^2+c d^2\right) \left(a^2 e^2 (4 A e-4 B d+3 B e x)+a c d e x (7 A e-B d)+3 A c^2 d^3 x\right)}{a^2 \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+3 c^2 d^4\right)+a B e \left(3 a^2 e^4-6 a c d^2 e^2-c^2 d^4\right)\right)}{a^{5/2} \sqrt{c}}+\frac{2 \left(a e^2+c d^2\right)^2 (a (A e-B d+B e x)+A c d x)}{a \left(a+c x^2\right)^2}+4 e^4 \log \left(a+c x^2\right) (B d-A e)+8 e^4 (A e-B d) \log (d+e x)}{8 \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{\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{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,"((2*(c*d^2 + a*e^2)^2*(A*c*d*x + a*(-(B*d) + A*e + B*e*x)))/(a*(a + c*x^2)^2) + ((c*d^2 + a*e^2)*(3*A*c^2*d^3*x + a*c*d*e*(-(B*d) + 7*A*e)*x + a^2*e^2*(-4*B*d + 4*A*e + 3*B*e*x)))/(a^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]])/(a^(5/2)*Sqrt[c]) + 8*e^4*(-(B*d) + A*e)*Log[d + e*x] + 4*e^4*(B*d - A*e)*Log[a + c*x^2])/(8*(c*d^2 + a*e^2)^3)","A",1
1353,1,378,443,0.4876401,"\int \frac{A+B x}{(d+e x)^2 \left(a+c x^2\right)^3} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(a + c*x^2)^3),x]","\frac{\frac{2 \left(a e^2+c d^2\right)^2 \left(a^2 B e^2-a c (A e (e x-2 d)+B d (d-2 e x))+A c^2 d^2 x\right)}{a \left(a+c x^2\right)^2}+\frac{\left(a e^2+c d^2\right) \left(4 a^3 B e^4+a^2 c e^2 (A e (16 d-7 e x)-2 B d (6 d-7 e x))-2 a c^2 d^2 e x (B d-6 A e)+3 A c^3 d^4 x\right)}{a^2 \left(a+c x^2\right)}+\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(-5 a^3 e^6+15 a^2 c d^2 e^4+5 a c^2 d^4 e^2+c^3 d^6\right)\right)}{a^{5/2}}-4 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)-\frac{8 e^4 \left(a e^2+c d^2\right) (A e-B d)}{d+e x}+8 e^4 \log (d+e x) \left(a B e^2+6 A c d e-5 B c d^2\right)}{8 \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{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{\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(-5 a^3 e^6+15 a^2 c d^2 e^4+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{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,"((-8*e^4*(-(B*d) + A*e)*(c*d^2 + a*e^2))/(d + e*x) + ((c*d^2 + a*e^2)*(4*a^3*B*e^4 + 3*A*c^3*d^4*x - 2*a*c^2*d^2*e*(B*d - 6*A*e)*x + a^2*c*e^2*(-2*B*d*(6*d - 7*e*x) + A*e*(16*d - 7*e*x))))/(a^2*(a + c*x^2)) + (2*(c*d^2 + a*e^2)^2*(a^2*B*e^2 + A*c^2*d^2*x - a*c*(B*d*(d - 2*e*x) + A*e*(-2*d + e*x))))/(a*(a + c*x^2)^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]])/a^(5/2) + 8*e^4*(-5*B*c*d^2 + 6*A*c*d*e + a*B*e^2)*Log[d + e*x] - 4*e^4*(-5*B*c*d^2 + 6*A*c*d*e + a*B*e^2)*Log[a + c*x^2])/(8*(c*d^2 + a*e^2)^4)","A",1
1354,1,31,29,0.0100215,"\int \frac{-11+6 x}{(-1+2 x) \left(-1+x^2\right)} \, dx","Integrate[(-11 + 6*x)/((-1 + 2*x)*(-1 + x^2)),x]","-\frac{5}{2} \log (2-2 x)+\frac{16}{3} \log (2 x-1)-\frac{17}{6} \log (2 x+2)","\frac{16}{3} \log (1-2 x)-\frac{5}{2} \log (1-x)-\frac{17}{6} \log (x+1)",1,"(-5*Log[2 - 2*x])/2 + (16*Log[-1 + 2*x])/3 - (17*Log[2 + 2*x])/6","A",1
1355,1,28,39,0.0148048,"\int \frac{x (1+x)^2}{\left(1+x^2\right)^3} \, dx","Integrate[(x*(1 + x)^2)/(1 + x^2)^3,x]","\frac{1}{4} \left(\frac{x^3-2 x^2-x-2}{\left(x^2+1\right)^2}+\tan ^{-1}(x)\right)","-\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,"((-2 - x - 2*x^2 + x^3)/(1 + x^2)^2 + ArcTan[x])/4","A",1
1356,1,65,122,0.0772165,"\int (5-x) (3+2 x)^4 \sqrt{2+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)^4*Sqrt[2 + 3*x^2],x]","\frac{\sqrt{3 x^2+2} \left(-12960 x^6-15120 x^5+297648 x^4+1222200 x^3+1956174 x^2+1558935 x+1167988\right)}{5670}+\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,"(Sqrt[2 + 3*x^2]*(1167988 + 1558935*x + 1956174*x^2 + 1222200*x^3 + 297648*x^4 - 15120*x^5 - 12960*x^6))/5670 + (2341*ArcSinh[Sqrt[3/2]*x])/(9*Sqrt[3])","A",1
1357,1,60,100,0.0498263,"\int (5-x) (3+2 x)^3 \sqrt{2+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)^3*Sqrt[2 + 3*x^2],x]","\frac{1}{270} \left(10220 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(360 x^5-216 x^4-8445 x^3-21918 x^2-21120 x-14516\right)\right)","-\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,"(-(Sqrt[2 + 3*x^2]*(-14516 - 21120*x - 21918*x^2 - 8445*x^3 - 216*x^4 + 360*x^5)) + 10220*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/270","A",1
1358,1,55,78,0.044689,"\int (5-x) (3+2 x)^2 \sqrt{2+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)^2*Sqrt[2 + 3*x^2],x]","\frac{1}{270} \left(3930 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(216 x^4-540 x^3-4542 x^2-6255 x-3124\right)\right)","-\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,"(-(Sqrt[2 + 3*x^2]*(-3124 - 6255*x - 4542*x^2 - 540*x^3 + 216*x^4)) + 3930*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/270","A",1
1359,1,50,56,0.0375215,"\int (5-x) (3+2 x) \sqrt{2+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)*Sqrt[2 + 3*x^2],x]","\frac{1}{18} \left(92 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(9 x^3-42 x^2-132 x-28\right)\right)","\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,"(-(Sqrt[2 + 3*x^2]*(-28 - 132*x - 42*x^2 + 9*x^3)) + 92*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/18","A",1
1360,1,43,49,0.0207966,"\int (5-x) \sqrt{2+3 x^2} \, dx","Integrate[(5 - x)*Sqrt[2 + 3*x^2],x]","\frac{5 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{3}}-\frac{1}{18} \sqrt{3 x^2+2} \left(6 x^2-45 x+4\right)","-\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,"-1/18*(Sqrt[2 + 3*x^2]*(4 - 45*x + 6*x^2)) + (5*ArcSinh[Sqrt[3/2]*x])/Sqrt[3]","A",1
1361,1,68,72,0.0414146,"\int \frac{(5-x) \sqrt{2+3 x^2}}{3+2 x} \, dx","Integrate[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x),x]","\frac{1}{24} \left(-6 \sqrt{3 x^2+2} (x-13)-39 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-121 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right)","\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,"(-6*(-13 + x)*Sqrt[2 + 3*x^2] - 121*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] - 39*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/24","A",1
1362,1,71,73,0.0942305,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^2} \, dx","Integrate[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^2,x]","-\frac{\sqrt{3 x^2+2} (x+8)}{4 x+6}+\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])/(6 + 4*x)) + 2*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] + (19*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/Sqrt[35]","A",1
1363,1,80,79,0.0993781,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^3} \, dx","Integrate[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^3,x]","\frac{\frac{70 (187 x+53) \sqrt{3 x^2+2}}{(2 x+3)^2}-471 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{9800}-\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,"-1/8*(Sqrt[3]*ArcSinh[Sqrt[3/2]*x]) + ((70*(53 + 187*x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^2 - 471*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/9800","A",1
1364,1,65,82,0.0516384,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^4} \, dx","Integrate[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^4,x]","\frac{-\frac{35 \sqrt{3 x^2+2} \left(516 x^2-2337 x+3296\right)}{(2 x+3)^3}-738 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{257250}","-\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,"((-35*Sqrt[2 + 3*x^2]*(3296 - 2337*x + 516*x^2))/(3 + 2*x)^3 - 738*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/257250","A",1
1365,1,70,104,0.0801049,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^5} \, dx","Integrate[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^5,x]","-\frac{198 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8575 \sqrt{35}}-\frac{\sqrt{3 x^2+2} \left(2217 x^3+10134 x^2-304 x+26028\right)}{51450 (2 x+3)^4}","-\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,"-1/51450*(Sqrt[2 + 3*x^2]*(26028 - 304*x + 10134*x^2 + 2217*x^3))/(3 + 2*x)^4 - (198*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(8575*Sqrt[35])","A",1
1366,1,75,126,0.0866628,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^6} \, dx","Integrate[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^6,x]","\frac{-2034 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{35 \sqrt{3 x^2+2} \left(11712 x^4+76992 x^3+186392 x^2+108167 x+222112\right)}{(2 x+3)^5}}{15006250}","-\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,"((-35*Sqrt[2 + 3*x^2]*(222112 + 108167*x + 186392*x^2 + 76992*x^3 + 11712*x^4))/(3 + 2*x)^5 - 2034*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/15006250","A",1
1367,1,80,148,0.0882516,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^7} \, dx","Integrate[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^7,x]","\frac{-36612 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{35 \sqrt{3 x^2+2} \left(642132 x^5+5388660 x^4+18236055 x^3+30753930 x^2+18651300 x+22308548\right)}{(2 x+3)^6}}{1575656250}","-\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,"((-35*Sqrt[2 + 3*x^2]*(22308548 + 18651300*x + 30753930*x^2 + 18236055*x^3 + 5388660*x^4 + 642132*x^5))/(3 + 2*x)^6 - 36612*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/1575656250","A",1
1368,1,75,138,0.0818343,"\int (5-x) (3+2 x)^4 \left(2+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^4*(2 + 3*x^2)^(3/2),x]","\frac{\sqrt{3 x^2+2} \left(-181440 x^8-204120 x^7+3676320 x^6+14492520 x^5+24490404 x^4+27468315 x^3+27537072 x^2+19683405 x+8598544\right)}{34020}+\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,"(Sqrt[2 + 3*x^2]*(8598544 + 19683405*x + 27537072*x^2 + 27468315*x^3 + 24490404*x^4 + 14492520*x^5 + 3676320*x^6 - 204120*x^7 - 181440*x^8))/34020 + (2777*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",1
1369,1,70,116,0.0628334,"\int (5-x) (3+2 x)^3 \left(2+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^3*(2 + 3*x^2)^(3/2),x]","\frac{76090 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(3780 x^7-2160 x^6-75600 x^5-186012 x^4-219975 x^3-245136 x^2-226065 x-81392\right)}{1260}","-\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,"(-(Sqrt[2 + 3*x^2]*(-81392 - 226065*x - 245136*x^2 - 219975*x^3 - 186012*x^4 - 75600*x^5 - 2160*x^6 + 3780*x^7)) + 76090*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/1260","A",1
1370,1,65,94,0.0528015,"\int (5-x) (3+2 x)^2 \left(2+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^2*(2 + 3*x^2)^(3/2),x]","\frac{27790 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(2160 x^6-5040 x^5-36252 x^4-48405 x^3-51216 x^2-71715 x-17392\right)}{1260}","-\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,"(-(Sqrt[2 + 3*x^2]*(-17392 - 71715*x - 51216*x^2 - 48405*x^3 - 36252*x^4 - 5040*x^5 + 2160*x^6)) + 27790*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/1260","A",1
1371,1,60,72,0.0565149,"\int (5-x) (3+2 x) \left(2+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)*(2 + 3*x^2)^(3/2),x]","\frac{1}{60} \sqrt{3 x^2+2} \left(-60 x^5+252 x^4+605 x^3+336 x^2+1115 x+112\right)+\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,"(Sqrt[2 + 3*x^2]*(112 + 1115*x + 336*x^2 + 605*x^3 + 252*x^4 - 60*x^5))/60 + (137*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",1
1372,1,55,67,0.0243376,"\int (5-x) \left(2+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(2 + 3*x^2)^(3/2),x]","\frac{5}{2} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\frac{1}{60} \sqrt{3 x^2+2} \left(36 x^4-225 x^3+48 x^2-375 x+16\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,"-1/60*(Sqrt[2 + 3*x^2]*(16 - 375*x + 48*x^2 - 225*x^3 + 36*x^4)) + (5*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/2","A",1
1373,1,80,92,0.0399305,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{3+2 x} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x),x]","\frac{1}{96} \left(-1365 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-2 \sqrt{3 x^2+2} \left(18 x^3-156 x^2+381 x-1469\right)-4587 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\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,"(-2*Sqrt[2 + 3*x^2]*(-1469 + 381*x - 156*x^2 + 18*x^3) - 4587*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] - 1365*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/96","A",1
1374,1,87,97,0.0984696,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^2} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^2,x]","\frac{1}{48} \left(579 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{2 \sqrt{3 x^2+2} \left(12 x^3-126 x^2+599 x+1905\right)}{2 x+3}+1989 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\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,"((-2*Sqrt[2 + 3*x^2]*(1905 + 599*x - 126*x^2 + 12*x^3))/(3 + 2*x) + 1989*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] + 579*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/48","A",1
1375,1,89,104,0.113017,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^3} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^3,x]","-\frac{1143 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8 \sqrt{35}}-\frac{\sqrt{3 x^2+2} \left(3 x^3-48 x^2-328 x-317\right)}{4 (2 x+3)^2}-\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,"-1/4*(Sqrt[2 + 3*x^2]*(-317 - 328*x - 48*x^2 + 3*x^3))/(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",1
1376,1,89,106,0.1208107,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^4} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^4,x]","\frac{11727 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{560 \sqrt{35}}-\frac{\sqrt{3 x^2+2} \left(1260 x^3+24474 x^2+48747 x+30269\right)}{840 (2 x+3)^3}+\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,"-1/840*(Sqrt[2 + 3*x^2]*(30269 + 48747*x + 24474*x^2 + 1260*x^3))/(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",1
1377,1,90,106,0.1478557,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^5} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^5,x]","\frac{\frac{70 \sqrt{3 x^2+2} \left(250602 x^3+559764 x^2+718441 x+245943\right)}{(2 x+3)^4}-118989 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{4116000}-\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*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/32 + ((70*Sqrt[2 + 3*x^2]*(245943 + 718441*x + 559764*x^2 + 250602*x^3))/(3 + 2*x)^4 - 118989*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/4116000","A",1
1378,1,112,109,0.0950384,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^6} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^6,x]","\frac{1}{350} \left(-\frac{26 \left(3 x^2+2\right)^{5/2}}{(2 x+3)^5}+\frac{41 (9 x-4) \left(3 x^2+2\right)^{3/2}}{14 (2 x+3)^4}-\frac{369 \left(6 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{35 (9 x-4) \sqrt{3 x^2+2}}{(2 x+3)^2}\right)}{17150}\right)","-\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,"((41*(-4 + 9*x)*(2 + 3*x^2)^(3/2))/(14*(3 + 2*x)^4) - (26*(2 + 3*x^2)^(5/2))/(3 + 2*x)^5 - (369*((-35*(-4 + 9*x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^2 + 6*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])]))/17150)/350","A",1
1379,1,137,131,0.1987499,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^7} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^7,x]","\frac{1}{210} \left(-\frac{13 \left(3 x^2+2\right)^{5/2}}{(2 x+3)^6}-\frac{3 \left(10150 \left(3 x^2+2\right)^{5/2}+(2 x+3) \left(-315 (9 x-4) \sqrt{3 x^2+2} (2 x+3)^2-1225 (9 x-4) \left(3 x^2+2\right)^{3/2}+54 \sqrt{35} (2 x+3)^4 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)\right)\right)}{8750 (2 x+3)^5}\right)","-\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,"((-13*(2 + 3*x^2)^(5/2))/(3 + 2*x)^6 - (3*(10150*(2 + 3*x^2)^(5/2) + (3 + 2*x)*(-315*(3 + 2*x)^2*(-4 + 9*x)*Sqrt[2 + 3*x^2] - 1225*(-4 + 9*x)*(2 + 3*x^2)^(3/2) + 54*Sqrt[35]*(3 + 2*x)^4*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])))/(8750*(3 + 2*x)^5))/210","A",1
1380,1,161,153,0.1465705,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^8} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^8,x]","\frac{1}{245} \left(-\frac{822 \left(3 x^2+2\right)^{5/2}}{875 (2 x+3)^5}-\frac{404 \left(3 x^2+2\right)^{5/2}}{105 (2 x+3)^6}-\frac{13 \left(3 x^2+2\right)^{5/2}}{(2 x+3)^7}-\frac{2689 \left(-315 (9 x-4) \sqrt{3 x^2+2} (2 x+3)^2-1225 (9 x-4) \left(3 x^2+2\right)^{3/2}+54 \sqrt{35} (2 x+3)^4 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)\right)}{30012500 (2 x+3)^4}\right)","-\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,"((-13*(2 + 3*x^2)^(5/2))/(3 + 2*x)^7 - (404*(2 + 3*x^2)^(5/2))/(105*(3 + 2*x)^6) - (822*(2 + 3*x^2)^(5/2))/(875*(3 + 2*x)^5) - (2689*(-315*(3 + 2*x)^2*(-4 + 9*x)*Sqrt[2 + 3*x^2] - 1225*(-4 + 9*x)*(2 + 3*x^2)^(3/2) + 54*Sqrt[35]*(3 + 2*x)^4*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])]))/(30012500*(3 + 2*x)^4))/245","A",1
1381,1,85,154,0.0891124,"\int (5-x) (3+2 x)^4 \left(2+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^4*(2 + 3*x^2)^(5/2),x]","\frac{\sqrt{3 x^2+2} \left(-699840 x^{10}-769824 x^9+12921120 x^8+50615928 x^7+93646260 x^6+129966606 x^5+150762600 x^4+127123425 x^3+92160240 x^2+64370295 x+19537120\right)}{53460}+\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,"(Sqrt[2 + 3*x^2]*(19537120 + 64370295*x + 92160240*x^2 + 127123425*x^3 + 150762600*x^4 + 129966606*x^5 + 93646260*x^6 + 50615928*x^7 + 12921120*x^8 - 769824*x^9 - 699840*x^10))/53460 + (4991*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",1
1382,1,80,132,0.0768882,"\int (5-x) (3+2 x)^3 \left(2+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^3*(2 + 3*x^2)^(5/2),x]","\frac{335790 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(23328 x^9-12960 x^8-418446 x^7-1035720 x^6-1503522 x^5-2036880 x^4-1922805 x^3-1350240 x^2-1245915 x-299200\right)}{3240}","-\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,"(-(Sqrt[2 + 3*x^2]*(-299200 - 1245915*x - 1350240*x^2 - 1922805*x^3 - 2036880*x^4 - 1503522*x^5 - 1035720*x^6 - 418446*x^7 - 12960*x^8 + 23328*x^9)) + 335790*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/3240","A",1
1383,1,75,110,0.0721378,"\int (5-x) (3+2 x)^2 \left(2+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^2*(2 + 3*x^2)^(5/2),x]","\frac{1}{324} \sqrt{3 x^2+2} \left(-1296 x^8+2916 x^7+18900 x^6+27378 x^5+41256 x^4+50571 x^3+28272 x^2+40365 x+6368\right)+\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,"(Sqrt[2 + 3*x^2]*(6368 + 40365*x + 28272*x^2 + 50571*x^3 + 41256*x^4 + 27378*x^5 + 18900*x^6 + 2916*x^7 - 1296*x^8))/324 + (665*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",1
1384,1,70,88,0.0613028,"\int (5-x) (3+2 x) \left(2+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)*(2 + 3*x^2)^(5/2),x]","\frac{1}{72} \left(910 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-3 \sqrt{3 x^2+2} \left(54 x^7-216 x^6-438 x^5-432 x^4-1111 x^3-288 x^2-985 x-64\right)\right)","\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,"(-3*Sqrt[2 + 3*x^2]*(-64 - 985*x - 288*x^2 - 1111*x^3 - 432*x^4 - 438*x^5 - 216*x^6 + 54*x^7) + 910*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/72","A",1
1385,1,65,83,0.0432774,"\int (5-x) \left(2+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(2 + 3*x^2)^(5/2),x]","\frac{1}{84} \left(350 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(108 x^6-630 x^5+216 x^4-1365 x^3+144 x^2-1155 x+32\right)\right)","-\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,"(-(Sqrt[2 + 3*x^2]*(32 - 1155*x + 144*x^2 - 1365*x^3 + 216*x^4 - 630*x^5 + 108*x^6)) + 350*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/84","A",1
1386,1,90,112,0.0546955,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{3+2 x} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x),x]","\frac{-238875 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-2 \sqrt{3 x^2+2} \left(720 x^5-5616 x^4+12090 x^3-34788 x^2+80295 x-259571\right)-813365 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{1920}","\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,"(-2*Sqrt[2 + 3*x^2]*(-259571 + 80295*x - 34788*x^2 + 12090*x^3 - 5616*x^4 + 720*x^5) - 813365*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] - 238875*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/1920","A",1
1387,1,97,117,0.133182,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^2} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^2,x]","\frac{1}{480} \left(81375 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{2 \sqrt{3 x^2+2} \left(216 x^5-1836 x^4+5118 x^3-19458 x^2+89521 x+265989\right)}{2 x+3}+278145 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\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,"((-2*Sqrt[2 + 3*x^2]*(265989 + 89521*x - 19458*x^2 + 5118*x^3 - 1836*x^4 + 216*x^5))/(3 + 2*x) + 278145*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] + 81375*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/480","A",1
1388,1,97,126,0.1481962,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^3} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^3,x]","\frac{1}{128} \left(-12885 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{2 \sqrt{3 x^2+2} \left(72 x^5-696 x^4+2826 x^3-19268 x^2-127403 x-126181\right)}{(2 x+3)^2}-43995 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\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,"((-2*Sqrt[2 + 3*x^2]*(-126181 - 127403*x - 19268*x^2 + 2826*x^3 - 696*x^4 + 72*x^5))/(3 + 2*x)^2 - 43995*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] - 12885*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/128","A",1
1389,1,97,133,0.1621542,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^4} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^4,x]","\frac{1}{336} \left(10971 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{14 \sqrt{3 x^2+2} \left(36 x^5-432 x^4+3408 x^3+37974 x^2+77061 x+46103\right)}{(2 x+3)^3}+37485 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\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,"((-14*Sqrt[2 + 3*x^2]*(46103 + 77061*x + 37974*x^2 + 3408*x^3 - 432*x^4 + 36*x^5))/(3 + 2*x)^3 + 37485*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] + 10971*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/336","A",1
1390,1,97,133,0.1599265,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^5} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^5,x]","\frac{-565137 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{70 \sqrt{3 x^2+2} \left(3024 x^5-57456 x^4-898734 x^3-2762820 x^2-3335009 x-1421955\right)}{(2 x+3)^4}-1929375 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{94080}","-\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,"((-70*Sqrt[2 + 3*x^2]*(-1421955 - 3335009*x - 2762820*x^2 - 898734*x^3 - 57456*x^4 + 3024*x^5))/(3 + 2*x)^4 - 1929375*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] - 565137*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/94080","A",1
1391,1,100,133,0.2004699,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^6} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^6,x]","\frac{789723 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{70 \sqrt{3 x^2+2} \left(88200 x^5+2740188 x^4+11367738 x^3+20911298 x^2+17940463 x+5999363\right)}{(2 x+3)^5}}{1372000}+\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,"(63*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/32 + ((-70*Sqrt[2 + 3*x^2]*(5999363 + 17940463*x + 20911298*x^2 + 11367738*x^3 + 2740188*x^4 + 88200*x^5))/(3 + 2*x)^5 + 789723*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/1372000","A",1
1392,1,100,133,0.2352481,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^7} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^7,x]","\frac{\frac{70 \sqrt{3 x^2+2} \left(4369608 x^5+18915336 x^4+47453802 x^3+59256588 x^2+39843609 x+10361807\right)}{(2 x+3)^6}-479277 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{23049600}-\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*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/128 + ((70*Sqrt[2 + 3*x^2]*(10361807 + 39843609*x + 59256588*x^2 + 47453802*x^3 + 18915336*x^4 + 4369608*x^5))/(3 + 2*x)^6 - 479277*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/23049600","A",1
1393,1,122,136,0.177396,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^8} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^8,x]","\frac{1}{490} \left(-\frac{26 \left(3 x^2+2\right)^{7/2}}{(2 x+3)^7}+\frac{41 (9 x-4) \left(3 x^2+2\right)^{5/2}}{15 (2 x+3)^6}+\frac{41 \left(\frac{35 \sqrt{3 x^2+2} \left(1269 x^3+408 x^2+927 x-604\right)}{(2 x+3)^4}-54 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)\right)}{85750}\right)","-\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,"((41*(-4 + 9*x)*(2 + 3*x^2)^(5/2))/(15*(3 + 2*x)^6) - (26*(2 + 3*x^2)^(7/2))/(3 + 2*x)^7 + (41*((35*Sqrt[2 + 3*x^2]*(-604 + 927*x + 408*x^2 + 1269*x^3))/(3 + 2*x)^4 - 54*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])]))/85750)/490","A",1
1394,1,144,158,0.2097334,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^9} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^9,x]","\frac{1}{280} \left(-\frac{773 \left(3 x^2+2\right)^{7/2}}{245 (2 x+3)^7}-\frac{13 \left(3 x^2+2\right)^{7/2}}{(2 x+3)^8}+\frac{466 (9 x-4) \left(3 x^2+2\right)^{5/2}}{1225 (2 x+3)^6}+\frac{699 \left(\frac{35 \sqrt{3 x^2+2} \left(1269 x^3+408 x^2+927 x-604\right)}{(2 x+3)^4}-54 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)\right)}{10504375}\right)","-\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,"((466*(-4 + 9*x)*(2 + 3*x^2)^(5/2))/(1225*(3 + 2*x)^6) - (13*(2 + 3*x^2)^(7/2))/(3 + 2*x)^8 - (773*(2 + 3*x^2)^(7/2))/(245*(3 + 2*x)^7) + (699*((35*Sqrt[2 + 3*x^2]*(-604 + 927*x + 408*x^2 + 1269*x^3))/(3 + 2*x)^4 - 54*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])]))/10504375)/280","A",1
1395,1,185,180,0.3060959,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^{10}} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^10,x]","\frac{1}{315} \left(-\frac{243 \left(3 x^2+2\right)^{7/2}}{70 (2 x+3)^8}-\frac{13 \left(3 x^2+2\right)^{7/2}}{(2 x+3)^9}-\frac{3 \left(406540750 \left(3 x^2+2\right)^{7/2}+2847 (2 x+3) \left(-945 (9 x-4) \sqrt{3 x^2+2} (2 x+3)^4-3675 (9 x-4) \left(3 x^2+2\right)^{3/2} (2 x+3)^2-17150 (9 x-4) \left(3 x^2+2\right)^{5/2}+162 \sqrt{35} (2 x+3)^6 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)\right)\right)}{1470612500 (2 x+3)^7}\right)","-\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,"((-13*(2 + 3*x^2)^(7/2))/(3 + 2*x)^9 - (243*(2 + 3*x^2)^(7/2))/(70*(3 + 2*x)^8) - (3*(406540750*(2 + 3*x^2)^(7/2) + 2847*(3 + 2*x)*(-945*(3 + 2*x)^4*(-4 + 9*x)*Sqrt[2 + 3*x^2] - 3675*(3 + 2*x)^2*(-4 + 9*x)*(2 + 3*x^2)^(3/2) - 17150*(-4 + 9*x)*(2 + 3*x^2)^(5/2) + 162*Sqrt[35]*(3 + 2*x)^6*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])))/(1470612500*(3 + 2*x)^7))/315","A",1
1396,1,207,202,0.2653169,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^{11}} \, dx","Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^11,x]","\frac{1}{350} \left(-\frac{4393 \left(3 x^2+2\right)^{7/2}}{4900 (2 x+3)^8}-\frac{1171 \left(3 x^2+2\right)^{7/2}}{315 (2 x+3)^9}-\frac{13 \left(3 x^2+2\right)^{7/2}}{(2 x+3)^{10}}-\frac{31711164625 \left(3 x^2+2\right)^{7/2}+219699 (2 x+3) \left(-945 (9 x-4) \sqrt{3 x^2+2} (2 x+3)^4-3675 (9 x-4) \left(3 x^2+2\right)^{3/2} (2 x+3)^2-17150 (9 x-4) \left(3 x^2+2\right)^{5/2}+162 \sqrt{35} (2 x+3)^6 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)\right)}{154414312500 (2 x+3)^7}\right)","-\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,"((-13*(2 + 3*x^2)^(7/2))/(3 + 2*x)^10 - (1171*(2 + 3*x^2)^(7/2))/(315*(3 + 2*x)^9) - (4393*(2 + 3*x^2)^(7/2))/(4900*(3 + 2*x)^8) - (31711164625*(2 + 3*x^2)^(7/2) + 219699*(3 + 2*x)*(-945*(3 + 2*x)^4*(-4 + 9*x)*Sqrt[2 + 3*x^2] - 3675*(3 + 2*x)^2*(-4 + 9*x)*(2 + 3*x^2)^(3/2) - 17150*(-4 + 9*x)*(2 + 3*x^2)^(5/2) + 162*Sqrt[35]*(3 + 2*x)^6*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])]))/(154414312500*(3 + 2*x)^7))/350","A",1
1397,1,55,106,0.0589175,"\int \frac{(5-x) (3+2 x)^4}{\sqrt{2+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^4)/Sqrt[2 + 3*x^2],x]","\frac{1}{405} \left(15435 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(432 x^4+540 x^3-12264 x^2-58860 x-118513\right)\right)","-\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,"(-(Sqrt[2 + 3*x^2]*(-118513 - 58860*x - 12264*x^2 + 540*x^3 + 432*x^4)) + 15435*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/405","A",1
1398,1,50,84,0.0440025,"\int \frac{(5-x) (3+2 x)^3}{\sqrt{2+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^3)/Sqrt[2 + 3*x^2],x]","\frac{1}{27} \left(825 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(18 x^3-12 x^2-585 x-2171\right)\right)","-\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,"(-(Sqrt[2 + 3*x^2]*(-2171 - 585*x - 12*x^2 + 18*x^3)) + 825*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/27","A",1
1399,1,45,62,0.0391955,"\int \frac{(5-x) (3+2 x)^2}{\sqrt{2+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^2)/Sqrt[2 + 3*x^2],x]","\frac{1}{27} \left(381 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-\sqrt{3 x^2+2} \left(12 x^2-36 x-475\right)\right)","-\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,"(-(Sqrt[2 + 3*x^2]*(-475 - 36*x + 12*x^2)) + 381*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/27","A",1
1400,1,38,40,0.0224813,"\int \frac{(5-x) (3+2 x)}{\sqrt{2+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x))/Sqrt[2 + 3*x^2],x]","\frac{1}{9} \left(47 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-3 (x-7) \sqrt{3 x^2+2}\right)","\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,"(-3*(-7 + x)*Sqrt[2 + 3*x^2] + 47*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/9","A",1
1401,1,33,33,0.0191882,"\int \frac{5-x}{\sqrt{2+3 x^2}} \, dx","Integrate[(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,"-1/3*Sqrt[2 + 3*x^2] + (5*ArcSinh[Sqrt[3/2]*x])/Sqrt[3]","A",1
1402,1,52,52,0.0171613,"\int \frac{5-x}{(3+2 x) \sqrt{2+3 x^2}} \, dx","Integrate[(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,"-1/2*ArcSinh[Sqrt[3/2]*x]/Sqrt[3] - (13*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(2*Sqrt[35])","A",1
1403,1,55,55,0.0224625,"\int \frac{5-x}{(3+2 x)^2 \sqrt{2+3 x^2}} \, dx","Integrate[(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",1
1404,1,60,77,0.0658519,"\int \frac{5-x}{(3+2 x)^3 \sqrt{2+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^3*Sqrt[2 + 3*x^2]),x]","\frac{-\frac{35 \sqrt{3 x^2+2} (281 x+649)}{(2 x+3)^2}-291 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{42875}","-\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,"((-35*(649 + 281*x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^2 - 291*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/42875","A",1
1405,1,65,99,0.0676986,"\int \frac{5-x}{(3+2 x)^4 \sqrt{2+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^4*Sqrt[2 + 3*x^2]),x]","-\frac{\sqrt{3 x^2+2} \left(600 x^2+2472 x+2995\right)}{5145 (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,"-1/5145*(Sqrt[2 + 3*x^2]*(2995 + 2472*x + 600*x^2))/(3 + 2*x)^3 - (57*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1715*Sqrt[35])","A",1
1406,1,70,121,0.0791559,"\int \frac{5-x}{(3+2 x)^5 \sqrt{2+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^5*Sqrt[2 + 3*x^2]),x]","\frac{81 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{35 \sqrt{3 x^2+2} \left(5946 x^3+35892 x^2+79423 x+70389\right)}{(2 x+3)^4}}{4501875}","-\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,"((-35*Sqrt[2 + 3*x^2]*(70389 + 79423*x + 35892*x^2 + 5946*x^3))/(3 + 2*x)^4 + 81*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/4501875","A",1
1407,1,75,143,0.0908007,"\int \frac{5-x}{(3+2 x)^6 \sqrt{2+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^6*Sqrt[2 + 3*x^2]),x]","\frac{19737 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{35 \sqrt{3 x^2+2} \left(80184 x^4+706644 x^3+2487944 x^2+4314244 x+3409859\right)}{(2 x+3)^5}}{262609375}","-\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,"((-35*Sqrt[2 + 3*x^2]*(3409859 + 4314244*x + 2487944*x^2 + 706644*x^3 + 80184*x^4))/(3 + 2*x)^5 + 19737*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/262609375","A",1
1408,1,58,89,0.0548618,"\int \frac{(5-x) (3+2 x)^4}{\left(2+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^4)/(2 + 3*x^2)^(3/2),x]","-\frac{288 x^4+432 x^3-15024 x^2-15840 \sqrt{9 x^2+6} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)+14715 x+33914}{162 \sqrt{3 x^2+2}}","-\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,"-1/162*(33914 + 14715*x - 15024*x^2 + 432*x^3 + 288*x^4 - 15840*Sqrt[6 + 9*x^2]*ArcSinh[Sqrt[3/2]*x])/Sqrt[2 + 3*x^2]","A",1
1409,1,53,67,0.0441158,"\int \frac{(5-x) (3+2 x)^3}{\left(2+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^3)/(2 + 3*x^2)^(3/2),x]","-\frac{24 x^3-24 x^2-268 \sqrt{9 x^2+6} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-411 x+1426}{18 \sqrt{3 x^2+2}}","-\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,"-1/18*(1426 - 411*x - 24*x^2 + 24*x^3 - 268*Sqrt[6 + 9*x^2]*ArcSinh[Sqrt[3/2]*x])/Sqrt[2 + 3*x^2]","A",1
1410,1,48,60,0.0405117,"\int \frac{(5-x) (3+2 x)^2}{\left(2+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^2)/(2 + 3*x^2)^(3/2),x]","-\frac{24 x^2-16 \sqrt{9 x^2+6} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-357 x+338}{18 \sqrt{3 x^2+2}}","-\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,"-1/18*(338 - 357*x + 24*x^2 - 16*Sqrt[6 + 9*x^2]*ArcSinh[Sqrt[3/2]*x])/Sqrt[2 + 3*x^2]","A",1
1411,1,43,40,0.0273668,"\int \frac{(5-x) (3+2 x)}{\left(2+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x))/(2 + 3*x^2)^(3/2),x]","-\frac{4 \sqrt{9 x^2+6} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-147 x+42}{18 \sqrt{3 x^2+2}}","-\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,"-1/18*(42 - 147*x + 4*Sqrt[6 + 9*x^2]*ArcSinh[Sqrt[3/2]*x])/Sqrt[2 + 3*x^2]","A",1
1412,1,20,20,0.0080597,"\int \frac{5-x}{\left(2+3 x^2\right)^{3/2}} \, dx","Integrate[(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
1413,1,53,53,0.0246577,"\int \frac{5-x}{(3+2 x) \left(2+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)*(2 + 3*x^2)^(3/2)),x]","\frac{123 x+78}{210 \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,"(78 + 123*x)/(210*Sqrt[2 + 3*x^2]) - (26*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(35*Sqrt[35])","A",1
1414,1,65,82,0.0357695,"\int \frac{5-x}{(3+2 x)^2 \left(2+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^2*(2 + 3*x^2)^(3/2)),x]","\frac{\frac{35 \left(114 x^2+1435 x+986\right)}{(2 x+3) \sqrt{3 x^2+2}}-1264 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{85750}","\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,"((35*(986 + 1435*x + 114*x^2))/((3 + 2*x)*Sqrt[2 + 3*x^2]) - 1264*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/85750","A",1
1415,1,70,104,0.0779011,"\int \frac{5-x}{(3+2 x)^3 \left(2+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^3*(2 + 3*x^2)^(3/2)),x]","\frac{-3924 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{35 \left(3972 x^3+4068 x^2-7397 x-3658\right)}{(2 x+3)^2 \sqrt{3 x^2+2}}}{600250}","\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,"((-35*(-3658 - 7397*x + 4068*x^2 + 3972*x^3))/((3 + 2*x)^2*Sqrt[2 + 3*x^2]) - 3924*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/600250","A",1
1416,1,75,126,0.0832617,"\int \frac{5-x}{(3+2 x)^4 \left(2+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^4*(2 + 3*x^2)^(3/2)),x]","\frac{-19872 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{35 \left(75672 x^4+261036 x^3+237930 x^2+23349 x+29438\right)}{(2 x+3)^3 \sqrt{3 x^2+2}}}{9003750}","\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,"((-35*(29438 + 23349*x + 237930*x^2 + 261036*x^3 + 75672*x^4))/((3 + 2*x)^3*Sqrt[2 + 3*x^2]) - 19872*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/9003750","A",1
1417,1,80,148,0.0932,"\int \frac{5-x}{(3+2 x)^5 \left(2+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^5*(2 + 3*x^2)^(3/2)),x]","\frac{-180468 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{35 \left(2151936 x^5+11467872 x^4+22188792 x^3+18957672 x^2+8562487 x+4197366\right)}{(2 x+3)^4 \sqrt{3 x^2+2}}}{315131250}","\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,"((-35*(4197366 + 8562487*x + 18957672*x^2 + 22188792*x^3 + 11467872*x^4 + 2151936*x^5))/((3 + 2*x)^4*Sqrt[2 + 3*x^2]) - 180468*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/315131250","A",1
1418,1,73,116,0.0763786,"\int \frac{(5-x) (3+2 x)^6}{\left(2+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^6)/(2 + 3*x^2)^(5/2),x]","-\frac{3456 x^6+20736 x^5-130464 x^4-1125999 x^3+2363976 x^2-124320 \sqrt{3} \left(3 x^2+2\right)^{3/2} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-139815 x+1798610}{486 \left(3 x^2+2\right)^{3/2}}","-\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,"-1/486*(1798610 - 139815*x + 2363976*x^2 - 1125999*x^3 - 130464*x^4 + 20736*x^5 + 3456*x^6 - 124320*Sqrt[3]*(2 + 3*x^2)^(3/2)*ArcSinh[Sqrt[3/2]*x])/(2 + 3*x^2)^(3/2)","A",1
1419,1,68,94,0.0679423,"\int \frac{(5-x) (3+2 x)^5}{\left(2+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^5)/(2 + 3*x^2)^(5/2),x]","-\frac{864 x^5+4320 x^4-183945 x^3+147600 x^2-3200 \sqrt{3} \left(3 x^2+2\right)^{3/2} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-79215 x+134126}{162 \left(3 x^2+2\right)^{3/2}}","-\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,"-1/162*(134126 - 79215*x + 147600*x^2 - 183945*x^3 + 4320*x^4 + 864*x^5 - 3200*Sqrt[3]*(2 + 3*x^2)^(3/2)*ArcSinh[Sqrt[3/2]*x])/(2 + 3*x^2)^(3/2)","A",1
1420,1,63,87,0.0633678,"\int \frac{(5-x) (3+2 x)^4}{\left(2+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^4)/(2 + 3*x^2)^(5/2),x]","-\frac{864 x^4-57285 x^3+16560 x^2+96 \sqrt{3} \left(3 x^2+2\right)^{3/2} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-33381 x+25342}{162 \left(3 x^2+2\right)^{3/2}}","-\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,"-1/162*(25342 - 33381*x + 16560*x^2 - 57285*x^3 + 864*x^4 + 96*Sqrt[3]*(2 + 3*x^2)^(3/2)*ArcSinh[Sqrt[3/2]*x])/(2 + 3*x^2)^(3/2)","A",1
1421,1,58,67,0.0597131,"\int \frac{(5-x) (3+2 x)^3}{\left(2+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^3)/(2 + 3*x^2)^(5/2),x]","-\frac{-4971 x^3+72 x^2+16 \sqrt{3} \left(3 x^2+2\right)^{3/2} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)-3741 x+1490}{54 \left(3 x^2+2\right)^{3/2}}","-\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,"-1/54*(1490 - 3741*x + 72*x^2 - 4971*x^3 + 16*Sqrt[3]*(2 + 3*x^2)^(3/2)*ArcSinh[Sqrt[3/2]*x])/(2 + 3*x^2)^(3/2)","A",1
1422,1,30,48,0.1274821,"\int \frac{(5-x) (3+2 x)^2}{\left(2+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^2)/(2 + 3*x^2)^(5/2),x]","-\frac{-1287 x^3-72 x^2-1215 x+274}{54 \left(3 x^2+2\right)^{3/2}}","\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,"-1/54*(274 - 1215*x - 72*x^2 - 1287*x^3)/(2 + 3*x^2)^(3/2)","A",1
1423,1,25,37,0.0159446,"\int \frac{(5-x) (3+2 x)}{\left(2+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x))/(2 + 3*x^2)^(5/2),x]","-\frac{-129 x^3-135 x+14}{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,"-1/18*(14 - 135*x - 129*x^3)/(2 + 3*x^2)^(3/2)","A",1
1424,1,25,37,0.0098422,"\int \frac{5-x}{\left(2+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/(2 + 3*x^2)^(5/2),x]","\frac{45 x^3+45 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 + 45*x + 45*x^3)/(18*(2 + 3*x^2)^(3/2))","A",1
1425,1,63,73,0.0397048,"\int \frac{5-x}{(3+2 x) \left(2+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)*(2 + 3*x^2)^(5/2)),x]","\frac{\frac{35 \left(6411 x^3+936 x^2+5709 x+1534\right)}{\left(3 x^2+2\right)^{3/2}}-624 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{257250}","\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,"((35*(1534 + 5709*x + 936*x^2 + 6411*x^3))/(2 + 3*x^2)^(3/2) - 624*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/257250","A",1
1426,1,101,109,0.0466948,"\int \frac{5-x}{(3+2 x)^2 \left(2+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^2*(2 + 3*x^2)^(5/2)),x]","\frac{35 \left(4986 x^4+10647 x^3+7362 x^2+9107 x+3966\right)-1056 \sqrt{35} \sqrt{3 x^2+2} \left(6 x^3+9 x^2+4 x+6\right) \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{360150 (2 x+3) \left(3 x^2+2\right)^{3/2}}","\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,"(35*(3966 + 9107*x + 7362*x^2 + 10647*x^3 + 4986*x^4) - 1056*Sqrt[35]*Sqrt[2 + 3*x^2]*(6 + 4*x + 9*x^2 + 6*x^3)*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(360150*(3 + 2*x)*(2 + 3*x^2)^(3/2))","A",1
1427,1,80,131,0.1065502,"\int \frac{5-x}{(3+2 x)^3 \left(2+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^3*(2 + 3*x^2)^(5/2)),x]","\frac{\frac{35 \left(10284 x^5+67716 x^4+116367 x^3+91268 x^2+89749 x+41366\right)}{(2 x+3)^2 \left(3 x^2+2\right)^{3/2}}-6144 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{3001250}","\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,"((35*(41366 + 89749*x + 91268*x^2 + 116367*x^3 + 67716*x^4 + 10284*x^5))/((3 + 2*x)^2*(2 + 3*x^2)^(3/2)) - 6144*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/3001250","A",1
1428,1,85,153,0.1165439,"\int \frac{5-x}{(3+2 x)^4 \left(2+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^4*(2 + 3*x^2)^(5/2)),x]","\frac{-332064 \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{35 \left(1293192 x^6+1834596 x^5-4920642 x^4-9795297 x^3-7866162 x^2-9103449 x-3788738\right)}{(2 x+3)^3 \left(3 x^2+2\right)^{3/2}}}{315131250}","-\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,"((-35*(-3788738 - 9103449*x - 7866162*x^2 - 9795297*x^3 - 4920642*x^4 + 1834596*x^5 + 1293192*x^6))/((3 + 2*x)^3*(2 + 3*x^2)^(3/2)) - 332064*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/315131250","A",1
1429,1,99,116,0.0891711,"\int (A+B x) (d+e x)^{3/2} \left(a+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^(3/2)*(a + c*x^2),x]","\frac{2 (d+e x)^{5/2} \left(11 A e \left(63 a e^2+c \left(8 d^2-20 d e x+35 e^2 x^2\right)\right)-3 B \left(33 a e^2 (2 d-5 e x)+c \left(16 d^3-40 d^2 e x+70 d e^2 x^2-105 e^3 x^3\right)\right)\right)}{3465 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*(d + e*x)^(5/2)*(11*A*e*(63*a*e^2 + c*(8*d^2 - 20*d*e*x + 35*e^2*x^2)) - 3*B*(33*a*e^2*(2*d - 5*e*x) + c*(16*d^3 - 40*d^2*e*x + 70*d*e^2*x^2 - 105*e^3*x^3))))/(3465*e^4)","A",1
1430,1,96,116,0.0684262,"\int (A+B x) \sqrt{d+e x} \left(a+c x^2\right) \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*(a + c*x^2),x]","\frac{2 (d+e x)^{3/2} \left(105 a A e^3+21 a B e^2 (3 e x-2 d)+3 A c e \left(8 d^2-12 d e x+15 e^2 x^2\right)+B c \left(-16 d^3+24 d^2 e x-30 d e^2 x^2+35 e^3 x^3\right)\right)}{315 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*(d + e*x)^(3/2)*(105*a*A*e^3 + 21*a*B*e^2*(-2*d + 3*e*x) + 3*A*c*e*(8*d^2 - 12*d*e*x + 15*e^2*x^2) + B*c*(-16*d^3 + 24*d^2*e*x - 30*d*e^2*x^2 + 35*e^3*x^3)))/(315*e^4)","A",1
1431,1,96,114,0.0783156,"\int \frac{(A+B x) \left(a+c x^2\right)}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(a + c*x^2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(105 a A e^3+35 a B e^2 (e x-2 d)+7 A c e \left(8 d^2-4 d e x+3 e^2 x^2\right)-3 B c \left(16 d^3-8 d^2 e x+6 d e^2 x^2-5 e^3 x^3\right)\right)}{105 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*Sqrt[d + e*x]*(105*a*A*e^3 + 35*a*B*e^2*(-2*d + e*x) + 7*A*c*e*(8*d^2 - 4*d*e*x + 3*e^2*x^2) - 3*B*c*(16*d^3 - 8*d^2*e*x + 6*d*e^2*x^2 - 5*e^3*x^3)))/(105*e^4)","A",1
1432,1,97,112,0.0721173,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x)^(3/2),x]","\frac{6 B \left(5 a e^2 (2 d+e x)+c \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)\right)-10 A e \left(3 a e^2+c \left(8 d^2+4 d e x-e^2 x^2\right)\right)}{15 e^4 \sqrt{d+e 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}",1,"(-10*A*e*(3*a*e^2 + c*(8*d^2 + 4*d*e*x - e^2*x^2)) + 6*B*(5*a*e^2*(2*d + e*x) + c*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3)))/(15*e^4*Sqrt[d + e*x])","A",1
1433,1,94,112,0.0695168,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x)^(5/2),x]","-\frac{2 \left(a A e^3+a B e^2 (2 d+3 e x)-A c e \left(8 d^2+12 d e x+3 e^2 x^2\right)+B c \left(16 d^3+24 d^2 e x+6 d e^2 x^2-e^3 x^3\right)\right)}{3 e^4 (d+e x)^{3/2}}","-\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*(a*A*e^3 + a*B*e^2*(2*d + 3*e*x) - A*c*e*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + B*c*(16*d^3 + 24*d^2*e*x + 6*d*e^2*x^2 - e^3*x^3)))/(3*e^4*(d + e*x)^(3/2))","A",1
1434,1,95,112,0.0718414,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2))/(d + e*x)^(7/2),x]","-\frac{2 \left(3 a A e^3+a B e^2 (2 d+5 e x)+A c e \left(8 d^2+20 d e x+15 e^2 x^2\right)-3 B c \left(16 d^3+40 d^2 e x+30 d e^2 x^2+5 e^3 x^3\right)\right)}{15 e^4 (d+e x)^{5/2}}","-\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*(3*a*A*e^3 + a*B*e^2*(2*d + 5*e*x) + A*c*e*(8*d^2 + 20*d*e*x + 15*e^2*x^2) - 3*B*c*(16*d^3 + 40*d^2*e*x + 30*d*e^2*x^2 + 5*e^3*x^3)))/(15*e^4*(d + e*x)^(5/2))","A",1
1435,1,214,218,0.1928706,"\int (A+B x) \sqrt{d+e x} \left(a+c x^2\right)^2 \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*(a + c*x^2)^2,x]","\frac{2 (d+e x)^{3/2} \left(13 A e \left(1155 a^2 e^4+66 a c e^2 \left(8 d^2-12 d e x+15 e^2 x^2\right)+c^2 \left(128 d^4-192 d^3 e x+240 d^2 e^2 x^2-280 d e^3 x^3+315 e^4 x^4\right)\right)+B \left(3003 a^2 e^4 (3 e x-2 d)+286 a c e^2 \left(-16 d^3+24 d^2 e x-30 d e^2 x^2+35 e^3 x^3\right)-5 c^2 \left(256 d^5-384 d^4 e x+480 d^3 e^2 x^2-560 d^2 e^3 x^3+630 d e^4 x^4-693 e^5 x^5\right)\right)\right)}{45045 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{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{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 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*(d + e*x)^(3/2)*(13*A*e*(1155*a^2*e^4 + 66*a*c*e^2*(8*d^2 - 12*d*e*x + 15*e^2*x^2) + c^2*(128*d^4 - 192*d^3*e*x + 240*d^2*e^2*x^2 - 280*d*e^3*x^3 + 315*e^4*x^4)) + B*(3003*a^2*e^4*(-2*d + 3*e*x) + 286*a*c*e^2*(-16*d^3 + 24*d^2*e*x - 30*d*e^2*x^2 + 35*e^3*x^3) - 5*c^2*(256*d^5 - 384*d^4*e*x + 480*d^3*e^2*x^2 - 560*d^2*e^3*x^3 + 630*d*e^4*x^4 - 693*e^5*x^5))))/(45045*e^6)","A",1
1436,1,213,216,0.1604353,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(11 A e \left(315 a^2 e^4+42 a c e^2 \left(8 d^2-4 d e x+3 e^2 x^2\right)+c^2 \left(128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right)\right)+B \left(1155 a^2 e^4 (e x-2 d)+198 a c e^2 \left(-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right)-5 c^2 \left(256 d^5-128 d^4 e x+96 d^3 e^2 x^2-80 d^2 e^3 x^3+70 d e^4 x^4-63 e^5 x^5\right)\right)\right)}{3465 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{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{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 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*Sqrt[d + e*x]*(11*A*e*(315*a^2*e^4 + 42*a*c*e^2*(8*d^2 - 4*d*e*x + 3*e^2*x^2) + c^2*(128*d^4 - 64*d^3*e*x + 48*d^2*e^2*x^2 - 40*d*e^3*x^3 + 35*e^4*x^4)) + B*(1155*a^2*e^4*(-2*d + e*x) + 198*a*c*e^2*(-16*d^3 + 8*d^2*e*x - 6*d*e^2*x^2 + 5*e^3*x^3) - 5*c^2*(256*d^5 - 128*d^4*e*x + 96*d^3*e^2*x^2 - 80*d^2*e^3*x^3 + 70*d*e^4*x^4 - 63*e^5*x^5))))/(3465*e^6)","A",1
1437,1,214,214,0.1448924,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^(3/2),x]","\frac{2 B \left(315 a^2 e^4 (2 d+e x)+126 a c e^2 \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)+5 c^2 \left(256 d^5+128 d^4 e x-32 d^3 e^2 x^2+16 d^2 e^3 x^3-10 d e^4 x^4+7 e^5 x^5\right)\right)-6 A e \left(105 a^2 e^4+70 a c e^2 \left(8 d^2+4 d e x-e^2 x^2\right)+3 c^2 \left(128 d^4+64 d^3 e x-16 d^2 e^2 x^2+8 d e^3 x^3-5 e^4 x^4\right)\right)}{315 e^6 \sqrt{d+e 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{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{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 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,"(-6*A*e*(105*a^2*e^4 + 70*a*c*e^2*(8*d^2 + 4*d*e*x - e^2*x^2) + 3*c^2*(128*d^4 + 64*d^3*e*x - 16*d^2*e^2*x^2 + 8*d*e^3*x^3 - 5*e^4*x^4)) + 2*B*(315*a^2*e^4*(2*d + e*x) + 126*a*c*e^2*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) + 5*c^2*(256*d^5 + 128*d^4*e*x - 32*d^3*e^2*x^2 + 16*d^2*e^3*x^3 - 10*d*e^4*x^4 + 7*e^5*x^5)))/(315*e^6*Sqrt[d + e*x])","A",1
1438,1,214,214,0.1428344,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^(5/2),x]","\frac{14 A e \left(-5 a^2 e^4+10 a c e^2 \left(8 d^2+12 d e x+3 e^2 x^2\right)+c^2 \left(128 d^4+192 d^3 e x+48 d^2 e^2 x^2-8 d e^3 x^3+3 e^4 x^4\right)\right)-10 B \left(7 a^2 e^4 (2 d+3 e x)+14 a c e^2 \left(16 d^3+24 d^2 e x+6 d e^2 x^2-e^3 x^3\right)+c^2 \left(256 d^5+384 d^4 e x+96 d^3 e^2 x^2-16 d^2 e^3 x^3+6 d e^4 x^4-3 e^5 x^5\right)\right)}{105 e^6 (d+e x)^{3/2}}","\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{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{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 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,"(14*A*e*(-5*a^2*e^4 + 10*a*c*e^2*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + c^2*(128*d^4 + 192*d^3*e*x + 48*d^2*e^2*x^2 - 8*d*e^3*x^3 + 3*e^4*x^4)) - 10*B*(7*a^2*e^4*(2*d + 3*e*x) + 14*a*c*e^2*(16*d^3 + 24*d^2*e*x + 6*d*e^2*x^2 - e^3*x^3) + c^2*(256*d^5 + 384*d^4*e*x + 96*d^3*e^2*x^2 - 16*d^2*e^3*x^3 + 6*d*e^4*x^4 - 3*e^5*x^5)))/(105*e^6*(d + e*x)^(3/2))","A",1
1439,1,212,214,0.1407988,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^(7/2),x]","-\frac{2 \left(3 a^2 A e^5+a^2 B e^4 (2 d+5 e x)+2 a A c e^3 \left(8 d^2+20 d e x+15 e^2 x^2\right)-6 a B c e^2 \left(16 d^3+40 d^2 e x+30 d e^2 x^2+5 e^3 x^3\right)+A c^2 e \left(128 d^4+320 d^3 e x+240 d^2 e^2 x^2+40 d e^3 x^3-5 e^4 x^4\right)-B c^2 \left(256 d^5+640 d^4 e x+480 d^3 e^2 x^2+80 d^2 e^3 x^3-10 d e^4 x^4+3 e^5 x^5\right)\right)}{15 e^6 (d+e x)^{5/2}}","\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{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{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 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*(3*a^2*A*e^5 + a^2*B*e^4*(2*d + 5*e*x) + 2*a*A*c*e^3*(8*d^2 + 20*d*e*x + 15*e^2*x^2) - 6*a*B*c*e^2*(16*d^3 + 40*d^2*e*x + 30*d*e^2*x^2 + 5*e^3*x^3) + A*c^2*e*(128*d^4 + 320*d^3*e*x + 240*d^2*e^2*x^2 + 40*d*e^3*x^3 - 5*e^4*x^4) - B*c^2*(256*d^5 + 640*d^4*e*x + 480*d^3*e^2*x^2 + 80*d^2*e^3*x^3 - 10*d*e^4*x^4 + 3*e^5*x^5)))/(15*e^6*(d + e*x)^(5/2))","A",1
1440,1,214,214,0.1527471,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{9/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^(9/2),x]","-\frac{2 \left(A e \left(15 a^2 e^4+2 a c e^2 \left(8 d^2+28 d e x+35 e^2 x^2\right)-3 c^2 \left(128 d^4+448 d^3 e x+560 d^2 e^2 x^2+280 d e^3 x^3+35 e^4 x^4\right)\right)+B \left(3 a^2 e^4 (2 d+7 e x)+6 a c e^2 \left(16 d^3+56 d^2 e x+70 d e^2 x^2+35 e^3 x^3\right)+5 c^2 \left(256 d^5+896 d^4 e x+1120 d^3 e^2 x^2+560 d^2 e^3 x^3+70 d e^4 x^4-7 e^5 x^5\right)\right)\right)}{105 e^6 (d+e x)^{7/2}}","-\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{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{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 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*(A*e*(15*a^2*e^4 + 2*a*c*e^2*(8*d^2 + 28*d*e*x + 35*e^2*x^2) - 3*c^2*(128*d^4 + 448*d^3*e*x + 560*d^2*e^2*x^2 + 280*d*e^3*x^3 + 35*e^4*x^4)) + B*(3*a^2*e^4*(2*d + 7*e*x) + 6*a*c*e^2*(16*d^3 + 56*d^2*e*x + 70*d*e^2*x^2 + 35*e^3*x^3) + 5*c^2*(256*d^5 + 896*d^4*e*x + 1120*d^3*e^2*x^2 + 560*d^2*e^3*x^3 + 70*d*e^4*x^4 - 7*e^5*x^5))))/(105*e^6*(d + e*x)^(7/2))","A",1
1441,1,373,348,0.3538381,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(3 A e \left(15015 a^3 e^6+3003 a^2 c e^4 \left(8 d^2-4 d e x+3 e^2 x^2\right)+143 a c^2 e^2 \left(128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right)+5 c^3 \left(1024 d^6-512 d^5 e x+384 d^4 e^2 x^2-320 d^3 e^3 x^3+280 d^2 e^4 x^4-252 d e^5 x^5+231 e^6 x^6\right)\right)+B \left(15015 a^3 e^6 (e x-2 d)+3861 a^2 c e^4 \left(-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right)+195 a c^2 e^2 \left(-256 d^5+128 d^4 e x-96 d^3 e^2 x^2+80 d^2 e^3 x^3-70 d e^4 x^4+63 e^5 x^5\right)-7 c^3 \left(2048 d^7-1024 d^6 e x+768 d^5 e^2 x^2-640 d^4 e^3 x^3+560 d^3 e^4 x^4-504 d^2 e^5 x^5+462 d e^6 x^6-429 e^7 x^7\right)\right)\right)}{45045 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{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{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 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*Sqrt[d + e*x]*(3*A*e*(15015*a^3*e^6 + 3003*a^2*c*e^4*(8*d^2 - 4*d*e*x + 3*e^2*x^2) + 143*a*c^2*e^2*(128*d^4 - 64*d^3*e*x + 48*d^2*e^2*x^2 - 40*d*e^3*x^3 + 35*e^4*x^4) + 5*c^3*(1024*d^6 - 512*d^5*e*x + 384*d^4*e^2*x^2 - 320*d^3*e^3*x^3 + 280*d^2*e^4*x^4 - 252*d*e^5*x^5 + 231*e^6*x^6)) + B*(15015*a^3*e^6*(-2*d + e*x) + 3861*a^2*c*e^4*(-16*d^3 + 8*d^2*e*x - 6*d*e^2*x^2 + 5*e^3*x^3) + 195*a*c^2*e^2*(-256*d^5 + 128*d^4*e*x - 96*d^3*e^2*x^2 + 80*d^2*e^3*x^3 - 70*d*e^4*x^4 + 63*e^5*x^5) - 7*c^3*(2048*d^7 - 1024*d^6*e*x + 768*d^5*e^2*x^2 - 640*d^4*e^3*x^3 + 560*d^3*e^4*x^4 - 504*d^2*e^5*x^5 + 462*d*e^6*x^6 - 429*e^7*x^7))))/(45045*e^8)","A",1
1442,1,373,344,0.289864,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(3/2),x]","\frac{2 B \left(15015 a^3 e^6 (2 d+e x)+9009 a^2 c e^4 \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)+715 a c^2 e^2 \left(256 d^5+128 d^4 e x-32 d^3 e^2 x^2+16 d^2 e^3 x^3-10 d e^4 x^4+7 e^5 x^5\right)+35 c^3 \left(2048 d^7+1024 d^6 e x-256 d^5 e^2 x^2+128 d^4 e^3 x^3-80 d^3 e^4 x^4+56 d^2 e^5 x^5-42 d e^6 x^6+33 e^7 x^7\right)\right)-26 A e \left(1155 a^3 e^6+1155 a^2 c e^4 \left(8 d^2+4 d e x-e^2 x^2\right)+99 a c^2 e^2 \left(128 d^4+64 d^3 e x-16 d^2 e^2 x^2+8 d e^3 x^3-5 e^4 x^4\right)+5 c^3 \left(1024 d^6+512 d^5 e x-128 d^4 e^2 x^2+64 d^3 e^3 x^3-40 d^2 e^4 x^4+28 d e^5 x^5-21 e^6 x^6\right)\right)}{15015 e^8 \sqrt{d+e 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 \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 (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 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,"(-26*A*e*(1155*a^3*e^6 + 1155*a^2*c*e^4*(8*d^2 + 4*d*e*x - e^2*x^2) + 99*a*c^2*e^2*(128*d^4 + 64*d^3*e*x - 16*d^2*e^2*x^2 + 8*d*e^3*x^3 - 5*e^4*x^4) + 5*c^3*(1024*d^6 + 512*d^5*e*x - 128*d^4*e^2*x^2 + 64*d^3*e^3*x^3 - 40*d^2*e^4*x^4 + 28*d*e^5*x^5 - 21*e^6*x^6)) + 2*B*(15015*a^3*e^6*(2*d + e*x) + 9009*a^2*c*e^4*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) + 715*a*c^2*e^2*(256*d^5 + 128*d^4*e*x - 32*d^3*e^2*x^2 + 16*d^2*e^3*x^3 - 10*d*e^4*x^4 + 7*e^5*x^5) + 35*c^3*(2048*d^7 + 1024*d^6*e*x - 256*d^5*e^2*x^2 + 128*d^4*e^3*x^3 - 80*d^3*e^4*x^4 + 56*d^2*e^5*x^5 - 42*d*e^6*x^6 + 33*e^7*x^7)))/(15015*e^8*Sqrt[d + e*x])","A",1
1443,1,375,346,0.2804062,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(5/2),x]","\frac{22 A e \left(-105 a^3 e^6+315 a^2 c e^4 \left(8 d^2+12 d e x+3 e^2 x^2\right)+63 a c^2 e^2 \left(128 d^4+192 d^3 e x+48 d^2 e^2 x^2-8 d e^3 x^3+3 e^4 x^4\right)+5 c^3 \left(1024 d^6+1536 d^5 e x+384 d^4 e^2 x^2-64 d^3 e^3 x^3+24 d^2 e^4 x^4-12 d e^5 x^5+7 e^6 x^6\right)\right)-10 B \left(231 a^3 e^6 (2 d+3 e x)+693 a^2 c e^4 \left(16 d^3+24 d^2 e x+6 d e^2 x^2-e^3 x^3\right)+99 a c^2 e^2 \left(256 d^5+384 d^4 e x+96 d^3 e^2 x^2-16 d^2 e^3 x^3+6 d e^4 x^4-3 e^5 x^5\right)+7 c^3 \left(2048 d^7+3072 d^6 e x+768 d^5 e^2 x^2-128 d^4 e^3 x^3+48 d^3 e^4 x^4-24 d^2 e^5 x^5+14 d e^6 x^6-9 e^7 x^7\right)\right)}{3465 e^8 (d+e x)^{3/2}}","-\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{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{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 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,"(22*A*e*(-105*a^3*e^6 + 315*a^2*c*e^4*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + 63*a*c^2*e^2*(128*d^4 + 192*d^3*e*x + 48*d^2*e^2*x^2 - 8*d*e^3*x^3 + 3*e^4*x^4) + 5*c^3*(1024*d^6 + 1536*d^5*e*x + 384*d^4*e^2*x^2 - 64*d^3*e^3*x^3 + 24*d^2*e^4*x^4 - 12*d*e^5*x^5 + 7*e^6*x^6)) - 10*B*(231*a^3*e^6*(2*d + 3*e*x) + 693*a^2*c*e^4*(16*d^3 + 24*d^2*e*x + 6*d*e^2*x^2 - e^3*x^3) + 99*a*c^2*e^2*(256*d^5 + 384*d^4*e*x + 96*d^3*e^2*x^2 - 16*d^2*e^3*x^3 + 6*d*e^4*x^4 - 3*e^5*x^5) + 7*c^3*(2048*d^7 + 3072*d^6*e*x + 768*d^5*e^2*x^2 - 128*d^4*e^3*x^3 + 48*d^3*e^4*x^4 - 24*d^2*e^5*x^5 + 14*d*e^6*x^6 - 9*e^7*x^7)))/(3465*e^8*(d + e*x)^(3/2))","A",1
1444,1,373,346,0.2768792,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(7/2),x]","\frac{2 \left(7 B \left(-3 a^3 e^6 (2 d+5 e x)+27 a^2 c e^4 \left(16 d^3+40 d^2 e x+30 d e^2 x^2+5 e^3 x^3\right)+9 a c^2 e^2 \left(256 d^5+640 d^4 e x+480 d^3 e^2 x^2+80 d^2 e^3 x^3-10 d e^4 x^4+3 e^5 x^5\right)+c^3 \left(2048 d^7+5120 d^6 e x+3840 d^5 e^2 x^2+640 d^4 e^3 x^3-80 d^3 e^4 x^4+24 d^2 e^5 x^5-10 d e^6 x^6+5 e^7 x^7\right)\right)-9 A e \left(7 a^3 e^6+7 a^2 c e^4 \left(8 d^2+20 d e x+15 e^2 x^2\right)+7 a c^2 e^2 \left(128 d^4+320 d^3 e x+240 d^2 e^2 x^2+40 d e^3 x^3-5 e^4 x^4\right)+c^3 \left(1024 d^6+2560 d^5 e x+1920 d^4 e^2 x^2+320 d^3 e^3 x^3-40 d^2 e^4 x^4+12 d e^5 x^5-5 e^6 x^6\right)\right)\right)}{315 e^8 (d+e x)^{5/2}}","-\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{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{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 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*(-9*A*e*(7*a^3*e^6 + 7*a^2*c*e^4*(8*d^2 + 20*d*e*x + 15*e^2*x^2) + 7*a*c^2*e^2*(128*d^4 + 320*d^3*e*x + 240*d^2*e^2*x^2 + 40*d*e^3*x^3 - 5*e^4*x^4) + c^3*(1024*d^6 + 2560*d^5*e*x + 1920*d^4*e^2*x^2 + 320*d^3*e^3*x^3 - 40*d^2*e^4*x^4 + 12*d*e^5*x^5 - 5*e^6*x^6)) + 7*B*(-3*a^3*e^6*(2*d + 5*e*x) + 27*a^2*c*e^4*(16*d^3 + 40*d^2*e*x + 30*d*e^2*x^2 + 5*e^3*x^3) + 9*a*c^2*e^2*(256*d^5 + 640*d^4*e*x + 480*d^3*e^2*x^2 + 80*d^2*e^3*x^3 - 10*d*e^4*x^4 + 3*e^5*x^5) + c^3*(2048*d^7 + 5120*d^6*e*x + 3840*d^5*e^2*x^2 + 640*d^4*e^3*x^3 - 80*d^3*e^4*x^4 + 24*d^2*e^5*x^5 - 10*d*e^6*x^6 + 5*e^7*x^7))))/(315*e^8*(d + e*x)^(5/2))","A",1
1445,1,372,342,0.2885473,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{9/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(9/2),x]","\frac{2 A e \left(-5 a^3 e^6-a^2 c e^4 \left(8 d^2+28 d e x+35 e^2 x^2\right)+3 a c^2 e^2 \left(128 d^4+448 d^3 e x+560 d^2 e^2 x^2+280 d e^3 x^3+35 e^4 x^4\right)+c^3 \left(1024 d^6+3584 d^5 e x+4480 d^4 e^2 x^2+2240 d^3 e^3 x^3+280 d^2 e^4 x^4-28 d e^5 x^5+7 e^6 x^6\right)\right)-2 B \left(a^3 e^6 (2 d+7 e x)+3 a^2 c e^4 \left(16 d^3+56 d^2 e x+70 d e^2 x^2+35 e^3 x^3\right)+5 a c^2 e^2 \left(256 d^5+896 d^4 e x+1120 d^3 e^2 x^2+560 d^2 e^3 x^3+70 d e^4 x^4-7 e^5 x^5\right)+c^3 \left(2048 d^7+7168 d^6 e x+8960 d^5 e^2 x^2+4480 d^4 e^3 x^3+560 d^3 e^4 x^4-56 d^2 e^5 x^5+14 d e^6 x^6-5 e^7 x^7\right)\right)}{35 e^8 (d+e x)^{7/2}}","\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 \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 \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 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*A*e*(-5*a^3*e^6 - a^2*c*e^4*(8*d^2 + 28*d*e*x + 35*e^2*x^2) + 3*a*c^2*e^2*(128*d^4 + 448*d^3*e*x + 560*d^2*e^2*x^2 + 280*d*e^3*x^3 + 35*e^4*x^4) + c^3*(1024*d^6 + 3584*d^5*e*x + 4480*d^4*e^2*x^2 + 2240*d^3*e^3*x^3 + 280*d^2*e^4*x^4 - 28*d*e^5*x^5 + 7*e^6*x^6)) - 2*B*(a^3*e^6*(2*d + 7*e*x) + 3*a^2*c*e^4*(16*d^3 + 56*d^2*e*x + 70*d*e^2*x^2 + 35*e^3*x^3) + 5*a*c^2*e^2*(256*d^5 + 896*d^4*e*x + 1120*d^3*e^2*x^2 + 560*d^2*e^3*x^3 + 70*d*e^4*x^4 - 7*e^5*x^5) + c^3*(2048*d^7 + 7168*d^6*e*x + 8960*d^5*e^2*x^2 + 4480*d^4*e^3*x^3 + 560*d^3*e^4*x^4 - 56*d^2*e^5*x^5 + 14*d*e^6*x^6 - 5*e^7*x^7)))/(35*e^8*(d + e*x)^(7/2))","A",1
1446,1,375,346,0.3003414,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{11/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(11/2),x]","\frac{2 B \left(-5 a^3 e^6 (2 d+9 e x)-3 a^2 c e^4 \left(16 d^3+72 d^2 e x+126 d e^2 x^2+105 e^3 x^3\right)+15 a c^2 e^2 \left(256 d^5+1152 d^4 e x+2016 d^3 e^2 x^2+1680 d^2 e^3 x^3+630 d e^4 x^4+63 e^5 x^5\right)+7 c^3 \left(2048 d^7+9216 d^6 e x+16128 d^5 e^2 x^2+13440 d^4 e^3 x^3+5040 d^3 e^4 x^4+504 d^2 e^5 x^5-42 d e^6 x^6+9 e^7 x^7\right)\right)-2 A e \left(35 a^3 e^6+3 a^2 c e^4 \left(8 d^2+36 d e x+63 e^2 x^2\right)+3 a c^2 e^2 \left(128 d^4+576 d^3 e x+1008 d^2 e^2 x^2+840 d e^3 x^3+315 e^4 x^4\right)+5 c^3 \left(1024 d^6+4608 d^5 e x+8064 d^4 e^2 x^2+6720 d^3 e^3 x^3+2520 d^2 e^4 x^4+252 d e^5 x^5-21 e^6 x^6\right)\right)}{315 e^8 (d+e x)^{9/2}}","\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{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{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 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*A*e*(35*a^3*e^6 + 3*a^2*c*e^4*(8*d^2 + 36*d*e*x + 63*e^2*x^2) + 3*a*c^2*e^2*(128*d^4 + 576*d^3*e*x + 1008*d^2*e^2*x^2 + 840*d*e^3*x^3 + 315*e^4*x^4) + 5*c^3*(1024*d^6 + 4608*d^5*e*x + 8064*d^4*e^2*x^2 + 6720*d^3*e^3*x^3 + 2520*d^2*e^4*x^4 + 252*d*e^5*x^5 - 21*e^6*x^6)) + 2*B*(-5*a^3*e^6*(2*d + 9*e*x) - 3*a^2*c*e^4*(16*d^3 + 72*d^2*e*x + 126*d*e^2*x^2 + 105*e^3*x^3) + 15*a*c^2*e^2*(256*d^5 + 1152*d^4*e*x + 2016*d^3*e^2*x^2 + 1680*d^2*e^3*x^3 + 630*d*e^4*x^4 + 63*e^5*x^5) + 7*c^3*(2048*d^7 + 9216*d^6*e*x + 16128*d^5*e^2*x^2 + 13440*d^4*e^3*x^3 + 5040*d^3*e^4*x^4 + 504*d^2*e^5*x^5 - 42*d*e^6*x^6 + 9*e^7*x^7)))/(315*e^8*(d + e*x)^(9/2))","A",1
1447,1,223,237,0.4602885,"\int \frac{(A+B x) (d+e x)^{5/2}}{a-c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a - c*x^2),x]","\frac{-2 \sqrt{a} \sqrt[4]{c} \sqrt{d+e x} \left(15 a B e^2+5 A c e (7 d+e x)+B c \left(23 d^2+11 d e x+3 e^2 x^2\right)\right)-15 \left(A \sqrt{c}-\sqrt{a} B\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)+15 \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)}{15 \sqrt{a} c^{9/4}}","\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 \sqrt{d+e x} \left(a B e^2+2 A c d e+B c d^2\right)}{c^2}-\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*Sqrt[a]*c^(1/4)*Sqrt[d + e*x]*(15*a*B*e^2 + 5*A*c*e*(7*d + e*x) + B*c*(23*d^2 + 11*d*e*x + 3*e^2*x^2)) - 15*(-(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]] + 15*(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]])/(15*Sqrt[a]*c^(9/4))","A",1
1448,1,194,202,0.2409768,"\int \frac{(A+B x) (d+e x)^{3/2}}{a-c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a - c*x^2),x]","\frac{-2 \sqrt{a} c^{3/4} \sqrt{d+e x} (3 A e+4 B d+B e x)-3 \left(A \sqrt{c}-\sqrt{a} B\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)+3 \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)}{3 \sqrt{a} c^{7/4}}","\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*Sqrt[a]*c^(3/4)*Sqrt[d + e*x]*(4*B*d + 3*A*e + B*e*x) - 3*(-(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]] + 3*(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]])/(3*Sqrt[a]*c^(7/4))","A",1
1449,1,178,179,0.1493598,"\int \frac{(A+B x) \sqrt{d+e x}}{a-c x^2} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a - c*x^2),x]","\frac{-\left(A \sqrt{c}-\sqrt{a} B\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)+\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)-2 \sqrt{a} B \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{a} c^{5/4}}","\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*Sqrt[a]*B*c^(1/4)*Sqrt[d + e*x] - (-(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]*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",1
1450,1,155,152,0.1822353,"\int \frac{A+B x}{\sqrt{d+e x} \left(a-c x^2\right)} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a - c*x^2)),x]","\frac{\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{\sqrt{c} d-\sqrt{a} e}}+\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{\sqrt{a} e+\sqrt{c} d}}}{\sqrt{a} c^{3/4}}","\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,"(((Sqrt[a]*B - A*Sqrt[c])*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/Sqrt[Sqrt[c]*d - Sqrt[a]*e] + ((Sqrt[a]*B + A*Sqrt[c])*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/Sqrt[Sqrt[c]*d + Sqrt[a]*e])/(Sqrt[a]*c^(3/4))","A",1
1451,1,271,197,0.3278282,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a-c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(a - c*x^2)),x]","\frac{\frac{B \left(\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt[4]{c}}-\frac{(B d-A e) \left(\left(\sqrt{a} e+\sqrt{c} d\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{a} e}\right)+\left(\sqrt{a} e-\sqrt{c} d\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{a} e}\right)\right)}{\sqrt{d+e x} \left(c d^2-a e^2\right)}}{\sqrt{a} e}","-\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,"((B*(-(ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]]/Sqrt[Sqrt[c]*d - Sqrt[a]*e]) + ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]/Sqrt[Sqrt[c]*d + Sqrt[a]*e]))/c^(1/4) - ((B*d - A*e)*((Sqrt[c]*d + Sqrt[a]*e)*Hypergeometric2F1[-1/2, 1, 1/2, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[a]*e)] + (-(Sqrt[c]*d) + Sqrt[a]*e)*Hypergeometric2F1[-1/2, 1, 1/2, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[a]*e)]))/((c*d^2 - a*e^2)*Sqrt[d + e*x]))/(Sqrt[a]*e)","C",1
1452,1,266,243,0.1423011,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a-c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*(a - c*x^2)),x]","\frac{3 B (d+e x) \left(\left(\sqrt{a} e+\sqrt{c} d\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{a} e}\right)+\left(\sqrt{a} e-\sqrt{c} d\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{a} e}\right)\right)-(B d-A e) \left(\left(\sqrt{a} e+\sqrt{c} d\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{a} e}\right)+\left(\sqrt{a} e-\sqrt{c} d\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{a} e}\right)\right)}{3 \sqrt{a} (d+e x)^{3/2} \left(c d^2 e-a e^3\right)}","-\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,"(-((B*d - A*e)*((Sqrt[c]*d + Sqrt[a]*e)*Hypergeometric2F1[-3/2, 1, -1/2, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[a]*e)] + (-(Sqrt[c]*d) + Sqrt[a]*e)*Hypergeometric2F1[-3/2, 1, -1/2, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[a]*e)])) + 3*B*(d + e*x)*((Sqrt[c]*d + Sqrt[a]*e)*Hypergeometric2F1[-1/2, 1, 1/2, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[a]*e)] + (-(Sqrt[c]*d) + Sqrt[a]*e)*Hypergeometric2F1[-1/2, 1, 1/2, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[a]*e)]))/(3*Sqrt[a]*(c*d^2*e - a*e^3)*(d + e*x)^(3/2))","C",1
1453,1,279,269,0.5626027,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a-c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a - c*x^2)^2,x]","\frac{2 \sqrt{a} \sqrt[4]{c} \sqrt{d+e x} \left(5 a^2 B e^2+a c \left(A e (2 d+e x)+B \left(d^2+2 d e x-4 e^2 x^2\right)\right)+A c^2 d^2 x\right)+\left(c x^2-a\right) \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)-\left(c x^2-a\right) \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} \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,"(2*Sqrt[a]*c^(1/4)*Sqrt[d + e*x]*(5*a^2*B*e^2 + A*c^2*d^2*x + a*c*(A*e*(2*d + e*x) + B*(d^2 + 2*d*e*x - 4*e^2*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)*(-a + c*x^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - (Sqrt[c]*d + Sqrt[a]*e)^(3/2)*(2*A*c*d - 5*a*B*e - 3*Sqrt[a]*A*Sqrt[c]*e)*(-a + c*x^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(9/4)*(a - c*x^2))","A",1
1454,1,244,238,0.3739758,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a-c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a - c*x^2)^2,x]","\frac{2 \sqrt{a} c^{3/4} \sqrt{d+e x} (a A e+a B (d+e x)+A c d x)+\left(c x^2-a\right) \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)-\left(c x^2-a\right) \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} \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,"(2*Sqrt[a]*c^(3/4)*Sqrt[d + e*x]*(a*A*e + A*c*d*x + a*B*(d + e*x)) + Sqrt[Sqrt[c]*d - Sqrt[a]*e]*(2*A*c*d - 3*a*B*e + Sqrt[a]*A*Sqrt[c]*e)*(-a + c*x^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - Sqrt[Sqrt[c]*d + Sqrt[a]*e]*(2*A*c*d - 3*a*B*e - Sqrt[a]*A*Sqrt[c]*e)*(-a + c*x^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(7/4)*(a - c*x^2))","A",1
1455,1,375,225,0.4726186,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a-c x^2\right)^2} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a - c*x^2)^2,x]","\frac{-\frac{\sqrt[4]{c} \left(a A e^2+2 a B d e-3 A c d^2\right) \left(\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{\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)\right)}{2 \sqrt{a}}+\frac{c (d+e x)^{3/2} (-a A e+a B (d-e x)+A c d x)}{c x^2-a}+\frac{(a B e-A c d) \left(2 \sqrt{a} \sqrt[4]{c} e \sqrt{d+e x}+\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)-\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)\right)}{2 \sqrt{a} \sqrt[4]{c}}}{2 a c \left(a e^2-c d^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,"((c*(d + e*x)^(3/2)*(-(a*A*e) + A*c*d*x + a*B*(d - e*x)))/(-a + c*x^2) - (c^(1/4)*(-3*A*c*d^2 + 2*a*B*d*e + a*A*e^2)*(Sqrt[Sqrt[c]*d - Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - Sqrt[Sqrt[c]*d + Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(2*Sqrt[a]) + ((-(A*c*d) + a*B*e)*(2*Sqrt[a]*c^(1/4)*e*Sqrt[d + e*x] + (Sqrt[c]*d - Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - (Sqrt[c]*d + Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(2*Sqrt[a]*c^(1/4)))/(2*a*c*(-(c*d^2) + a*e^2))","A",1
1456,1,353,250,0.4484229,"\int \frac{A+B x}{\sqrt{d+e x} \left(a-c x^2\right)^2} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a - c*x^2)^2),x]","\frac{-\frac{c^{3/4} \left(-3 a A e^2+2 a B d e+A c d^2\right) \left(\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{2 \sqrt{a}}+\frac{c \sqrt{d+e x} (-a A e+a B (d-e x)+A c d x)}{c x^2-a}+\frac{\sqrt[4]{c} (A c d-a B e) \left(\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{\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)\right)}{2 \sqrt{a}}}{2 a c \left(a e^2-c d^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,"((c*Sqrt[d + e*x]*(-(a*A*e) + A*c*d*x + a*B*(d - e*x)))/(-a + c*x^2) - (c^(3/4)*(A*c*d^2 + 2*a*B*d*e - 3*a*A*e^2)*(-(ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]]/Sqrt[Sqrt[c]*d - Sqrt[a]*e]) + ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]/Sqrt[Sqrt[c]*d + Sqrt[a]*e]))/(2*Sqrt[a]) + (c^(1/4)*(A*c*d - a*B*e)*(Sqrt[Sqrt[c]*d - Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - Sqrt[Sqrt[c]*d + Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(2*Sqrt[a]))/(2*a*c*(-(c*d^2) + a*e^2))","A",1
1457,1,365,303,0.6114065,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a-c x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(a - c*x^2)^2),x]","\frac{-\frac{3 c^{3/4} (A c d-a B e) \left(\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{2 \sqrt{a}}+\frac{c \left(5 a A e^2-6 a B d e+A c d^2\right) \left(\left(\sqrt{a} e+\sqrt{c} d\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{a} e}\right)+\left(\sqrt{a} e-\sqrt{c} d\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{a} e}\right)\right)}{2 \sqrt{a} \sqrt{d+e x} \left(c d^2-a e^2\right)}+\frac{c (-a A e+a B (d-e x)+A c d x)}{\left(c x^2-a\right) \sqrt{d+e x}}}{2 a c \left(a e^2-c d^2\right)}","-\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,"((c*(-(a*A*e) + A*c*d*x + a*B*(d - e*x)))/(Sqrt[d + e*x]*(-a + c*x^2)) - (3*c^(3/4)*(A*c*d - a*B*e)*(-(ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]]/Sqrt[Sqrt[c]*d - Sqrt[a]*e]) + ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]/Sqrt[Sqrt[c]*d + Sqrt[a]*e]))/(2*Sqrt[a]) + (c*(A*c*d^2 - 6*a*B*d*e + 5*a*A*e^2)*((Sqrt[c]*d + Sqrt[a]*e)*Hypergeometric2F1[-1/2, 1, 1/2, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[a]*e)] + (-(Sqrt[c]*d) + Sqrt[a]*e)*Hypergeometric2F1[-1/2, 1, 1/2, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[a]*e)]))/(2*Sqrt[a]*(c*d^2 - a*e^2)*Sqrt[d + e*x]))/(2*a*c*(-(c*d^2) + a*e^2))","C",1
1458,1,802,396,2.9597713,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(a-c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a - c*x^2)^3,x]","\frac{\frac{2 a c^2 \left(c d^2-a e^2\right) (-a A e+A c d x+a B (d-e x)) (d+e x)^{9/2}}{\left(a-c x^2\right)^2}+\frac{c^2 \left(6 A c^2 x d^3+a c e (-9 A d-7 B x d+4 A e x) d-a^2 e^2 (-10 B d+A e+3 B e x)\right) (d+e x)^{9/2}}{2 \left(a-c x^2\right)}-\frac{\left(A \left(54 c^2 d^4+81 a c e^2 d^2+5 a^2 e^4\right)-7 a B d e \left(9 c d^2+11 a e^2\right)\right) \left(15 \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right) \left(\sqrt{c} d-\sqrt{a} e\right)^{7/2}+2 \sqrt{a} \sqrt[4]{c} e \sqrt{d+e x} \left(15 a e^2+c \left(58 d^2+16 e x d+3 e^2 x^2\right)\right)-15 \left(\sqrt{c} d+\sqrt{a} e\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d+\sqrt{a} e}}\right)\right)}{60 \sqrt{a} \sqrt[4]{c}}-\frac{\left(2 A c d \left(3 c d^2+2 a e^2\right)-a B e \left(7 c d^2+3 a e^2\right)\right) \left(\left(\sqrt{c} d-\sqrt{a} e\right) \left(15 c^{7/4} (d+e x)^{7/2}+7 \left(\sqrt{c} d-\sqrt{a} e\right) \left(3 c^{5/4} (d+e x)^{5/2}+5 \left(\sqrt{c} d-\sqrt{a} e\right) \left(\sqrt[4]{c} \sqrt{d+e x} \left(\sqrt{c} (4 d+e x)-3 \sqrt{a} e\right)-3 \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)\right)\right)\right)-\left(\sqrt{c} d+\sqrt{a} e\right) \left(15 c^{7/4} (d+e x)^{7/2}+7 \left(\sqrt{c} d+\sqrt{a} e\right) \left(3 c^{5/4} (d+e x)^{5/2}+5 \left(\sqrt{c} d+\sqrt{a} e\right) \left(\sqrt[4]{c} \sqrt{d+e x} \left(3 \sqrt{a} e+\sqrt{c} (4 d+e x)\right)-3 \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)\right)\right)\right)\right)}{60 \sqrt{a} c^{3/4}}}{8 a^2 c^2 \left(c d^2-a e^2\right)^2}","\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{\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{(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,"((2*a*c^2*(c*d^2 - a*e^2)*(d + e*x)^(9/2)*(-(a*A*e) + A*c*d*x + a*B*(d - e*x)))/(a - c*x^2)^2 + (c^2*(d + e*x)^(9/2)*(6*A*c^2*d^3*x + a*c*d*e*(-9*A*d - 7*B*d*x + 4*A*e*x) - a^2*e^2*(-10*B*d + A*e + 3*B*e*x)))/(2*(a - c*x^2)) - ((-7*a*B*d*e*(9*c*d^2 + 11*a*e^2) + A*(54*c^2*d^4 + 81*a*c*d^2*e^2 + 5*a^2*e^4))*(2*Sqrt[a]*c^(1/4)*e*Sqrt[d + e*x]*(15*a*e^2 + c*(58*d^2 + 16*d*e*x + 3*e^2*x^2)) + 15*(Sqrt[c]*d - Sqrt[a]*e)^(7/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - 15*(Sqrt[c]*d + Sqrt[a]*e)^(7/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(60*Sqrt[a]*c^(1/4)) - ((2*A*c*d*(3*c*d^2 + 2*a*e^2) - a*B*e*(7*c*d^2 + 3*a*e^2))*((Sqrt[c]*d - Sqrt[a]*e)*(15*c^(7/4)*(d + e*x)^(7/2) + 7*(Sqrt[c]*d - Sqrt[a]*e)*(3*c^(5/4)*(d + e*x)^(5/2) + 5*(Sqrt[c]*d - Sqrt[a]*e)*(c^(1/4)*Sqrt[d + e*x]*(-3*Sqrt[a]*e + Sqrt[c]*(4*d + e*x)) - 3*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]]))) - (Sqrt[c]*d + Sqrt[a]*e)*(15*c^(7/4)*(d + e*x)^(7/2) + 7*(Sqrt[c]*d + Sqrt[a]*e)*(3*c^(5/4)*(d + e*x)^(5/2) + 5*(Sqrt[c]*d + Sqrt[a]*e)*(c^(1/4)*Sqrt[d + e*x]*(3*Sqrt[a]*e + Sqrt[c]*(4*d + e*x)) - 3*(Sqrt[c]*d + Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])))))/(60*Sqrt[a]*c^(3/4)))/(8*a^2*c^2*(c*d^2 - a*e^2)^2)","B",1
1459,1,569,372,1.5629821,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a-c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a - c*x^2)^3,x]","\frac{\frac{c^2 (d+e x)^{7/2} \left(a^2 e^2 (A e+6 B d-B e x)-a c d^2 e (7 A+5 B x)+6 A c^2 d^3 x\right)}{2 \left(a-c x^2\right)}+\frac{\sqrt[4]{c} \left(5 a B d e \left(5 a e^2+7 c d^2\right)-3 A \left(-a^2 e^4+7 a c d^2 e^2+14 c^2 d^4\right)\right) \left(2 \sqrt{a} c^{3/4} e \sqrt{d+e x} (7 d+e x)+3 \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)-3 \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)\right)}{12 \sqrt{a}}+\frac{2 a c^2 (d+e x)^{7/2} \left(c d^2-a e^2\right) (-a A e+a B (d-e x)+A c d x)}{\left(a-c x^2\right)^2}+\frac{\left(6 A c^2 d^3-a B e \left(a e^2+5 c d^2\right)\right) \left(2 \sqrt{a} \sqrt[4]{c} e \sqrt{d+e x} \left(15 a e^2+c \left(58 d^2+16 d e x+3 e^2 x^2\right)\right)+15 \left(\sqrt{c} d-\sqrt{a} e\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)-15 \left(\sqrt{a} e+\sqrt{c} d\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)\right)}{12 \sqrt{a} \sqrt[4]{c}}}{8 a^2 c^2 \left(c d^2-a e^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,"((2*a*c^2*(c*d^2 - a*e^2)*(d + e*x)^(7/2)*(-(a*A*e) + A*c*d*x + a*B*(d - e*x)))/(a - c*x^2)^2 + (c^2*(d + e*x)^(7/2)*(6*A*c^2*d^3*x - a*c*d^2*e*(7*A + 5*B*x) + a^2*e^2*(6*B*d + A*e - B*e*x)))/(2*(a - c*x^2)) + (c^(1/4)*(5*a*B*d*e*(7*c*d^2 + 5*a*e^2) - 3*A*(14*c^2*d^4 + 7*a*c*d^2*e^2 - a^2*e^4))*(2*Sqrt[a]*c^(3/4)*e*Sqrt[d + e*x]*(7*d + e*x) + 3*(Sqrt[c]*d - Sqrt[a]*e)^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - 3*(Sqrt[c]*d + Sqrt[a]*e)^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(12*Sqrt[a]) + ((6*A*c^2*d^3 - a*B*e*(5*c*d^2 + a*e^2))*(2*Sqrt[a]*c^(1/4)*e*Sqrt[d + e*x]*(15*a*e^2 + c*(58*d^2 + 16*d*e*x + 3*e^2*x^2)) + 15*(Sqrt[c]*d - Sqrt[a]*e)^(7/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - 15*(Sqrt[c]*d + Sqrt[a]*e)^(7/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(12*Sqrt[a]*c^(1/4)))/(8*a^2*c^2*(c*d^2 - a*e^2)^2)","A",1
1460,1,550,350,1.4241838,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a-c x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a - c*x^2)^3,x]","\frac{\frac{c^2 (d+e x)^{5/2} \left(a^2 e^2 (3 A e+2 B d+B e x)-a c d e (5 A d+4 A e x+3 B d x)+6 A c^2 d^3 x\right)}{2 \left(a-c x^2\right)}+\frac{3 c^{3/4} \left(A \left(a^2 e^4+5 a c d^2 e^2-10 c^2 d^4\right)+a B d e \left(5 c d^2-a e^2\right)\right) \left(2 \sqrt{a} \sqrt[4]{c} e \sqrt{d+e x}+\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)-\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)\right)}{4 \sqrt{a}}+\frac{\sqrt[4]{c} \left(2 A c d \left(3 c d^2-2 a e^2\right)+a B e \left(a e^2-3 c d^2\right)\right) \left(2 \sqrt{a} c^{3/4} e \sqrt{d+e x} (7 d+e x)+3 \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)-3 \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)\right)}{4 \sqrt{a}}+\frac{2 a c^2 (d+e x)^{5/2} \left(c d^2-a e^2\right) (-a A e+a B (d-e x)+A c d x)}{\left(a-c x^2\right)^2}}{8 a^2 c^2 \left(c d^2-a e^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,"((2*a*c^2*(c*d^2 - a*e^2)*(d + e*x)^(5/2)*(-(a*A*e) + A*c*d*x + a*B*(d - e*x)))/(a - c*x^2)^2 + (c^2*(d + e*x)^(5/2)*(6*A*c^2*d^3*x - a*c*d*e*(5*A*d + 3*B*d*x + 4*A*e*x) + a^2*e^2*(2*B*d + 3*A*e + B*e*x)))/(2*(a - c*x^2)) + (3*c^(3/4)*(a*B*d*e*(5*c*d^2 - a*e^2) + A*(-10*c^2*d^4 + 5*a*c*d^2*e^2 + a^2*e^4))*(2*Sqrt[a]*c^(1/4)*e*Sqrt[d + e*x] + (Sqrt[c]*d - Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - (Sqrt[c]*d + Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(4*Sqrt[a]) + (c^(1/4)*(2*A*c*d*(3*c*d^2 - 2*a*e^2) + a*B*e*(-3*c*d^2 + a*e^2))*(2*Sqrt[a]*c^(3/4)*e*Sqrt[d + e*x]*(7*d + e*x) + 3*(Sqrt[c]*d - Sqrt[a]*e)^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - 3*(Sqrt[c]*d + Sqrt[a]*e)^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(4*Sqrt[a]))/(8*a^2*c^2*(c*d^2 - a*e^2)^2)","A",1
1461,1,522,372,1.0441007,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a-c x^2\right)^3} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a - c*x^2)^3,x]","\frac{\frac{c^2 (d+e x)^{3/2} \left(a^2 e^2 (5 A e-2 B d+3 B e x)-a c d e (3 A d+8 A e x+B d x)+6 A c^2 d^3 x\right)}{2 \left(a-c x^2\right)}-\frac{c^{5/4} \left(A \left(5 a^2 e^4-27 a c d^2 e^2+18 c^2 d^4\right)+a B d e \left(7 a e^2-3 c d^2\right)\right) \left(\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{\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)\right)}{4 \sqrt{a}}+\frac{c^{3/4} \left(2 A c d \left(3 c d^2-4 a e^2\right)+a B e \left(3 a e^2-c d^2\right)\right) \left(2 \sqrt{a} \sqrt[4]{c} e \sqrt{d+e x}+\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)-\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)\right)}{4 \sqrt{a}}+\frac{2 a c^2 (d+e x)^{3/2} \left(c d^2-a e^2\right) (-a A e+a B (d-e x)+A c d x)}{\left(a-c x^2\right)^2}}{8 a^2 c^2 \left(c d^2-a e^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,"((2*a*c^2*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*(-(a*A*e) + A*c*d*x + a*B*(d - e*x)))/(a - c*x^2)^2 + (c^2*(d + e*x)^(3/2)*(6*A*c^2*d^3*x - a*c*d*e*(3*A*d + B*d*x + 8*A*e*x) + a^2*e^2*(-2*B*d + 5*A*e + 3*B*e*x)))/(2*(a - c*x^2)) - (c^(5/4)*(a*B*d*e*(-3*c*d^2 + 7*a*e^2) + A*(18*c^2*d^4 - 27*a*c*d^2*e^2 + 5*a^2*e^4))*(Sqrt[Sqrt[c]*d - Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - Sqrt[Sqrt[c]*d + Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(4*Sqrt[a]) + (c^(3/4)*(2*A*c*d*(3*c*d^2 - 4*a*e^2) + a*B*e*(-(c*d^2) + 3*a*e^2))*(2*Sqrt[a]*c^(1/4)*e*Sqrt[d + e*x] + (Sqrt[c]*d - Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - (Sqrt[c]*d + Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(4*Sqrt[a]))/(8*a^2*c^2*(c*d^2 - a*e^2)^2)","A",1
1462,1,536,417,1.0597747,"\int \frac{A+B x}{\sqrt{d+e x} \left(a-c x^2\right)^3} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a - c*x^2)^3),x]","\frac{\frac{c^2 \sqrt{d+e x} \left(a^2 e^2 (7 A e-6 B d+5 B e x)+a c d e (B d x-A (d+12 e x))+6 A c^2 d^3 x\right)}{2 \left(a-c x^2\right)}+\frac{c^{7/4} \left(3 A \left(7 a^2 e^4-5 a c d^2 e^2+2 c^2 d^4\right)+a B d e \left(c d^2-13 a e^2\right)\right) \left(\sqrt{\sqrt{c} d-\sqrt{a} e} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)-\sqrt{\sqrt{a} e+\sqrt{c} d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)\right)}{4 \sqrt{a} \sqrt{\sqrt{c} d-\sqrt{a} e} \sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{c^{5/4} \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) \left(\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{\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)\right)}{4 \sqrt{a}}+\frac{2 a c^2 \sqrt{d+e x} \left(c d^2-a e^2\right) (-a A e+a B (d-e x)+A c d x)}{\left(a-c x^2\right)^2}}{8 a^2 c^2 \left(c d^2-a e^2\right)^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(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,"((2*a*c^2*(c*d^2 - a*e^2)*Sqrt[d + e*x]*(-(a*A*e) + A*c*d*x + a*B*(d - e*x)))/(a - c*x^2)^2 + (c^2*Sqrt[d + e*x]*(6*A*c^2*d^3*x + a^2*e^2*(-6*B*d + 7*A*e + 5*B*e*x) + a*c*d*e*(B*d*x - A*(d + 12*e*x))))/(2*(a - c*x^2)) + (c^(7/4)*(a*B*d*e*(c*d^2 - 13*a*e^2) + 3*A*(2*c^2*d^4 - 5*a*c*d^2*e^2 + 7*a^2*e^4))*(-(Sqrt[Sqrt[c]*d + Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]]) + Sqrt[Sqrt[c]*d - Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(4*Sqrt[a]*Sqrt[Sqrt[c]*d - Sqrt[a]*e]*Sqrt[Sqrt[c]*d + Sqrt[a]*e]) - (c^(5/4)*(6*A*c*d*(c*d^2 - 2*a*e^2) + a*B*e*(c*d^2 + 5*a*e^2))*(Sqrt[Sqrt[c]*d - Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]] - Sqrt[Sqrt[c]*d + Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]))/(4*Sqrt[a]))/(8*a^2*c^2*(c*d^2 - a*e^2)^2)","A",1
1463,1,302,155,1.2328297,"\int \frac{A+B x}{\sqrt{d+e x} \left(2 A B d-A^2 e-B^2 e x^2\right)} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(2*A*B*d - A^2*e - B^2*e*x^2)),x]","-\frac{\left(\sqrt{A} \sqrt{e} \sqrt{2 B d-A e}+A e-2 B d\right) \left(\sqrt{B d-\sqrt{A} \sqrt{e} \sqrt{2 B d-A e}} \sqrt{\sqrt{A} \sqrt{e} \sqrt{2 B d-A e}+B d} \tanh ^{-1}\left(\frac{\sqrt{B} \sqrt{d+e x}}{\sqrt{B d-\sqrt{A} \sqrt{e} \sqrt{2 B d-A e}}}\right)+(B d-A e) \tanh ^{-1}\left(\frac{\sqrt{B} \sqrt{d+e x}}{\sqrt{\sqrt{A} \sqrt{e} \sqrt{2 B d-A e}+B d}}\right)\right)}{\sqrt{B} \sqrt{2 B d-A e} \sqrt{\sqrt{A} \sqrt{e} \sqrt{2 B d-A e}+B d} \left(A^{3/2} e^{5/2}-2 \sqrt{A} B d e^{3/2}+B d e \sqrt{2 B d-A e}\right)}","\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,"-(((-2*B*d + A*e + Sqrt[A]*Sqrt[e]*Sqrt[2*B*d - A*e])*(Sqrt[B*d - Sqrt[A]*Sqrt[e]*Sqrt[2*B*d - A*e]]*Sqrt[B*d + Sqrt[A]*Sqrt[e]*Sqrt[2*B*d - A*e]]*ArcTanh[(Sqrt[B]*Sqrt[d + e*x])/Sqrt[B*d - Sqrt[A]*Sqrt[e]*Sqrt[2*B*d - A*e]]] + (B*d - A*e)*ArcTanh[(Sqrt[B]*Sqrt[d + e*x])/Sqrt[B*d + Sqrt[A]*Sqrt[e]*Sqrt[2*B*d - A*e]]]))/(Sqrt[B]*Sqrt[2*B*d - A*e]*Sqrt[B*d + Sqrt[A]*Sqrt[e]*Sqrt[2*B*d - A*e]]*(-2*Sqrt[A]*B*d*e^(3/2) + A^(3/2)*e^(5/2) + B*d*e*Sqrt[2*B*d - A*e])))","A",1
1464,1,142,133,0.1762002,"\int \frac{A+B x}{\sqrt{\frac{A^2 e-B^2 e}{2 A B}+e x} \left(1+x^2\right)} \, dx","Integrate[(A + B*x)/(Sqrt[(A^2*e - B^2*e)/(2*A*B) + e*x]*(1 + x^2)),x]","-\frac{i \sqrt{2} \sqrt{A} \sqrt{B} \sqrt{\frac{A}{B}-\frac{B}{A}+2 x} \left(\tanh ^{-1}\left(\frac{\sqrt{A} \sqrt{B} \sqrt{\frac{A}{B}-\frac{B}{A}+2 x}}{A-i B}\right)-\tanh ^{-1}\left(\frac{\sqrt{A} \sqrt{B} \sqrt{\frac{A}{B}-\frac{B}{A}+2 x}}{A+i B}\right)\right)}{\sqrt{e \left(\frac{A}{B}-\frac{B}{A}+2 x\right)}}","\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,"((-I)*Sqrt[2]*Sqrt[A]*Sqrt[B]*Sqrt[A/B - B/A + 2*x]*(ArcTanh[(Sqrt[A]*Sqrt[B]*Sqrt[A/B - B/A + 2*x])/(A - I*B)] - ArcTanh[(Sqrt[A]*Sqrt[B]*Sqrt[A/B - B/A + 2*x])/(A + I*B)]))/Sqrt[e*(A/B - B/A + 2*x)]","C",1
1465,1,66,66,0.0741282,"\int \frac{A+B x}{\sqrt{d+e x} \left(1-x^2\right)} \, dx","Integrate[(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",1
1466,1,89,440,0.0914217,"\int \frac{A+B x}{\sqrt{d+e x} \left(1+x^2\right)} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(1 + x^2)),x]","\frac{i (A+i B) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d+i e}}\right)}{\sqrt{d+i e}}-\frac{i (A-i B) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d-i e}}\right)}{\sqrt{d-i e}}","-\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,"((-I)*(A - I*B)*ArcTanh[Sqrt[d + e*x]/Sqrt[d - I*e]])/Sqrt[d - I*e] + (I*(A + I*B)*ArcTanh[Sqrt[d + e*x]/Sqrt[d + I*e]])/Sqrt[d + I*e]","C",1
1467,1,58,202,0.0458942,"\int \frac{(1-x) \sqrt{1+x}}{1+x^2} \, dx","Integrate[((1 - x)*Sqrt[1 + x])/(1 + x^2),x]","-2 \sqrt{x+1}+(1-i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{1-i}}\right)+(1+i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{1+i}}\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] + (1 - I)^(3/2)*ArcTanh[Sqrt[1 + x]/Sqrt[1 - I]] + (1 + I)^(3/2)*ArcTanh[Sqrt[1 + x]/Sqrt[1 + I]]","C",1
1468,1,63,45,0.0446874,"\int \frac{3+x}{\sqrt{4+3 x} \left(1+x^2\right)} \, dx","Integrate[(3 + x)/(Sqrt[4 + 3*x]*(1 + x^2)),x]","\frac{1}{5} \left((1-3 i) \sqrt{4-3 i} \tanh ^{-1}\left(\frac{\sqrt{3 x+4}}{\sqrt{4-3 i}}\right)+(1+3 i) \sqrt{4+3 i} \tanh ^{-1}\left(\frac{\sqrt{3 x+4}}{\sqrt{4+3 i}}\right)\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,"((1 - 3*I)*Sqrt[4 - 3*I]*ArcTanh[Sqrt[4 + 3*x]/Sqrt[4 - 3*I]] + (1 + 3*I)*Sqrt[4 + 3*I]*ArcTanh[Sqrt[4 + 3*x]/Sqrt[4 + 3*I]])/5","C",1
1469,1,63,53,0.0288109,"\int \frac{1-3 x}{\sqrt{4+3 x} \left(1+x^2\right)} \, dx","Integrate[(1 - 3*x)/(Sqrt[4 + 3*x]*(1 + x^2)),x]","\frac{1}{5} \left((3+i) \sqrt{4-3 i} \tanh ^{-1}\left(\frac{\sqrt{3 x+4}}{\sqrt{4-3 i}}\right)+(3-i) \sqrt{4+3 i} \tanh ^{-1}\left(\frac{\sqrt{3 x+4}}{\sqrt{4+3 i}}\right)\right)","\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,"((3 + I)*Sqrt[4 - 3*I]*ArcTanh[Sqrt[4 + 3*x]/Sqrt[4 - 3*I]] + (3 - I)*Sqrt[4 + 3*I]*ArcTanh[Sqrt[4 + 3*x]/Sqrt[4 + 3*I]])/5","C",1
1470,1,41,29,0.0189196,"\int \frac{2+x}{\sqrt{3+4 x} \left(1+x^2\right)} \, dx","Integrate[(2 + x)/(Sqrt[3 + 4*x]*(1 + x^2)),x]","\tan ^{-1}\left(\left(\frac{1}{5}+\frac{2 i}{5}\right) \sqrt{4 x+3}\right)-i \tanh ^{-1}\left(\left(\frac{2}{5}+\frac{i}{5}\right) \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[(1/5 + (2*I)/5)*Sqrt[3 + 4*x]] - I*ArcTanh[(2/5 + I/5)*Sqrt[3 + 4*x]]","C",1
1471,1,69,45,0.1368264,"\int \frac{-2+x}{\sqrt{-3+x} \left(-8+x^2\right)} \, dx","Integrate[(-2 + x)/(Sqrt[-3 + x]*(-8 + x^2)),x]","\frac{\left(2+\sqrt{2}\right) \left(\tan ^{-1}\left(\sqrt{3-2 \sqrt{2}} \sqrt{x-3}\right)+\tan ^{-1}\left(\sqrt{3+2 \sqrt{2}} \sqrt{x-3}\right)\right)}{2 \sqrt{3+2 \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,"((2 + Sqrt[2])*(ArcTan[Sqrt[3 - 2*Sqrt[2]]*Sqrt[-3 + x]] + ArcTan[Sqrt[3 + 2*Sqrt[2]]*Sqrt[-3 + x]]))/(2*Sqrt[3 + 2*Sqrt[2]])","A",0
1472,1,622,438,4.5486092,"\int (A+B x) \sqrt{d+e x} \sqrt{a+c x^2} \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*Sqrt[a + c*x^2],x]","\frac{\sqrt{d+e x} \left(\frac{2 \left(a+c x^2\right) \left(10 a B e^2+7 A c e (d+3 e x)+B c \left(-4 d^2+3 d e x+15 e^2 x^2\right)\right)}{c e^2}+\frac{4 \left(\sqrt{a} e (d+e x)^{3/2} \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(7 A \left(c d e+3 i \sqrt{a} \sqrt{c} e^2\right)+B \left(3 i \sqrt{a} \sqrt{c} d e-5 a e^2-4 c d^2\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+e^2 \left(a+c x^2\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \left(21 a A e^3+8 a B d e^2-7 A c d^2 e+4 B c d^3\right)-\sqrt{c} (d+e x)^{3/2} \left(-\sqrt{a} e+i \sqrt{c} d\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{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(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{c e^4 (d+e x) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}\right)}{105 \sqrt{a+c x^2}}","\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,"(Sqrt[d + e*x]*((2*(a + c*x^2)*(10*a*B*e^2 + 7*A*c*e*(d + 3*e*x) + B*c*(-4*d^2 + 3*d*e*x + 15*e^2*x^2)))/(c*e^2) + (4*(e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(4*B*c*d^3 - 7*A*c*d^2*e + 8*a*B*d*e^2 + 21*a*A*e^3)*(a + c*x^2) - Sqrt[c]*(I*Sqrt[c]*d - Sqrt[a]*e)*(4*B*c*d^3 - 7*A*c*d^2*e + 8*a*B*d*e^2 + 21*a*A*e^3)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] + Sqrt[a]*e*(Sqrt[c]*d + I*Sqrt[a]*e)*(B*(-4*c*d^2 + (3*I)*Sqrt[a]*Sqrt[c]*d*e - 5*a*e^2) + 7*A*(c*d*e + (3*I)*Sqrt[a]*Sqrt[c]*e^2))*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(c*e^4*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(d + e*x))))/(105*Sqrt[a + c*x^2])","C",1
1473,1,549,365,3.9130691,"\int \frac{(A+B x) \sqrt{a+c x^2}}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/Sqrt[d + e*x],x]","\frac{\sqrt{d+e x} \left(\frac{2 \left(a+c x^2\right) (5 A e-4 B d+3 B e x)}{e^2}-\frac{4 \left(e^2 \left(a+c x^2\right) \left(-\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}\right) \left(3 a B e^2-5 A c d e+4 B c d^2\right)+\sqrt{c} (d+e x)^{3/2} \left(\sqrt{a} e-i \sqrt{c} d\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(-3 a B e^2+5 A c d e-4 B c d^2\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+\sqrt{a} \sqrt{c} e (d+e x)^{3/2} \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(-3 i \sqrt{a} B e-5 A \sqrt{c} e+4 B \sqrt{c} d\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{c e^4 (d+e x) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}\right)}{15 \sqrt{a+c x^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,"(Sqrt[d + e*x]*((2*(-4*B*d + 5*A*e + 3*B*e*x)*(a + c*x^2))/e^2 - (4*(-(e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(4*B*c*d^2 - 5*A*c*d*e + 3*a*B*e^2)*(a + c*x^2)) + Sqrt[c]*((-I)*Sqrt[c]*d + Sqrt[a]*e)*(-4*B*c*d^2 + 5*A*c*d*e - 3*a*B*e^2)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] + Sqrt[a]*Sqrt[c]*e*(Sqrt[c]*d + I*Sqrt[a]*e)*(4*B*Sqrt[c]*d - (3*I)*Sqrt[a]*B*e - 5*A*Sqrt[c]*e)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(c*e^4*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(d + e*x))))/(15*Sqrt[a + c*x^2])","C",1
1474,1,512,352,3.2830122,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/(d + e*x)^(3/2),x]","\frac{\sqrt{d+e x} \left(\frac{2 \left(a+c x^2\right) (-3 A e+4 B d+B e x)}{e^2 (d+e x)}+\frac{2 (d+e x) \left(\frac{2 e^2 \left(a+c x^2\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} (3 A e-4 B d)}{(d+e x)^2}-\frac{2 \sqrt{a} e \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(-i \sqrt{a} B e+3 A \sqrt{c} e-4 B \sqrt{c} d\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)}{\sqrt{d+e x}}+\frac{2 \sqrt{c} \left(\sqrt{a} e-i \sqrt{c} d\right) (3 A e-4 B d) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)}{\sqrt{d+e x}}\right)}{e^4 \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}\right)}{3 \sqrt{a+c x^2}}","-\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{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{2 \sqrt{a+c x^2} (-3 A e+4 B d+B e x)}{3 e^2 \sqrt{d+e x}}",1,"(Sqrt[d + e*x]*((2*(4*B*d - 3*A*e + B*e*x)*(a + c*x^2))/(e^2*(d + e*x)) + (2*(d + e*x)*((2*e^2*(-4*B*d + 3*A*e)*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(a + c*x^2))/(d + e*x)^2 + (2*Sqrt[c]*((-I)*Sqrt[c]*d + Sqrt[a]*e)*(-4*B*d + 3*A*e)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)])/Sqrt[d + e*x] - (2*Sqrt[a]*e*(-4*B*Sqrt[c]*d - I*Sqrt[a]*B*e + 3*A*Sqrt[c]*e)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)])/Sqrt[d + e*x]))/(e^4*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]])))/(3*Sqrt[a + c*x^2])","C",1
1475,1,609,420,4.6407565,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[a + c*x^2])/(d + e*x)^(5/2),x]","-\frac{2 \sqrt{a+c x^2} \left(a A e^3+a B e^2 (2 d+3 e x)-A c d e (d+2 e x)+B c d^2 (4 d+5 e x)\right)}{3 e^2 (d+e x)^{3/2} \left(a e^2+c d^2\right)}+\frac{4 \left(e^2 \left(a+c x^2\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \left(3 a B e^2-A c d e+4 B c d^2\right)-\sqrt{c} (d+e x)^{3/2} \left(\sqrt{a} e-i \sqrt{c} d\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(-3 a B e^2+A c d e-4 B c d^2\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+\sqrt{a} \sqrt{c} e (d+e x)^{3/2} \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(3 i \sqrt{a} B e+A \sqrt{c} e-4 B \sqrt{c} d\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{3 e^4 \sqrt{a+c x^2} \sqrt{d+e x} \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \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{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} (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*Sqrt[a + c*x^2]*(a*A*e^3 - A*c*d*e*(d + 2*e*x) + a*B*e^2*(2*d + 3*e*x) + B*c*d^2*(4*d + 5*e*x)))/(3*e^2*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) + (4*(e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(4*B*c*d^2 - A*c*d*e + 3*a*B*e^2)*(a + c*x^2) - Sqrt[c]*((-I)*Sqrt[c]*d + Sqrt[a]*e)*(-4*B*c*d^2 + A*c*d*e - 3*a*B*e^2)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] + Sqrt[a]*Sqrt[c]*e*(Sqrt[c]*d + I*Sqrt[a]*e)*(-4*B*Sqrt[c]*d + (3*I)*Sqrt[a]*B*e + A*Sqrt[c]*e)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(3*e^4*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(c*d^2 + a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","C",1
1476,1,730,498,5.4467433,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/Sqrt[d + e*x],x]","\frac{\sqrt{d+e x} \left(\frac{2 \left(a+c x^2\right) \left(135 a A e^3+a B e^2 (77 e x-106 d)+9 A c e \left(8 d^2-6 d e x+5 e^2 x^2\right)+B c \left(-64 d^3+48 d^2 e x-40 d e^2 x^2+35 e^3 x^3\right)\right)}{e^4}-\frac{8 \left(-\sqrt{a} \sqrt{c} e (d+e x)^{3/2} \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(B \left(21 i a^{3/2} e^3+24 i \sqrt{a} c d^2 e-33 a \sqrt{c} d e^2-32 c^{3/2} d^3\right)+9 A \sqrt{c} e \left(-3 i \sqrt{a} \sqrt{c} d e+5 a e^2+4 c d^2\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+e^2 \left(a+c x^2\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \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)+\sqrt{c} (d+e x)^{3/2} \left(\sqrt{a} e-i \sqrt{c} d\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{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(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{c e^6 (d+e x) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}\right)}{315 \sqrt{a+c x^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{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{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{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,"(Sqrt[d + e*x]*((2*(a + c*x^2)*(135*a*A*e^3 + a*B*e^2*(-106*d + 77*e*x) + 9*A*c*e*(8*d^2 - 6*d*e*x + 5*e^2*x^2) + B*c*(-64*d^3 + 48*d^2*e*x - 40*d*e^2*x^2 + 35*e^3*x^3)))/e^4 - (8*(e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(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))*(a + c*x^2) + Sqrt[c]*((-I)*Sqrt[c]*d + Sqrt[a]*e)*(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[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] - Sqrt[a]*Sqrt[c]*e*(Sqrt[c]*d + I*Sqrt[a]*e)*(9*A*Sqrt[c]*e*(4*c*d^2 - (3*I)*Sqrt[a]*Sqrt[c]*d*e + 5*a*e^2) + B*(-32*c^(3/2)*d^3 + (24*I)*Sqrt[a]*c*d^2*e - 33*a*Sqrt[c]*d*e^2 + (21*I)*a^(3/2)*e^3))*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(c*e^6*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(d + e*x))))/(315*Sqrt[a + c*x^2])","C",1
1477,1,661,448,4.8708881,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{\sqrt{d+e x} \left(\frac{2 \left(a+c x^2\right) \left(B \left(5 a e^2 (10 d+3 e x)+c \left(64 d^3+16 d^2 e x-8 d e^2 x^2+5 e^3 x^3\right)\right)-7 A e \left(5 a e^2+c \left(8 d^2+2 d e x-e^2 x^2\right)\right)\right)}{e^4 (d+e x)}+\frac{8 \left(\sqrt{a} e (d+e x)^{3/2} \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(21 i \sqrt{a} A \sqrt{c} e^2-24 i \sqrt{a} B \sqrt{c} d e+5 a B e^2-28 A c d e+32 B c d^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+e^2 \left(a+c x^2\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \left(21 a A e^3-29 a B d e^2+28 A c d^2 e-32 B c d^3\right)+\sqrt{c} (d+e x)^{3/2} \left(\sqrt{a} e-i \sqrt{c} d\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{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(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{e^6 (d+e x) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}\right)}{35 \sqrt{a+c x^2}}","-\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,"(Sqrt[d + e*x]*((2*(a + c*x^2)*(-7*A*e*(5*a*e^2 + c*(8*d^2 + 2*d*e*x - e^2*x^2)) + B*(5*a*e^2*(10*d + 3*e*x) + c*(64*d^3 + 16*d^2*e*x - 8*d*e^2*x^2 + 5*e^3*x^3))))/(e^4*(d + e*x)) + (8*(e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(-32*B*c*d^3 + 28*A*c*d^2*e - 29*a*B*d*e^2 + 21*a*A*e^3)*(a + c*x^2) + Sqrt[c]*((-I)*Sqrt[c]*d + Sqrt[a]*e)*(-32*B*c*d^3 + 28*A*c*d^2*e - 29*a*B*d*e^2 + 21*a*A*e^3)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] + Sqrt[a]*e*(Sqrt[c]*d + I*Sqrt[a]*e)*(32*B*c*d^2 - (24*I)*Sqrt[a]*B*Sqrt[c]*d*e - 28*A*c*d*e + 5*a*B*e^2 + (21*I)*Sqrt[a]*A*Sqrt[c]*e^2)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(e^6*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(d + e*x))))/(35*Sqrt[a + c*x^2])","C",1
1478,1,628,437,4.5425892,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/(d + e*x)^(5/2),x]","\frac{\sqrt{d+e x} \left(-\frac{2 \left(a+c x^2\right) \left(5 a A e^3+5 a B e^2 (2 d+3 e x)-5 A c e \left(8 d^2+10 d e x+e^2 x^2\right)+B c \left(64 d^3+80 d^2 e x+8 d e^2 x^2-3 e^3 x^3\right)\right)}{e^4 (d+e x)^2}-\frac{8 \left(e^2 \left(a+c x^2\right) \left(-\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}\right) \left(9 a B e^2-20 A c d e+32 B c d^2\right)+\sqrt{a} \sqrt{c} e (d+e x)^{3/2} \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(B \left(8 i \sqrt{a} \sqrt{c} d e+9 a e^2+32 c d^2\right)-5 A \left(4 c d e+i \sqrt{a} \sqrt{c} e^2\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+\sqrt{c} (d+e x)^{3/2} \left(\sqrt{a} e-i \sqrt{c} d\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(-9 a B e^2+20 A c d e-32 B c d^2\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{e^6 (d+e x) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}\right)}{15 \sqrt{a+c x^2}}","\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{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{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}}",1,"(Sqrt[d + e*x]*((-2*(a + c*x^2)*(5*a*A*e^3 + 5*a*B*e^2*(2*d + 3*e*x) - 5*A*c*e*(8*d^2 + 10*d*e*x + e^2*x^2) + B*c*(64*d^3 + 80*d^2*e*x + 8*d*e^2*x^2 - 3*e^3*x^3)))/(e^4*(d + e*x)^2) - (8*(-(e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(32*B*c*d^2 - 20*A*c*d*e + 9*a*B*e^2)*(a + c*x^2)) + Sqrt[c]*((-I)*Sqrt[c]*d + Sqrt[a]*e)*(-32*B*c*d^2 + 20*A*c*d*e - 9*a*B*e^2)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] + Sqrt[a]*Sqrt[c]*e*(B*(32*c*d^2 + (8*I)*Sqrt[a]*Sqrt[c]*d*e + 9*a*e^2) - 5*A*(4*c*d*e + I*Sqrt[a]*Sqrt[c]*e^2))*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(e^6*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(d + e*x))))/(15*Sqrt[a + c*x^2])","C",1
1479,1,705,541,5.4141055,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(a + c*x^2)^(3/2))/(d + e*x)^(7/2),x]","\frac{\sqrt{d+e x} \left(\frac{2 \left(a+c x^2\right) \left(\frac{-5 a B e^2+12 A c d e-17 B c d^2}{(d+e x)^2}+\frac{3 \left(a e^2+c d^2\right) (B d-A e)}{(d+e x)^3}+\frac{c \left(-21 a A e^3+61 a B d e^2-33 A c d^2 e+73 B c d^3\right)}{(d+e x) \left(a e^2+c d^2\right)}+5 B c\right)}{e^4}-\frac{8 c \left(-\sqrt{a} e (d+e x)^{3/2} \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(9 i \sqrt{a} A \sqrt{c} e^2-24 i \sqrt{a} B \sqrt{c} d e+5 a B e^2-12 A c d e+32 B c d^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+e^2 \left(a+c x^2\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \left(-9 a A e^3+29 a B d e^2-12 A c d^2 e+32 B c d^3\right)+i \sqrt{c} (d+e x)^{3/2} \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{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(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{e^6 (d+e x) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \left(a e^2+c d^2\right)}\right)}{15 \sqrt{a+c x^2}}","\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{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{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{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)}",1,"(Sqrt[d + e*x]*((2*(a + c*x^2)*(5*B*c + (3*(B*d - A*e)*(c*d^2 + a*e^2))/(d + e*x)^3 + (-17*B*c*d^2 + 12*A*c*d*e - 5*a*B*e^2)/(d + e*x)^2 + (c*(73*B*c*d^3 - 33*A*c*d^2*e + 61*a*B*d*e^2 - 21*a*A*e^3))/((c*d^2 + a*e^2)*(d + e*x))))/e^4 - (8*c*(e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(32*B*c*d^3 - 12*A*c*d^2*e + 29*a*B*d*e^2 - 9*a*A*e^3)*(a + c*x^2) + I*Sqrt[c]*(Sqrt[c]*d + I*Sqrt[a]*e)*(-32*B*c*d^3 + 12*A*c*d^2*e - 29*a*B*d*e^2 + 9*a*A*e^3)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] - Sqrt[a]*e*(Sqrt[c]*d + I*Sqrt[a]*e)*(32*B*c*d^2 - (24*I)*Sqrt[a]*B*Sqrt[c]*d*e - 12*A*c*d*e + 5*a*B*e^2 + (9*I)*Sqrt[a]*A*Sqrt[c]*e^2)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(e^6*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(c*d^2 + a*e^2)*(d + e*x))))/(15*Sqrt[a + c*x^2])","C",1
1480,1,550,388,4.266181,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{a+c x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/Sqrt[a + c*x^2],x]","\frac{\sqrt{d+e x} \left(\frac{2 \left(a+c x^2\right) (5 A e+6 B d+3 B e x)}{c}+\frac{2 \left(e^2 \left(a+c x^2\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \left(-9 a B e^2+20 A c d e+3 B c d^2\right)+\sqrt{c} (d+e x)^{3/2} \left(\sqrt{a} e-i \sqrt{c} d\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(-9 a B e^2+20 A c d e+3 B c d^2\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+i \sqrt{c} e (d+e x)^{3/2} \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(i \sqrt{a} \sqrt{c} (5 A e+3 B d)-9 a B e+15 A c d\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{c^2 e^2 (d+e x) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}\right)}{15 \sqrt{a+c x^2}}","\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,"(Sqrt[d + e*x]*((2*(6*B*d + 5*A*e + 3*B*e*x)*(a + c*x^2))/c + (2*(e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(3*B*c*d^2 + 20*A*c*d*e - 9*a*B*e^2)*(a + c*x^2) + Sqrt[c]*((-I)*Sqrt[c]*d + Sqrt[a]*e)*(3*B*c*d^2 + 20*A*c*d*e - 9*a*B*e^2)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] + I*Sqrt[c]*e*(Sqrt[c]*d + I*Sqrt[a]*e)*(15*A*c*d - 9*a*B*e + I*Sqrt[a]*Sqrt[c]*(3*B*d + 5*A*e))*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(c^2*e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(d + e*x))))/(15*Sqrt[a + c*x^2])","C",1
1481,1,464,331,3.2707537,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{a+c x^2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/Sqrt[a + c*x^2],x]","\frac{2 \sqrt{d+e x} \left(\frac{i c \sqrt{d+e x} \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} (3 A e+B d) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)}{e^2}+\frac{\left(a+c x^2\right) (3 A e+B d)}{d+e x}+\frac{i \sqrt{d+e x} \left(3 A \sqrt{c}+i \sqrt{a} B\right) \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)}{e \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}+B \left(a+c x^2\right)\right)}{3 c \sqrt{a+c x^2}}","-\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*Sqrt[d + e*x]*(B*(a + c*x^2) + ((B*d + 3*A*e)*(a + c*x^2))/(d + e*x) + (I*c*(B*d + 3*A*e)*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*Sqrt[d + e*x]*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)])/e^2 + (I*(I*Sqrt[a]*B + 3*A*Sqrt[c])*(Sqrt[c]*d + I*Sqrt[a]*e)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*Sqrt[d + e*x]*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)])/(e*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]])))/(3*c*Sqrt[a + c*x^2])","C",1
1482,1,439,288,1.5874304,"\int \frac{A+B x}{\sqrt{d+e x} \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*Sqrt[a + c*x^2]),x]","-\frac{2 \left(\sqrt{c} e (d+e x)^{3/2} \left(\sqrt{a} B-i A \sqrt{c}\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)-B e^2 \left(a+c x^2\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}+i B \sqrt{c} (d+e x)^{3/2} \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{c e^2 \sqrt{a+c x^2} \sqrt{d+e x} \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}","\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*(-(B*e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(a + c*x^2)) + I*B*Sqrt[c]*(Sqrt[c]*d + I*Sqrt[a]*e)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] + (Sqrt[a]*B - I*A*Sqrt[c])*Sqrt[c]*e*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(c*e^2*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*Sqrt[d + e*x]*Sqrt[a + c*x^2])","C",1
1483,1,320,344,1.4980881,"\int \frac{A+B x}{(d+e x)^{3/2} \sqrt{a+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*Sqrt[a + c*x^2]),x]","\frac{2 (d+e x) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} \left(e \left(\sqrt{a} B+i A \sqrt{c}\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+i \sqrt{c} (B d-A e) E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{e^2 \sqrt{a+c x^2} \left(\sqrt{c} d-i \sqrt{a} e\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}","\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*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)*(I*Sqrt[c]*(B*d - A*e)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] + (Sqrt[a]*B + I*A*Sqrt[c])*e*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(e^2*(Sqrt[c]*d - I*Sqrt[a]*e)*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*Sqrt[a + c*x^2])","C",1
1484,1,465,345,4.7993674,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a + c*x^2)^(3/2),x]","\frac{\sqrt{d+e x} \left(\frac{e \left(a+c x^2\right) (3 a B e-A c d)}{d+e x}+c (A c d x-a (A e+B (d+e x)))-\sqrt{a} c \sqrt{d+e x} \left(A \sqrt{c}+3 i \sqrt{a} B\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)-\frac{i c \sqrt{d+e x} \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} (A c d-3 a B e) E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)}{e}\right)}{a c^2 \sqrt{a+c x^2}}","-\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]*((e*(-(A*c*d) + 3*a*B*e)*(a + c*x^2))/(d + e*x) + c*(A*c*d*x - a*(A*e + B*(d + e*x))) - (I*c*(A*c*d - 3*a*B*e)*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*Sqrt[d + e*x]*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)])/e - Sqrt[a]*((3*I)*Sqrt[a]*B + A*Sqrt[c])*c*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*Sqrt[d + e*x]*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(a*c^2*Sqrt[a + c*x^2])","C",1
1485,1,431,319,3.9754642,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a + c*x^2)^(3/2),x]","\frac{\sqrt{d+e x} \left(\frac{\sqrt{a} \sqrt{d+e x} \left(A \sqrt{c}+i \sqrt{a} B\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)}{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}-\frac{A e \left(a+c x^2\right)}{d+e x}-\frac{i A c \sqrt{d+e x} \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)}{e}-a B+A c x\right)}{a c \sqrt{a+c x^2}}","\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,"(Sqrt[d + e*x]*(-(a*B) + A*c*x - (A*e*(a + c*x^2))/(d + e*x) - (I*A*c*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*Sqrt[d + e*x]*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)])/e + (Sqrt[a]*(I*Sqrt[a]*B + A*Sqrt[c])*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*Sqrt[d + e*x]*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)])/Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]))/(a*c*Sqrt[a + c*x^2])","C",1
1486,1,525,356,3.2464891,"\int \frac{A+B x}{\sqrt{d+e x} \left(a+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a + c*x^2)^(3/2)),x]","\frac{\sqrt{d+e x} \left(2 (a (A e-B d+B e x)+A c d x)-\frac{2 \left(e^2 \left(a+c x^2\right) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}} (a B e+A c d)+\sqrt{a} \sqrt{c} e (d+e x)^{3/2} \left(-A \sqrt{c}+i \sqrt{a} B\right) \left(\sqrt{c} d+i \sqrt{a} e\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)+\sqrt{c} (d+e x)^{3/2} \left(\sqrt{a} e-i \sqrt{c} d\right) \sqrt{\frac{e \left(x+\frac{i \sqrt{a}}{\sqrt{c}}\right)}{d+e x}} \sqrt{-\frac{-e x+\frac{i \sqrt{a} e}{\sqrt{c}}}{d+e x}} (a B e+A c d) E\left(i \sinh ^{-1}\left(\frac{\sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}{\sqrt{d+e x}}\right)|\frac{\sqrt{c} d-i \sqrt{a} e}{\sqrt{c} d+i \sqrt{a} e}\right)\right)}{c e (d+e x) \sqrt{-d-\frac{i \sqrt{a} e}{\sqrt{c}}}}\right)}{2 a \sqrt{a+c x^2} \left(a e^2+c d^2\right)}","-\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]*(2*(A*c*d*x + a*(-(B*d) + A*e + B*e*x)) - (2*(e^2*(A*c*d + a*B*e)*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(a + c*x^2) + Sqrt[c]*((-I)*Sqrt[c]*d + Sqrt[a]*e)*(A*c*d + a*B*e)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticE[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)] + Sqrt[a]*(I*Sqrt[a]*B - A*Sqrt[c])*Sqrt[c]*e*(Sqrt[c]*d + I*Sqrt[a]*e)*Sqrt[(e*((I*Sqrt[a])/Sqrt[c] + x))/(d + e*x)]*Sqrt[-(((I*Sqrt[a]*e)/Sqrt[c] - e*x)/(d + e*x))]*(d + e*x)^(3/2)*EllipticF[I*ArcSinh[Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]/Sqrt[d + e*x]], (Sqrt[c]*d - I*Sqrt[a]*e)/(Sqrt[c]*d + I*Sqrt[a]*e)]))/(c*e*Sqrt[-d - (I*Sqrt[a]*e)/Sqrt[c]]*(d + e*x))))/(2*a*(c*d^2 + a*e^2)*Sqrt[a + c*x^2])","C",1
1487,1,773,372,1.6156173,"\int (A+B x) (d+e x)^m \left(a+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a + c*x^2)^3,x]","\frac{(d+e x)^{m+1} \left(B (m+1) (d+e x) \left(6 (m+7) \left(a e^2+c d^2\right) \left(4 (m+5) \left(a e^2+c d^2\right) \left(a e^2 \left(m^2+7 m+12\right)+c \left(2 d^2-2 d e (m+2) x+e^2 \left(m^2+5 m+6\right) x^2\right)\right)-4 c d (m+2) (d+e x) \left(a e^2 \left(m^2+9 m+20\right)+c \left(2 d^2-2 d e (m+3) x+e^2 \left(m^2+7 m+12\right) x^2\right)\right)+e^4 (m+2) (m+3) (m+4) (m+5) \left(a+c x^2\right)^2\right)-6 c d (m+2) (d+e x) \left(4 (m+6) \left(a e^2+c d^2\right) \left(a e^2 \left(m^2+9 m+20\right)+c \left(2 d^2-2 d e (m+3) x+e^2 \left(m^2+7 m+12\right) x^2\right)\right)-4 c d (m+3) (d+e x) \left(a e^2 \left(m^2+11 m+30\right)+c \left(2 d^2-2 d e (m+4) x+e^2 \left(m^2+9 m+20\right) x^2\right)\right)+e^4 (m+3) (m+4) (m+5) (m+6) \left(a+c x^2\right)^2\right)+e^6 (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) \left(a+c x^2\right)^3\right)-(m+8) (B d-A e) \left(6 (m+6) \left(a e^2+c d^2\right) \left(4 (m+4) \left(a e^2+c d^2\right) \left(a e^2 \left(m^2+5 m+6\right)+c \left(2 d^2-2 d e (m+1) x+e^2 \left(m^2+3 m+2\right) x^2\right)\right)-4 c d (m+1) (d+e x) \left(a e^2 \left(m^2+7 m+12\right)+c \left(2 d^2-2 d e (m+2) x+e^2 \left(m^2+5 m+6\right) x^2\right)\right)+e^4 (m+1) (m+2) (m+3) (m+4) \left(a+c x^2\right)^2\right)-6 c d (m+1) (d+e x) \left(4 (m+5) \left(a e^2+c d^2\right) \left(a e^2 \left(m^2+7 m+12\right)+c \left(2 d^2-2 d e (m+2) x+e^2 \left(m^2+5 m+6\right) x^2\right)\right)-4 c d (m+2) (d+e x) \left(a e^2 \left(m^2+9 m+20\right)+c \left(2 d^2-2 d e (m+3) x+e^2 \left(m^2+7 m+12\right) x^2\right)\right)+e^4 (m+2) (m+3) (m+4) (m+5) \left(a+c x^2\right)^2\right)+e^6 (m+1) (m+2) (m+3) (m+4) (m+5) (m+6) \left(a+c x^2\right)^3\right)\right)}{e^8 (m+1) (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) (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{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{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{\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,"((d + e*x)^(1 + m)*(-((B*d - A*e)*(8 + m)*(e^6*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(a + c*x^2)^3 + 6*(c*d^2 + a*e^2)*(6 + m)*(e^4*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(a + c*x^2)^2 + 4*(c*d^2 + a*e^2)*(4 + m)*(a*e^2*(6 + 5*m + m^2) + c*(2*d^2 - 2*d*e*(1 + m)*x + e^2*(2 + 3*m + m^2)*x^2)) - 4*c*d*(1 + m)*(d + e*x)*(a*e^2*(12 + 7*m + m^2) + c*(2*d^2 - 2*d*e*(2 + m)*x + e^2*(6 + 5*m + m^2)*x^2))) - 6*c*d*(1 + m)*(d + e*x)*(e^4*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(a + c*x^2)^2 + 4*(c*d^2 + a*e^2)*(5 + m)*(a*e^2*(12 + 7*m + m^2) + c*(2*d^2 - 2*d*e*(2 + m)*x + e^2*(6 + 5*m + m^2)*x^2)) - 4*c*d*(2 + m)*(d + e*x)*(a*e^2*(20 + 9*m + m^2) + c*(2*d^2 - 2*d*e*(3 + m)*x + e^2*(12 + 7*m + m^2)*x^2))))) + B*(1 + m)*(d + e*x)*(e^6*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)*(a + c*x^2)^3 + 6*(c*d^2 + a*e^2)*(7 + m)*(e^4*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(a + c*x^2)^2 + 4*(c*d^2 + a*e^2)*(5 + m)*(a*e^2*(12 + 7*m + m^2) + c*(2*d^2 - 2*d*e*(2 + m)*x + e^2*(6 + 5*m + m^2)*x^2)) - 4*c*d*(2 + m)*(d + e*x)*(a*e^2*(20 + 9*m + m^2) + c*(2*d^2 - 2*d*e*(3 + m)*x + e^2*(12 + 7*m + m^2)*x^2))) - 6*c*d*(2 + m)*(d + e*x)*(e^4*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(a + c*x^2)^2 + 4*(c*d^2 + a*e^2)*(6 + m)*(a*e^2*(20 + 9*m + m^2) + c*(2*d^2 - 2*d*e*(3 + m)*x + e^2*(12 + 7*m + m^2)*x^2)) - 4*c*d*(3 + m)*(d + e*x)*(a*e^2*(30 + 11*m + m^2) + c*(2*d^2 - 2*d*e*(4 + m)*x + e^2*(20 + 9*m + m^2)*x^2))))))/(e^8*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)*(8 + m))","B",1
1488,1,355,234,0.5342458,"\int (A+B x) (d+e x)^m \left(a+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a + c*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(B (m+1) (d+e x) \left(4 (m+5) \left(a e^2+c d^2\right) \left(a e^2 \left(m^2+7 m+12\right)+c \left(2 d^2-2 d e (m+2) x+e^2 \left(m^2+5 m+6\right) x^2\right)\right)-4 c d (m+2) (d+e x) \left(a e^2 \left(m^2+9 m+20\right)+c \left(2 d^2-2 d e (m+3) x+e^2 \left(m^2+7 m+12\right) x^2\right)\right)+e^4 (m+2) (m+3) (m+4) (m+5) \left(a+c x^2\right)^2\right)-(m+6) (B d-A e) \left(4 (m+4) \left(a e^2+c d^2\right) \left(a e^2 \left(m^2+5 m+6\right)+c \left(2 d^2-2 d e (m+1) x+e^2 \left(m^2+3 m+2\right) x^2\right)\right)-4 c d (m+1) (d+e x) \left(a e^2 \left(m^2+7 m+12\right)+c \left(2 d^2-2 d e (m+2) x+e^2 \left(m^2+5 m+6\right) x^2\right)\right)+e^4 (m+1) (m+2) (m+3) (m+4) \left(a+c x^2\right)^2\right)\right)}{e^6 (m+1) (m+2) (m+3) (m+4) (m+5) (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+4} \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6 (m+4)}-\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{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,"((d + e*x)^(1 + m)*(-((B*d - A*e)*(6 + m)*(e^4*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(a + c*x^2)^2 + 4*(c*d^2 + a*e^2)*(4 + m)*(a*e^2*(6 + 5*m + m^2) + c*(2*d^2 - 2*d*e*(1 + m)*x + e^2*(2 + 3*m + m^2)*x^2)) - 4*c*d*(1 + m)*(d + e*x)*(a*e^2*(12 + 7*m + m^2) + c*(2*d^2 - 2*d*e*(2 + m)*x + e^2*(6 + 5*m + m^2)*x^2)))) + B*(1 + m)*(d + e*x)*(e^4*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(a + c*x^2)^2 + 4*(c*d^2 + a*e^2)*(5 + m)*(a*e^2*(12 + 7*m + m^2) + c*(2*d^2 - 2*d*e*(2 + m)*x + e^2*(6 + 5*m + m^2)*x^2)) - 4*c*d*(2 + m)*(d + e*x)*(a*e^2*(20 + 9*m + m^2) + c*(2*d^2 - 2*d*e*(3 + m)*x + e^2*(12 + 7*m + m^2)*x^2)))))/(e^6*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m))","A",1
1489,1,122,126,0.1989119,"\int (A+B x) (d+e x)^m \left(a+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a + c*x^2),x]","\frac{(d+e x)^{m+1} \left((A e-B d) \left(\frac{a e^2+c d^2}{m+1}+\frac{c (d+e x)^2}{m+3}-\frac{2 c d (d+e x)}{m+2}\right)+B (d+e x) \left(\frac{a e^2+c d^2}{m+2}+\frac{c (d+e x)^2}{m+4}-\frac{2 c d (d+e x)}{m+3}\right)\right)}{e^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,"((d + e*x)^(1 + m)*((-(B*d) + A*e)*((c*d^2 + a*e^2)/(1 + m) - (2*c*d*(d + e*x))/(2 + m) + (c*(d + e*x)^2)/(3 + m)) + B*(d + e*x)*((c*d^2 + a*e^2)/(2 + m) - (2*c*d*(d + e*x))/(3 + m) + (c*(d + e*x)^2)/(4 + m))))/e^4","A",1
1490,1,182,202,0.2511454,"\int \frac{(A+B x) (d+e x)^m}{a+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^m)/(a + c*x^2),x]","\frac{(d+e x)^{m+1} \left(\frac{\left(\sqrt{-a} A \sqrt{c}+a B\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{\sqrt{-a} e-\sqrt{c} d}+\frac{\left(\sqrt{-a} A \sqrt{c}-a B\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{\sqrt{-a} e+\sqrt{c} d}\right)}{2 a \sqrt{c} (m+1)}","-\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,"((d + e*x)^(1 + m)*(((a*B + Sqrt[-a]*A*Sqrt[c])*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(-(Sqrt[c]*d) + Sqrt[-a]*e) + ((-(a*B) + Sqrt[-a]*A*Sqrt[c])*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(Sqrt[c]*d + Sqrt[-a]*e)))/(2*a*Sqrt[c]*(1 + m))","A",1
1491,1,310,361,0.7510597,"\int \frac{(A+B x) (d+e x)^m}{\left(a+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^m)/(a + c*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(\frac{\sqrt{c} \left(a e m (a B e+A c d)-\sqrt{-a} \sqrt{c} \left(-a A e^2 (m-1)+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)}{a (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}+\frac{\sqrt{c} \left(\sqrt{-a} \sqrt{c} \left(-a A e^2 (m-1)+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)}{a (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}+\frac{2 c (a (A e-B d+B e x)+A c d x)}{a+c x^2}\right)}{4 a c \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)*((2*c*(A*c*d*x + a*(-(B*d) + A*e + B*e*x)))/(a + c*x^2) + (Sqrt[c]*(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))*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(a*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + m)) + (Sqrt[c]*(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))*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(a*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + m))))/(4*a*c*(c*d^2 + a*e^2))","A",1
1492,1,182,202,0.1725058,"\int \frac{(A+B x) (d+e x)^{1+m}}{a+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(1 + m))/(a + c*x^2),x]","\frac{(d+e x)^{m+2} \left(\frac{\left(\sqrt{-a} A \sqrt{c}+a B\right) \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{\sqrt{-a} e-\sqrt{c} d}+\frac{\left(\sqrt{-a} A \sqrt{c}-a B\right) \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{\sqrt{-a} e+\sqrt{c} d}\right)}{2 a \sqrt{c} (m+2)}","-\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,"((d + e*x)^(2 + m)*(((a*B + Sqrt[-a]*A*Sqrt[c])*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(-(Sqrt[c]*d) + Sqrt[-a]*e) + ((-(a*B) + Sqrt[-a]*A*Sqrt[c])*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(Sqrt[c]*d + Sqrt[-a]*e)))/(2*a*Sqrt[c]*(2 + m))","A",1
1493,1,31,31,0.061256,"\int (-a e+c d x) (d+e x)^{-3-2 p} \left(a+c x^2\right)^p \, dx","Integrate[(-(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-2}}{2 (p+1)}","\frac{\left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)}}{2 (p+1)}",1,"((d + e*x)^(-2 - 2*p)*(a + c*x^2)^(1 + p))/(2*(1 + p))","A",1
1494,1,229,124,0.0743082,"\int (b+2 c x) (d+e x)^4 \left(a+b x+c x^2\right) \, dx","Integrate[(b + 2*c*x)*(d + e*x)^4*(a + b*x + c*x^2),x]","\frac{1}{6} e^2 x^6 \left(2 c e (a e+6 b d)+b^2 e^2+12 c^2 d^2\right)+\frac{1}{2} d^3 x^2 \left(4 a b e+2 a c d+b^2 d\right)+\frac{1}{3} d^2 x^3 \left(6 a b e^2+8 a c d e+4 b^2 d e+3 b c d^2\right)+\frac{1}{5} e x^5 \left(2 c d e (4 a e+9 b d)+b e^2 (a e+4 b d)+8 c^2 d^3\right)+\frac{1}{2} d x^4 \left(6 c d e (a e+b d)+b e^2 (2 a e+3 b d)+c^2 d^3\right)+a b d^4 x+\frac{1}{7} c e^3 x^7 (3 b e+8 c d)+\frac{1}{4} c^2 e^4 x^8","\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,"a*b*d^4*x + (d^3*(b^2*d + 2*a*c*d + 4*a*b*e)*x^2)/2 + (d^2*(3*b*c*d^2 + 4*b^2*d*e + 8*a*c*d*e + 6*a*b*e^2)*x^3)/3 + (d*(c^2*d^3 + 6*c*d*e*(b*d + a*e) + b*e^2*(3*b*d + 2*a*e))*x^4)/2 + (e*(8*c^2*d^3 + b*e^2*(4*b*d + a*e) + 2*c*d*e*(9*b*d + 4*a*e))*x^5)/5 + (e^2*(12*c^2*d^2 + b^2*e^2 + 2*c*e*(6*b*d + a*e))*x^6)/6 + (c*e^3*(8*c*d + 3*b*e)*x^7)/7 + (c^2*e^4*x^8)/4","A",1
1495,1,175,124,0.0549454,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right) \, dx","Integrate[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2),x]","\frac{1}{5} e x^5 \left(c e (2 a e+9 b d)+b^2 e^2+6 c^2 d^2\right)+d x^3 \left(a b e^2+2 a c d e+b^2 d e+b c d^2\right)+\frac{1}{2} d^2 x^2 \left(3 a b e+2 a c d+b^2 d\right)+\frac{1}{4} x^4 \left(3 c d e (2 a e+3 b d)+b e^2 (a e+3 b d)+2 c^2 d^3\right)+a b d^3 x+\frac{1}{2} c e^2 x^6 (b e+2 c d)+\frac{2}{7} c^2 e^3 x^7","\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,"a*b*d^3*x + (d^2*(b^2*d + 2*a*c*d + 3*a*b*e)*x^2)/2 + d*(b*c*d^2 + b^2*d*e + 2*a*c*d*e + a*b*e^2)*x^3 + ((2*c^2*d^3 + b*e^2*(3*b*d + a*e) + 3*c*d*e*(3*b*d + 2*a*e))*x^4)/4 + (e*(6*c^2*d^2 + b^2*e^2 + c*e*(9*b*d + 2*a*e))*x^5)/5 + (c*e^2*(2*c*d + b*e)*x^6)/2 + (2*c^2*e^3*x^7)/7","A",1
1496,1,133,124,0.0398786,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right) \, dx","Integrate[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2),x]","\frac{1}{4} x^4 \left(2 a c e^2+b^2 e^2+6 b c d e+2 c^2 d^2\right)+\frac{1}{3} x^3 \left(a b e^2+4 a c d e+2 b^2 d e+3 b c d^2\right)+\frac{1}{2} d x^2 \left(2 a b e+2 a c d+b^2 d\right)+a b d^2 x+\frac{1}{5} c e x^5 (3 b e+4 c d)+\frac{1}{3} c^2 e^2 x^6","\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,"a*b*d^2*x + (d*(b^2*d + 2*a*c*d + 2*a*b*e)*x^2)/2 + ((3*b*c*d^2 + 2*b^2*d*e + 4*a*c*d*e + a*b*e^2)*x^3)/3 + ((2*c^2*d^2 + 6*b*c*d*e + b^2*e^2 + 2*a*c*e^2)*x^4)/4 + (c*e*(4*c*d + 3*b*e)*x^5)/5 + (c^2*e^2*x^6)/3","A",1
1497,1,79,79,0.0181314,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right) \, dx","Integrate[(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",1
1498,1,21,16,0.0046918,"\int (b+2 c x) \left(a+b x+c x^2\right) \, dx","Integrate[(b + 2*c*x)*(a + b*x + c*x^2),x]","\frac{1}{2} x (b+c x) (2 a+x (b+c x))","\frac{1}{2} \left(a+b x+c x^2\right)^2",1,"(x*(b + c*x)*(2*a + x*(b + c*x)))/2","A",1
1499,1,95,104,0.0393467,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{d+e x} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x),x]","\frac{e x \left(3 c e (4 a e-6 b d+3 b e x)+6 b^2 e^2+2 c^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)-6 (2 c d-b e) \log (d+e x) \left(e (a e-b d)+c d^2\right)}{6 e^4}","\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,"(e*x*(6*b^2*e^2 + 3*c*e*(-6*b*d + 4*a*e + 3*b*e*x) + 2*c^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) - 6*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))*Log[d + e*x])/(6*e^4)","A",1
1500,1,97,102,0.0638662,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^2} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^2,x]","\frac{\log (d+e x) \left(2 c e (a e-3 b d)+b^2 e^2+6 c^2 d^2\right)+\frac{(2 c d-b e) \left(e (a e-b d)+c d^2\right)}{d+e x}-c e x (4 c d-3 b e)+c^2 e^2 x^2}{e^4}","\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*e*(4*c*d - 3*b*e)*x) + c^2*e^2*x^2 + ((2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e)))/(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",1
1501,1,118,111,0.0481807,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^3} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^3,x]","\frac{c e (3 b d (3 d+4 e x)-2 a e (d+2 e x))-b e^2 (a e+b (d+2 e x))-6 c (d+e x)^2 (2 c d-b e) \log (d+e x)+c^2 \left(-10 d^3-8 d^2 e x+8 d e^2 x^2+4 e^3 x^3\right)}{2 e^4 (d+e x)^2}","-\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,"(c^2*(-10*d^3 - 8*d^2*e*x + 8*d*e^2*x^2 + 4*e^3*x^3) - b*e^2*(a*e + b*(d + 2*e*x)) + c*e*(-2*a*e*(d + 2*e*x) + 3*b*d*(3*d + 4*e*x)) - 6*c*(2*c*d - b*e)*(d + e*x)^2*Log[d + e*x])/(2*e^4*(d + e*x)^2)","A",1
1502,1,111,119,0.0452175,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^4} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^4,x]","\frac{-2 c e \left(a e (d+3 e x)+3 b \left(d^2+3 d e x+3 e^2 x^2\right)\right)-b e^2 (2 a e+b (d+3 e x))+2 c^2 d \left(11 d^2+27 d e x+18 e^2 x^2\right)+12 c^2 (d+e x)^3 \log (d+e x)}{6 e^4 (d+e x)^3}","-\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^2*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2) - b*e^2*(2*a*e + b*(d + 3*e*x)) - 2*c*e*(a*e*(d + 3*e*x) + 3*b*(d^2 + 3*d*e*x + 3*e^2*x^2)) + 12*c^2*(d + e*x)^3*Log[d + e*x])/(6*e^4*(d + e*x)^3)","A",1
1503,1,100,122,0.0393119,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^5} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^5,x]","-\frac{c e \left(2 a e (d+4 e x)+3 b \left(d^2+4 d e x+6 e^2 x^2\right)\right)+b e^2 (3 a e+b (d+4 e x))+6 c^2 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)}{12 e^4 (d+e x)^4}","-\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,"-1/12*(6*c^2*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) + b*e^2*(3*a*e + b*(d + 4*e*x)) + c*e*(2*a*e*(d + 4*e*x) + 3*b*(d^2 + 4*d*e*x + 6*e^2*x^2)))/(e^4*(d + e*x)^4)","A",1
1504,1,433,240,0.156663,"\int (b+2 c x) (d+e x)^4 \left(a+b x+c x^2\right)^2 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^4*(a + b*x + c*x^2)^2,x]","\frac{1}{3} x^6 \left(c e^2 \left(a^2 e^2+12 a b d e+12 b^2 d^2\right)+b^2 e^3 (a e+2 b d)+2 c^2 d^2 e (6 a e+5 b d)+c^3 d^4\right)+\frac{1}{5} x^5 \left(b \left(a^2 e^4+36 a c d^2 e^2+5 c^2 d^4\right)+8 b^2 \left(a d e^3+2 c d^3 e\right)+8 a c d e \left(a e^2+2 c d^2\right)+6 b^3 d^2 e^2\right)+\frac{1}{3} d^2 x^3 \left(8 a^2 c d e+8 a b^2 d e+6 a b \left(a e^2+c d^2\right)+b^3 d^2\right)+a^2 b d^4 x+\frac{1}{7} e x^7 \left(2 c^2 d e (8 a e+15 b d)+2 b c e^2 (3 a e+8 b d)+b^3 e^3+8 c^3 d^3\right)+\frac{1}{2} c e^2 x^8 \left(c e (a e+5 b d)+b^2 e^2+3 c^2 d^2\right)+a d^3 x^2 \left(2 a b e+a c d+b^2 d\right)+d x^4 \left(b^2 \left(3 a d e^2+c d^3\right)+a b e \left(a e^2+6 c d^2\right)+a c d \left(3 a e^2+c d^2\right)+b^3 d^2 e\right)+\frac{1}{9} c^2 e^3 x^9 (5 b e+8 c d)+\frac{1}{5} c^3 e^4 x^{10}","\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,"a^2*b*d^4*x + a*d^3*(b^2*d + a*c*d + 2*a*b*e)*x^2 + (d^2*(b^3*d^2 + 8*a*b^2*d*e + 8*a^2*c*d*e + 6*a*b*(c*d^2 + a*e^2))*x^3)/3 + d*(b^3*d^2*e + a*b*e*(6*c*d^2 + a*e^2) + a*c*d*(c*d^2 + 3*a*e^2) + b^2*(c*d^3 + 3*a*d*e^2))*x^4 + ((6*b^3*d^2*e^2 + 8*a*c*d*e*(2*c*d^2 + a*e^2) + 8*b^2*(2*c*d^3*e + a*d*e^3) + b*(5*c^2*d^4 + 36*a*c*d^2*e^2 + a^2*e^4))*x^5)/5 + ((c^3*d^4 + b^2*e^3*(2*b*d + a*e) + 2*c^2*d^2*e*(5*b*d + 6*a*e) + c*e^2*(12*b^2*d^2 + 12*a*b*d*e + a^2*e^2))*x^6)/3 + (e*(8*c^3*d^3 + b^3*e^3 + 2*b*c*e^2*(8*b*d + 3*a*e) + 2*c^2*d*e*(15*b*d + 8*a*e))*x^7)/7 + (c*e^2*(3*c^2*d^2 + b^2*e^2 + c*e*(5*b*d + a*e))*x^8)/2 + (c^2*e^3*(8*c*d + 5*b*e)*x^9)/9 + (c^3*e^4*x^10)/5","A",1
1505,1,351,240,0.1232443,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right)^2 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2)^2,x]","\frac{1}{3} d x^3 \left(6 a^2 c d e+6 a b^2 d e+3 a b \left(a e^2+2 c d^2\right)+b^3 d^2\right)+a^2 b d^3 x+\frac{1}{6} x^6 \left(3 c^2 d e (4 a e+5 b d)+6 b c e^2 (a e+2 b d)+b^3 e^3+2 c^3 d^3\right)+\frac{1}{7} c e x^7 \left(c e (4 a e+15 b d)+4 b^2 e^2+6 c^2 d^2\right)+\frac{1}{2} a d^2 x^2 \left(3 a b e+2 a c d+2 b^2 d\right)+\frac{1}{5} x^5 \left(2 b^2 \left(a e^3+6 c d^2 e\right)+b c d \left(18 a e^2+5 c d^2\right)+2 a c e \left(a e^2+6 c d^2\right)+3 b^3 d e^2\right)+\frac{1}{4} x^4 \left(b^2 \left(6 a d e^2+4 c d^3\right)+a b e \left(a e^2+18 c d^2\right)+2 a c d \left(3 a e^2+2 c d^2\right)+3 b^3 d^2 e\right)+\frac{1}{8} c^2 e^2 x^8 (5 b e+6 c d)+\frac{2}{9} c^3 e^3 x^9","\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,"a^2*b*d^3*x + (a*d^2*(2*b^2*d + 2*a*c*d + 3*a*b*e)*x^2)/2 + (d*(b^3*d^2 + 6*a*b^2*d*e + 6*a^2*c*d*e + 3*a*b*(2*c*d^2 + a*e^2))*x^3)/3 + ((3*b^3*d^2*e + a*b*e*(18*c*d^2 + a*e^2) + 2*a*c*d*(2*c*d^2 + 3*a*e^2) + b^2*(4*c*d^3 + 6*a*d*e^2))*x^4)/4 + ((3*b^3*d*e^2 + 2*a*c*e*(6*c*d^2 + a*e^2) + b*c*d*(5*c*d^2 + 18*a*e^2) + 2*b^2*(6*c*d^2*e + a*e^3))*x^5)/5 + ((2*c^3*d^3 + b^3*e^3 + 6*b*c*e^2*(2*b*d + a*e) + 3*c^2*d*e*(5*b*d + 4*a*e))*x^6)/6 + (c*e*(6*c^2*d^2 + 4*b^2*e^2 + c*e*(15*b*d + 4*a*e))*x^7)/7 + (c^2*e^2*(6*c*d + 5*b*e)*x^8)/8 + (2*c^3*e^3*x^9)/9","A",1
1506,1,244,240,0.0840663,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right)^2 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2)^2,x]","\frac{1}{3} x^3 \left(4 a^2 c d e+4 a b^2 d e+a b \left(a e^2+6 c d^2\right)+b^3 d^2\right)+a^2 b d^2 x+\frac{1}{3} c x^6 \left(c e (2 a e+5 b d)+2 b^2 e^2+c^2 d^2\right)+a d x^2 \left(a b e+a c d+b^2 d\right)+\frac{1}{5} x^5 \left(b c \left(6 a e^2+5 c d^2\right)+8 a c^2 d e+b^3 e^2+8 b^2 c d e\right)+\frac{1}{2} x^4 \left(b^2 \left(a e^2+2 c d^2\right)+6 a b c d e+a c \left(a e^2+2 c d^2\right)+b^3 d e\right)+\frac{1}{7} c^2 e x^7 (5 b e+4 c d)+\frac{1}{4} c^3 e^2 x^8","\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,"a^2*b*d^2*x + a*d*(b^2*d + a*c*d + a*b*e)*x^2 + ((b^3*d^2 + 4*a*b^2*d*e + 4*a^2*c*d*e + a*b*(6*c*d^2 + a*e^2))*x^3)/3 + ((b^3*d*e + 6*a*b*c*d*e + b^2*(2*c*d^2 + a*e^2) + a*c*(2*c*d^2 + a*e^2))*x^4)/2 + ((8*b^2*c*d*e + 8*a*c^2*d*e + b^3*e^2 + b*c*(5*c*d^2 + 6*a*e^2))*x^5)/5 + (c*(c^2*d^2 + 2*b^2*e^2 + c*e*(5*b*d + 2*a*e))*x^6)/3 + (c^2*e*(4*c*d + 5*b*e)*x^7)/7 + (c^3*e^2*x^8)/4","A",1
1507,1,153,153,0.0432311,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[(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}{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}{4} x^4 \left(6 a b c e+4 a c^2 d+b^3 e+4 b^2 c 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}{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}{4} x^4 \left(6 a b c e+4 a c^2 d+b^3 e+4 b^2 c 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",1
1508,1,36,16,0.0098342,"\int (b+2 c x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[(b + 2*c*x)*(a + b*x + c*x^2)^2,x]","\frac{1}{3} x (b+c x) \left(3 a^2+3 a x (b+c x)+x^2 (b+c x)^2\right)","\frac{1}{3} \left(a+b x+c x^2\right)^3",1,"(x*(b + c*x)*(3*a^2 + 3*a*x*(b + c*x) + x^2*(b + c*x)^2))/3","B",1
1509,1,228,229,0.1116867,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{d+e x} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x),x]","\frac{e x \left(20 c e^2 \left(6 a^2 e^2+9 a b e (e x-2 d)+2 b^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+30 b^2 e^3 (4 a e-2 b d+b e x)+5 c^2 e \left(8 a e \left(6 d^2-3 d e x+2 e^2 x^2\right)-5 b \left(12 d^3-6 d^2 e x+4 d e^2 x^2-3 e^3 x^3\right)\right)+2 c^3 \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)-60 (2 c d-b e) \log (d+e x) \left(e (a e-b d)+c d^2\right)^2}{60 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,"(e*x*(30*b^2*e^3*(-2*b*d + 4*a*e + b*e*x) + 2*c^3*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + 20*c*e^2*(6*a^2*e^2 + 9*a*b*e*(-2*d + e*x) + 2*b^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + 5*c^2*e*(8*a*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) - 5*b*(12*d^3 - 6*d^2*e*x + 4*d*e^2*x^2 - 3*e^3*x^3))) - 60*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^2*Log[d + e*x])/(60*e^6)","A",1
1510,1,241,223,0.1849864,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^2} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^2,x]","\frac{12 \log (d+e x) \left(c e^2 \left(a^2 e^2-6 a b d e+6 b^2 d^2\right)+b^2 e^3 (a e-b d)+2 c^2 d^2 e (3 a e-5 b d)+5 c^3 d^4\right)+6 e x \left(c^2 d e (15 b d-8 a e)+2 b c e^2 (3 a e-4 b d)+b^3 e^3-8 c^3 d^3\right)+6 c e^2 x^2 \left(c e (2 a e-5 b d)+2 b^2 e^2+3 c^2 d^2\right)+\frac{6 (2 c d-b e) \left(e (a e-b d)+c d^2\right)^2}{d+e x}-2 c^2 e^3 x^3 (4 c d-5 b e)+3 c^3 e^4 x^4}{6 e^6}","-\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{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{(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,"(6*e*(-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 + 6*c*e^2*(3*c^2*d^2 + 2*b^2*e^2 + c*e*(-5*b*d + 2*a*e))*x^2 - 2*c^2*e^3*(4*c*d - 5*b*e)*x^3 + 3*c^3*e^4*x^4 + (6*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^2)/(d + e*x) + 12*(5*c^3*d^4 + b^2*e^3*(-(b*d) + a*e) + 2*c^2*d^2*e*(-5*b*d + 3*a*e) + c*e^2*(6*b^2*d^2 - 6*a*b*d*e + a^2*e^2))*Log[d + e*x])/(6*e^6)","A",1
1511,1,233,219,0.0806513,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^3} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^3,x]","\frac{-\frac{12 \left(c e^2 \left(a^2 e^2-6 a b d e+6 b^2 d^2\right)+b^2 e^3 (a e-b d)+2 c^2 d^2 e (3 a e-5 b d)+5 c^3 d^4\right)}{d+e x}+6 c e x \left(c e (4 a e-15 b d)+4 b^2 e^2+12 c^2 d^2\right)-6 (2 c d-b e) \log (d+e x) \left(2 c e (3 a e-5 b d)+b^2 e^2+10 c^2 d^2\right)+\frac{3 (2 c d-b e) \left(e (a e-b d)+c d^2\right)^2}{(d+e x)^2}-3 c^2 e^2 x^2 (6 c d-5 b e)+4 c^3 e^3 x^3}{6 e^6}","-\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{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 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,"(6*c*e*(12*c^2*d^2 + 4*b^2*e^2 + c*e*(-15*b*d + 4*a*e))*x - 3*c^2*e^2*(6*c*d - 5*b*e)*x^2 + 4*c^3*e^3*x^3 + (3*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^2)/(d + e*x)^2 - (12*(5*c^3*d^4 + b^2*e^3*(-(b*d) + a*e) + 2*c^2*d^2*e*(-5*b*d + 3*a*e) + c*e^2*(6*b^2*d^2 - 6*a*b*d*e + a^2*e^2)))/(d + e*x) - 6*(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])/(6*e^6)","A",1
1512,1,300,217,0.1281313,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^4} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^4,x]","\frac{-c e^2 \left(a^2 e^2 (d+3 e x)+6 a b e \left(d^2+3 d e x+3 e^2 x^2\right)-2 b^2 d \left(11 d^2+27 d e x+18 e^2 x^2\right)\right)-b e^3 \left(a^2 e^2+a b e (d+3 e x)+b^2 \left(d^2+3 d e x+3 e^2 x^2\right)\right)+12 c (d+e x)^3 \log (d+e x) \left(c e (a e-5 b d)+b^2 e^2+5 c^2 d^2\right)+c^2 e \left(2 a d e \left(11 d^2+27 d e x+18 e^2 x^2\right)-5 b \left(13 d^4+27 d^3 e x+9 d^2 e^2 x^2-9 d e^3 x^3-3 e^4 x^4\right)\right)+c^3 \left(47 d^5+81 d^4 e x-9 d^3 e^2 x^2-63 d^2 e^3 x^3-15 d e^4 x^4+3 e^5 x^5\right)}{3 e^6 (d+e x)^3}","\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^3*(47*d^5 + 81*d^4*e*x - 9*d^3*e^2*x^2 - 63*d^2*e^3*x^3 - 15*d*e^4*x^4 + 3*e^5*x^5) - b*e^3*(a^2*e^2 + a*b*e*(d + 3*e*x) + b^2*(d^2 + 3*d*e*x + 3*e^2*x^2)) - c*e^2*(a^2*e^2*(d + 3*e*x) + 6*a*b*e*(d^2 + 3*d*e*x + 3*e^2*x^2) - 2*b^2*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) + c^2*e*(2*a*d*e*(11*d^2 + 27*d*e*x + 18*e^2*x^2) - 5*b*(13*d^4 + 27*d^3*e*x + 9*d^2*e^2*x^2 - 9*d*e^3*x^3 - 3*e^4*x^4)) + 12*c*(5*c^2*d^2 + b^2*e^2 + c*e*(-5*b*d + a*e))*(d + e*x)^3*Log[d + e*x])/(3*e^6*(d + e*x)^3)","A",1
1513,1,292,227,0.1750603,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^5} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^5,x]","-\frac{2 c e^2 \left(a^2 e^2 (d+4 e x)+3 a b e \left(d^2+4 d e x+6 e^2 x^2\right)+6 b^2 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+b e^3 \left(3 a^2 e^2+2 a b e (d+4 e x)+b^2 \left(d^2+4 d e x+6 e^2 x^2\right)\right)+c^2 e \left(12 a e \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)-5 b d \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)\right)+60 c^2 (d+e x)^4 (2 c d-b e) \log (d+e x)+2 c^3 \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)}{12 e^6 (d+e x)^4}","-\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,"-1/12*(2*c^3*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5) + b*e^3*(3*a^2*e^2 + 2*a*b*e*(d + 4*e*x) + b^2*(d^2 + 4*d*e*x + 6*e^2*x^2)) + 2*c*e^2*(a^2*e^2*(d + 4*e*x) + 3*a*b*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 6*b^2*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)) + c^2*e*(12*a*e*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) - 5*b*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) + 60*c^2*(2*c*d - b*e)*(d + e*x)^4*Log[d + e*x])/(e^6*(d + e*x)^4)","A",1
1514,1,735,411,0.2371504,"\int (b+2 c x) (d+e x)^4 \left(a+b x+c x^2\right)^3 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^4*(a + b*x + c*x^2)^3,x]","a^3 b d^4 x+\frac{1}{2} a^2 d^3 x^2 \left(4 a b e+2 a c d+3 b^2 d\right)+\frac{1}{8} x^8 \left(6 c^2 e^2 \left(a^2 e^2+10 a b d e+9 b^2 d^2\right)+4 b^2 c e^3 (3 a e+5 b d)+4 c^3 d^2 e (9 a e+7 b d)+b^4 e^4+2 c^4 d^4\right)+\frac{1}{3} a d^2 x^3 \left(8 a^2 c d e+12 a b^2 d e+3 a b \left(2 a e^2+3 c d^2\right)+3 b^3 d^2\right)+\frac{1}{7} x^7 \left(b c \left(9 a^2 e^4+90 a c d^2 e^2+7 c^2 d^4\right)+3 b^3 \left(a e^4+10 c d^2 e^2\right)+12 b^2 c d e \left(4 a e^2+3 c d^2\right)+24 a c^2 d e \left(a e^2+c d^2\right)+4 b^4 d e^3\right)+\frac{1}{5} x^5 \left(a b \left(a^2 e^4+54 a c d^2 e^2+15 c^2 d^4\right)+8 a^2 c d e \left(a e^2+3 c d^2\right)+b^3 \left(18 a d^2 e^2+5 c d^4\right)+12 a b^2 d e \left(a e^2+4 c d^2\right)+4 b^4 d^3 e\right)+\frac{1}{6} x^6 \left(3 b^2 \left(a^2 e^4+24 a c d^2 e^2+3 c^2 d^4\right)+2 a c \left(a^2 e^4+18 a c d^2 e^2+3 c^2 d^4\right)+4 b^3 \left(3 a d e^3+5 c d^3 e\right)+12 a b c d e \left(3 a e^2+5 c d^2\right)+6 b^4 d^2 e^2\right)+\frac{1}{4} d x^4 \left(4 a^2 b e \left(a e^2+9 c d^2\right)+6 a^2 c d \left(2 a e^2+c d^2\right)+12 a b^3 d^2 e+6 a b^2 d \left(3 a e^2+2 c d^2\right)+b^4 d^3\right)+\frac{1}{9} c e x^9 \left(6 c^2 d e (4 a e+7 b d)+3 b c e^2 (5 a e+12 b d)+5 b^3 e^3+8 c^3 d^3\right)+\frac{1}{10} c^2 e^2 x^{10} \left(2 c e (3 a e+14 b d)+9 b^2 e^2+12 c^2 d^2\right)+\frac{1}{11} c^3 e^3 x^{11} (7 b e+8 c d)+\frac{1}{6} c^4 e^4 x^{12}","\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,"a^3*b*d^4*x + (a^2*d^3*(3*b^2*d + 2*a*c*d + 4*a*b*e)*x^2)/2 + (a*d^2*(3*b^3*d^2 + 12*a*b^2*d*e + 8*a^2*c*d*e + 3*a*b*(3*c*d^2 + 2*a*e^2))*x^3)/3 + (d*(b^4*d^3 + 12*a*b^3*d^2*e + 4*a^2*b*e*(9*c*d^2 + a*e^2) + 6*a^2*c*d*(c*d^2 + 2*a*e^2) + 6*a*b^2*d*(2*c*d^2 + 3*a*e^2))*x^4)/4 + ((4*b^4*d^3*e + 8*a^2*c*d*e*(3*c*d^2 + a*e^2) + 12*a*b^2*d*e*(4*c*d^2 + a*e^2) + b^3*(5*c*d^4 + 18*a*d^2*e^2) + a*b*(15*c^2*d^4 + 54*a*c*d^2*e^2 + a^2*e^4))*x^5)/5 + ((6*b^4*d^2*e^2 + 12*a*b*c*d*e*(5*c*d^2 + 3*a*e^2) + 4*b^3*(5*c*d^3*e + 3*a*d*e^3) + 2*a*c*(3*c^2*d^4 + 18*a*c*d^2*e^2 + a^2*e^4) + 3*b^2*(3*c^2*d^4 + 24*a*c*d^2*e^2 + a^2*e^4))*x^6)/6 + ((4*b^4*d*e^3 + 24*a*c^2*d*e*(c*d^2 + a*e^2) + 12*b^2*c*d*e*(3*c*d^2 + 4*a*e^2) + 3*b^3*(10*c*d^2*e^2 + a*e^4) + b*c*(7*c^2*d^4 + 90*a*c*d^2*e^2 + 9*a^2*e^4))*x^7)/7 + ((2*c^4*d^4 + b^4*e^4 + 4*b^2*c*e^3*(5*b*d + 3*a*e) + 4*c^3*d^2*e*(7*b*d + 9*a*e) + 6*c^2*e^2*(9*b^2*d^2 + 10*a*b*d*e + a^2*e^2))*x^8)/8 + (c*e*(8*c^3*d^3 + 5*b^3*e^3 + 6*c^2*d*e*(7*b*d + 4*a*e) + 3*b*c*e^2*(12*b*d + 5*a*e))*x^9)/9 + (c^2*e^2*(12*c^2*d^2 + 9*b^2*e^2 + 2*c*e*(14*b*d + 3*a*e))*x^10)/10 + (c^3*e^3*(8*c*d + 7*b*e)*x^11)/11 + (c^4*e^4*x^12)/6","A",1
1515,1,562,411,0.1979049,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right)^3 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2)^3,x]","a^3 b d^3 x+\frac{1}{2} a^2 d^2 x^2 \left(3 a b e+2 a c d+3 b^2 d\right)+a d x^3 \left(2 a^2 c d e+3 a b^2 d e+a b \left(a e^2+3 c d^2\right)+b^3 d^2\right)+\frac{1}{5} x^5 \left(2 a^2 c e \left(a e^2+9 c d^2\right)+b^3 \left(9 a d e^2+5 c d^3\right)+3 a b^2 e \left(a e^2+12 c d^2\right)+3 a b c d \left(9 a e^2+5 c d^2\right)+3 b^4 d^2 e\right)+\frac{1}{4} x^4 \left(a^2 b e \left(a e^2+27 c d^2\right)+6 a^2 c d \left(a e^2+c d^2\right)+9 a b^3 d^2 e+3 a b^2 d \left(3 a e^2+4 c d^2\right)+b^4 d^3\right)+\frac{1}{8} c x^8 \left(3 c^2 d e (6 a e+7 b d)+3 b c e^2 (5 a e+9 b d)+5 b^3 e^3+2 c^3 d^3\right)+\frac{1}{3} c^2 e x^9 \left(c e (2 a e+7 b d)+3 b^2 e^2+2 c^2 d^2\right)+\frac{1}{7} x^7 \left(3 b^2 c e \left(4 a e^2+9 c d^2\right)+b c^2 d \left(45 a e^2+7 c d^2\right)+6 a c^2 e \left(a e^2+3 c d^2\right)+b^4 e^3+15 b^3 c d e^2\right)+\frac{1}{2} x^6 \left(b^3 \left(a e^3+5 c d^2 e\right)+3 b^2 c d \left(4 a e^2+c d^2\right)+3 a b c e \left(a e^2+5 c d^2\right)+2 a c^2 d \left(3 a e^2+c d^2\right)+b^4 d e^2\right)+\frac{1}{10} c^3 e^2 x^{10} (7 b e+6 c d)+\frac{2}{11} c^4 e^3 x^{11}","\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,"a^3*b*d^3*x + (a^2*d^2*(3*b^2*d + 2*a*c*d + 3*a*b*e)*x^2)/2 + a*d*(b^3*d^2 + 3*a*b^2*d*e + 2*a^2*c*d*e + a*b*(3*c*d^2 + a*e^2))*x^3 + ((b^4*d^3 + 9*a*b^3*d^2*e + 6*a^2*c*d*(c*d^2 + a*e^2) + a^2*b*e*(27*c*d^2 + a*e^2) + 3*a*b^2*d*(4*c*d^2 + 3*a*e^2))*x^4)/4 + ((3*b^4*d^2*e + 2*a^2*c*e*(9*c*d^2 + a*e^2) + 3*a*b^2*e*(12*c*d^2 + a*e^2) + 3*a*b*c*d*(5*c*d^2 + 9*a*e^2) + b^3*(5*c*d^3 + 9*a*d*e^2))*x^5)/5 + ((b^4*d*e^2 + 3*a*b*c*e*(5*c*d^2 + a*e^2) + 2*a*c^2*d*(c*d^2 + 3*a*e^2) + 3*b^2*c*d*(c*d^2 + 4*a*e^2) + b^3*(5*c*d^2*e + a*e^3))*x^6)/2 + ((15*b^3*c*d*e^2 + b^4*e^3 + 6*a*c^2*e*(3*c*d^2 + a*e^2) + 3*b^2*c*e*(9*c*d^2 + 4*a*e^2) + b*c^2*d*(7*c*d^2 + 45*a*e^2))*x^7)/7 + (c*(2*c^3*d^3 + 5*b^3*e^3 + 3*b*c*e^2*(9*b*d + 5*a*e) + 3*c^2*d*e*(7*b*d + 6*a*e))*x^8)/8 + (c^2*e*(2*c^2*d^2 + 3*b^2*e^2 + c*e*(7*b*d + 2*a*e))*x^9)/3 + (c^3*e^2*(6*c*d + 7*b*e)*x^10)/10 + (2*c^4*e^3*x^11)/11","A",1
1516,1,413,411,0.1353615,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right)^3 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2)^3,x]","a^3 b d^2 x+\frac{1}{2} a^2 d x^2 \left(2 a b e+2 a c d+3 b^2 d\right)+\frac{1}{3} a x^3 \left(4 a^2 c d e+6 a b^2 d e+a b \left(a e^2+9 c d^2\right)+3 b^3 d^2\right)+\frac{1}{5} x^5 \left(12 a^2 c^2 d e+b^3 \left(3 a e^2+5 c d^2\right)+24 a b^2 c d e+3 a b c \left(3 a e^2+5 c d^2\right)+2 b^4 d e\right)+\frac{1}{4} x^4 \left(18 a^2 b c d e+2 a^2 c \left(a e^2+3 c d^2\right)+6 a b^3 d e+3 a b^2 \left(a e^2+4 c d^2\right)+b^4 d^2\right)+\frac{1}{8} c^2 x^8 \left(2 c e (3 a e+7 b d)+9 b^2 e^2+2 c^2 d^2\right)+\frac{1}{7} c x^7 \left(b c \left(15 a e^2+7 c d^2\right)+12 a c^2 d e+5 b^3 e^2+18 b^2 c d e\right)+\frac{1}{6} x^6 \left(3 b^2 c \left(4 a e^2+3 c d^2\right)+30 a b c^2 d e+6 a c^2 \left(a e^2+c d^2\right)+b^4 e^2+10 b^3 c d e\right)+\frac{1}{9} c^3 e x^9 (7 b e+4 c d)+\frac{1}{5} c^4 e^2 x^{10}","\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,"a^3*b*d^2*x + (a^2*d*(3*b^2*d + 2*a*c*d + 2*a*b*e)*x^2)/2 + (a*(3*b^3*d^2 + 6*a*b^2*d*e + 4*a^2*c*d*e + a*b*(9*c*d^2 + a*e^2))*x^3)/3 + ((b^4*d^2 + 6*a*b^3*d*e + 18*a^2*b*c*d*e + 2*a^2*c*(3*c*d^2 + a*e^2) + 3*a*b^2*(4*c*d^2 + a*e^2))*x^4)/4 + ((2*b^4*d*e + 24*a*b^2*c*d*e + 12*a^2*c^2*d*e + b^3*(5*c*d^2 + 3*a*e^2) + 3*a*b*c*(5*c*d^2 + 3*a*e^2))*x^5)/5 + ((10*b^3*c*d*e + 30*a*b*c^2*d*e + b^4*e^2 + 6*a*c^2*(c*d^2 + a*e^2) + 3*b^2*c*(3*c*d^2 + 4*a*e^2))*x^6)/6 + (c*(18*b^2*c*d*e + 12*a*c^2*d*e + 5*b^3*e^2 + b*c*(7*c*d^2 + 15*a*e^2))*x^7)/7 + (c^2*(2*c^2*d^2 + 9*b^2*e^2 + 2*c*e*(7*b*d + 3*a*e))*x^8)/8 + (c^3*e*(4*c*d + 7*b*e)*x^9)/9 + (c^4*e^2*x^10)/5","A",1
1517,1,251,251,0.0570737,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[(b + 2*c*x)*(d + e*x)*(a + b*x + c*x^2)^3,x]","a^3 b d x+\frac{1}{2} a^2 x^2 \left(a b e+2 a c d+3 b^2 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}{5} x^5 \left(6 a^2 c^2 e+12 a b^2 c e+15 a b c^2 d+b^4 e+5 b^3 c d\right)+\frac{1}{4} x^4 \left(9 a^2 b c e+6 a^2 c^2 d+3 a b^3 e+12 a b^2 c d+b^4 d\right)+\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+5 b^3 e+9 b^2 c d\right)+\frac{1}{8} c^3 x^8 (7 b e+2 c d)+\frac{2}{9} c^4 e x^9","a^3 b d x+\frac{1}{2} a^2 x^2 \left(a b e+2 a c d+3 b^2 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}{5} x^5 \left(6 a^2 c^2 e+12 a b^2 c e+15 a b c^2 d+b^4 e+5 b^3 c d\right)+\frac{1}{4} x^4 \left(9 a^2 b c e+6 a^2 c^2 d+3 a b^3 e+12 a b^2 c d+b^4 d\right)+\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+5 b^3 e+9 b^2 c d\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",1
1518,1,51,16,0.0187302,"\int (b+2 c x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[(b + 2*c*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{4} x (b+c x) \left(4 a^3+6 a^2 x (b+c x)+4 a x^2 (b+c x)^2+x^3 (b+c x)^3\right)","\frac{1}{4} \left(a+b x+c x^2\right)^4",1,"(x*(b + c*x)*(4*a^3 + 6*a^2*x*(b + c*x) + 4*a*x^2*(b + c*x)^2 + x^3*(b + c*x)^3))/4","B",1
1519,1,483,399,0.2440448,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{d+e x} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x),x]","\frac{e x \left(21 c^2 e^2 \left(20 a^2 e^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)+25 a b e \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+3 b^2 \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)+70 b^2 e^4 \left(18 a^2 e^2+9 a b e (e x-2 d)+b^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+35 c e^3 \left(24 a^3 e^3+54 a^2 b e^2 (e x-2 d)+24 a b^2 e \left(6 d^2-3 d e x+2 e^2 x^2\right)-5 b^3 \left(12 d^3-6 d^2 e x+4 d e^2 x^2-3 e^3 x^3\right)\right)+7 c^3 e \left(6 a e \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)-7 b \left(60 d^5-30 d^4 e x+20 d^3 e^2 x^2-15 d^2 e^3 x^3+12 d e^4 x^4-10 e^5 x^5\right)\right)+2 c^4 \left(420 d^6-210 d^5 e x+140 d^4 e^2 x^2-105 d^3 e^3 x^3+84 d^2 e^4 x^4-70 d e^5 x^5+60 e^6 x^6\right)\right)-420 (2 c d-b e) \log (d+e x) \left(e (a e-b d)+c d^2\right)^3}{420 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,"(e*x*(2*c^4*(420*d^6 - 210*d^5*e*x + 140*d^4*e^2*x^2 - 105*d^3*e^3*x^3 + 84*d^2*e^4*x^4 - 70*d*e^5*x^5 + 60*e^6*x^6) + 70*b^2*e^4*(18*a^2*e^2 + 9*a*b*e*(-2*d + e*x) + b^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + 35*c*e^3*(24*a^3*e^3 + 54*a^2*b*e^2*(-2*d + e*x) + 24*a*b^2*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) - 5*b^3*(12*d^3 - 6*d^2*e*x + 4*d*e^2*x^2 - 3*e^3*x^3)) + 21*c^2*e^2*(20*a^2*e^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + 25*a*b*e*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + 3*b^2*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4)) + 7*c^3*e*(6*a*e*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) - 7*b*(60*d^5 - 30*d^4*e*x + 20*d^3*e^2*x^2 - 15*d^2*e^3*x^3 + 12*d*e^4*x^4 - 10*e^5*x^5))) - 420*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^3*Log[d + e*x])/(420*e^8)","A",1
1520,1,637,396,0.2508508,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^2} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^2,x]","\frac{15 c^2 e^2 \left(12 a^2 e^2 \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+20 a b e \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)+3 b^2 \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)\right)+20 c e^3 \left(6 a^3 d e^3+27 a^2 b e^2 \left(-d^2+d e x+e^2 x^2\right)+18 a b^2 e \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)-5 b^3 \left(3 d^4-9 d^3 e x-6 d^2 e^2 x^2+2 d e^3 x^3-e^4 x^4\right)\right)+30 b e^4 \left(-2 a^3 e^3+6 a^2 b d e^2+6 a b^2 e \left(-d^2+d e x+e^2 x^2\right)+b^3 \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)\right)+60 (d+e x) \log (d+e x) \left(2 c e (a e-7 b d)+3 b^2 e^2+14 c^2 d^2\right) \left(e (a e-b d)+c d^2\right)^2+6 c^3 e \left(5 a e \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)-7 b \left(10 d^6-50 d^5 e x-30 d^4 e^2 x^2+10 d^3 e^3 x^3-5 d^2 e^4 x^4+3 d e^5 x^5-2 e^6 x^6\right)\right)+2 c^4 \left(60 d^7-360 d^6 e x-210 d^5 e^2 x^2+70 d^4 e^3 x^3-35 d^3 e^4 x^4+21 d^2 e^5 x^5-14 d e^6 x^6+10 e^7 x^7\right)}{60 e^8 (d+e 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{\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{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{(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,"(2*c^4*(60*d^7 - 360*d^6*e*x - 210*d^5*e^2*x^2 + 70*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 - 14*d*e^6*x^6 + 10*e^7*x^7) + 30*b*e^4*(6*a^2*b*d*e^2 - 2*a^3*e^3 + 6*a*b^2*e*(-d^2 + d*e*x + e^2*x^2) + b^3*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3)) + 20*c*e^3*(6*a^3*d*e^3 + 27*a^2*b*e^2*(-d^2 + d*e*x + e^2*x^2) + 18*a*b^2*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) - 5*b^3*(3*d^4 - 9*d^3*e*x - 6*d^2*e^2*x^2 + 2*d*e^3*x^3 - e^4*x^4)) + 15*c^2*e^2*(12*a^2*e^2*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 20*a*b*e*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + 3*b^2*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5)) + 6*c^3*e*(5*a*e*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5) - 7*b*(10*d^6 - 50*d^5*e*x - 30*d^4*e^2*x^2 + 10*d^3*e^3*x^3 - 5*d^2*e^4*x^4 + 3*d*e^5*x^5 - 2*e^6*x^6)) + 60*(14*c^2*d^2 + 3*b^2*e^2 + 2*c*e*(-7*b*d + a*e))*(c*d^2 + e*(-(b*d) + a*e))^2*(d + e*x)*Log[d + e*x])/(60*e^8*(d + e*x))","A",1
1521,1,403,390,0.1648338,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^3} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^3,x]","\frac{-60 (2 c d-b e) \log (d+e x) \left(c e^2 \left(3 a^2 e^2-10 a b d e+8 b^2 d^2\right)+b^2 e^3 (a e-b d)-2 c^2 d^2 e (7 b d-5 a e)+7 c^3 d^4\right)+20 e 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 (18 a e-35 b d)+b^4 e^4+30 c^4 d^4\right)-10 c e^2 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)-\frac{20 \left(2 c e (a e-7 b d)+3 b^2 e^2+14 c^2 d^2\right) \left(e (a e-b d)+c d^2\right)^2}{d+e x}+20 c^2 e^3 x^3 \left(c e (2 a e-7 b d)+3 b^2 e^2+4 c^2 d^2\right)+\frac{10 (2 c d-b e) \left(e (a e-b d)+c d^2\right)^3}{(d+e x)^2}-5 c^3 e^4 x^4 (6 c d-7 b e)+8 c^4 e^5 x^5}{20 e^8}","\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 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{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{(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,"(20*e*(30*c^4*d^4 + b^4*e^4 - 3*b^2*c*e^3*(5*b*d - 4*a*e) + 2*c^3*d^2*e*(-35*b*d + 18*a*e) + 3*c^2*e^2*(18*b^2*d^2 - 15*a*b*d*e + 2*a^2*e^2))*x - 10*c*e^2*(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 + 20*c^2*e^3*(4*c^2*d^2 + 3*b^2*e^2 + c*e*(-7*b*d + 2*a*e))*x^3 - 5*c^3*e^4*(6*c*d - 7*b*e)*x^4 + 8*c^4*e^5*x^5 + (10*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^3)/(d + e*x)^2 - (20*(14*c^2*d^2 + 3*b^2*e^2 + 2*c*e*(-7*b*d + a*e))*(c*d^2 + e*(-(b*d) + a*e))^2)/(d + e*x) - 60*(2*c*d - b*e)*(7*c^3*d^4 - 2*c^2*d^2*e*(7*b*d - 5*a*e) + b^2*e^3*(-(b*d) + a*e) + c*e^2*(8*b^2*d^2 - 10*a*b*d*e + 3*a^2*e^2))*Log[d + e*x])/(20*e^8)","A",1
1522,1,404,396,0.1549892,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^4} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^4,x]","\frac{\frac{18 (2 c d-b e) \left(c e^2 \left(3 a^2 e^2-10 a b d e+8 b^2 d^2\right)+b^2 e^3 (a e-b d)-2 c^2 d^2 e (7 b d-5 a e)+7 c^3 d^4\right)}{d+e x}+6 \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)-6 c e x \left(2 c^2 d e (12 a e-35 b d)+3 b c e^2 (12 b d-5 a e)-5 b^3 e^3+40 c^3 d^3\right)+3 c^2 e^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)-\frac{3 \left(2 c e (a e-7 b d)+3 b^2 e^2+14 c^2 d^2\right) \left(e (a e-b d)+c d^2\right)^2}{(d+e x)^2}+\frac{2 (2 c d-b e) \left(e (a e-b d)+c d^2\right)^3}{(d+e x)^3}-2 c^3 e^3 x^3 (8 c d-7 b e)+3 c^4 e^4 x^4}{6 e^8}","\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 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{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{(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,"(-6*c*e*(40*c^3*d^3 - 5*b^3*e^3 + 3*b*c*e^2*(12*b*d - 5*a*e) + 2*c^2*d*e*(-35*b*d + 12*a*e))*x + 3*c^2*e^2*(20*c^2*d^2 - 28*b*c*d*e + 9*b^2*e^2 + 6*a*c*e^2)*x^2 - 2*c^3*e^3*(8*c*d - 7*b*e)*x^3 + 3*c^4*e^4*x^4 + (2*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^3)/(d + e*x)^3 - (3*(14*c^2*d^2 + 3*b^2*e^2 + 2*c*e*(-7*b*d + a*e))*(c*d^2 + e*(-(b*d) + a*e))^2)/(d + e*x)^2 + (18*(2*c*d - b*e)*(7*c^3*d^4 - 2*c^2*d^2*e*(7*b*d - 5*a*e) + b^2*e^3*(-(b*d) + a*e) + c*e^2*(8*b^2*d^2 - 10*a*b*d*e + 3*a^2*e^2)))/(d + e*x) + 6*(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])/(6*e^8)","A",1
1523,1,614,389,0.3028648,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^5} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^5,x]","-\frac{3 c^2 e^2 \left(6 a^2 e^2 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)-5 a b d e \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)+3 b^2 \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)\right)+c e^3 \left(2 a^3 e^3 (d+4 e x)+9 a^2 b e^2 \left(d^2+4 d e x+6 e^2 x^2\right)+36 a b^2 e \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)-5 b^3 d \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)\right)+3 b e^4 \left(a^3 e^3+a^2 b e^2 (d+4 e x)+a b^2 e \left(d^2+4 d e x+6 e^2 x^2\right)+b^3 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+60 c (d+e x)^4 (2 c d-b e) \log (d+e x) \left(c e (3 a e-7 b d)+b^2 e^2+7 c^2 d^2\right)-3 c^3 e \left(2 a e \left(-77 d^5-248 d^4 e x-252 d^3 e^2 x^2-48 d^2 e^3 x^3+48 d e^4 x^4+12 e^5 x^5\right)+7 b \left(57 d^6+168 d^5 e x+132 d^4 e^2 x^2-32 d^3 e^3 x^3-68 d^2 e^4 x^4-12 d e^5 x^5+2 e^6 x^6\right)\right)+2 c^4 \left(319 d^7+856 d^6 e x+444 d^5 e^2 x^2-544 d^4 e^3 x^3-556 d^3 e^4 x^4-84 d^2 e^5 x^5+14 d e^6 x^6-4 e^7 x^7\right)}{12 e^8 (d+e x)^4}","-\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{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{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{(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,"-1/12*(2*c^4*(319*d^7 + 856*d^6*e*x + 444*d^5*e^2*x^2 - 544*d^4*e^3*x^3 - 556*d^3*e^4*x^4 - 84*d^2*e^5*x^5 + 14*d*e^6*x^6 - 4*e^7*x^7) + 3*b*e^4*(a^3*e^3 + a^2*b*e^2*(d + 4*e*x) + a*b^2*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + b^3*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)) + c*e^3*(2*a^3*e^3*(d + 4*e*x) + 9*a^2*b*e^2*(d^2 + 4*d*e*x + 6*e^2*x^2) + 36*a*b^2*e*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) - 5*b^3*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) + 3*c^2*e^2*(6*a^2*e^2*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) - 5*a*b*d*e*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3) + 3*b^2*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5)) - 3*c^3*e*(2*a*e*(-77*d^5 - 248*d^4*e*x - 252*d^3*e^2*x^2 - 48*d^2*e^3*x^3 + 48*d*e^4*x^4 + 12*e^5*x^5) + 7*b*(57*d^6 + 168*d^5*e*x + 132*d^4*e^2*x^2 - 32*d^3*e^3*x^3 - 68*d^2*e^4*x^4 - 12*d*e^5*x^5 + 2*e^6*x^6)) + 60*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*Log[d + e*x])/(e^8*(d + e*x)^4)","A",1
1524,1,297,299,0.2225326,"\int \frac{(b+2 c x) (d+e x)^4}{a+b x+c x^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2),x]","\frac{3 \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 (a+x (b+c x))+6 c 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)+3 c^2 e^2 x^2 \left(-2 c e (a e+2 b d)+b^2 e^2+12 c^2 d^2\right)-6 e \sqrt{4 a c-b^2} (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)+2 c^3 e^3 x^3 (8 c d-b e)+3 c^4 e^4 x^4}{6 c^4}","\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 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^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 \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,"(6*c*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 + 3*c^2*e^2*(12*c^2*d^2 + b^2*e^2 - 2*c*e*(2*b*d + a*e))*x^2 + 2*c^3*e^3*(8*c*d - b*e)*x^3 + 3*c^4*e^4*x^4 - 6*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))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]] + 3*(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 + x*(b + c*x)])/(6*c^4)","A",1
1525,1,177,188,0.1822456,"\int \frac{(b+2 c x) (d+e x)^3}{a+b x+c x^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^3)/(a + b*x + c*x^2),x]","\frac{c e x \left(-3 c e (4 a e+6 b d+b e x)+6 b^2 e^2+2 c^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+3 (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log (a+x (b+c x))-6 e \sqrt{4 a c-b^2} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{6 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{(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 \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,"(c*e*x*(6*b^2*e^2 - 3*c*e*(6*b*d + 4*a*e + b*e*x) + 2*c^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2)) - 6*Sqrt[-b^2 + 4*a*c]*e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]] + 3*(2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Log[a + x*(b + c*x)])/(6*c^3)","A",1
1526,1,111,114,0.0941504,"\int \frac{(b+2 c x) (d+e x)^2}{a+b x+c x^2} \, dx","Integrate[((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 (a+x (b+c x))+2 e \sqrt{4 a c-b^2} (b e-2 c d) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)+2 c e x (-b e+4 c d+c e x)}{2 c^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,"(2*c*e*x*(4*c*d - b*e + c*e*x) + 2*Sqrt[-b^2 + 4*a*c]*e*(-2*c*d + b*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]] + (2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*Log[a + x*(b + c*x)])/(2*c^2)","A",1
1527,1,72,70,0.0629369,"\int \frac{(b+2 c x) (d+e x)}{a+b x+c x^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2),x]","\frac{-2 e \sqrt{4 a c-b^2} \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)+(2 c d-b e) \log (a+x (b+c x))+4 c e x}{2 c}","-\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,"(4*c*e*x - 2*Sqrt[-b^2 + 4*a*c]*e*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]] + (2*c*d - b*e)*Log[a + x*(b + c*x)])/(2*c)","A",1
1528,1,10,11,0.0020364,"\int \frac{b+2 c x}{a+b x+c x^2} \, dx","Integrate[(b + 2*c*x)/(a + b*x + c*x^2),x]","\log (a+x (b+c x))","\log \left(a+b x+c x^2\right)",1,"Log[a + x*(b + c*x)]","A",1
1529,1,116,130,0.1154386,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)} \, dx","Integrate[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)),x]","\frac{\sqrt{4 a c-b^2} (2 c d-b e) (2 \log (d+e x)-\log (a+x (b+c x)))+2 e \left(b^2-4 a c\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{2 \sqrt{4 a c-b^2} \left(e (b d-a e)-c d^2\right)}","\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,"(2*(b^2 - 4*a*c)*e*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]] + Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)*(2*Log[d + e*x] - Log[a + x*(b + c*x)]))/(2*Sqrt[-b^2 + 4*a*c]*(-(c*d^2) + e*(b*d - a*e)))","A",1
1530,1,177,210,0.2868195,"\int \frac{b+2 c x}{(d+e x)^2 \left(a+b x+c x^2\right)} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^2*(a + b*x + c*x^2)),x]","\frac{\log (d+e x) \left(4 c e (a e+b d)-2 b^2 e^2-4 c^2 d^2\right)+\left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log (a+x (b+c x))-2 e \sqrt{4 a c-b^2} (b e-2 c d) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)+\frac{2 (2 c d-b e) \left(e (a e-b d)+c d^2\right)}{d+e x}}{2 \left(e (a e-b d)+c d^2\right)^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 \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*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e)))/(d + e*x) - 2*Sqrt[-b^2 + 4*a*c]*e*(-2*c*d + b*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]] + (-4*c^2*d^2 - 2*b^2*e^2 + 4*c*e*(b*d + a*e))*Log[d + e*x] + (2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*Log[a + x*(b + c*x)])/(2*(c*d^2 + e*(-(b*d) + a*e))^2)","A",1
1531,1,268,303,0.3740239,"\int \frac{b+2 c x}{(d+e x)^3 \left(a+b x+c x^2\right)} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^3*(a + b*x + c*x^2)),x]","\frac{\frac{2 \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \left(e (a e-b d)+c d^2\right)}{d+e x}-2 (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)+(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log (a+x (b+c x))+2 e \sqrt{4 a c-b^2} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)+\frac{(2 c d-b e) \left(e (a e-b d)+c d^2\right)^2}{(d+e x)^2}}{2 \left(e (a e-b d)+c d^2\right)^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 \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)*(c*d^2 + e*(-(b*d) + a*e))^2)/(d + e*x)^2 + (2*(c*d^2 + e*(-(b*d) + a*e))*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e)))/(d + e*x) + 2*Sqrt[-b^2 + 4*a*c]*e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]] - 2*(2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Log[d + e*x] + (2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Log[a + x*(b + c*x)])/(2*(c*d^2 + e*(-(b*d) + a*e))^3)","A",1
1532,1,241,172,0.276571,"\int \frac{(b+2 c x) (d+e x)^4}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2)^2,x]","\frac{\frac{-c e^3 \left(a^2 e+2 a b (2 d+e x)+4 b^2 d x\right)+b^2 e^4 (a+b x)+2 c^2 d e^2 (3 a d+2 a e x+3 b d x)-c^3 d^3 (d+4 e x)}{a+x (b+c x)}+2 e^2 \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log (a+x (b+c x))+\frac{4 e (b e-2 c d) \left(c e (3 a e+b d)-b^2 e^2-c^2 d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+c e^3 x (8 c d-3 b e)+c^2 e^4 x^2}{c^3}","\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,"(c*e^3*(8*c*d - 3*b*e)*x + c^2*e^4*x^2 + (b^2*e^4*(a + b*x) - c^3*d^3*(d + 4*e*x) + 2*c^2*d*e^2*(3*a*d + 3*b*d*x + 2*a*e*x) - c*e^3*(a^2*e + 4*b^2*d*x + 2*a*b*(2*d + e*x)))/(a + x*(b + c*x)) + (4*e*(-2*c*d + b*e)*(-(c^2*d^2) - b^2*e^2 + c*e*(b*d + 3*a*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/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 + x*(b + c*x)])/c^3","A",1
1533,1,161,126,0.1724005,"\int \frac{(b+2 c x) (d+e x)^3}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^3)/(a + b*x + c*x^2)^2,x]","\frac{\frac{6 e \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}-\frac{2 \left(-c e^2 (3 a d+a e x+3 b d x)+b e^3 (a+b x)+c^2 d^2 (d+3 e x)\right)}{a+x (b+c x)}-3 e^2 (b e-2 c d) \log (a+x (b+c x))+4 c e^3 x}{2 c^2}","-\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,"(4*c*e^3*x - (2*(b*e^3*(a + b*x) + c^2*d^2*(d + 3*e*x) - c*e^2*(3*a*d + 3*b*d*x + a*e*x)))/(a + x*(b + c*x)) + (6*e*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] - 3*e^2*(-2*c*d + b*e)*Log[a + x*(b + c*x)])/(2*c^2)","A",1
1534,1,98,87,0.113514,"\int \frac{(b+2 c x) (d+e x)^2}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^2)/(a + b*x + c*x^2)^2,x]","\frac{-\frac{2 e (b e-2 c d) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+\frac{e^2 (a+b x)-c d (d+2 e x)}{a+x (b+c x)}+e^2 \log (a+x (b+c x))}{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,"((e^2*(a + b*x) - c*d*(d + 2*e*x))/(a + x*(b + c*x)) - (2*e*(-2*c*d + b*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + e^2*Log[a + x*(b + c*x)])/c","A",1
1535,1,58,55,0.028156,"\int \frac{(b+2 c x) (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2)^2,x]","\frac{2 e \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}-\frac{d+e x}{a+x (b+c 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}",1,"-((d + e*x)/(a + x*(b + c*x))) + (2*e*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c]","A",1
1536,1,13,14,0.0036,"\int \frac{b+2 c x}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(b + 2*c*x)/(a + b*x + c*x^2)^2,x]","-\frac{1}{a+x (b+c x)}","-\frac{1}{a+b x+c x^2}",1,"-(a + x*(b + c*x))^(-1)","A",1
1537,1,173,236,0.2426997,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)^2} \, dx","Integrate[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)^2),x]","\frac{\frac{2 e \left(2 c e (a e+b d)-b^2 e^2-2 c^2 d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+\frac{2 \left(e (a e-b d)+c d^2\right) (b e-c d+c e x)}{a+x (b+c x)}-e^2 (b e-2 c d) \log (a+x (b+c x))+2 e^2 (b e-2 c d) \log (d+e x)}{2 \left(e (a e-b d)+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,"((2*(c*d^2 + e*(-(b*d) + a*e))*(-(c*d) + b*e + c*e*x))/(a + x*(b + c*x)) + (2*e*(-2*c^2*d^2 - b^2*e^2 + 2*c*e*(b*d + a*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + 2*e^2*(-2*c*d + b*e)*Log[d + e*x] - e^2*(-2*c*d + b*e)*Log[a + x*(b + c*x)])/(2*(c*d^2 + e*(-(b*d) + a*e))^2)","A",1
1538,1,275,327,0.601818,"\int \frac{b+2 c x}{(d+e x)^2 \left(a+b x+c x^2\right)^2} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^2*(a + b*x + c*x^2)^2),x]","\frac{-\frac{\left(e (a e-b d)+c d^2\right) \left(c e (-a e-2 b d+b e x)+b^2 e^2+c^2 d (d-2 e x)\right)}{a+x (b+c x)}-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)+e^2 \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log (a+x (b+c x))+\frac{2 e (b e-2 c d) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}-\frac{e^2 (b e-2 c d) \left(e (a e-b d)+c d^2\right)}{d+e x}}{\left(e (a e-b d)+c d^2\right)^3}","\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,"(-((e^2*(-2*c*d + b*e)*(c*d^2 + e*(-(b*d) + a*e)))/(d + e*x)) - ((c*d^2 + e*(-(b*d) + a*e))*(b^2*e^2 + c^2*d*(d - 2*e*x) + c*e*(-2*b*d - a*e + b*e*x)))/(a + x*(b + c*x)) + (2*e*(-2*c*d + b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/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[d + e*x] + e^2*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*Log[a + x*(b + c*x)])/(c*d^2 + e*(-(b*d) + a*e))^3","A",1
1539,1,480,293,0.8041801,"\int \frac{(b+2 c x) (d+e x)^5}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^5)/(a + b*x + c*x^2)^3,x]","\frac{-\frac{c^2 e^3 \left(a^2 e (5 d+e x)+10 a b d (d+e x)+10 b^2 d^2 x\right)-b c e^4 \left(2 a^2 e+a b (5 d+3 e x)+5 b^2 d x\right)+b^3 e^5 (a+b x)-10 c^3 d^2 e^2 (a (d+e x)+b d x)+c^4 d^4 (d+5 e x)}{(a+x (b+c x))^2}+\frac{e \left(b c^2 \left(31 a^2 e^4-10 a c d e^2 (7 d+10 e x)-5 c^2 d^3 (d-4 e x)\right)-2 c^3 \left(a^2 e^3 (40 d+9 e x)-10 a c d^2 e (4 d+5 e x)+5 c^2 d^4 x\right)+b^3 c e^2 \left(10 c d (d+3 e x)-13 a e^2\right)+2 b^2 c^2 e \left(a e^2 (25 d+17 e x)-5 c d^2 (d+4 e x)\right)+b^5 e^4-b^4 c e^3 (5 d+8 e x)\right)}{\left(b^2-4 a c\right) (a+x (b+c x))}-\frac{10 c 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) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}+5 c e^4 (2 c d-b e) \log (a+x (b+c x))+4 c^2 e^5 x}{2 c^4}","\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^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 \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 (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,"(4*c^2*e^5*x - (b^3*e^5*(a + b*x) + c^4*d^4*(d + 5*e*x) - 10*c^3*d^2*e^2*(b*d*x + a*(d + e*x)) + c^2*e^3*(10*b^2*d^2*x + 10*a*b*d*(d + e*x) + a^2*e*(5*d + e*x)) - b*c*e^4*(2*a^2*e + 5*b^2*d*x + a*b*(5*d + 3*e*x)))/(a + x*(b + c*x))^2 + (e*(b^5*e^4 - b^4*c*e^3*(5*d + 8*e*x) + b^3*c*e^2*(-13*a*e^2 + 10*c*d*(d + 3*e*x)) - 2*c^3*(5*c^2*d^4*x - 10*a*c*d^2*e*(4*d + 5*e*x) + a^2*e^3*(40*d + 9*e*x)) + b*c^2*(31*a^2*e^4 - 5*c^2*d^3*(d - 4*e*x) - 10*a*c*d*e^2*(7*d + 10*e*x)) + 2*b^2*c^2*e*(-5*c*d^2*(d + 4*e*x) + a*e^2*(25*d + 17*e*x))))/((b^2 - 4*a*c)*(a + x*(b + c*x))) - (10*c*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))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2) + 5*c*e^4*(2*c*d - b*e)*Log[a + x*(b + c*x)])/(2*c^4)","A",1
1540,1,334,197,0.5448192,"\int \frac{(b+2 c x) (d+e x)^4}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2)^3,x]","\frac{\frac{-c e^3 \left(a^2 e+2 a b (2 d+e x)+4 b^2 d x\right)+b^2 e^4 (a+b x)+2 c^2 d e^2 (3 a d+2 a e x+3 b d x)-c^3 d^3 (d+4 e x)}{(a+x (b+c x))^2}-\frac{e \left(8 c^2 \left(2 a^2 e^3-a c d e (6 d+5 e x)+c^2 d^3 x\right)+2 b^2 c e \left(c d (3 d+8 e x)-5 a e^2\right)+4 b c^2 \left(a e^2 (7 d+5 e x)+c d^2 (d-3 e x)\right)+b^4 e^3-2 b^3 c e^2 (2 d+3 e x)\right)}{\left(b^2-4 a c\right) (a+x (b+c x))}+\frac{4 c e (b e-2 c d) \left(2 c e (b d-3 a e)+b^2 e^2-2 c^2 d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}+2 c e^4 \log (a+x (b+c x))}{2 c^3}","\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,"((b^2*e^4*(a + b*x) - c^3*d^3*(d + 4*e*x) + 2*c^2*d*e^2*(3*a*d + 3*b*d*x + 2*a*e*x) - c*e^3*(a^2*e + 4*b^2*d*x + 2*a*b*(2*d + e*x)))/(a + x*(b + c*x))^2 - (e*(b^4*e^3 - 2*b^3*c*e^2*(2*d + 3*e*x) + 8*c^2*(2*a^2*e^3 + c^2*d^3*x - a*c*d*e*(6*d + 5*e*x)) + 4*b*c^2*(c*d^2*(d - 3*e*x) + a*e^2*(7*d + 5*e*x)) + 2*b^2*c*e*(-5*a*e^2 + c*d*(3*d + 8*e*x))))/((b^2 - 4*a*c)*(a + x*(b + c*x))) + (4*c*e*(-2*c*d + b*e)*(-2*c^2*d^2 + b^2*e^2 + 2*c*e*(b*d - 3*a*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2) + 2*c*e^4*Log[a + x*(b + c*x)])/(2*c^3)","A",1
1541,1,216,126,0.2764379,"\int \frac{(b+2 c x) (d+e x)^3}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^3)/(a + b*x + c*x^2)^3,x]","\frac{1}{2} \left(\frac{12 e \left(e (a e-b d)+c d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}+\frac{e \left(b c \left(7 a e^2+3 c d (d-2 e x)\right)+2 c^2 \left(3 c d^2 x-a e (12 d+5 e x)\right)+b^3 \left(-e^2\right)+b^2 c e (3 d+4 e x)\right)}{c^2 \left(4 a c-b^2\right) (a+x (b+c x))}+\frac{c e^2 (3 a d+a e x+3 b d x)-b e^3 (a+b x)-c^2 d^2 (d+3 e x)}{c^2 (a+x (b+c x))^2}\right)","\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,"((-(b*e^3*(a + b*x)) - c^2*d^2*(d + 3*e*x) + c*e^2*(3*a*d + 3*b*d*x + a*e*x))/(c^2*(a + x*(b + c*x))^2) + (e*(-(b^3*e^2) + b^2*c*e*(3*d + 4*e*x) + b*c*(7*a*e^2 + 3*c*d*(d - 2*e*x)) + 2*c^2*(3*c*d^2*x - a*e*(12*d + 5*e*x))))/(c^2*(-b^2 + 4*a*c)*(a + x*(b + c*x))) + (12*e*(c*d^2 + e*(-(b*d) + a*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2))/2","A",1
1542,1,143,112,0.1823853,"\int \frac{(b+2 c x) (d+e x)^2}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^2)/(a + b*x + c*x^2)^3,x]","\frac{1}{2} \left(\frac{e \left(4 c (c d x-2 a e)+b^2 e+2 b c (d-e x)\right)}{c \left(4 a c-b^2\right) (a+x (b+c x))}-\frac{4 e (b e-2 c d) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}+\frac{e^2 (a+b x)-c d (d+2 e x)}{c (a+x (b+c x))^2}\right)","-\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,"((e*(b^2*e + 4*c*(-2*a*e + c*d*x) + 2*b*c*(d - e*x)))/(c*(-b^2 + 4*a*c)*(a + x*(b + c*x))) + (e^2*(a + b*x) - c*d*(d + 2*e*x))/(c*(a + x*(b + c*x))^2) - (4*e*(-2*c*d + b*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2))/2","A",1
1543,1,93,94,0.1236342,"\int \frac{(b+2 c x) (d+e x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2)^3,x]","\frac{1}{2} \left(-\frac{e (b+2 c x)}{\left(b^2-4 a c\right) (a+x (b+c x))}+\frac{4 c e \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2}}-\frac{d+e x}{(a+x (b+c x))^2}\right)","-\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)/(a + x*(b + c*x))^2) - (e*(b + 2*c*x))/((b^2 - 4*a*c)*(a + x*(b + c*x))) + (4*c*e*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2))/2","A",1
1544,1,15,16,0.0051752,"\int \frac{b+2 c x}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[(b + 2*c*x)/(a + b*x + c*x^2)^3,x]","-\frac{1}{2 (a+x (b+c x))^2}","-\frac{1}{2 \left(a+b x+c x^2\right)^2}",1,"-1/2*1/(a + x*(b + c*x))^2","A",1
1545,1,356,397,1.1113968,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)^3} \, dx","Integrate[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)^3),x]","\frac{1}{2} \left(-\frac{2 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) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{3/2} \left(e (b d-a e)-c d^2\right)^3}+\frac{e \left(b c \left(c d (d-2 e x)-7 a e^2\right)+2 c^2 \left(a e (4 d-3 e x)+c d^2 x\right)+2 b^3 e^2+b^2 c e (2 e x-3 d)\right)}{\left(b^2-4 a c\right) (a+x (b+c x)) \left(e (a e-b d)+c d^2\right)^2}+\frac{2 e^4 (b e-2 c d) \log (d+e x)}{\left(e (a e-b d)+c d^2\right)^3}+\frac{e^4 (2 c d-b e) \log (a+x (b+c x))}{\left(e (a e-b d)+c d^2\right)^3}+\frac{b e-c d+c e x}{(a+x (b+c x))^2 \left(e (a e-b d)+c d^2\right)}\right)","\frac{c e x \left(b^2-4 a c\right)-\left(b^2-4 a c\right) (c d-b e)}{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 \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{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-2 b^3 e^2+3 b^2 c d e\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^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,"((-(c*d) + b*e + c*e*x)/((c*d^2 + e*(-(b*d) + a*e))*(a + x*(b + c*x))^2) + (e*(2*b^3*e^2 + b^2*c*e*(-3*d + 2*e*x) + 2*c^2*(c*d^2*x + a*e*(4*d - 3*e*x)) + b*c*(-7*a*e^2 + c*d*(d - 2*e*x))))/((b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e))^2*(a + x*(b + 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))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/((-b^2 + 4*a*c)^(3/2)*(-(c*d^2) + e*(b*d - a*e))^3) + (2*e^4*(-2*c*d + b*e)*Log[d + e*x])/(c*d^2 + e*(-(b*d) + a*e))^3 + (e^4*(2*c*d - b*e)*Log[a + x*(b + c*x)])/(c*d^2 + e*(-(b*d) + a*e))^3)/2","A",1
1546,1,549,431,0.8477673,"\int (b+2 c x) (d+e x)^4 \sqrt{a+b x+c x^2} \, dx","Integrate[(b + 2*c*x)*(d + e*x)^4*Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+x (b+c x)} \left(2048 a^3 c^3 e^4-16 a^2 c^2 e^2 \left(343 b^2 e^2-2 b c e (567 d+73 e x)+4 c^2 \left(336 d^2+105 d e x+16 e^2 x^2\right)\right)+8 a c \left(315 b^4 e^4-14 b^3 c e^3 (95 d+13 e x)+4 b^2 c^2 e^2 \left(525 d^2+189 d e x+31 e^2 x^2\right)-8 b c^3 e \left(175 d^3+147 d^2 e x+63 d e^2 x^2+11 e^3 x^3\right)+16 c^4 \left(70 d^4+105 d^3 e x+84 d^2 e^2 x^2+35 d e^3 x^3+6 e^4 x^4\right)\right)-315 b^6 e^4+210 b^5 c e^3 (7 d+e x)-28 b^4 c^2 e^2 \left(90 d^2+35 d e x+6 e^2 x^2\right)+16 b^3 c^3 e \left(105 d^3+105 d^2 e x+49 d e^2 x^2+9 e^3 x^3\right)-32 b^2 c^4 e x \left(35 d^3+42 d^2 e x+21 d e^2 x^2+4 e^3 x^3\right)+128 b c^5 x \left(70 d^4+175 d^3 e x+189 d^2 e^2 x^2+98 d e^3 x^3+20 e^4 x^4\right)+256 c^6 x^2 \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)\right)}{13440 c^5}+\frac{e \left(b^2-4 a c\right)^2 (b e-2 c d) \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+x (b+c x)}}\right)}{256 c^{11/2}}","\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)^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{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{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,"(Sqrt[a + x*(b + c*x)]*(-315*b^6*e^4 + 2048*a^3*c^3*e^4 + 210*b^5*c*e^3*(7*d + e*x) - 28*b^4*c^2*e^2*(90*d^2 + 35*d*e*x + 6*e^2*x^2) - 32*b^2*c^4*e*x*(35*d^3 + 42*d^2*e*x + 21*d*e^2*x^2 + 4*e^3*x^3) + 16*b^3*c^3*e*(105*d^3 + 105*d^2*e*x + 49*d*e^2*x^2 + 9*e^3*x^3) + 256*c^6*x^2*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4) + 128*b*c^5*x*(70*d^4 + 175*d^3*e*x + 189*d^2*e^2*x^2 + 98*d*e^3*x^3 + 20*e^4*x^4) - 16*a^2*c^2*e^2*(343*b^2*e^2 - 2*b*c*e*(567*d + 73*e*x) + 4*c^2*(336*d^2 + 105*d*e*x + 16*e^2*x^2)) + 8*a*c*(315*b^4*e^4 - 14*b^3*c*e^3*(95*d + 13*e*x) + 4*b^2*c^2*e^2*(525*d^2 + 189*d*e*x + 31*e^2*x^2) - 8*b*c^3*e*(175*d^3 + 147*d^2*e*x + 63*d*e^2*x^2 + 11*e^3*x^3) + 16*c^4*(70*d^4 + 105*d^3*e*x + 84*d^2*e^2*x^2 + 35*d*e^3*x^3 + 6*e^4*x^4))))/(13440*c^5) + ((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 + x*(b + c*x)])])/(256*c^(11/2))","A",1
1547,1,270,312,0.5129971,"\int (b+2 c x) (d+e x)^3 \sqrt{a+b x+c x^2} \, dx","Integrate[(b + 2*c*x)*(d + e*x)^3*Sqrt[a + b*x + c*x^2],x]","\frac{1}{6} \left(\frac{(a+x (b+c x))^{3/2} \left(-24 c^2 e (a e (16 d+5 e x)+b d (3 d+2 e x))+6 b c e^2 (22 a e+20 b d+7 b e x)-35 b^3 e^3+16 c^3 d^2 (4 d+3 e x)\right)}{80 c^3}-\frac{3 e \left(b^2-4 a c\right) \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{256 c^{9/2}}+2 (d+e x)^3 (a+x (b+c x))^{3/2}+\frac{3 (d+e x)^2 (a+x (b+c x))^{3/2} (2 c d-b e)}{5 c}\right)","-\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{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{\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{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,"((3*(2*c*d - b*e)*(d + e*x)^2*(a + x*(b + c*x))^(3/2))/(5*c) + 2*(d + e*x)^3*(a + x*(b + c*x))^(3/2) + ((a + x*(b + c*x))^(3/2)*(-35*b^3*e^3 + 16*c^3*d^2*(4*d + 3*e*x) + 6*b*c*e^2*(20*b*d + 22*a*e + 7*b*e*x) - 24*c^2*e*(b*d*(3*d + 2*e*x) + a*e*(16*d + 5*e*x))))/(80*c^3) - (3*(b^2 - 4*a*c)*e*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(256*c^(9/2)))/6","A",1
1548,1,177,195,0.2509258,"\int (b+2 c x) (d+e x)^2 \sqrt{a+b x+c x^2} \, dx","Integrate[(b + 2*c*x)*(d + e*x)^2*Sqrt[a + b*x + c*x^2],x]","\frac{e \left(b^2-4 a c\right) (b e-2 c d) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{64 c^{7/2}}+\frac{(a+x (b+c x))^{3/2} \left(-2 c e (8 a e+5 b d+3 b e x)+5 b^2 e^2+4 c^2 d (4 d+3 e x)\right)}{60 c^2}+\frac{2}{5} (d+e x)^2 (a+x (b+c x))^{3/2}","-\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{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{\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{2}{5} (d+e x)^2 \left(a+b x+c x^2\right)^{3/2}",1,"(2*(d + e*x)^2*(a + x*(b + c*x))^(3/2))/5 + ((a + x*(b + c*x))^(3/2)*(5*b^2*e^2 + 4*c^2*d*(4*d + 3*e*x) - 2*c*e*(5*b*d + 8*a*e + 3*b*e*x)))/(60*c^2) + ((b^2 - 4*a*c)*e*(-2*c*d + b*e)*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(64*c^(7/2))","A",1
1549,1,134,122,0.1446871,"\int (b+2 c x) (d+e x) \sqrt{a+b x+c x^2} \, dx","Integrate[(b + 2*c*x)*(d + e*x)*Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+x (b+c x)} \left(4 a c (-5 b e+16 c d+6 c e x)+3 b^3 e-2 b^2 c e x+8 b c^2 x (8 d+5 e x)+16 c^3 x^2 (4 d+3 e x)\right)}{96 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+x (b+c x)}}\right)}{64 c^{5/2}}","-\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{e \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}{32 c^2}+\frac{\left(a+b x+c x^2\right)^{3/2} (-b e+8 c d+6 c e x)}{12 c}",1,"(Sqrt[a + x*(b + c*x)]*(3*b^3*e - 2*b^2*c*e*x + 16*c^3*x^2*(4*d + 3*e*x) + 8*b*c^2*x*(8*d + 5*e*x) + 4*a*c*(16*c*d - 5*b*e + 6*c*e*x)))/(96*c^2) - ((b^2 - 4*a*c)^2*e*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(64*c^(5/2))","A",1
1550,1,17,18,0.0095787,"\int (b+2 c x) \sqrt{a+b x+c x^2} \, dx","Integrate[(b + 2*c*x)*Sqrt[a + b*x + c*x^2],x]","\frac{2}{3} (a+x (b+c x))^{3/2}","\frac{2}{3} \left(a+b x+c x^2\right)^{3/2}",1,"(2*(a + x*(b + c*x))^(3/2))/3","A",1
1551,1,195,199,0.2521416,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{d+e x} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x),x]","\frac{\left(4 c e (a e-2 b d)+b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)+2 \sqrt{c} \left(2 (2 c d-b e) \sqrt{e (a e-b d)+c d^2} \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)+e \sqrt{a+x (b+c x)} (3 b e-4 c d+2 c e x)\right)}{4 \sqrt{c} 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{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,"((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 + x*(b + c*x)])] + 2*Sqrt[c]*(e*(-4*c*d + 3*b*e + 2*c*e*x)*Sqrt[a + x*(b + c*x)] + 2*(2*c*d - b*e)*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])]))/(4*Sqrt[c]*e^3)","A",1
1552,1,280,203,0.4073063,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^2} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^2,x]","\frac{\frac{\left(4 c e (a e-2 b d)+b^2 e^2+8 c^2 d^2\right) \sqrt{e (a e-b d)+c d^2} \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)+4 \sqrt{c} (2 c d-b e) \left(e (a e-b d)+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{2 e^3}-\frac{\sqrt{a+x (b+c x)} \left(c e (2 a e-5 b d+b e x)+b^2 e^2+2 c^2 d (2 d-e x)\right)}{e^2}+\frac{(a+x (b+c x))^{3/2} (b e-2 c d)}{d+e x}}{e (b d-a e)-c d^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{-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{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{\sqrt{a+b x+c x^2} (-b e+4 c d+2 c e x)}{e^2 (d+e x)}",1,"(((-2*c*d + b*e)*(a + x*(b + c*x))^(3/2))/(d + e*x) - (Sqrt[a + x*(b + c*x)]*(b^2*e^2 + 2*c^2*d*(2*d - e*x) + c*e*(-5*b*d + 2*a*e + b*e*x)))/e^2 + (4*Sqrt[c]*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])] + (8*c^2*d^2 + b^2*e^2 + 4*c*e*(-2*b*d + a*e))*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(2*e^3))/(-(c*d^2) + e*(b*d - a*e))","A",1
1553,1,389,280,1.2135607,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^3} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^3,x]","\frac{\frac{2 (a+x (b+c x))^{3/2} \left(4 c e (b d-2 a e)+b^2 e^2-4 c^2 d^2\right)}{d+e x}+\frac{-2 c e \sqrt{a+x (b+c x)} \left(-2 c^2 e (2 a e (2 e x-3 d)+b d (7 d-2 e x))+b c e^2 (-10 a e+5 b d+b e x)+b^3 e^3+4 c^3 d^2 (2 d-e x)\right)+c (2 c d-b e) \sqrt{e (a e-b d)+c d^2} \left(4 c e (3 a e-2 b d)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)+16 c^{5/2} \left(e (a e-b d)+c d^2\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{c e^3}+\frac{4 (a+x (b+c x))^{3/2} (2 c d-b e) \left(e (a e-b d)+c d^2\right)}{(d+e x)^2}}{8 \left(e (a e-b d)+c d^2\right)^2}","-\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{\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^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^3}",1,"((4*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))*(a + x*(b + c*x))^(3/2))/(d + e*x)^2 + (2*(-4*c^2*d^2 + b^2*e^2 + 4*c*e*(b*d - 2*a*e))*(a + x*(b + c*x))^(3/2))/(d + e*x) + (-2*c*e*Sqrt[a + x*(b + c*x)]*(b^3*e^3 + 4*c^3*d^2*(2*d - e*x) + b*c*e^2*(5*b*d - 10*a*e + b*e*x) - 2*c^2*e*(b*d*(7*d - 2*e*x) + 2*a*e*(-3*d + 2*e*x))) + 16*c^(5/2)*(c*d^2 + e*(-(b*d) + a*e))^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])] + c*(2*c*d - b*e)*Sqrt[c*d^2 + e*(-(b*d) + a*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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(c*e^3))/(8*(c*d^2 + e*(-(b*d) + a*e))^2)","A",1
1554,1,214,217,0.4689752,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^4} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^4,x]","\frac{\frac{2 (a+x (b+c x))^{3/2} (2 c d-b e)}{(d+e x)^3}-3 e \left(b^2-4 a c\right) \left(\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{8 \left(e (a e-b d)+c d^2\right)^{3/2}}+\frac{\sqrt{a+x (b+c x)} (-2 a e+b (d-e x)+2 c d x)}{4 (d+e x)^2 \left(e (a e-b d)+c d^2\right)}\right)}{6 \left(e (a e-b d)+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,"((2*(2*c*d - b*e)*(a + x*(b + c*x))^(3/2))/(d + e*x)^3 - 3*(b^2 - 4*a*c)*e*((Sqrt[a + x*(b + c*x)]*(-2*a*e + 2*c*d*x + b*(d - e*x)))/(4*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)^2) + ((b^2 - 4*a*c)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(8*(c*d^2 + e*(-(b*d) + a*e))^(3/2))))/(6*(c*d^2 + e*(-(b*d) + a*e)))","A",1
1555,1,290,307,0.7364471,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^5} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^5,x]","\frac{\frac{(a+x (b+c x))^{3/2} \left(-4 c e (4 a e+b d)+5 b^2 e^2+4 c^2 d^2\right)}{(d+e x)^3}+\frac{15}{2} e \left(b^2-4 a c\right) (b e-2 c d) \left(\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{8 \left(e (a e-b d)+c d^2\right)^{3/2}}+\frac{\sqrt{a+x (b+c x)} (-2 a e+b (d-e x)+2 c d x)}{4 (d+e x)^2 \left(e (a e-b d)+c d^2\right)}\right)+\frac{6 (a+x (b+c x))^{3/2} (2 c d-b e) \left(e (a e-b d)+c d^2\right)}{(d+e x)^4}}{24 \left(e (a e-b d)+c d^2\right)^2}","\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,"((6*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))*(a + x*(b + c*x))^(3/2))/(d + e*x)^4 + ((4*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(b*d + 4*a*e))*(a + x*(b + c*x))^(3/2))/(d + e*x)^3 + (15*(b^2 - 4*a*c)*e*(-2*c*d + b*e)*((Sqrt[a + x*(b + c*x)]*(-2*a*e + 2*c*d*x + b*(d - e*x)))/(4*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)^2) + ((b^2 - 4*a*c)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(8*(c*d^2 + e*(-(b*d) + a*e))^(3/2))))/2)/(24*(c*d^2 + e*(-(b*d) + a*e))^2)","A",1
1556,1,401,430,3.1127766,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^6} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^6,x]","\frac{\frac{(a+x (b+c x))^{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)}{48 (d+e x)^3 \left(e (a e-b d)+c d^2\right)^2}+\frac{(a+x (b+c x))^{3/2} \left(-4 c e (5 a e+2 b d)+7 b^2 e^2+8 c^2 d^2\right)}{8 (d+e x)^4 \left(e (a e-b d)+c d^2\right)}-\frac{5 e \left(b^2-4 a c\right) \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \left(\left(b^2-4 a c\right) (d+e x)^2 \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)+2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2} (-2 a e+b (d-e x)+2 c d x)\right)}{256 (d+e x)^2 \left(e (a e-b d)+c d^2\right)^{7/2}}+\frac{(a+x (b+c x))^{3/2} (2 c d-b e)}{(d+e x)^5}}{5 \left(e (a e-b d)+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,"(((2*c*d - b*e)*(a + x*(b + c*x))^(3/2))/(d + e*x)^5 + ((8*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(2*b*d + 5*a*e))*(a + x*(b + c*x))^(3/2))/(8*(c*d^2 + e*(-(b*d) + a*e))*(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 + x*(b + c*x))^(3/2))/(48*(c*d^2 + e*(-(b*d) + a*e))^2*(d + e*x)^3) - (5*(b^2 - 4*a*c)*e*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)]*(-2*a*e + 2*c*d*x + b*(d - e*x)) + (b^2 - 4*a*c)*(d + e*x)^2*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])]))/(256*(c*d^2 + e*(-(b*d) + a*e))^(7/2)*(d + e*x)^2))/(5*(c*d^2 + e*(-(b*d) + a*e)))","A",1
1557,1,297,379,0.6894167,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2)^(3/2),x]","\frac{1}{8} \left(\frac{(a+x (b+c x))^{5/2} \left(-8 c^2 e (a e (96 d+35 e x)+b d (13 d+10 e x))+2 b c e^2 (122 a e+112 b d+45 b e x)-63 b^3 e^3+16 c^3 d^2 (6 d+5 e x)\right)}{280 c^3}+\frac{e \left(b^2-4 a c\right) \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)} \left(4 c \left(5 a+2 c x^2\right)-3 b^2+8 b c x\right)+3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{2048 c^{11/2}}+2 (d+e x)^3 (a+x (b+c x))^{5/2}+\frac{3 (d+e x)^2 (a+x (b+c x))^{5/2} (2 c d-b e)}{7 c}\right)","\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{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{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*(2*c*d - b*e)*(d + e*x)^2*(a + x*(b + c*x))^(5/2))/(7*c) + 2*(d + e*x)^3*(a + x*(b + c*x))^(5/2) + ((a + x*(b + c*x))^(5/2)*(-63*b^3*e^3 + 16*c^3*d^2*(6*d + 5*e*x) + 2*b*c*e^2*(112*b*d + 122*a*e + 45*b*e*x) - 8*c^2*e*(b*d*(13*d + 10*e*x) + a*e*(96*d + 35*e*x))))/(280*c^3) + ((b^2 - 4*a*c)*e*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)]*(-3*b^2 + 8*b*c*x + 4*c*(5*a + 2*c*x^2)) + 3*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(2048*c^(11/2)))/8","A",1
1558,1,204,242,0.3412254,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2)^(3/2),x]","-\frac{e \left(b^2-4 a c\right) (b e-2 c d) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)} \left(4 c \left(5 a+2 c x^2\right)-3 b^2+8 b c x\right)+3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{1536 c^{9/2}}+\frac{(a+x (b+c x))^{5/2} \left(-2 c e (12 a e+7 b d+5 b e x)+7 b^2 e^2+4 c^2 d (6 d+5 e x)\right)}{210 c^2}+\frac{2}{7} (d+e x)^2 (a+x (b+c x))^{5/2}","\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{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{\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{2}{7} (d+e x)^2 \left(a+b x+c x^2\right)^{5/2}",1,"(2*(d + e*x)^2*(a + x*(b + c*x))^(5/2))/7 + ((a + x*(b + c*x))^(5/2)*(7*b^2*e^2 + 4*c^2*d*(6*d + 5*e*x) - 2*c*e*(7*b*d + 12*a*e + 5*b*e*x)))/(210*c^2) - ((b^2 - 4*a*c)*e*(-2*c*d + b*e)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)]*(-3*b^2 + 8*b*c*x + 4*c*(5*a + 2*c*x^2)) + 3*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(1536*c^(9/2))","A",1
1559,1,147,160,0.190481,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[(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) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)} \left(4 c \left(5 a+2 c x^2\right)-3 b^2+8 b c x\right)+3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{1536 c^{7/2}}+\frac{(a+x (b+c x))^{5/2} (2 c (6 d+5 e x)-b e)}{30 c}","\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{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{\left(a+b x+c x^2\right)^{5/2} (-b e+12 c d+10 c e x)}{30 c}",1,"((a + x*(b + c*x))^(5/2)*(-(b*e) + 2*c*(6*d + 5*e*x)))/(30*c) + ((b^2 - 4*a*c)*e*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)]*(-3*b^2 + 8*b*c*x + 4*c*(5*a + 2*c*x^2)) + 3*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(1536*c^(7/2))","A",1
1560,1,17,18,0.0149491,"\int (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[(b + 2*c*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{2}{5} (a+x (b+c x))^{5/2}","\frac{2}{5} \left(a+b x+c x^2\right)^{5/2}",1,"(2*(a + x*(b + c*x))^(5/2))/5","A",1
1561,1,342,360,0.741819,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{d+e x} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x),x]","\frac{3 \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+x (b+c x)}}\right)+2 \sqrt{c} \left(e \sqrt{a+x (b+c x)} \left(8 c^2 e \left(a e (15 e x-32 d)+b \left(42 d^2-20 d e x+13 e^2 x^2\right)\right)+2 b c e^2 (94 a e-72 b d+31 b e x)+3 b^3 e^3-16 c^3 \left(12 d^3-6 d^2 e x+4 d e^2 x^2-3 e^3 x^3\right)\right)+96 c (2 c d-b e) \left(e (a e-b d)+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)\right)}{192 c^{3/2} 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{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,"(3*(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 + x*(b + c*x)])] + 2*Sqrt[c]*(e*Sqrt[a + x*(b + c*x)]*(3*b^3*e^3 + 2*b*c*e^2*(-72*b*d + 94*a*e + 31*b*e*x) - 16*c^3*(12*d^3 - 6*d^2*e*x + 4*d*e^2*x^2 - 3*e^3*x^3) + 8*c^2*e*(a*e*(-32*d + 15*e*x) + b*(42*d^2 - 20*d*e*x + 13*e^2*x^2))) + 96*c*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^(3/2)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])]))/(192*c^(3/2)*e^5)","A",1
1562,1,395,303,1.0566263,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^2} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^2,x]","\frac{\frac{(a+x (b+c x))^{3/2} \left(c e (-2 a e+11 b d-3 b e x)-3 b^2 e^2+c^2 \left(6 d e x-8 d^2\right)\right)}{3 e^2}+\frac{-2 c^2 e \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right) \left(4 c e (a e-5 b d+b e x)+5 b^2 e^2+8 c^2 d (2 d-e x)\right)+2 c^2 \left(4 c e (a e-4 b d)+3 b^2 e^2+16 c^2 d^2\right) \left(e (a e-b d)+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)+c^{3/2} (2 c d-b e) \left(e (a e-b d)+c d^2\right) \left(4 c e (3 a e-4 b d)+b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{4 c^2 e^5}+\frac{(a+x (b+c x))^{5/2} (b e-2 c d)}{d+e x}}{e (b d-a e)-c d^2}","-\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{\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{\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,"(((-2*c*d + b*e)*(a + x*(b + c*x))^(5/2))/(d + e*x) + ((a + x*(b + c*x))^(3/2)*(-3*b^2*e^2 + c*e*(11*b*d - 2*a*e - 3*b*e*x) + c^2*(-8*d^2 + 6*d*e*x)))/(3*e^2) + (-2*c^2*e*(c*d^2 + e*(-(b*d) + a*e))*Sqrt[a + x*(b + c*x)]*(5*b^2*e^2 + 8*c^2*d*(2*d - e*x) + 4*c*e*(-5*b*d + a*e + b*e*x)) + c^(3/2)*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*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 + x*(b + c*x)])] + 2*c^2*(16*c^2*d^2 + 3*b^2*e^2 + 4*c*e*(-4*b*d + a*e))*(c*d^2 + e*(-(b*d) + a*e))^(3/2)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(4*c^2*e^5))/(-(c*d^2) + e*(b*d - a*e))","A",1
1563,1,544,309,2.3054961,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^3} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^3,x]","\frac{-\frac{(a+x (b+c x))^{5/2} \left(4 c e (2 a e-3 b d)+b^2 e^2+12 c^2 d^2\right)}{2 (d+e x) \left(e (a e-b d)+c d^2\right)}-\frac{2 e^3 (a+x (b+c x))^{3/2} \left(2 c^2 e (2 a e (2 e x-3 d)+3 b d (5 d-2 e x))+b c e^2 (10 a e-15 b d+b e x)+b^3 e^3-4 c^3 d^2 (4 d-3 e x)\right)+6 e \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right) \left(4 c^2 e (a e (e x-3 d)+b d (7 d-2 e x))+b c e^2 (8 a e-13 b d+b e x)+b^3 e^3+8 c^3 d^2 (e x-2 d)\right)+6 \sqrt{c} \left(4 c e (a e-4 b d)+3 b^2 e^2+16 c^2 d^2\right) \left(e (a e-b d)+c d^2\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)+3 (2 c d-b e) \left(e (a e-b d)+c d^2\right)^{3/2} \left(4 c e (3 a e-4 b d)+b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{4 e^5 \left(e (b d-a e)-c d^2\right)}+\frac{(a+x (b+c x))^{5/2} (2 c d-b e)}{(d+e x)^2}}{2 \left(e (a e-b d)+c d^2\right)}","\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{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{\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,"(((2*c*d - b*e)*(a + x*(b + c*x))^(5/2))/(d + e*x)^2 - ((12*c^2*d^2 + b^2*e^2 + 4*c*e*(-3*b*d + 2*a*e))*(a + x*(b + c*x))^(5/2))/(2*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)) - (6*e*(c*d^2 + e*(-(b*d) + a*e))*Sqrt[a + x*(b + c*x)]*(b^3*e^3 + 8*c^3*d^2*(-2*d + e*x) + b*c*e^2*(-13*b*d + 8*a*e + b*e*x) + 4*c^2*e*(b*d*(7*d - 2*e*x) + a*e*(-3*d + e*x))) + 2*e^3*(a + x*(b + c*x))^(3/2)*(b^3*e^3 - 4*c^3*d^2*(4*d - 3*e*x) + b*c*e^2*(-15*b*d + 10*a*e + b*e*x) + 2*c^2*e*(3*b*d*(5*d - 2*e*x) + 2*a*e*(-3*d + 2*e*x))) + 6*Sqrt[c]*(16*c^2*d^2 + 3*b^2*e^2 + 4*c*e*(-4*b*d + a*e))*(c*d^2 + e*(-(b*d) + a*e))^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])] + 3*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^(3/2)*(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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(4*e^5*(-(c*d^2) + e*(b*d - a*e))))/(2*(c*d^2 + e*(-(b*d) + a*e)))","A",1
1564,1,485,462,2.9647561,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^4} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^4,x]","\frac{\frac{2 e \sqrt{a+x (b+c x)} \left(2 c e^2 \left(-4 a^2 e^2 (d+3 e x)-2 a b e \left(9 d^2+20 d e x+23 e^2 x^2\right)+b^2 d \left(24 d^2+63 d e x+55 e^2 x^2\right)\right)+b e^3 \left(-8 a^2 e^2+2 a b e (d-7 e x)+b^2 \left(3 d^2+8 d e x-3 e^2 x^2\right)\right)-8 c^2 e \left(b d \left(30 d^3+76 d^2 e x+57 d e^2 x^2+6 e^3 x^3\right)-a e \left(20 d^3+51 d^2 e x+41 d e^2 x^2+6 e^3 x^3\right)\right)+16 c^3 d^2 \left(12 d^3+30 d^2 e x+22 d e^2 x^2+3 e^3 x^3\right)\right)}{(d+e x)^3 \left(e (a e-b d)+c d^2\right)}-\frac{3 \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-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{\left(e (a e-b d)+c d^2\right)^{3/2}}-192 c^{3/2} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{48 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,"((2*e*Sqrt[a + x*(b + c*x)]*(16*c^3*d^2*(12*d^3 + 30*d^2*e*x + 22*d*e^2*x^2 + 3*e^3*x^3) + b*e^3*(-8*a^2*e^2 + 2*a*b*e*(d - 7*e*x) + b^2*(3*d^2 + 8*d*e*x - 3*e^2*x^2)) + 2*c*e^2*(-4*a^2*e^2*(d + 3*e*x) - 2*a*b*e*(9*d^2 + 20*d*e*x + 23*e^2*x^2) + b^2*d*(24*d^2 + 63*d*e*x + 55*e^2*x^2)) - 8*c^2*e*(-(a*e*(20*d^3 + 51*d^2*e*x + 41*d*e^2*x^2 + 6*e^3*x^3)) + b*d*(30*d^3 + 76*d^2*e*x + 57*d*e^2*x^2 + 6*e^3*x^3))))/((c*d^2 + e*(-(b*d) + a*e))*(d + e*x)^3) - 192*c^(3/2)*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])] - (3*(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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(c*d^2 + e*(-(b*d) + a*e))^(3/2))/(48*e^5)","A",1
1565,1,345,446,1.1012792,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2)^(5/2),x]","\frac{1}{10} \left(-\frac{e \left(b^2-4 a c\right) \left(-4 c e (a e+10 b d)+11 b^2 e^2+40 c^2 d^2\right) \left(15 \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)} \left(16 c^2 \left(33 a^2+26 a c x^2+8 c^2 x^4\right)+8 b^2 c \left(11 c x^2-20 a\right)+32 b c^2 x \left(13 a+8 c x^2\right)+15 b^4-40 b^3 c x\right)\right)}{65536 c^{13/2}}+\frac{(a+x (b+c x))^{7/2} \left(-8 c^2 e (a e (160 d+63 e x)+b d (17 d+14 e x))+2 b c e^2 (194 a e+180 b d+77 b e x)-99 b^3 e^3+16 c^3 d^2 (8 d+7 e x)\right)}{672 c^3}+2 (d+e x)^3 (a+x (b+c x))^{7/2}+\frac{(d+e x)^2 (a+x (b+c x))^{7/2} (2 c d-b e)}{3 c}\right)","-\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{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{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,"(((2*c*d - b*e)*(d + e*x)^2*(a + x*(b + c*x))^(7/2))/(3*c) + 2*(d + e*x)^3*(a + x*(b + c*x))^(7/2) + ((a + x*(b + c*x))^(7/2)*(-99*b^3*e^3 + 16*c^3*d^2*(8*d + 7*e*x) + 2*b*c*e^2*(180*b*d + 194*a*e + 77*b*e*x) - 8*c^2*e*(b*d*(17*d + 14*e*x) + a*e*(160*d + 63*e*x))))/(672*c^3) - ((b^2 - 4*a*c)*e*(40*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(10*b*d + a*e))*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)]*(15*b^4 - 40*b^3*c*x + 32*b*c^2*x*(13*a + 8*c*x^2) + 8*b^2*c*(-20*a + 11*c*x^2) + 16*c^2*(33*a^2 + 26*a*c*x^2 + 8*c^2*x^4)) + 15*(b^2 - 4*a*c)^3*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(65536*c^(13/2)))/10","A",1
1566,1,252,289,0.6770802,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2)^(5/2),x]","-\frac{e \left(b^2-4 a c\right) (b e-2 c d) \left(256 c^{5/2} (b+2 c x) (a+x (b+c x))^{5/2}-5 \left(b^2-4 a c\right) \left(16 c^{3/2} (b+2 c x) (a+x (b+c x))^{3/2}-3 \left(b^2-4 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{49152 c^{11/2}}+\frac{(a+x (b+c x))^{7/2} \left(-2 c e (16 a e+9 b d+7 b e x)+9 b^2 e^2+4 c^2 d (8 d+7 e x)\right)}{504 c^2}+\frac{2}{9} (d+e x)^2 (a+x (b+c x))^{7/2}","-\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{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{\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{2}{9} (d+e x)^2 \left(a+b x+c x^2\right)^{7/2}",1,"(2*(d + e*x)^2*(a + x*(b + c*x))^(7/2))/9 + ((a + x*(b + c*x))^(7/2)*(9*b^2*e^2 + 4*c^2*d*(8*d + 7*e*x) - 2*c*e*(9*b*d + 16*a*e + 7*b*e*x)))/(504*c^2) - ((b^2 - 4*a*c)*e*(-2*c*d + b*e)*(256*c^(5/2)*(b + 2*c*x)*(a + x*(b + c*x))^(5/2) - 5*(b^2 - 4*a*c)*(16*c^(3/2)*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))))/(49152*c^(11/2))","A",1
1567,1,194,198,0.5173998,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[(b + 2*c*x)*(d + e*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{\frac{7}{24} e \left(b^2-4 a c\right) \left(2 (b+2 c x) (a+x (b+c x))^{5/2}-5 \left(b^2-4 a c\right) \left(\frac{3 \left(b^2-4 a c\right) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{128 c^{5/2}}+\frac{(b+2 c x) (a+x (b+c x))^{3/2}}{8 c}\right)\right)+2 c (a+x (b+c x))^{7/2} (2 c (8 d+7 e x)-b e)}{112 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{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{\left(a+b x+c x^2\right)^{7/2} (-b e+16 c d+14 c e x)}{56 c}",1,"(2*c*(a + x*(b + c*x))^(7/2)*(-(b*e) + 2*c*(8*d + 7*e*x)) + (7*(b^2 - 4*a*c)*e*(2*(b + 2*c*x)*(a + x*(b + c*x))^(5/2) - 5*(b^2 - 4*a*c)*(((b + 2*c*x)*(a + x*(b + c*x))^(3/2))/(8*c) + (3*(b^2 - 4*a*c)*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(128*c^(5/2)))))/24)/(112*c^2)","A",1
1568,1,17,18,0.01195,"\int (b+2 c x) \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[(b + 2*c*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{2}{7} (a+x (b+c x))^{7/2}","\frac{2}{7} \left(a+b x+c x^2\right)^{7/2}",1,"(2*(a + x*(b + c*x))^(7/2))/7","A",1
1569,1,607,627,1.6301685,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{d+e x} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x),x]","\frac{\sqrt{c} \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 (a e-4 b d)+b^6 e^6+1024 c^6 d^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 c e \sqrt{a+x (b+c x)} \left(16 c^3 e^2 \left(2 a^2 e^2 (16 d-5 e x)+2 a b d e (14 e x-55 d)+b^2 d^2 (80 d-17 e x)\right)-8 b c^2 e^3 \left(42 a^2 e^2+4 a b e (e x-23 d)+b^2 d (49 d-2 e x)\right)+2 b^3 c e^4 (-8 a e+4 b d+b e x)-64 c^4 d^2 e (a e (7 e x-16 d)+2 b d (11 d-4 e x))+b^5 e^5+256 c^5 d^4 (2 d-e x)\right)+512 c^3 (2 c d-b e) \left(e (a e-b d)+c d^2\right)^{5/2} \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{512 c^3 e^7}+\frac{(a+x (b+c x))^{3/2} \left(8 c^2 e (a e (5 e x-8 d)+3 b d (5 d-2 e x))+2 b c e^2 (26 a e-28 b d+b e x)+b^3 e^3+16 c^3 d^2 (3 e x-4 d)\right)}{96 c e^4}+\frac{(a+x (b+c x))^{5/2} (11 b e-12 c d+10 c e x)}{30 e^2}","\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{\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)+8 b^3 c e^4 (b d-2 a e)-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)-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(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,"((-12*c*d + 11*b*e + 10*c*e*x)*(a + x*(b + c*x))^(5/2))/(30*e^2) + ((a + x*(b + c*x))^(3/2)*(b^3*e^3 + 16*c^3*d^2*(-4*d + 3*e*x) + 2*b*c*e^2*(-28*b*d + 26*a*e + b*e*x) + 8*c^2*e*(3*b*d*(5*d - 2*e*x) + a*e*(-8*d + 5*e*x))))/(96*c*e^4) + (-2*c*e*Sqrt[a + x*(b + c*x)]*(b^5*e^5 + 256*c^5*d^4*(2*d - e*x) + 2*b^3*c*e^4*(4*b*d - 8*a*e + b*e*x) - 8*b*c^2*e^3*(42*a^2*e^2 + b^2*d*(49*d - 2*e*x) + 4*a*b*e*(-23*d + e*x)) - 64*c^4*d^2*e*(2*b*d*(11*d - 4*e*x) + a*e*(-16*d + 7*e*x)) + 16*c^3*e^2*(b^2*d^2*(80*d - 17*e*x) + 2*a^2*e^2*(16*d - 5*e*x) + 2*a*b*d*e*(-55*d + 14*e*x))) + Sqrt[c]*(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 + x*(b + c*x)])] + 512*c^3*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))^(5/2)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(512*c^3*e^7)","A",1
1570,1,659,508,2.4518529,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{(d+e x)^2} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x)^2,x]","\frac{\frac{-2 c^2 e \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right) \left(4 c^2 e^2 \left(16 a^2 e^2+2 a b e (11 e x-67 d)+b^2 d (152 d-25 e x)\right)+2 b^2 c e^3 (62 a e-65 b d+b e x)-16 c^3 d e (a e (11 e x-28 d)+18 b d (3 d-e x))+b^4 e^4+192 c^4 d^3 (2 d-e x)\right)+c^{3/2} (2 c d-b e) \left(16 c^3 d^2 e^2 \left(55 a^2 e^2-128 a b d e+74 b^2 d^2\right)+b^2 c e^4 \left(40 a^2 e^2-72 a b d e+31 b^2 d^2\right)+8 c^2 e^3 \left(30 a^3 e^3-110 a^2 b d e^2+137 a b^2 d^2 e-56 b^3 d^3\right)+b^4 e^5 (b d-a e)-128 c^4 d^4 e (9 b d-8 a e)+384 c^5 d^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)+32 c^3 \left(4 c e (a e-6 b d)+5 b^2 e^2+24 c^2 d^2\right) \left(e (a e-b d)+c d^2\right)^{5/2} \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{64 c^3 e^7}-\frac{(a+x (b+c x))^{3/2} \left(e (a e-b d)+c d^2\right) \left(2 c e (4 a e-33 b d+9 b e x)+19 b^2 e^2+12 c^2 d (4 d-3 e x)\right)}{12 e^4}+\frac{(a+x (b+c x))^{5/2} \left(c e (-2 a e+17 b d-5 b e x)-5 b^2 e^2-2 c^2 d (6 d-5 e x)\right)}{5 e^2}+\frac{(a+x (b+c x))^{7/2} (b e-2 c d)}{d+e x}}{e (b d-a e)-c d^2}","\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 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)^{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+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,"(((-2*c*d + b*e)*(a + x*(b + c*x))^(7/2))/(d + e*x) + ((a + x*(b + c*x))^(5/2)*(-5*b^2*e^2 - 2*c^2*d*(6*d - 5*e*x) + c*e*(17*b*d - 2*a*e - 5*b*e*x)))/(5*e^2) - ((c*d^2 + e*(-(b*d) + a*e))*(a + x*(b + c*x))^(3/2)*(19*b^2*e^2 + 12*c^2*d*(4*d - 3*e*x) + 2*c*e*(-33*b*d + 4*a*e + 9*b*e*x)))/(12*e^4) + (-2*c^2*e*(c*d^2 + e*(-(b*d) + a*e))*Sqrt[a + x*(b + c*x)]*(b^4*e^4 + 192*c^4*d^3*(2*d - e*x) + 2*b^2*c*e^3*(-65*b*d + 62*a*e + b*e*x) + 4*c^2*e^2*(16*a^2*e^2 + b^2*d*(152*d - 25*e*x) + 2*a*b*e*(-67*d + 11*e*x)) - 16*c^3*d*e*(18*b*d*(3*d - e*x) + a*e*(-28*d + 11*e*x))) + c^(3/2)*(2*c*d - b*e)*(384*c^5*d^6 - 128*c^4*d^4*e*(9*b*d - 8*a*e) + b^4*e^5*(b*d - a*e) + b^2*c*e^4*(31*b^2*d^2 - 72*a*b*d*e + 40*a^2*e^2) + 16*c^3*d^2*e^2*(74*b^2*d^2 - 128*a*b*d*e + 55*a^2*e^2) + 8*c^2*e^3*(-56*b^3*d^3 + 137*a*b^2*d^2*e - 110*a^2*b*d*e^2 + 30*a^3*e^3))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])] + 32*c^3*(24*c^2*d^2 + 5*b^2*e^2 + 4*c*e*(-6*b*d + a*e))*(c*d^2 + e*(-(b*d) + a*e))^(5/2)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(64*c^3*e^7))/(-(c*d^2) + e*(b*d - a*e))","A",1
1571,1,535,464,2.1336672,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{(d+e x)^3} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x)^3,x]","\frac{-\frac{2 e \sqrt{a+x (b+c x)} \left(2 c e^2 \left(16 a^2 e^2 (d+2 e x)-2 a b e \left(145 d^2+234 d e x+65 e^2 x^2\right)+b^2 \left(420 d^3+655 d^2 e x+166 d e^2 x^2-37 e^3 x^3\right)\right)+b e^3 \left(16 a^2 e^2+8 a b e (5 d+9 e x)-\left(b^2 \left(105 d^2+170 d e x+49 e^2 x^2\right)\right)\right)-8 c^2 e \left(a e \left(-100 d^3-155 d^2 e x-38 d e^2 x^2+9 e^3 x^3\right)+b \left(210 d^4+320 d^3 e x+75 d^2 e^2 x^2-18 d e^3 x^3+7 e^4 x^4\right)\right)+16 c^3 \left(60 d^5+90 d^4 e x+20 d^3 e^2 x^2-5 d^2 e^3 x^3+2 d e^4 x^4-e^5 x^5\right)\right)}{(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+x (b+c x)}}\right)}{\sqrt{c}}+120 (2 c d-b e) \left(4 c e (a e-2 b d)+b^2 e^2+8 c^2 d^2\right) \sqrt{e (a e-b d)+c d^2} \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{64 e^7}","\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{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{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{\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,"((-2*e*Sqrt[a + x*(b + c*x)]*(16*c^3*(60*d^5 + 90*d^4*e*x + 20*d^3*e^2*x^2 - 5*d^2*e^3*x^3 + 2*d*e^4*x^4 - e^5*x^5) + b*e^3*(16*a^2*e^2 + 8*a*b*e*(5*d + 9*e*x) - b^2*(105*d^2 + 170*d*e*x + 49*e^2*x^2)) + 2*c*e^2*(16*a^2*e^2*(d + 2*e*x) - 2*a*b*e*(145*d^2 + 234*d*e*x + 65*e^2*x^2) + b^2*(420*d^3 + 655*d^2*e*x + 166*d*e^2*x^2 - 37*e^3*x^3)) - 8*c^2*e*(a*e*(-100*d^3 - 155*d^2*e*x - 38*d*e^2*x^2 + 9*e^3*x^3) + b*(210*d^4 + 320*d^3*e*x + 75*d^2*e^2*x^2 - 18*d*e^3*x^3 + 7*e^4*x^4))))/(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 + x*(b + c*x)])])/Sqrt[c] + 120*(2*c*d - b*e)*(8*c^2*d^2 + b^2*e^2 + 4*c*e*(-2*b*d + a*e))*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(64*e^7)","A",1
1572,1,823,473,2.6235555,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{(d+e x)^4} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x)^4,x]","\frac{-120 \sqrt{c} (2 c d-b e) \left(8 c^3 d^4-4 c^2 e (4 b d-3 a e) d^2+c e^2 (3 b d-2 a e)^2+b^2 e^3 (a e-b d)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right) (d+e x)^3-15 \sqrt{c d^2+e (a e-b d)} \left(128 c^4 d^4-128 c^3 e (2 b d-a e) d^2+b^4 e^4-8 b^2 c e^3 (4 b d-3 a e)+16 c^2 e^2 \left(10 b^2 d^2-8 a b e d+a^2 e^2\right)\right) \tanh ^{-1}\left(\frac{-b d-2 c x d+2 a e+b e x}{2 \sqrt{c d^2+e (a e-b d)} \sqrt{a+x (b+c x)}}\right) (d+e x)^3+2 e \sqrt{a+x (b+c x)} \left(16 d^2 \left(60 d^5+150 e x d^4+110 e^2 x^2 d^3+15 e^3 x^3 d^2-3 e^4 x^4 d+e^5 x^5\right) c^4+8 e \left(a e \left(160 d^5+405 e x d^4+303 e^2 x^2 d^3+44 e^3 x^3 d^2-6 e^4 x^4 d+2 e^5 x^5\right)-b d \left(270 d^5+680 e x d^4+505 e^2 x^2 d^3+72 e^3 x^3 d^2-14 e^4 x^4 d+2 e^5 x^5\right)\right) c^3+2 e^2 \left(d \left(780 d^4+1985 e x d^3+1501 e^2 x^2 d^2+228 e^3 x^3 d-32 e^4 x^4\right) b^2-2 a e \left(395 d^4+1014 e x d^3+777 e^2 x^2 d^2+112 e^3 x^3 d-16 e^4 x^4\right) b+4 a^2 e^2 \left(39 d^3+102 e x d^2+83 e^2 x^2 d+14 e^3 x^3\right)\right) c^2-e^3 \left(5 d \left(75 d^3+194 e x d^2+151 e^2 x^2 d+24 e^3 x^3\right) b^3-2 a e \left(205 d^3+540 e x d^2+443 e^2 x^2 d+60 e^3 x^3\right) b^2+4 a^2 e^2 \left(15 d^2+38 e x d+41 e^2 x^2\right) b+8 a^3 e^3 (d+3 e x)\right) c+b e^4 (b d-a e) \left(\left(15 d^2+40 e x d+33 e^2 x^2\right) b^2+2 a e (5 d+13 e x) b+8 a^2 e^2\right)\right)}{48 e^7 \left(c d^2+e (a e-b d)\right) (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 \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{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{\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,"(2*e*Sqrt[a + x*(b + c*x)]*(16*c^4*d^2*(60*d^5 + 150*d^4*e*x + 110*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 3*d*e^4*x^4 + e^5*x^5) + b*e^4*(b*d - a*e)*(8*a^2*e^2 + 2*a*b*e*(5*d + 13*e*x) + b^2*(15*d^2 + 40*d*e*x + 33*e^2*x^2)) - c*e^3*(8*a^3*e^3*(d + 3*e*x) + 4*a^2*b*e^2*(15*d^2 + 38*d*e*x + 41*e^2*x^2) + 5*b^3*d*(75*d^3 + 194*d^2*e*x + 151*d*e^2*x^2 + 24*e^3*x^3) - 2*a*b^2*e*(205*d^3 + 540*d^2*e*x + 443*d*e^2*x^2 + 60*e^3*x^3)) + 2*c^2*e^2*(4*a^2*e^2*(39*d^3 + 102*d^2*e*x + 83*d*e^2*x^2 + 14*e^3*x^3) + b^2*d*(780*d^4 + 1985*d^3*e*x + 1501*d^2*e^2*x^2 + 228*d*e^3*x^3 - 32*e^4*x^4) - 2*a*b*e*(395*d^4 + 1014*d^3*e*x + 777*d^2*e^2*x^2 + 112*d*e^3*x^3 - 16*e^4*x^4)) + 8*c^3*e*(-(b*d*(270*d^5 + 680*d^4*e*x + 505*d^3*e^2*x^2 + 72*d^2*e^3*x^3 - 14*d*e^4*x^4 + 2*e^5*x^5)) + a*e*(160*d^5 + 405*d^4*e*x + 303*d^3*e^2*x^2 + 44*d^2*e^3*x^3 - 6*d*e^4*x^4 + 2*e^5*x^5))) - 120*Sqrt[c]*(2*c*d - b*e)*(8*c^3*d^4 - 4*c^2*d^2*e*(4*b*d - 3*a*e) + c*e^2*(3*b*d - 2*a*e)^2 + b^2*e^3*(-(b*d) + a*e))*(d + e*x)^3*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])] - 15*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*(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))*(d + e*x)^3*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(48*e^7*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)^3)","A",1
1573,1,302,245,0.3930409,"\int \frac{(b+2 c x) (d+e x)^3}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^3)/Sqrt[a + b*x + c*x^2],x]","\frac{-4 a^2 c e^2 (-13 b e+32 c d+6 c e x)+a \left(-15 b^3 e^3+2 b^2 c e^2 (24 d+31 e x)+4 b c^2 e \left(-12 d^2-40 d e x+5 e^2 x^2\right)+8 c^3 \left(8 d^3+12 d^2 e x-8 d e^2 x^2-e^3 x^3\right)\right)+x (b+c x) \left(-15 b^3 e^3+2 b^2 c e^2 (24 d+5 e x)-8 b c^2 e \left(6 d^2+4 d e x+e^2 x^2\right)+16 c^3 \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)\right)}{32 c^3 \sqrt{a+x (b+c x)}}+\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+x (b+c x)}}\right)}{64 c^{7/2}}","\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{\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{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,"(-4*a^2*c*e^2*(32*c*d - 13*b*e + 6*c*e*x) + a*(-15*b^3*e^3 + 2*b^2*c*e^2*(24*d + 31*e*x) + 4*b*c^2*e*(-12*d^2 - 40*d*e*x + 5*e^2*x^2) + 8*c^3*(8*d^3 + 12*d^2*e*x - 8*d*e^2*x^2 - e^3*x^3)) + x*(b + c*x)*(-15*b^3*e^3 + 2*b^2*c*e^2*(24*d + 5*e*x) - 8*b*c^2*e*(6*d^2 + 4*d*e*x + e^2*x^2) + 16*c^3*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3)))/(32*c^3*Sqrt[a + x*(b + c*x)]) + (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 + x*(b + c*x)])])/(64*c^(7/2))","A",1
1574,1,185,148,0.181593,"\int \frac{(b+2 c x) (d+e x)^2}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^2)/Sqrt[a + b*x + c*x^2],x]","\frac{-8 a^2 c e^2+a \left(3 b^2 e^2-2 b c e (3 d+5 e x)+4 c^2 \left(3 d^2+3 d e x-e^2 x^2\right)\right)+x (b+c x) \left(3 b^2 e^2-2 b c e (3 d+e x)+4 c^2 \left(3 d^2+3 d e x+e^2 x^2\right)\right)}{6 c^2 \sqrt{a+x (b+c x)}}-\frac{e \left(b^2-4 a c\right) (b e-2 c d) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{4 c^{5/2}}","\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{\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{2}{3} (d+e x)^2 \sqrt{a+b x+c x^2}",1,"(-8*a^2*c*e^2 + a*(3*b^2*e^2 - 2*b*c*e*(3*d + 5*e*x) + 4*c^2*(3*d^2 + 3*d*e*x - e^2*x^2)) + x*(b + c*x)*(3*b^2*e^2 - 2*b*c*e*(3*d + e*x) + 4*c^2*(3*d^2 + 3*d*e*x + e^2*x^2)))/(6*c^2*Sqrt[a + x*(b + c*x)]) - ((b^2 - 4*a*c)*e*(-2*c*d + b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(4*c^(5/2))","A",1
1575,1,82,84,0.1235884,"\int \frac{(b+2 c x) (d+e x)}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((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+x (b+c x)}}\right)}{4 c^{3/2}}+\frac{\sqrt{a+x (b+c x)} (-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 + x*(b + c*x)])/(2*c) + ((b^2 - 4*a*c)*e*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(4*c^(3/2))","A",1
1576,1,15,16,0.006727,"\int \frac{b+2 c x}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(b + 2*c*x)/Sqrt[a + b*x + c*x^2],x]","2 \sqrt{a+x (b+c x)}","2 \sqrt{a+b x+c x^2}",1,"2*Sqrt[a + x*(b + c*x)]","A",1
1577,1,127,133,0.1439893,"\int \frac{b+2 c x}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{\sqrt{e (a e-b d)+c d^2}}+2 \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{e}","\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 + x*(b + c*x)])] + ((2*c*d - b*e)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/Sqrt[c*d^2 + e*(-(b*d) + a*e)])/e","A",1
1578,1,138,141,0.1072174,"\int \frac{b+2 c x}{(d+e x)^2 \sqrt{a+b x+c x^2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^2*Sqrt[a + b*x + c*x^2]),x]","\frac{e \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{2 \left(e (a e-b d)+c d^2\right)^{3/2}}+\frac{\sqrt{a+x (b+c x)} (2 c d-b e)}{(d+e x) \left(e (a e-b d)+c d^2\right)}","\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 + x*(b + c*x)])/((c*d^2 + e*(-(b*d) + a*e))*(d + e*x)) + ((b^2 - 4*a*c)*e*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(2*(c*d^2 + e*(-(b*d) + a*e))^(3/2))","A",1
1579,1,220,225,0.317911,"\int \frac{b+2 c x}{(d+e x)^3 \sqrt{a+b x+c x^2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^3*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+x (b+c x)} \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(e (a e-b d)+c d^2\right)^2}-\frac{3 e \left(b^2-4 a c\right) (b e-2 c d) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{8 \left(e (a e-b d)+c d^2\right)^{5/2}}+\frac{\sqrt{a+x (b+c x)} (2 c d-b e)}{2 (d+e x)^2 \left(e (a e-b d)+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 + x*(b + c*x)])/(2*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)^2) + ((4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*Sqrt[a + x*(b + c*x)])/(4*(c*d^2 + e*(-(b*d) + a*e))^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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(8*(c*d^2 + e*(-(b*d) + a*e))^(5/2))","A",1
1580,1,323,328,0.5590863,"\int \frac{b+2 c x}{(d+e x)^4 \sqrt{a+b x+c x^2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^4*Sqrt[a + b*x + c*x^2]),x]","\frac{\frac{\sqrt{a+x (b+c x)} \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)}{2 (d+e x)^2}+\frac{\sqrt{a+x (b+c x)} (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)}{4 (d+e x) \left(e (a e-b d)+c d^2\right)}+\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{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{8 \left(e (a e-b d)+c d^2\right)^{3/2}}+\frac{2 \sqrt{a+x (b+c x)} (2 c d-b e) \left(e (a e-b d)+c d^2\right)}{(d+e x)^3}}{6 \left(e (a e-b d)+c d^2\right)^2}","\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*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))*Sqrt[a + x*(b + c*x)])/(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 + x*(b + c*x)])/(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 + x*(b + c*x)])/(4*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)) + (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*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(8*(c*d^2 + e*(-(b*d) + a*e))^(3/2)))/(6*(c*d^2 + e*(-(b*d) + a*e))^2)","A",1
1581,1,248,202,0.3319826,"\int \frac{(b+2 c x) (d+e x)^4}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2)^(3/2),x]","\frac{-c e^3 \left(16 a^2 e+a b (54 d+26 e x)+b^2 x (54 d-5 e x)\right)+15 b^2 e^4 (a+b x)+2 c^2 e^2 \left(2 a \left(18 d^2+9 d e x-2 e^2 x^2\right)-b x \left(-36 d^2+9 d e x+e^2 x^2\right)\right)+c^3 \left(-6 d^4-24 d^3 e x+36 d^2 e^2 x^2+12 d e^3 x^3+2 e^4 x^4\right)}{3 c^3 \sqrt{a+x (b+c x)}}+\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+x (b+c x)}}\right)}{2 c^{7/2}}","\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{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{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,"(15*b^2*e^4*(a + b*x) + c^3*(-6*d^4 - 24*d^3*e*x + 36*d^2*e^2*x^2 + 12*d*e^3*x^3 + 2*e^4*x^4) - c*e^3*(16*a^2*e + b^2*x*(54*d - 5*e*x) + a*b*(54*d + 26*e*x)) + 2*c^2*e^2*(2*a*(18*d^2 + 9*d*e*x - 2*e^2*x^2) - b*x*(-36*d^2 + 9*d*e*x + e^2*x^2)))/(3*c^3*Sqrt[a + x*(b + c*x)]) + (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 + x*(b + c*x)])])/(2*c^(7/2))","A",1
1582,1,164,153,0.2189574,"\int \frac{(b+2 c x) (d+e x)^3}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((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+x (b+c x)}}\right)}{4 c^{5/2}}+\frac{3 c e^2 (2 a (4 d+e x)+b x (8 d-e x))-9 b e^3 (a+b x)-2 c^2 \left(2 d^3+6 d^2 e x-6 d e^2 x^2-e^3 x^3\right)}{2 c^2 \sqrt{a+x (b+c 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}}",1,"(-9*b*e^3*(a + b*x) - 2*c^2*(2*d^3 + 6*d^2*e*x - 6*d*e^2*x^2 - e^3*x^3) + 3*c*e^2*(b*x*(8*d - e*x) + 2*a*(4*d + e*x)))/(2*c^2*Sqrt[a + x*(b + c*x)]) + (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 + x*(b + c*x)])])/(4*c^(5/2))","A",1
1583,1,95,93,0.1662969,"\int \frac{(b+2 c x) (d+e x)^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((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+x (b+c x)}}\right)}{c^{3/2}}+\frac{4 e^2 (a+b x)-2 c \left(d^2+2 d e x-e^2 x^2\right)}{c \sqrt{a+x (b+c 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}",1,"(4*e^2*(a + b*x) - 2*c*(d^2 + 2*d*e*x - e^2*x^2))/(c*Sqrt[a + x*(b + c*x)]) + (2*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/c^(3/2)","A",1
1584,1,56,60,0.2713047,"\int \frac{(b+2 c x) (d+e x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{2 e \log \left(2 \sqrt{c} \sqrt{a+x (b+c x)}+b+2 c x\right)}{\sqrt{c}}-\frac{2 (d+e x)}{\sqrt{a+x (b+c 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}}",1,"(-2*(d + e*x))/Sqrt[a + x*(b + c*x)] + (2*e*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/Sqrt[c]","A",1
1585,1,15,16,0.0070185,"\int \frac{b+2 c x}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(b + 2*c*x)/(a + b*x + c*x^2)^(3/2),x]","-\frac{2}{\sqrt{a+x (b+c x)}}","-\frac{2}{\sqrt{a+b x+c x^2}}",1,"-2/Sqrt[a + x*(b + c*x)]","A",1
1586,1,133,166,0.1912284,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 (b e-c d+c e x)}{\sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right)}+\frac{e (2 c d-b e) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{\left(e (a e-b d)+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*(-(c*d) + b*e + c*e*x))/((c*d^2 + e*(-(b*d) + a*e))*Sqrt[a + x*(b + c*x)]) + (e*(2*c*d - b*e)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(c*d^2 + e*(-(b*d) + a*e))^(3/2)","A",1
1587,1,215,248,0.5383277,"\int \frac{b+2 c x}{(d+e x)^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(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-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{2 \left(e (a e-b d)+c d^2\right)^{5/2}}+\frac{3 e^2 \sqrt{a+x (b+c x)} (2 c d-b e)}{(d+e x) \left(e (a e-b d)+c d^2\right)^2}+\frac{2 (b e-c d+c e x)}{(d+e x) \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right)}","-\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*(-(c*d) + b*e + c*e*x))/((c*d^2 + e*(-(b*d) + a*e))*(d + e*x)*Sqrt[a + x*(b + c*x)]) + (3*e^2*(2*c*d - b*e)*Sqrt[a + x*(b + c*x)])/((c*d^2 + e*(-(b*d) + a*e))^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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(2*(c*d^2 + e*(-(b*d) + a*e))^(5/2))","A",1
1588,1,354,208,1.0081398,"\int \frac{(b+2 c x) (d+e x)^4}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2)^(5/2),x]","\frac{2 \left(\frac{\sqrt{c} \left(b^2 \left(-12 a^2 e^4+24 a c e^3 x (2 d+e x)+c^2 \left(d^4+12 d^3 e x-18 d^2 e^2 x^2+28 d e^3 x^3-3 e^4 x^4\right)\right)+8 b c e \left(3 a^2 e^2 (d+3 e x)+a c \left(d^3-9 d^2 e x-3 d e^2 x^2+7 e^3 x^3\right)+3 c^2 d^2 x^2 (d-e x)\right)+4 c \left(8 a^3 e^4-12 a^2 c e^2 \left(d^2+d e x-e^2 x^2\right)-a c^2 \left(d^4+18 d^2 e^2 x^2+16 d e^3 x^3-3 e^4 x^4\right)+4 c^3 d^3 e x^3\right)-8 b^3 e^3 x (3 a e+c x (2 e x-3 d))-12 b^4 e^4 x^2\right)}{(a+x (b+c x))^{3/2}}+6 e^3 \left(b^2-4 a c\right) (b e-2 c d) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)}{3 c^{5/2} \left(4 a c-b^2\right)}","\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*((Sqrt[c]*(-12*b^4*e^4*x^2 - 8*b^3*e^3*x*(3*a*e + c*x*(-3*d + 2*e*x)) + 8*b*c*e*(3*c^2*d^2*x^2*(d - e*x) + 3*a^2*e^2*(d + 3*e*x) + a*c*(d^3 - 9*d^2*e*x - 3*d*e^2*x^2 + 7*e^3*x^3)) + 4*c*(8*a^3*e^4 + 4*c^3*d^3*e*x^3 - 12*a^2*c*e^2*(d^2 + d*e*x - e^2*x^2) - a*c^2*(d^4 + 18*d^2*e^2*x^2 + 16*d*e^3*x^3 - 3*e^4*x^4)) + b^2*(-12*a^2*e^4 + 24*a*c*e^3*x*(2*d + e*x) + c^2*(d^4 + 12*d^3*e*x - 18*d^2*e^2*x^2 + 28*d*e^3*x^3 - 3*e^4*x^4))))/(a + x*(b + c*x))^(3/2) + 6*(b^2 - 4*a*c)*e^3*(-2*c*d + b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/(3*c^(5/2)*(-b^2 + 4*a*c))","A",1
1589,1,285,158,0.490459,"\int \frac{(b+2 c x) (d+e x)^3}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^3)/(a + b*x + c*x^2)^(5/2),x]","\frac{6 e^3 \sqrt{a+x (b+c x)} \left(4 a^2 c+a \left(-b^2+4 b c x+4 c^2 x^2\right)-b^2 x (b+c x)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)+2 \sqrt{c} \left(6 b e \left(a^2 e^2+a c \left(d^2-6 d e x-e^2 x^2\right)+c^2 d x^2 (3 d-2 e x)\right)-4 c \left(3 a^2 e^2 (2 d+e x)+a c \left(d^3+9 d e^2 x^2+4 e^3 x^3\right)-3 c^2 d^2 e x^3\right)+b^2 \left(12 a e^3 x+c \left(d^3+9 d^2 e x-9 d e^2 x^2+7 e^3 x^3\right)\right)+6 b^3 e^3 x^2\right)}{3 c^{3/2} \left(4 a c-b^2\right) (a+x (b+c x))^{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*Sqrt[c]*(6*b^3*e^3*x^2 + 6*b*e*(a^2*e^2 + c^2*d*x^2*(3*d - 2*e*x) + a*c*(d^2 - 6*d*e*x - e^2*x^2)) - 4*c*(-3*c^2*d^2*e*x^3 + 3*a^2*e^2*(2*d + e*x) + a*c*(d^3 + 9*d*e^2*x^2 + 4*e^3*x^3)) + b^2*(12*a*e^3*x + c*(d^3 + 9*d^2*e*x - 9*d*e^2*x^2 + 7*e^3*x^3))) + 6*e^3*Sqrt[a + x*(b + c*x)]*(4*a^2*c - b^2*x*(b + c*x) + a*(-b^2 + 4*b*c*x + 4*c^2*x^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(3*c^(3/2)*(-b^2 + 4*a*c)*(a + x*(b + c*x))^(3/2))","A",1
1590,1,110,74,0.7858443,"\int \frac{(b+2 c x) (d+e x)^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^2)/(a + b*x + c*x^2)^(5/2),x]","\frac{2 \left(8 a^2 e^2+4 b e \left(c x^2 (e x-3 d)-a (d-3 e x)\right)+4 a c \left(d^2+3 e^2 x^2\right)-b^2 \left(d^2+6 d e x-3 e^2 x^2\right)-8 c^2 d e x^3\right)}{3 \left(b^2-4 a c\right) (a+x (b+c x))^{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*(8*a^2*e^2 - 8*c^2*d*e*x^3 - b^2*(d^2 + 6*d*e*x - 3*e^2*x^2) + 4*a*c*(d^2 + 3*e^2*x^2) + 4*b*e*(-(a*(d - 3*e*x)) + c*x^2*(-3*d + e*x))))/(3*(b^2 - 4*a*c)*(a + x*(b + c*x))^(3/2))","A",1
1591,1,64,59,0.2040734,"\int \frac{(b+2 c x) (d+e x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \left(2 b e \left(a+3 c x^2\right)+4 c \left(c e x^3-a d\right)+b^2 (d+3 e x)\right)}{3 \left(b^2-4 a c\right) (a+x (b+c x))^{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*(b^2*(d + 3*e*x) + 2*b*e*(a + 3*c*x^2) + 4*c*(-(a*d) + c*e*x^3)))/(3*(b^2 - 4*a*c)*(a + x*(b + c*x))^(3/2))","A",1
1592,1,17,18,0.010134,"\int \frac{b+2 c x}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(b + 2*c*x)/(a + b*x + c*x^2)^(5/2),x]","-\frac{2}{3 (a+x (b+c x))^{3/2}}","-\frac{2}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"-2/(3*(a + x*(b + c*x))^(3/2))","A",1
1593,1,249,291,0.4195104,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)^(5/2)),x]","\frac{2 e \left(2 b c \left(c d (d-2 e x)-5 a e^2\right)+4 c^2 \left(a e (3 d-2 e x)+c d^2 x\right)+3 b^3 e^2+b^2 c e (3 e x-5 d)\right)}{3 \left(b^2-4 a c\right) \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right)^2}+\frac{e^3 (2 c d-b e) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{\left(e (a e-b d)+c d^2\right)^{5/2}}+\frac{2 (b e-c d+c e x)}{3 (a+x (b+c x))^{3/2} \left(e (a e-b d)+c d^2\right)}","-\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{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-3 b^3 e^2+5 b^2 c d e\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{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*(-(c*d) + b*e + c*e*x))/(3*(c*d^2 + e*(-(b*d) + a*e))*(a + x*(b + c*x))^(3/2)) + (2*e*(3*b^3*e^2 + b^2*c*e*(-5*d + 3*e*x) + 2*b*c*(-5*a*e^2 + c*d*(d - 2*e*x)) + 4*c^2*(c*d^2*x + a*e*(3*d - 2*e*x))))/(3*(b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e))^2*Sqrt[a + x*(b + c*x)]) + (e^3*(2*c*d - b*e)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(c*d^2 + e*(-(b*d) + a*e))^(5/2)","A",1
1594,1,384,423,1.3471727,"\int \frac{b+2 c x}{(d+e x)^2 \left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^2*(a + b*x + c*x^2)^(5/2)),x]","\frac{2 \left(\frac{1}{4} e^2 \left(\frac{2 \sqrt{a+x (b+c x)} (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)}{(d+e x) \left(e (a e-b d)+c d^2\right)^2}+\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{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{\left(e (a e-b d)+c d^2\right)^{5/2}}\right)+\frac{\left(b^2-4 a c\right) (b e-c d+c e x)}{(d+e x) (a+x (b+c x))^{3/2}}+\frac{e \left(4 b c \left(c d (d-2 e x)-4 a e^2\right)+4 c^2 \left(a e (5 d-3 e x)+2 c d^2 x\right)+5 b^3 e^2+b^2 c e (5 e x-9 d)\right)}{(d+e x) \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right)}\right)}{3 \left(b^2-4 a c\right) \left(e (a e-b d)+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{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{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-5 b^3 e^2+9 b^2 c d e\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}",1,"(2*(((b^2 - 4*a*c)*(-(c*d) + b*e + c*e*x))/((d + e*x)*(a + x*(b + c*x))^(3/2)) + (e*(5*b^3*e^2 + b^2*c*e*(-9*d + 5*e*x) + 4*c^2*(2*c*d^2*x + a*e*(5*d - 3*e*x)) + 4*b*c*(-4*a*e^2 + c*d*(d - 2*e*x))))/((c*d^2 + e*(-(b*d) + a*e))*(d + e*x)*Sqrt[a + x*(b + c*x)]) + (e^2*((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 + x*(b + c*x)])/((c*d^2 + e*(-(b*d) + a*e))^2*(d + e*x)) + (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*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(c*d^2 + e*(-(b*d) + a*e))^(5/2)))/4))/(3*(b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e)))","A",1
1595,1,111,132,0.13632,"\int (b+2 c x) (d+e x)^{5/2} \left(a+b x+c x^2\right) \, dx","Integrate[(b + 2*c*x)*(d + e*x)^(5/2)*(a + b*x + c*x^2),x]","\frac{2 (d+e x)^{7/2} \left(13 c e \left(22 a e (7 e x-2 d)+3 b \left(8 d^2-28 d e x+63 e^2 x^2\right)\right)+143 b e^2 (9 a e-2 b d+7 b e x)-6 c^2 \left(16 d^3-56 d^2 e x+126 d e^2 x^2-231 e^3 x^3\right)\right)}{9009 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*(d + e*x)^(7/2)*(143*b*e^2*(-2*b*d + 9*a*e + 7*b*e*x) - 6*c^2*(16*d^3 - 56*d^2*e*x + 126*d*e^2*x^2 - 231*e^3*x^3) + 13*c*e*(22*a*e*(-2*d + 7*e*x) + 3*b*(8*d^2 - 28*d*e*x + 63*e^2*x^2))))/(9009*e^4)","A",1
1596,1,109,132,0.1273051,"\int (b+2 c x) (d+e x)^{3/2} \left(a+b x+c x^2\right) \, dx","Integrate[(b + 2*c*x)*(d + e*x)^(3/2)*(a + b*x + c*x^2),x]","\frac{2 (d+e x)^{5/2} \left(11 c e \left(6 a e (5 e x-2 d)+b \left(8 d^2-20 d e x+35 e^2 x^2\right)\right)+33 b e^2 (7 a e-2 b d+5 b e x)+c^2 \left(-32 d^3+80 d^2 e x-140 d e^2 x^2+210 e^3 x^3\right)\right)}{1155 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*(d + e*x)^(5/2)*(33*b*e^2*(-2*b*d + 7*a*e + 5*b*e*x) + c^2*(-32*d^3 + 80*d^2*e*x - 140*d*e^2*x^2 + 210*e^3*x^3) + 11*c*e*(6*a*e*(-2*d + 5*e*x) + b*(8*d^2 - 20*d*e*x + 35*e^2*x^2))))/(1155*e^4)","A",1
1597,1,110,132,0.1191282,"\int (b+2 c x) \sqrt{d+e x} \left(a+b x+c x^2\right) \, dx","Integrate[(b + 2*c*x)*Sqrt[d + e*x]*(a + b*x + c*x^2),x]","\frac{2 (d+e x)^{3/2} \left(3 c e \left(14 a e (3 e x-2 d)+3 b \left(8 d^2-12 d e x+15 e^2 x^2\right)\right)+21 b e^2 (5 a e-2 b d+3 b e x)+c^2 \left(-32 d^3+48 d^2 e x-60 d e^2 x^2+70 e^3 x^3\right)\right)}{315 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*(d + e*x)^(3/2)*(21*b*e^2*(-2*b*d + 5*a*e + 3*b*e*x) + c^2*(-32*d^3 + 48*d^2*e*x - 60*d*e^2*x^2 + 70*e^3*x^3) + 3*c*e*(14*a*e*(-2*d + 3*e*x) + 3*b*(8*d^2 - 12*d*e*x + 15*e^2*x^2))))/(315*e^4)","A",1
1598,1,109,130,0.1120089,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{\sqrt{d+e x}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(7 c e \left(10 a e (e x-2 d)+3 b \left(8 d^2-4 d e x+3 e^2 x^2\right)\right)+35 b e^2 (3 a e-2 b d+b e x)-6 c^2 \left(16 d^3-8 d^2 e x+6 d e^2 x^2-5 e^3 x^3\right)\right)}{105 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*Sqrt[d + e*x]*(35*b*e^2*(-2*b*d + 3*a*e + b*e*x) - 6*c^2*(16*d^3 - 8*d^2*e*x + 6*d*e^2*x^2 - 5*e^3*x^3) + 7*c*e*(10*a*e*(-2*d + e*x) + 3*b*(8*d^2 - 4*d*e*x + 3*e^2*x^2))))/(105*e^4)","A",1
1599,1,106,126,0.105317,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^{3/2}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^(3/2),x]","\frac{2 \left(5 c e \left(2 a e (2 d+e x)+b \left(-8 d^2-4 d e x+e^2 x^2\right)\right)+5 b e^2 (-a e+2 b d+b e x)+2 c^2 \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)\right)}{5 e^4 \sqrt{d+e 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}",1,"(2*(5*b*e^2*(2*b*d - a*e + b*e*x) + 2*c^2*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) + 5*c*e*(2*a*e*(2*d + e*x) + b*(-8*d^2 - 4*d*e*x + e^2*x^2))))/(5*e^4*Sqrt[d + e*x])","A",1
1600,1,108,128,0.115022,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^(5/2),x]","-\frac{2 \left(c e \left(2 a e (2 d+3 e x)-3 b \left(8 d^2+12 d e x+3 e^2 x^2\right)\right)+b e^2 (a e+2 b d+3 b e x)+2 c^2 \left(16 d^3+24 d^2 e x+6 d e^2 x^2-e^3 x^3\right)\right)}{3 e^4 (d+e x)^{3/2}}","-\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*(b*e^2*(2*b*d + a*e + 3*b*e*x) + 2*c^2*(16*d^3 + 24*d^2*e*x + 6*d*e^2*x^2 - e^3*x^3) + c*e*(2*a*e*(2*d + 3*e*x) - 3*b*(8*d^2 + 12*d*e*x + 3*e^2*x^2))))/(3*e^4*(d + e*x)^(3/2))","A",1
1601,1,291,252,0.409767,"\int (b+2 c x) (d+e x)^{5/2} \left(a+b x+c x^2\right)^2 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^(5/2)*(a + b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{7/2} \left(-34 c e^2 \left(143 a^2 e^2 (2 d-7 e x)-39 a b e \left(8 d^2-28 d e x+63 e^2 x^2\right)+6 b^2 \left(16 d^3-56 d^2 e x+126 d e^2 x^2-231 e^3 x^3\right)\right)+221 b e^3 \left(99 a^2 e^2+22 a b e (7 e x-2 d)+b^2 \left(8 d^2-28 d e x+63 e^2 x^2\right)\right)+17 c^2 e \left(12 a e \left(-16 d^3+56 d^2 e x-126 d e^2 x^2+231 e^3 x^3\right)+b \left(128 d^4-448 d^3 e x+1008 d^2 e^2 x^2-1848 d e^3 x^3+3003 e^4 x^4\right)\right)-2 c^3 \left(256 d^5-896 d^4 e x+2016 d^3 e^2 x^2-3696 d^2 e^3 x^3+6006 d e^4 x^4-9009 e^5 x^5\right)\right)}{153153 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*(d + e*x)^(7/2)*(-2*c^3*(256*d^5 - 896*d^4*e*x + 2016*d^3*e^2*x^2 - 3696*d^2*e^3*x^3 + 6006*d*e^4*x^4 - 9009*e^5*x^5) + 221*b*e^3*(99*a^2*e^2 + 22*a*b*e*(-2*d + 7*e*x) + b^2*(8*d^2 - 28*d*e*x + 63*e^2*x^2)) - 34*c*e^2*(143*a^2*e^2*(2*d - 7*e*x) - 39*a*b*e*(8*d^2 - 28*d*e*x + 63*e^2*x^2) + 6*b^2*(16*d^3 - 56*d^2*e*x + 126*d*e^2*x^2 - 231*e^3*x^3)) + 17*c^2*e*(12*a*e*(-16*d^3 + 56*d^2*e*x - 126*d*e^2*x^2 + 231*e^3*x^3) + b*(128*d^4 - 448*d^3*e*x + 1008*d^2*e^2*x^2 - 1848*d*e^3*x^3 + 3003*e^4*x^4))))/(153153*e^6)","A",1
1602,1,291,252,0.3566764,"\int (b+2 c x) (d+e x)^{3/2} \left(a+b x+c x^2\right)^2 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^(3/2)*(a + b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{5/2} \left(-78 c e^2 \left(33 a^2 e^2 (2 d-5 e x)-11 a b e \left(8 d^2-20 d e x+35 e^2 x^2\right)+2 b^2 \left(16 d^3-40 d^2 e x+70 d e^2 x^2-105 e^3 x^3\right)\right)+143 b e^3 \left(63 a^2 e^2+18 a b e (5 e x-2 d)+b^2 \left(8 d^2-20 d e x+35 e^2 x^2\right)\right)+3 c^2 e \left(52 a e \left(-16 d^3+40 d^2 e x-70 d e^2 x^2+105 e^3 x^3\right)+5 b \left(128 d^4-320 d^3 e x+560 d^2 e^2 x^2-840 d e^3 x^3+1155 e^4 x^4\right)\right)+c^3 \left(-512 d^5+1280 d^4 e x-2240 d^3 e^2 x^2+3360 d^2 e^3 x^3-4620 d e^4 x^4+6006 e^5 x^5\right)\right)}{45045 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*(d + e*x)^(5/2)*(c^3*(-512*d^5 + 1280*d^4*e*x - 2240*d^3*e^2*x^2 + 3360*d^2*e^3*x^3 - 4620*d*e^4*x^4 + 6006*e^5*x^5) + 143*b*e^3*(63*a^2*e^2 + 18*a*b*e*(-2*d + 5*e*x) + b^2*(8*d^2 - 20*d*e*x + 35*e^2*x^2)) - 78*c*e^2*(33*a^2*e^2*(2*d - 5*e*x) - 11*a*b*e*(8*d^2 - 20*d*e*x + 35*e^2*x^2) + 2*b^2*(16*d^3 - 40*d^2*e*x + 70*d*e^2*x^2 - 105*e^3*x^3)) + 3*c^2*e*(52*a*e*(-16*d^3 + 40*d^2*e*x - 70*d*e^2*x^2 + 105*e^3*x^3) + 5*b*(128*d^4 - 320*d^3*e*x + 560*d^2*e^2*x^2 - 840*d*e^3*x^3 + 1155*e^4*x^4))))/(45045*e^6)","A",1
1603,1,291,252,0.3626749,"\int (b+2 c x) \sqrt{d+e x} \left(a+b x+c x^2\right)^2 \, dx","Integrate[(b + 2*c*x)*Sqrt[d + e*x]*(a + b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{3/2} \left(-286 c e^2 \left(21 a^2 e^2 (2 d-3 e x)-9 a b e \left(8 d^2-12 d e x+15 e^2 x^2\right)+b^2 \left(32 d^3-48 d^2 e x+60 d e^2 x^2-70 e^3 x^3\right)\right)+429 b e^3 \left(35 a^2 e^2+14 a b e (3 e x-2 d)+b^2 \left(8 d^2-12 d e x+15 e^2 x^2\right)\right)+13 c^2 e \left(44 a e \left(-16 d^3+24 d^2 e x-30 d e^2 x^2+35 e^3 x^3\right)+5 b \left(128 d^4-192 d^3 e x+240 d^2 e^2 x^2-280 d e^3 x^3+315 e^4 x^4\right)\right)-10 c^3 \left(256 d^5-384 d^4 e x+480 d^3 e^2 x^2-560 d^2 e^3 x^3+630 d e^4 x^4-693 e^5 x^5\right)\right)}{45045 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*(d + e*x)^(3/2)*(-10*c^3*(256*d^5 - 384*d^4*e*x + 480*d^3*e^2*x^2 - 560*d^2*e^3*x^3 + 630*d*e^4*x^4 - 693*e^5*x^5) + 429*b*e^3*(35*a^2*e^2 + 14*a*b*e*(-2*d + 3*e*x) + b^2*(8*d^2 - 12*d*e*x + 15*e^2*x^2)) - 286*c*e^2*(21*a^2*e^2*(2*d - 3*e*x) - 9*a*b*e*(8*d^2 - 12*d*e*x + 15*e^2*x^2) + b^2*(32*d^3 - 48*d^2*e*x + 60*d*e^2*x^2 - 70*e^3*x^3)) + 13*c^2*e*(44*a*e*(-16*d^3 + 24*d^2*e*x - 30*d*e^2*x^2 + 35*e^3*x^3) + 5*b*(128*d^4 - 192*d^3*e*x + 240*d^2*e^2*x^2 - 280*d*e^3*x^3 + 315*e^4*x^4))))/(45045*e^6)","A",1
1604,1,290,250,0.3908488,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{\sqrt{d+e x}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-66 c e^2 \left(-35 a^2 e^2 (e x-2 d)-21 a b e \left(8 d^2-4 d e x+3 e^2 x^2\right)+6 b^2 \left(16 d^3-8 d^2 e x+6 d e^2 x^2-5 e^3 x^3\right)\right)+231 b e^3 \left(15 a^2 e^2+10 a b e (e x-2 d)+b^2 \left(8 d^2-4 d e x+3 e^2 x^2\right)\right)+11 c^2 e \left(36 a e \left(-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right)+5 b \left(128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right)\right)-10 c^3 \left(256 d^5-128 d^4 e x+96 d^3 e^2 x^2-80 d^2 e^3 x^3+70 d e^4 x^4-63 e^5 x^5\right)\right)}{3465 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*Sqrt[d + e*x]*(-10*c^3*(256*d^5 - 128*d^4*e*x + 96*d^3*e^2*x^2 - 80*d^2*e^3*x^3 + 70*d*e^4*x^4 - 63*e^5*x^5) + 231*b*e^3*(15*a^2*e^2 + 10*a*b*e*(-2*d + e*x) + b^2*(8*d^2 - 4*d*e*x + 3*e^2*x^2)) - 66*c*e^2*(-35*a^2*e^2*(-2*d + e*x) - 21*a*b*e*(8*d^2 - 4*d*e*x + 3*e^2*x^2) + 6*b^2*(16*d^3 - 8*d^2*e*x + 6*d*e^2*x^2 - 5*e^3*x^3)) + 11*c^2*e*(36*a*e*(-16*d^3 + 8*d^2*e*x - 6*d*e^2*x^2 + 5*e^3*x^3) + 5*b*(128*d^4 - 64*d^3*e*x + 48*d^2*e^2*x^2 - 40*d*e^3*x^3 + 35*e^4*x^4))))/(3465*e^6)","A",1
1605,1,287,248,0.343606,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^{3/2}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^(3/2),x]","\frac{252 c e^2 \left(5 a^2 e^2 (2 d+e x)+5 a b e \left(-8 d^2-4 d e x+e^2 x^2\right)+2 b^2 \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)\right)-210 b e^3 \left(3 a^2 e^2-6 a b e (2 d+e x)+b^2 \left(8 d^2+4 d e x-e^2 x^2\right)\right)-18 c^2 e \left(5 b \left(128 d^4+64 d^3 e x-16 d^2 e^2 x^2+8 d e^3 x^3-5 e^4 x^4\right)-28 a e \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)\right)+20 c^3 \left(256 d^5+128 d^4 e x-32 d^3 e^2 x^2+16 d^2 e^3 x^3-10 d e^4 x^4+7 e^5 x^5\right)}{315 e^6 \sqrt{d+e 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}",1,"(20*c^3*(256*d^5 + 128*d^4*e*x - 32*d^3*e^2*x^2 + 16*d^2*e^3*x^3 - 10*d*e^4*x^4 + 7*e^5*x^5) - 210*b*e^3*(3*a^2*e^2 - 6*a*b*e*(2*d + e*x) + b^2*(8*d^2 + 4*d*e*x - e^2*x^2)) + 252*c*e^2*(5*a^2*e^2*(2*d + e*x) + 5*a*b*e*(-8*d^2 - 4*d*e*x + e^2*x^2) + 2*b^2*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3)) - 18*c^2*e*(-28*a*e*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) + 5*b*(128*d^4 + 64*d^3*e*x - 16*d^2*e^2*x^2 + 8*d*e^3*x^3 - 5*e^4*x^4)))/(315*e^6*Sqrt[d + e*x])","A",1
1606,1,289,246,0.3338882,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^(5/2),x]","-\frac{2 \left(14 c e^2 \left(a^2 e^2 (2 d+3 e x)-3 a b e \left(8 d^2+12 d e x+3 e^2 x^2\right)+2 b^2 \left(16 d^3+24 d^2 e x+6 d e^2 x^2-e^3 x^3\right)\right)+7 b e^3 \left(a^2 e^2+2 a b e (2 d+3 e x)-\left(b^2 \left(8 d^2+12 d e x+3 e^2 x^2\right)\right)\right)-7 c^2 e \left(4 a e \left(-16 d^3-24 d^2 e x-6 d e^2 x^2+e^3 x^3\right)+b \left(128 d^4+192 d^3 e x+48 d^2 e^2 x^2-8 d e^3 x^3+3 e^4 x^4\right)\right)+2 c^3 \left(256 d^5+384 d^4 e x+96 d^3 e^2 x^2-16 d^2 e^3 x^3+6 d e^4 x^4-3 e^5 x^5\right)\right)}{21 e^6 (d+e x)^{3/2}}","\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^3*(256*d^5 + 384*d^4*e*x + 96*d^3*e^2*x^2 - 16*d^2*e^3*x^3 + 6*d*e^4*x^4 - 3*e^5*x^5) + 7*b*e^3*(a^2*e^2 + 2*a*b*e*(2*d + 3*e*x) - b^2*(8*d^2 + 12*d*e*x + 3*e^2*x^2)) + 14*c*e^2*(a^2*e^2*(2*d + 3*e*x) - 3*a*b*e*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + 2*b^2*(16*d^3 + 24*d^2*e*x + 6*d*e^2*x^2 - e^3*x^3)) - 7*c^2*e*(4*a*e*(-16*d^3 - 24*d^2*e*x - 6*d*e^2*x^2 + e^3*x^3) + b*(128*d^4 + 192*d^3*e*x + 48*d^2*e^2*x^2 - 8*d*e^3*x^3 + 3*e^4*x^4))))/(21*e^6*(d + e*x)^(3/2))","A",1
1607,1,600,427,0.6155565,"\int (b+2 c x) (d+e x)^{5/2} \left(a+b x+c x^2\right)^3 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^(5/2)*(a + b*x + c*x^2)^3,x]","\frac{2 (d+e x)^{7/2} \left(-57 c^2 e^2 \left(102 a^2 e^2 \left(16 d^3-56 d^2 e x+126 d e^2 x^2-231 e^3 x^3\right)-17 a b e \left(128 d^4-448 d^3 e x+1008 d^2 e^2 x^2-1848 d e^3 x^3+3003 e^4 x^4\right)+3 b^2 \left(256 d^5-896 d^4 e x+2016 d^3 e^2 x^2-3696 d^2 e^3 x^3+6006 d e^4 x^4-9009 e^5 x^5\right)\right)+323 c e^3 \left(286 a^3 e^3 (7 e x-2 d)+117 a^2 b e^2 \left(8 d^2-28 d e x+63 e^2 x^2\right)+36 a b^2 e \left(-16 d^3+56 d^2 e x-126 d e^2 x^2+231 e^3 x^3\right)+b^3 \left(128 d^4-448 d^3 e x+1008 d^2 e^2 x^2-1848 d e^3 x^3+3003 e^4 x^4\right)\right)+969 b e^4 \left(429 a^3 e^3+143 a^2 b e^2 (7 e x-2 d)+13 a b^2 e \left(8 d^2-28 d e x+63 e^2 x^2\right)+b^3 \left(-16 d^3+56 d^2 e x-126 d e^2 x^2+231 e^3 x^3\right)\right)+3 c^3 e \left(38 a e \left(-256 d^5+896 d^4 e x-2016 d^3 e^2 x^2+3696 d^2 e^3 x^3-6006 d e^4 x^4+9009 e^5 x^5\right)+7 b \left(1024 d^6-3584 d^5 e x+8064 d^4 e^2 x^2-14784 d^3 e^3 x^3+24024 d^2 e^4 x^4-36036 d e^5 x^5+51051 e^6 x^6\right)\right)-2 c^4 \left(2048 d^7-7168 d^6 e x+16128 d^5 e^2 x^2-29568 d^4 e^3 x^3+48048 d^3 e^4 x^4-72072 d^2 e^5 x^5+102102 d e^6 x^6-138567 e^7 x^7\right)\right)}{2909907 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*(d + e*x)^(7/2)*(-2*c^4*(2048*d^7 - 7168*d^6*e*x + 16128*d^5*e^2*x^2 - 29568*d^4*e^3*x^3 + 48048*d^3*e^4*x^4 - 72072*d^2*e^5*x^5 + 102102*d*e^6*x^6 - 138567*e^7*x^7) + 969*b*e^4*(429*a^3*e^3 + 143*a^2*b*e^2*(-2*d + 7*e*x) + 13*a*b^2*e*(8*d^2 - 28*d*e*x + 63*e^2*x^2) + b^3*(-16*d^3 + 56*d^2*e*x - 126*d*e^2*x^2 + 231*e^3*x^3)) + 323*c*e^3*(286*a^3*e^3*(-2*d + 7*e*x) + 117*a^2*b*e^2*(8*d^2 - 28*d*e*x + 63*e^2*x^2) + 36*a*b^2*e*(-16*d^3 + 56*d^2*e*x - 126*d*e^2*x^2 + 231*e^3*x^3) + b^3*(128*d^4 - 448*d^3*e*x + 1008*d^2*e^2*x^2 - 1848*d*e^3*x^3 + 3003*e^4*x^4)) - 57*c^2*e^2*(102*a^2*e^2*(16*d^3 - 56*d^2*e*x + 126*d*e^2*x^2 - 231*e^3*x^3) - 17*a*b*e*(128*d^4 - 448*d^3*e*x + 1008*d^2*e^2*x^2 - 1848*d*e^3*x^3 + 3003*e^4*x^4) + 3*b^2*(256*d^5 - 896*d^4*e*x + 2016*d^3*e^2*x^2 - 3696*d^2*e^3*x^3 + 6006*d*e^4*x^4 - 9009*e^5*x^5)) + 3*c^3*e*(38*a*e*(-256*d^5 + 896*d^4*e*x - 2016*d^3*e^2*x^2 + 3696*d^2*e^3*x^3 - 6006*d*e^4*x^4 + 9009*e^5*x^5) + 7*b*(1024*d^6 - 3584*d^5*e*x + 8064*d^4*e^2*x^2 - 14784*d^3*e^3*x^3 + 24024*d^2*e^4*x^4 - 36036*d*e^5*x^5 + 51051*e^6*x^6))))/(2909907*e^8)","A",1
1608,1,600,427,0.6162509,"\int (b+2 c x) (d+e x)^{3/2} \left(a+b x+c x^2\right)^3 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^(3/2)*(a + b*x + c*x^2)^3,x]","\frac{2 (d+e x)^{5/2} \left(-969 c^2 e^2 \left(26 a^2 e^2 \left(16 d^3-40 d^2 e x+70 d e^2 x^2-105 e^3 x^3\right)-5 a b e \left(128 d^4-320 d^3 e x+560 d^2 e^2 x^2-840 d e^3 x^3+1155 e^4 x^4\right)+b^2 \left(256 d^5-640 d^4 e x+1120 d^3 e^2 x^2-1680 d^2 e^3 x^3+2310 d e^4 x^4-3003 e^5 x^5\right)\right)+323 c e^3 \left(858 a^3 e^3 (5 e x-2 d)+429 a^2 b e^2 \left(8 d^2-20 d e x+35 e^2 x^2\right)+156 a b^2 e \left(-16 d^3+40 d^2 e x-70 d e^2 x^2+105 e^3 x^3\right)+5 b^3 \left(128 d^4-320 d^3 e x+560 d^2 e^2 x^2-840 d e^3 x^3+1155 e^4 x^4\right)\right)+4199 b e^4 \left(231 a^3 e^3+99 a^2 b e^2 (5 e x-2 d)+11 a b^2 e \left(8 d^2-20 d e x+35 e^2 x^2\right)+b^3 \left(-16 d^3+40 d^2 e x-70 d e^2 x^2+105 e^3 x^3\right)\right)+19 c^3 e \left(34 a e \left(-256 d^5+640 d^4 e x-1120 d^3 e^2 x^2+1680 d^2 e^3 x^3-2310 d e^4 x^4+3003 e^5 x^5\right)+7 b \left(1024 d^6-2560 d^5 e x+4480 d^4 e^2 x^2-6720 d^3 e^3 x^3+9240 d^2 e^4 x^4-12012 d e^5 x^5+15015 e^6 x^6\right)\right)-14 c^4 \left(2048 d^7-5120 d^6 e x+8960 d^5 e^2 x^2-13440 d^4 e^3 x^3+18480 d^3 e^4 x^4-24024 d^2 e^5 x^5+30030 d e^6 x^6-36465 e^7 x^7\right)\right)}{4849845 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*(d + e*x)^(5/2)*(-14*c^4*(2048*d^7 - 5120*d^6*e*x + 8960*d^5*e^2*x^2 - 13440*d^4*e^3*x^3 + 18480*d^3*e^4*x^4 - 24024*d^2*e^5*x^5 + 30030*d*e^6*x^6 - 36465*e^7*x^7) + 4199*b*e^4*(231*a^3*e^3 + 99*a^2*b*e^2*(-2*d + 5*e*x) + 11*a*b^2*e*(8*d^2 - 20*d*e*x + 35*e^2*x^2) + b^3*(-16*d^3 + 40*d^2*e*x - 70*d*e^2*x^2 + 105*e^3*x^3)) + 323*c*e^3*(858*a^3*e^3*(-2*d + 5*e*x) + 429*a^2*b*e^2*(8*d^2 - 20*d*e*x + 35*e^2*x^2) + 156*a*b^2*e*(-16*d^3 + 40*d^2*e*x - 70*d*e^2*x^2 + 105*e^3*x^3) + 5*b^3*(128*d^4 - 320*d^3*e*x + 560*d^2*e^2*x^2 - 840*d*e^3*x^3 + 1155*e^4*x^4)) - 969*c^2*e^2*(26*a^2*e^2*(16*d^3 - 40*d^2*e*x + 70*d*e^2*x^2 - 105*e^3*x^3) - 5*a*b*e*(128*d^4 - 320*d^3*e*x + 560*d^2*e^2*x^2 - 840*d*e^3*x^3 + 1155*e^4*x^4) + b^2*(256*d^5 - 640*d^4*e*x + 1120*d^3*e^2*x^2 - 1680*d^2*e^3*x^3 + 2310*d*e^4*x^4 - 3003*e^5*x^5)) + 19*c^3*e*(34*a*e*(-256*d^5 + 640*d^4*e*x - 1120*d^3*e^2*x^2 + 1680*d^2*e^3*x^3 - 2310*d*e^4*x^4 + 3003*e^5*x^5) + 7*b*(1024*d^6 - 2560*d^5*e*x + 4480*d^4*e^2*x^2 - 6720*d^3*e^3*x^3 + 9240*d^2*e^4*x^4 - 12012*d*e^5*x^5 + 15015*e^6*x^6))))/(4849845*e^8)","A",1
1609,1,601,427,0.6015913,"\int (b+2 c x) \sqrt{d+e x} \left(a+b x+c x^2\right)^3 \, dx","Integrate[(b + 2*c*x)*Sqrt[d + e*x]*(a + b*x + c*x^2)^3,x]","\frac{2 (d+e x)^{3/2} \left(-51 c^2 e^2 \left(286 a^2 e^2 \left(16 d^3-24 d^2 e x+30 d e^2 x^2-35 e^3 x^3\right)-65 a b e \left(128 d^4-192 d^3 e x+240 d^2 e^2 x^2-280 d e^3 x^3+315 e^4 x^4\right)+15 b^2 \left(256 d^5-384 d^4 e x+480 d^3 e^2 x^2-560 d^2 e^3 x^3+630 d e^4 x^4-693 e^5 x^5\right)\right)+221 c e^3 \left(462 a^3 e^3 (3 e x-2 d)+297 a^2 b e^2 \left(8 d^2-12 d e x+15 e^2 x^2\right)+132 a b^2 e \left(-16 d^3+24 d^2 e x-30 d e^2 x^2+35 e^3 x^3\right)+5 b^3 \left(128 d^4-192 d^3 e x+240 d^2 e^2 x^2-280 d e^3 x^3+315 e^4 x^4\right)\right)+2431 b e^4 \left(105 a^3 e^3+63 a^2 b e^2 (3 e x-2 d)+9 a b^2 e \left(8 d^2-12 d e x+15 e^2 x^2\right)+b^3 \left(-16 d^3+24 d^2 e x-30 d e^2 x^2+35 e^3 x^3\right)\right)+17 c^3 e \left(30 a e \left(-256 d^5+384 d^4 e x-480 d^3 e^2 x^2+560 d^2 e^3 x^3-630 d e^4 x^4+693 e^5 x^5\right)+7 b \left(1024 d^6-1536 d^5 e x+1920 d^4 e^2 x^2-2240 d^3 e^3 x^3+2520 d^2 e^4 x^4-2772 d e^5 x^5+3003 e^6 x^6\right)\right)-14 c^4 \left(2048 d^7-3072 d^6 e x+3840 d^5 e^2 x^2-4480 d^4 e^3 x^3+5040 d^3 e^4 x^4-5544 d^2 e^5 x^5+6006 d e^6 x^6-6435 e^7 x^7\right)\right)}{765765 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*(d + e*x)^(3/2)*(-14*c^4*(2048*d^7 - 3072*d^6*e*x + 3840*d^5*e^2*x^2 - 4480*d^4*e^3*x^3 + 5040*d^3*e^4*x^4 - 5544*d^2*e^5*x^5 + 6006*d*e^6*x^6 - 6435*e^7*x^7) + 2431*b*e^4*(105*a^3*e^3 + 63*a^2*b*e^2*(-2*d + 3*e*x) + 9*a*b^2*e*(8*d^2 - 12*d*e*x + 15*e^2*x^2) + b^3*(-16*d^3 + 24*d^2*e*x - 30*d*e^2*x^2 + 35*e^3*x^3)) + 221*c*e^3*(462*a^3*e^3*(-2*d + 3*e*x) + 297*a^2*b*e^2*(8*d^2 - 12*d*e*x + 15*e^2*x^2) + 132*a*b^2*e*(-16*d^3 + 24*d^2*e*x - 30*d*e^2*x^2 + 35*e^3*x^3) + 5*b^3*(128*d^4 - 192*d^3*e*x + 240*d^2*e^2*x^2 - 280*d*e^3*x^3 + 315*e^4*x^4)) - 51*c^2*e^2*(286*a^2*e^2*(16*d^3 - 24*d^2*e*x + 30*d*e^2*x^2 - 35*e^3*x^3) - 65*a*b*e*(128*d^4 - 192*d^3*e*x + 240*d^2*e^2*x^2 - 280*d*e^3*x^3 + 315*e^4*x^4) + 15*b^2*(256*d^5 - 384*d^4*e*x + 480*d^3*e^2*x^2 - 560*d^2*e^3*x^3 + 630*d*e^4*x^4 - 693*e^5*x^5)) + 17*c^3*e*(30*a*e*(-256*d^5 + 384*d^4*e*x - 480*d^3*e^2*x^2 + 560*d^2*e^3*x^3 - 630*d*e^4*x^4 + 693*e^5*x^5) + 7*b*(1024*d^6 - 1536*d^5*e*x + 1920*d^4*e^2*x^2 - 2240*d^3*e^3*x^3 + 2520*d^2*e^4*x^4 - 2772*d*e^5*x^5 + 3003*e^6*x^6))))/(765765*e^8)","A",1
1610,1,599,425,0.6177234,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{\sqrt{d+e x}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^3)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-39 c^2 e^2 \left(198 a^2 e^2 \left(16 d^3-8 d^2 e x+6 d e^2 x^2-5 e^3 x^3\right)-55 a b e \left(128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right)+15 b^2 \left(256 d^5-128 d^4 e x+96 d^3 e^2 x^2-80 d^2 e^3 x^3+70 d e^4 x^4-63 e^5 x^5\right)\right)+143 c e^3 \left(210 a^3 e^3 (e x-2 d)+189 a^2 b e^2 \left(8 d^2-4 d e x+3 e^2 x^2\right)+108 a b^2 e \left(-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right)+5 b^3 \left(128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right)\right)+1287 b e^4 \left(35 a^3 e^3+35 a^2 b e^2 (e x-2 d)+7 a b^2 e \left(8 d^2-4 d e x+3 e^2 x^2\right)+b^3 \left(-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right)\right)+15 c^3 e \left(26 a e \left(-256 d^5+128 d^4 e x-96 d^3 e^2 x^2+80 d^2 e^3 x^3-70 d e^4 x^4+63 e^5 x^5\right)+7 b \left(1024 d^6-512 d^5 e x+384 d^4 e^2 x^2-320 d^3 e^3 x^3+280 d^2 e^4 x^4-252 d e^5 x^5+231 e^6 x^6\right)\right)-14 c^4 \left(2048 d^7-1024 d^6 e x+768 d^5 e^2 x^2-640 d^4 e^3 x^3+560 d^3 e^4 x^4-504 d^2 e^5 x^5+462 d e^6 x^6-429 e^7 x^7\right)\right)}{45045 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*Sqrt[d + e*x]*(-14*c^4*(2048*d^7 - 1024*d^6*e*x + 768*d^5*e^2*x^2 - 640*d^4*e^3*x^3 + 560*d^3*e^4*x^4 - 504*d^2*e^5*x^5 + 462*d*e^6*x^6 - 429*e^7*x^7) + 1287*b*e^4*(35*a^3*e^3 + 35*a^2*b*e^2*(-2*d + e*x) + 7*a*b^2*e*(8*d^2 - 4*d*e*x + 3*e^2*x^2) + b^3*(-16*d^3 + 8*d^2*e*x - 6*d*e^2*x^2 + 5*e^3*x^3)) + 143*c*e^3*(210*a^3*e^3*(-2*d + e*x) + 189*a^2*b*e^2*(8*d^2 - 4*d*e*x + 3*e^2*x^2) + 108*a*b^2*e*(-16*d^3 + 8*d^2*e*x - 6*d*e^2*x^2 + 5*e^3*x^3) + 5*b^3*(128*d^4 - 64*d^3*e*x + 48*d^2*e^2*x^2 - 40*d*e^3*x^3 + 35*e^4*x^4)) - 39*c^2*e^2*(198*a^2*e^2*(16*d^3 - 8*d^2*e*x + 6*d*e^2*x^2 - 5*e^3*x^3) - 55*a*b*e*(128*d^4 - 64*d^3*e*x + 48*d^2*e^2*x^2 - 40*d*e^3*x^3 + 35*e^4*x^4) + 15*b^2*(256*d^5 - 128*d^4*e*x + 96*d^3*e^2*x^2 - 80*d^2*e^3*x^3 + 70*d*e^4*x^4 - 63*e^5*x^5)) + 15*c^3*e*(26*a*e*(-256*d^5 + 128*d^4*e*x - 96*d^3*e^2*x^2 + 80*d^2*e^3*x^3 - 70*d*e^4*x^4 + 63*e^5*x^5) + 7*b*(1024*d^6 - 512*d^5*e*x + 384*d^4*e^2*x^2 - 320*d^3*e^3*x^3 + 280*d^2*e^4*x^4 - 252*d*e^5*x^5 + 231*e^6*x^6))))/(45045*e^8)","A",1
1611,1,594,421,0.5396631,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^{3/2}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^(3/2),x]","\frac{2 \left(429 c^2 e^2 \left(42 a^2 e^2 \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)+15 a b e \left(-128 d^4-64 d^3 e x+16 d^2 e^2 x^2-8 d e^3 x^3+5 e^4 x^4\right)+5 b^2 \left(256 d^5+128 d^4 e x-32 d^3 e^2 x^2+16 d^2 e^3 x^3-10 d e^4 x^4+7 e^5 x^5\right)\right)+429 c e^3 \left(70 a^3 e^3 (2 d+e x)+105 a^2 b e^2 \left(-8 d^2-4 d e x+e^2 x^2\right)+84 a b^2 e \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)-5 b^3 \left(128 d^4+64 d^3 e x-16 d^2 e^2 x^2+8 d e^3 x^3-5 e^4 x^4\right)\right)+3003 b e^4 \left(-5 a^3 e^3+15 a^2 b e^2 (2 d+e x)+5 a b^2 e \left(-8 d^2-4 d e x+e^2 x^2\right)+b^3 \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)\right)-65 c^3 e \left(7 b \left(1024 d^6+512 d^5 e x-128 d^4 e^2 x^2+64 d^3 e^3 x^3-40 d^2 e^4 x^4+28 d e^5 x^5-21 e^6 x^6\right)-22 a e \left(256 d^5+128 d^4 e x-32 d^3 e^2 x^2+16 d^2 e^3 x^3-10 d e^4 x^4+7 e^5 x^5\right)\right)+70 c^4 \left(2048 d^7+1024 d^6 e x-256 d^5 e^2 x^2+128 d^4 e^3 x^3-80 d^3 e^4 x^4+56 d^2 e^5 x^5-42 d e^6 x^6+33 e^7 x^7\right)\right)}{15015 e^8 \sqrt{d+e 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}",1,"(2*(70*c^4*(2048*d^7 + 1024*d^6*e*x - 256*d^5*e^2*x^2 + 128*d^4*e^3*x^3 - 80*d^3*e^4*x^4 + 56*d^2*e^5*x^5 - 42*d*e^6*x^6 + 33*e^7*x^7) + 3003*b*e^4*(-5*a^3*e^3 + 15*a^2*b*e^2*(2*d + e*x) + 5*a*b^2*e*(-8*d^2 - 4*d*e*x + e^2*x^2) + b^3*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3)) + 429*c*e^3*(70*a^3*e^3*(2*d + e*x) + 105*a^2*b*e^2*(-8*d^2 - 4*d*e*x + e^2*x^2) + 84*a*b^2*e*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) - 5*b^3*(128*d^4 + 64*d^3*e*x - 16*d^2*e^2*x^2 + 8*d*e^3*x^3 - 5*e^4*x^4)) + 429*c^2*e^2*(42*a^2*e^2*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) + 15*a*b*e*(-128*d^4 - 64*d^3*e*x + 16*d^2*e^2*x^2 - 8*d*e^3*x^3 + 5*e^4*x^4) + 5*b^2*(256*d^5 + 128*d^4*e*x - 32*d^3*e^2*x^2 + 16*d^2*e^3*x^3 - 10*d*e^4*x^4 + 7*e^5*x^5)) - 65*c^3*e*(-22*a*e*(256*d^5 + 128*d^4*e*x - 32*d^3*e^2*x^2 + 16*d^2*e^3*x^3 - 10*d*e^4*x^4 + 7*e^5*x^5) + 7*b*(1024*d^6 + 512*d^5*e*x - 128*d^4*e^2*x^2 + 64*d^3*e^3*x^3 - 40*d^2*e^4*x^4 + 28*d*e^5*x^5 - 21*e^6*x^6))))/(15015*e^8*Sqrt[d + e*x])","A",1
1612,1,598,421,0.5927408,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^(5/2),x]","\frac{-198 c^2 e^2 \left(14 a^2 e^2 \left(16 d^3+24 d^2 e x+6 d e^2 x^2-e^3 x^3\right)-7 a b e \left(128 d^4+192 d^3 e x+48 d^2 e^2 x^2-8 d e^3 x^3+3 e^4 x^4\right)+3 b^2 \left(256 d^5+384 d^4 e x+96 d^3 e^2 x^2-16 d^2 e^3 x^3+6 d e^4 x^4-3 e^5 x^5\right)\right)+462 c e^3 \left(-2 a^3 e^3 (2 d+3 e x)+9 a^2 b e^2 \left(8 d^2+12 d e x+3 e^2 x^2\right)+12 a b^2 e \left(-16 d^3-24 d^2 e x-6 d e^2 x^2+e^3 x^3\right)+b^3 \left(128 d^4+192 d^3 e x+48 d^2 e^2 x^2-8 d e^3 x^3+3 e^4 x^4\right)\right)-462 b e^4 \left(a^3 e^3+3 a^2 b e^2 (2 d+3 e x)-3 a b^2 e \left(8 d^2+12 d e x+3 e^2 x^2\right)+b^3 \left(16 d^3+24 d^2 e x+6 d e^2 x^2-e^3 x^3\right)\right)+22 c^3 e \left(7 b \left(1024 d^6+1536 d^5 e x+384 d^4 e^2 x^2-64 d^3 e^3 x^3+24 d^2 e^4 x^4-12 d e^5 x^5+7 e^6 x^6\right)-18 a e \left(256 d^5+384 d^4 e x+96 d^3 e^2 x^2-16 d^2 e^3 x^3+6 d e^4 x^4-3 e^5 x^5\right)\right)-28 c^4 \left(2048 d^7+3072 d^6 e x+768 d^5 e^2 x^2-128 d^4 e^3 x^3+48 d^3 e^4 x^4-24 d^2 e^5 x^5+14 d e^6 x^6-9 e^7 x^7\right)}{693 e^8 (d+e x)^{3/2}}","\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,"(-28*c^4*(2048*d^7 + 3072*d^6*e*x + 768*d^5*e^2*x^2 - 128*d^4*e^3*x^3 + 48*d^3*e^4*x^4 - 24*d^2*e^5*x^5 + 14*d*e^6*x^6 - 9*e^7*x^7) - 462*b*e^4*(a^3*e^3 + 3*a^2*b*e^2*(2*d + 3*e*x) - 3*a*b^2*e*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + b^3*(16*d^3 + 24*d^2*e*x + 6*d*e^2*x^2 - e^3*x^3)) + 462*c*e^3*(-2*a^3*e^3*(2*d + 3*e*x) + 9*a^2*b*e^2*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + 12*a*b^2*e*(-16*d^3 - 24*d^2*e*x - 6*d*e^2*x^2 + e^3*x^3) + b^3*(128*d^4 + 192*d^3*e*x + 48*d^2*e^2*x^2 - 8*d*e^3*x^3 + 3*e^4*x^4)) - 198*c^2*e^2*(14*a^2*e^2*(16*d^3 + 24*d^2*e*x + 6*d*e^2*x^2 - e^3*x^3) - 7*a*b*e*(128*d^4 + 192*d^3*e*x + 48*d^2*e^2*x^2 - 8*d*e^3*x^3 + 3*e^4*x^4) + 3*b^2*(256*d^5 + 384*d^4*e*x + 96*d^3*e^2*x^2 - 16*d^2*e^3*x^3 + 6*d*e^4*x^4 - 3*e^5*x^5)) + 22*c^3*e*(-18*a*e*(256*d^5 + 384*d^4*e*x + 96*d^3*e^2*x^2 - 16*d^2*e^3*x^3 + 6*d*e^4*x^4 - 3*e^5*x^5) + 7*b*(1024*d^6 + 1536*d^5*e*x + 384*d^4*e^2*x^2 - 64*d^3*e^3*x^3 + 24*d^2*e^4*x^4 - 12*d*e^5*x^5 + 7*e^6*x^6)))/(693*e^8*(d + e*x)^(3/2))","A",1
1613,1,782,422,2.4218548,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{a+b x+c x^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2),x]","\frac{\frac{(b e-2 c d) \left(\frac{\sqrt{2} \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{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)}{\sqrt{b^2-4 a c} \sqrt{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}}+\frac{\sqrt{2} \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{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+2 \sqrt{c} e \sqrt{d+e x}\right)}{c^{3/2}}-\frac{2 \sqrt{2} \left(3 c^2 d e \left(d \sqrt{b^2-4 a c}-2 a e-b d\right)+c e^2 \left(-3 b d \sqrt{b^2-4 a c}-a e \sqrt{b^2-4 a c}+3 a b e+3 b^2 d\right)+b^2 e^3 \left(\sqrt{b^2-4 a c}-b\right)+2 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}}+\frac{2 \sqrt{2} \left(-3 c^2 d e \left(d \sqrt{b^2-4 a c}+2 a e+b d\right)+c e^2 \left(3 b \left(d \sqrt{b^2-4 a c}+a e\right)+a e \sqrt{b^2-4 a c}+3 b^2 d\right)-b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+2 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)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{4 e \sqrt{d+e x} (b e-2 c d)}{c}+\frac{4}{3} e (d+e x)^{3/2}}{e}","\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,"((-4*e*(-2*c*d + b*e)*Sqrt[d + e*x])/c + (4*e*(d + e*x)^(3/2))/3 - (2*Sqrt[2]*(2*c^3*d^3 + b^2*(-b + Sqrt[b^2 - 4*a*c])*e^3 + 3*c^2*d*e*(-(b*d) + Sqrt[b^2 - 4*a*c]*d - 2*a*e) + c*e^2*(3*b^2*d - 3*b*Sqrt[b^2 - 4*a*c]*d + 3*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*e + 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]) + (2*Sqrt[2]*(2*c^3*d^3 - b^2*(b + Sqrt[b^2 - 4*a*c])*e^3 - 3*c^2*d*e*(b*d + Sqrt[b^2 - 4*a*c]*d + 2*a*e) + c*e^2*(3*b^2*d + a*Sqrt[b^2 - 4*a*c]*e + 3*b*(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]])/(c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]) + ((-2*c*d + b*e)*(2*Sqrt[c]*e*Sqrt[d + e*x] + (Sqrt[2]*(-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*e + 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]*(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[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])))/c^(3/2))/e","A",1
1614,1,288,291,0.3482196,"\int \frac{(b+2 c x) \sqrt{d+e x}}{a+b x+c x^2} \, dx","Integrate[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(c \left(4 a e-2 d \sqrt{b^2-4 a c}\right)+b e \left(\sqrt{b^2-4 a c}-b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)}{\sqrt{c} \sqrt{b^2-4 a c} \sqrt{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}}+\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 + c*(-2*Sqrt[b^2 - 4*a*c]*d + 4*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + 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",1
1615,1,165,175,0.6306816,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)} \, dx","Integrate[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)),x]","2 \sqrt{2} \sqrt{c} \left(-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)}{\sqrt{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}}-\frac{\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)}}\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*e + Sqrt[b^2 - 4*a*c]*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*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",1
1616,1,317,354,0.4983884,"\int \frac{b+2 c x}{(d+e x)^{3/2} \left(a+b x+c x^2\right)} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^(3/2)*(a + b*x + c*x^2)),x]","\frac{2 \left(\frac{\sqrt{c} \left(2 c \left(d \sqrt{b^2-4 a c}+2 a e\right)-b e \left(\sqrt{b^2-4 a c}+b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}}+\frac{\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{2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{b e-2 c d}{\sqrt{d+e x}}\right)}{e (b d-a e)-c d^2}","\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)/Sqrt[d + e*x] + (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*e + 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]) + (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[2]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])))/(-(c*d^2) + e*(b*d - a*e))","A",1
1617,1,481,518,1.6736068,"\int \frac{b+2 c x}{(d+e x)^{5/2} \left(a+b x+c x^2\right)} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x]","\frac{2 \left(\frac{-6 c e (a e+b d)+3 b^2 e^2+6 c^2 d^2}{\sqrt{d+e x} \left(e (a e-b d)+c d^2\right)}-\frac{3 \sqrt{c} \left(-\frac{\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{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)}{\sqrt{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}}-\frac{\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)}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \left(e (b d-a e)-c d^2\right)}+\frac{2 c d-b e}{(d+e x)^{3/2}}\right)}{3 \left(e (a e-b d)+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)/(d + e*x)^(3/2) + (6*c^2*d^2 + 3*b^2*e^2 - 6*c*e*(b*d + a*e))/((c*d^2 + e*(-(b*d) + a*e))*Sqrt[d + e*x]) - (3*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*e + Sqrt[b^2 - 4*a*c]*e]])/Sqrt[2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e]) - ((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[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]))/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*(-(c*d^2) + e*(b*d - a*e)))))/(3*(c*d^2 + e*(-(b*d) + a*e)))","A",1
1618,1,297,350,1.8360383,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^2,x]","-\frac{5 e \left(-4 \sqrt{c} e \sqrt{b^2-4 a c} \sqrt{d+e x}+\sqrt{2} \left(e \left(\sqrt{b^2-4 a c}-b\right)+2 c d\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)-\sqrt{2} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)^{3/2} \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)\right)}{4 c^{3/2} \sqrt{b^2-4 a c}}-\frac{e^2 (d+e x)^{5/2}}{e (a e-b d)+c d^2}+\frac{(d+e x)^{7/2} (b e-c d+c e x)}{(a+x (b+c x)) \left(e (a e-b d)+c d^2\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(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,"-((e^2*(d + e*x)^(5/2))/(c*d^2 + e*(-(b*d) + a*e))) + ((d + e*x)^(7/2)*(-(c*d) + b*e + c*e*x))/((c*d^2 + e*(-(b*d) + a*e))*(a + x*(b + c*x))) - (5*e*(-4*Sqrt[c]*Sqrt[b^2 - 4*a*c]*e*Sqrt[d + e*x] + Sqrt[2]*(2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]] - Sqrt[2]*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]]))/(4*c^(3/2)*Sqrt[b^2 - 4*a*c])","A",1
1619,1,221,224,0.4175355,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^2,x]","-\frac{3 e \sqrt{e \sqrt{b^2-4 a c}-b e+2 c d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{e \sqrt{b^2-4 a c}-b e+2 c d}}\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+x (b+c 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}",1,"-((d + e*x)^(3/2)/(a + x*(b + c*x))) - (3*e*Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + 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",1
1620,1,221,223,0.7548069,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^2,x]","\frac{-\frac{\sqrt{b^2-4 a c} \sqrt{d+e x}}{a+x (b+c x)}-\frac{\sqrt{2} \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)}{\sqrt{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}}+\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{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}{\sqrt{b^2-4 a c}}","-\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[b^2 - 4*a*c]*Sqrt[d + e*x])/(a + x*(b + c*x))) - (Sqrt[2]*Sqrt[c]*e*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]])/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[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])/Sqrt[b^2 - 4*a*c]","A",1
1621,1,278,364,1.2109101,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^2} \, dx","Integrate[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^2),x]","\frac{\frac{\sqrt{2} \sqrt{c} e \left(\frac{\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{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)}{\sqrt{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}}-\frac{\left(e \left(\sqrt{b^2-4 a c}-b\right)+2 c d\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 d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c}}+\frac{2 \sqrt{d+e x} (b e-c d+c e x)}{a+x (b+c x)}}{2 \left(e (a e-b d)+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,"((2*Sqrt[d + e*x]*(-(c*d) + b*e + c*e*x))/(a + x*(b + c*x)) + (Sqrt[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*e + Sqrt[b^2 - 4*a*c]*e]])/Sqrt[2*c*d + (-b + Sqrt[b^2 - 4*a*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*c*d - (b + Sqrt[b^2 - 4*a*c])*e]))/Sqrt[b^2 - 4*a*c])/(2*(c*d^2 + e*(-(b*d) + a*e)))","A",1
1622,1,381,469,2.6332006,"\int \frac{b+2 c x}{(d+e x)^{3/2} \left(a+b x+c x^2\right)^2} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^(3/2)*(a + b*x + c*x^2)^2),x]","\frac{\frac{3 \sqrt{2} \sqrt{c} e \left(\frac{\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{e \sqrt{b^2-4 a c}-b e+2 c d}}\right)}{\sqrt{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}}-\frac{\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 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c}}+\frac{2 \left(e (a e-b d)+c d^2\right) (b e-c d+c e x)}{\sqrt{d+e x} (a+x (b+c x))}-\frac{6 e^2 (b e-2 c d)}{\sqrt{d+e x}}}{2 \left(e (a e-b d)+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,"((-6*e^2*(-2*c*d + b*e))/Sqrt[d + e*x] + (2*(c*d^2 + e*(-(b*d) + a*e))*(-(c*d) + b*e + c*e*x))/(Sqrt[d + e*x]*(a + x*(b + c*x))) + (3*Sqrt[2]*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*e + Sqrt[b^2 - 4*a*c]*e]])/Sqrt[2*c*d + (-b + Sqrt[b^2 - 4*a*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*c*d - (b + Sqrt[b^2 - 4*a*c])*e]))/Sqrt[b^2 - 4*a*c])/(2*(c*d^2 + e*(-(b*d) + a*e))^2)","A",1
1623,1,1403,543,6.7459251,"\int \frac{(b+2 c x) (d+e x)^{7/2}}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(7/2))/(a + b*x + c*x^2)^3,x]","-\frac{\left(-2 a c (2 c d-b e)+b \left(-e b^2+c d b+2 a c e\right)+c (b (2 c d-b e)-2 c (b d-2 a e)) x\right) (d+e x)^{9/2}}{2 \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)^2}-\frac{-\frac{\left(-\frac{3}{2} a c \left(b^2-4 a c\right) (2 c d-b e) e^2-\frac{1}{2} \left(b^2-4 a c\right) (7 c d-5 b e) \left(-e b^2+c d b+2 a c e\right) e+c \left(-\frac{3}{2} c \left(b^2-4 a c\right) (b d-2 a e) e^2-\frac{1}{2} \left(b^2-4 a c\right) (7 c d-5 b e) (2 c d-b e) e\right) x\right) (d+e x)^{9/2}}{\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)}-\frac{\frac{1}{2} \left(b^2-4 a c\right) e^2 \left(14 c^2 d^2+5 b^2 e^2-2 c e (7 b d+3 a e)\right) (d+e x)^{7/2}+\frac{2 \left(\frac{49}{4} c \left(b^2-4 a c\right) e^2 (2 c d-b e) \left(c d^2-e (b d-a e)\right) (d+e x)^{5/2}+\frac{2 \left(\frac{245}{4} c^2 \left(b^2-4 a c\right) e^2 (d+e x)^{3/2} \left(c d^2-e (b d-a e)\right)^2+\frac{2 \left(\frac{735}{16} c^2 \left(b^2-4 a c\right) e^2 (2 c d-b e) \sqrt{d+e x} \left(c d^2-e (b d-a e)\right)^2+\frac{4 \left(\frac{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e} \left(-\frac{735}{64} \left(b^2-4 a c\right) e^2 \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) \left(c d^2-e (b d-a e)\right)^2 c^3-\frac{\frac{735}{64} \left(b^2-4 a c\right) e^2 (b e-2 c d) \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) \left(c d^2-e (b d-a e)\right)^2 c^3+2 \left(\frac{735}{64} c^3 \left(b^2-4 a c\right) d e^2 \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) \left(c d^2-e (b d-a e)\right)^2-\frac{735}{64} c^3 \left(b^2-4 a c\right) e^2 \left(4 c^2 d^3-c e (5 b d-8 a e) d-a b e^3\right) \left(c d^2-e (b d-a e)\right)^2\right) c}{\sqrt{b^2-4 a c} e}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e+\sqrt{b^2-4 a c} e\right)}+\frac{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e} \left(\frac{\frac{735}{64} \left(b^2-4 a c\right) e^2 (b e-2 c d) \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) \left(c d^2-e (b d-a e)\right)^2 c^3+2 \left(\frac{735}{64} c^3 \left(b^2-4 a c\right) d e^2 \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) \left(c d^2-e (b d-a e)\right)^2-\frac{735}{64} c^3 \left(b^2-4 a c\right) e^2 \left(4 c^2 d^3-c e (5 b d-8 a e) d-a b e^3\right) \left(c d^2-e (b d-a e)\right)^2\right) c}{\sqrt{b^2-4 a c} e}-\frac{735}{64} c^3 \left(b^2-4 a c\right) e^2 \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) \left(c d^2-e (b d-a e)\right)^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e-\sqrt{b^2-4 a c} e\right)}\right)}{c}\right)}{3 c}\right)}{5 c}\right)}{7 c}}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)}}{2 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\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(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,"-1/2*((d + e*x)^(9/2)*(-2*a*c*(2*c*d - b*e) + b*(b*c*d - b^2*e + 2*a*c*e) + c*(-2*c*(b*d - 2*a*e) + b*(2*c*d - b*e))*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (-(((d + e*x)^(9/2)*((-3*a*c*(b^2 - 4*a*c)*e^2*(2*c*d - b*e))/2 - ((b^2 - 4*a*c)*e*(7*c*d - 5*b*e)*(b*c*d - b^2*e + 2*a*c*e))/2 + c*((-3*c*(b^2 - 4*a*c)*e^2*(b*d - 2*a*e))/2 - ((b^2 - 4*a*c)*e*(7*c*d - 5*b*e)*(2*c*d - b*e))/2)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) - (((b^2 - 4*a*c)*e^2*(14*c^2*d^2 + 5*b^2*e^2 - 2*c*e*(7*b*d + 3*a*e))*(d + e*x)^(7/2))/2 + (2*((49*c*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))*(d + e*x)^(5/2))/4 + (2*((245*c^2*(b^2 - 4*a*c)*e^2*(c*d^2 - e*(b*d - a*e))^2*(d + e*x)^(3/2))/4 + (2*((735*c^2*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))^2*Sqrt[d + e*x])/16 + (4*((Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]*((-735*c^3*(b^2 - 4*a*c)*e^2*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*(c*d^2 - e*(b*d - a*e))^2)/64 - ((735*c^3*(b^2 - 4*a*c)*e^2*(-2*c*d + b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*(c*d^2 - e*(b*d - a*e))^2)/64 + 2*c*((-735*c^3*(b^2 - 4*a*c)*e^2*(4*c^2*d^3 - a*b*e^3 - c*d*e*(5*b*d - 8*a*e))*(c*d^2 - e*(b*d - a*e))^2)/64 + (735*c^3*(b^2 - 4*a*c)*d*e^2*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*(c*d^2 - e*(b*d - a*e))^2)/64))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e + Sqrt[b^2 - 4*a*c]*e)) + (Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]*((-735*c^3*(b^2 - 4*a*c)*e^2*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*(c*d^2 - e*(b*d - a*e))^2)/64 + ((735*c^3*(b^2 - 4*a*c)*e^2*(-2*c*d + b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*(c*d^2 - e*(b*d - a*e))^2)/64 + 2*c*((-735*c^3*(b^2 - 4*a*c)*e^2*(4*c^2*d^3 - a*b*e^3 - c*d*e*(5*b*d - 8*a*e))*(c*d^2 - e*(b*d - a*e))^2)/64 + (735*c^3*(b^2 - 4*a*c)*d*e^2*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*(c*d^2 - e*(b*d - a*e))^2)/64))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e))))/c))/(3*c)))/(5*c)))/(7*c))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2))","B",1
1624,1,1197,398,6.5862233,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^3,x]","-\frac{\left(-2 a c (2 c d-b e)+b \left(-e b^2+c d b+2 a c e\right)+c (b (2 c d-b e)-2 c (b d-2 a e)) x\right) (d+e x)^{7/2}}{2 \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)^2}-\frac{-\frac{\left(-\frac{1}{2} a c \left(b^2-4 a c\right) (2 c d-b e) e^2-\frac{1}{2} \left(b^2-4 a c\right) (5 c d-3 b e) \left(-e b^2+c d b+2 a c e\right) e+c \left(-\frac{1}{2} c \left(b^2-4 a c\right) (b d-2 a e) e^2-\frac{1}{2} \left(b^2-4 a c\right) (5 c d-3 b e) (2 c d-b e) e\right) x\right) (d+e x)^{7/2}}{\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)}-\frac{\frac{1}{2} \left(b^2-4 a c\right) e^2 \left(10 c^2 d^2+3 b^2 e^2-2 c e (5 b d+a e)\right) (d+e x)^{5/2}+\frac{2 \left(\frac{25}{4} c \left(b^2-4 a c\right) (2 c d-b e) \left(c d^2-e (b d-a e)\right) (d+e x)^{3/2} e^2+\frac{2 \left(\frac{75}{4} c^2 \left(b^2-4 a c\right) e^2 \sqrt{d+e x} \left(c d^2-e (b d-a e)\right)^2+\frac{4 \left(\frac{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e} \left(-\frac{75}{32} \left(b^2-4 a c\right) e^2 (2 c d-b e) \left(c d^2-e (b d-a e)\right)^2 c^3-\frac{\frac{75}{32} \left(b^2-4 a c\right) e^2 (2 c d-b e) (b e-2 c d) \left(c d^2-e (b d-a e)\right)^2 c^3+2 \left(\frac{75}{32} c^3 \left(b^2-4 a c\right) d e^2 (2 c d-b e) \left(c d^2-e (b d-a e)\right)^2-\frac{75}{32} c^3 \left(b^2-4 a c\right) e^2 \left(4 c d^2-e (3 b d-2 a e)\right) \left(c d^2-e (b d-a e)\right)^2\right) c}{\sqrt{b^2-4 a c} e}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e+\sqrt{b^2-4 a c} e\right)}+\frac{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e} \left(\frac{\frac{75}{32} \left(b^2-4 a c\right) e^2 (2 c d-b e) (b e-2 c d) \left(c d^2-e (b d-a e)\right)^2 c^3+2 \left(\frac{75}{32} c^3 \left(b^2-4 a c\right) d e^2 (2 c d-b e) \left(c d^2-e (b d-a e)\right)^2-\frac{75}{32} c^3 \left(b^2-4 a c\right) e^2 \left(4 c d^2-e (3 b d-2 a e)\right) \left(c d^2-e (b d-a e)\right)^2\right) c}{\sqrt{b^2-4 a c} e}-\frac{75}{32} c^3 \left(b^2-4 a c\right) e^2 (2 c d-b e) \left(c d^2-e (b d-a e)\right)^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e-\sqrt{b^2-4 a c} e\right)}\right)}{c}\right)}{3 c}\right)}{5 c}}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)}}{2 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\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(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,"-1/2*((d + e*x)^(7/2)*(-2*a*c*(2*c*d - b*e) + b*(b*c*d - b^2*e + 2*a*c*e) + c*(-2*c*(b*d - 2*a*e) + b*(2*c*d - b*e))*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (-(((d + e*x)^(7/2)*(-1/2*(a*c*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)) - ((b^2 - 4*a*c)*e*(5*c*d - 3*b*e)*(b*c*d - b^2*e + 2*a*c*e))/2 + c*(-1/2*(c*(b^2 - 4*a*c)*e^2*(b*d - 2*a*e)) - ((b^2 - 4*a*c)*e*(5*c*d - 3*b*e)*(2*c*d - b*e))/2)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) - (((b^2 - 4*a*c)*e^2*(10*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(5*b*d + a*e))*(d + e*x)^(5/2))/2 + (2*((25*c*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))*(d + e*x)^(3/2))/4 + (2*((75*c^2*(b^2 - 4*a*c)*e^2*(c*d^2 - e*(b*d - a*e))^2*Sqrt[d + e*x])/4 + (4*((Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]*((-75*c^3*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))^2)/32 - ((75*c^3*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(-2*c*d + b*e)*(c*d^2 - e*(b*d - a*e))^2)/32 + 2*c*((75*c^3*(b^2 - 4*a*c)*d*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))^2)/32 - (75*c^3*(b^2 - 4*a*c)*e^2*(4*c*d^2 - e*(3*b*d - 2*a*e))*(c*d^2 - e*(b*d - a*e))^2)/32))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e + Sqrt[b^2 - 4*a*c]*e)) + (Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]*((-75*c^3*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))^2)/32 + ((75*c^3*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(-2*c*d + b*e)*(c*d^2 - e*(b*d - a*e))^2)/32 + 2*c*((75*c^3*(b^2 - 4*a*c)*d*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))^2)/32 - (75*c^3*(b^2 - 4*a*c)*e^2*(4*c*d^2 - e*(3*b*d - 2*a*e))*(c*d^2 - e*(b*d - a*e))^2)/32))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e))))/c))/(3*c)))/(5*c))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2))","B",1
1625,1,1069,322,6.4614752,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^3,x]","-\frac{\left(-2 a c (2 c d-b e)+b \left(-e b^2+c d b+2 a c e\right)+c (b (2 c d-b e)-2 c (b d-2 a e)) x\right) (d+e x)^{5/2}}{2 \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)^2}-\frac{-\frac{\left(\frac{1}{2} a c \left(b^2-4 a c\right) (2 c d-b e) e^2-\frac{1}{2} \left(b^2-4 a c\right) (3 c d-b e) \left(-e b^2+c d b+2 a c e\right) e+c \left(\frac{1}{2} c \left(b^2-4 a c\right) e^2 (b d-2 a e)-\frac{1}{2} \left(b^2-4 a c\right) e (2 c d-b e) (3 c d-b e)\right) x\right) (d+e x)^{5/2}}{\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)}-\frac{\frac{1}{2} \left(b^2-4 a c\right) \left(6 c^2 d^2+b^2 e^2-2 c e (3 b d-a e)\right) (d+e x)^{3/2} e^2+\frac{2 \left(\frac{9}{4} c \left(b^2-4 a c\right) (2 c d-b e) \left(c d^2-e (b d-a e)\right) \sqrt{d+e x} e^2+\frac{4 \left(\frac{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e} \left(-\frac{9}{8} \left(b^2-4 a c\right) e^2 \left(c d^2-e (b d-a e)\right)^2 c^3-\frac{\frac{9}{8} \left(b^2-4 a c\right) e^2 (b e-2 c d) \left(c d^2-e (b d-a e)\right)^2 c^3+2 \left(\frac{9}{8} c^3 \left(b^2-4 a c\right) d e^2 \left(c d^2-e (b d-a e)\right)^2-\frac{9}{16} c^2 \left(b^2-4 a c\right) e^2 (4 c d-b e) \left(c d^2-e (b d-a e)\right)^2\right) c}{\sqrt{b^2-4 a c} e}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e+\sqrt{b^2-4 a c} e\right)}+\frac{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e} \left(\frac{\frac{9}{8} \left(b^2-4 a c\right) e^2 (b e-2 c d) \left(c d^2-e (b d-a e)\right)^2 c^3+2 \left(\frac{9}{8} c^3 \left(b^2-4 a c\right) d e^2 \left(c d^2-e (b d-a e)\right)^2-\frac{9}{16} c^2 \left(b^2-4 a c\right) e^2 (4 c d-b e) \left(c d^2-e (b d-a e)\right)^2\right) c}{\sqrt{b^2-4 a c} e}-\frac{9}{8} c^3 \left(b^2-4 a c\right) e^2 \left(c d^2-e (b d-a e)\right)^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e-\sqrt{b^2-4 a c} e\right)}\right)}{c}\right)}{3 c}}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)}}{2 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)}","-\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,"-1/2*((d + e*x)^(5/2)*(-2*a*c*(2*c*d - b*e) + b*(b*c*d - b^2*e + 2*a*c*e) + c*(-2*c*(b*d - 2*a*e) + b*(2*c*d - b*e))*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (-(((d + e*x)^(5/2)*((a*c*(b^2 - 4*a*c)*e^2*(2*c*d - b*e))/2 - ((b^2 - 4*a*c)*e*(3*c*d - b*e)*(b*c*d - b^2*e + 2*a*c*e))/2 + c*((c*(b^2 - 4*a*c)*e^2*(b*d - 2*a*e))/2 - ((b^2 - 4*a*c)*e*(2*c*d - b*e)*(3*c*d - b*e))/2)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) - (((b^2 - 4*a*c)*e^2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(3/2))/2 + (2*((9*c*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))*Sqrt[d + e*x])/4 + (4*((Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]*((-9*c^3*(b^2 - 4*a*c)*e^2*(c*d^2 - e*(b*d - a*e))^2)/8 - ((9*c^3*(b^2 - 4*a*c)*e^2*(-2*c*d + b*e)*(c*d^2 - e*(b*d - a*e))^2)/8 + 2*c*((9*c^3*(b^2 - 4*a*c)*d*e^2*(c*d^2 - e*(b*d - a*e))^2)/8 - (9*c^2*(b^2 - 4*a*c)*e^2*(4*c*d - b*e)*(c*d^2 - e*(b*d - a*e))^2)/16))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e + Sqrt[b^2 - 4*a*c]*e)) + (Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]*((-9*c^3*(b^2 - 4*a*c)*e^2*(c*d^2 - e*(b*d - a*e))^2)/8 + ((9*c^3*(b^2 - 4*a*c)*e^2*(-2*c*d + b*e)*(c*d^2 - e*(b*d - a*e))^2)/8 + 2*c*((9*c^3*(b^2 - 4*a*c)*d*e^2*(c*d^2 - e*(b*d - a*e))^2)/8 - (9*c^2*(b^2 - 4*a*c)*e^2*(4*c*d - b*e)*(c*d^2 - e*(b*d - a*e))^2)/16))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e))))/c))/(3*c))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2))","B",1
1626,1,1080,463,6.4118599,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^3,x]","-\frac{\left(-2 a c (2 c d-b e)+b \left(-e b^2+c d b+2 a c e\right)+c (b (2 c d-b e)-2 c (b d-2 a e)) x\right) (d+e x)^{3/2}}{2 \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)^2}-\frac{-\frac{\left(\frac{3}{2} a c \left(b^2-4 a c\right) (2 c d-b e) e^2-\frac{1}{2} \left(b^2-4 a c\right) (c d+b e) \left(-e b^2+c d b+2 a c e\right) e+c \left(\frac{3}{2} c \left(b^2-4 a c\right) e^2 (b d-2 a e)-\frac{1}{2} \left(b^2-4 a c\right) e (2 c d-b e) (c d+b e)\right) x\right) (d+e x)^{3/2}}{\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)}-\frac{\frac{1}{2} \left(b^2-4 a c\right) \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) \sqrt{d+e x} e^2+\frac{4 \left(\frac{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e} \left(-\frac{1}{8} c^2 \left(b^2-4 a c\right) (2 c d-b e) \left(c d^2-e (b d-a e)\right) e^2-\frac{\frac{1}{8} c^2 \left(b^2-4 a c\right) (2 c d-b e) (b e-2 c d) \left(c d^2-e (b d-a e)\right) e^2+2 c \left(\frac{1}{8} c^2 \left(b^2-4 a c\right) d e^2 (2 c d-b e) \left(c d^2-e (b d-a e)\right)-\frac{1}{8} c \left(b^2-4 a c\right) e^2 \left(c d^2-b e d+a e^2\right) \left(4 c^2 d^2-3 b c e d-b^2 e^2+6 a c e^2\right)\right)}{\sqrt{b^2-4 a c} e}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e+\sqrt{b^2-4 a c} e\right)}+\frac{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e} \left(\frac{\frac{1}{8} c^2 \left(b^2-4 a c\right) (2 c d-b e) (b e-2 c d) \left(c d^2-e (b d-a e)\right) e^2+2 c \left(\frac{1}{8} c^2 \left(b^2-4 a c\right) d e^2 (2 c d-b e) \left(c d^2-e (b d-a e)\right)-\frac{1}{8} c \left(b^2-4 a c\right) e^2 \left(c d^2-b e d+a e^2\right) \left(4 c^2 d^2-3 b c e d-b^2 e^2+6 a c e^2\right)\right)}{\sqrt{b^2-4 a c} e}-\frac{1}{8} c^2 \left(b^2-4 a c\right) e^2 (2 c d-b e) \left(c d^2-e (b d-a e)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e-\sqrt{b^2-4 a c} e\right)}\right)}{c}}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)}}{2 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^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(\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,"-1/2*((d + e*x)^(3/2)*(-2*a*c*(2*c*d - b*e) + b*(b*c*d - b^2*e + 2*a*c*e) + c*(-2*c*(b*d - 2*a*e) + b*(2*c*d - b*e))*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (-(((d + e*x)^(3/2)*((3*a*c*(b^2 - 4*a*c)*e^2*(2*c*d - b*e))/2 - ((b^2 - 4*a*c)*e*(c*d + b*e)*(b*c*d - b^2*e + 2*a*c*e))/2 + c*((3*c*(b^2 - 4*a*c)*e^2*(b*d - 2*a*e))/2 - ((b^2 - 4*a*c)*e*(2*c*d - b*e)*(c*d + b*e))/2)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) - (((b^2 - 4*a*c)*e^2*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*Sqrt[d + e*x])/2 + (4*((Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]*(-1/8*(c^2*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))) - ((c^2*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(-2*c*d + b*e)*(c*d^2 - e*(b*d - a*e)))/8 + 2*c*(-1/8*(c*(b^2 - 4*a*c)*e^2*(c*d^2 - b*d*e + a*e^2)*(4*c^2*d^2 - 3*b*c*d*e - b^2*e^2 + 6*a*c*e^2)) + (c^2*(b^2 - 4*a*c)*d*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e)))/8))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e + Sqrt[b^2 - 4*a*c]*e)) + (Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]*(-1/8*(c^2*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))) + ((c^2*(b^2 - 4*a*c)*e^2*(2*c*d - b*e)*(-2*c*d + b*e)*(c*d^2 - e*(b*d - a*e)))/8 + 2*c*(-1/8*(c*(b^2 - 4*a*c)*e^2*(c*d^2 - b*d*e + a*e^2)*(4*c^2*d^2 - 3*b*c*d*e - b^2*e^2 + 6*a*c*e^2)) + (c^2*(b^2 - 4*a*c)*d*e^2*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e)))/8))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e))))/c)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2))","B",1
1627,1,1033,673,6.2004805,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^3} \, dx","Integrate[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^3),x]","-\frac{\sqrt{d+e x} \left(-2 a c (2 c d-b e)+b \left(-e b^2+c d b+2 a c e\right)+c (b (2 c d-b e)-2 c (b d-2 a e)) x\right)}{2 \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)^2}-\frac{-\frac{\sqrt{d+e x} \left(\frac{5}{2} a c \left(b^2-4 a c\right) (2 c d-b e) e^2+\frac{1}{2} \left(b^2-4 a c\right) (c d-3 b e) \left(-e b^2+c d b+2 a c e\right) e+c \left(\frac{5}{2} c \left(b^2-4 a c\right) (b d-2 a e) e^2+\frac{1}{2} \left(b^2-4 a c\right) (c d-3 b e) (2 c d-b e) e\right) x\right)}{\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)}-\frac{2 \left(\frac{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e} \left(\frac{1}{4} c \left(b^2-4 a c\right) e^2 \left(2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right)-\frac{2 c \left(\frac{1}{4} \left(b^2-4 a c\right) e^2 \left(4 c^3 d^3-c^2 e (5 b d-16 a e) d+3 b^3 e^3-b c e^2 (2 b d+13 a e)\right)-\frac{1}{4} c \left(b^2-4 a c\right) d e^2 \left(2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right)\right)-\frac{1}{4} c \left(b^2-4 a c\right) e^2 (b e-2 c d) \left(2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right)}{\sqrt{b^2-4 a c} e}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e-\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e+\sqrt{b^2-4 a c} e\right)}+\frac{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e} \left(\frac{1}{4} c \left(b^2-4 a c\right) \left(2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right) e^2+\frac{2 c \left(\frac{1}{4} \left(b^2-4 a c\right) e^2 \left(4 c^3 d^3-c^2 e (5 b d-16 a e) d+3 b^3 e^3-b c e^2 (2 b d+13 a e)\right)-\frac{1}{4} c \left(b^2-4 a c\right) d e^2 \left(2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right)\right)-\frac{1}{4} c \left(b^2-4 a c\right) e^2 (b e-2 c d) \left(2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right)}{\sqrt{b^2-4 a c} e}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-b e+\sqrt{b^2-4 a c} e}}\right)}{\sqrt{2} \sqrt{c} \left(-2 c d+b e-\sqrt{b^2-4 a c} e\right)}\right)}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)}}{2 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^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,"-1/2*(Sqrt[d + e*x]*(-2*a*c*(2*c*d - b*e) + b*(b*c*d - b^2*e + 2*a*c*e) + c*(-2*c*(b*d - 2*a*e) + b*(2*c*d - b*e))*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (-((Sqrt[d + e*x]*((5*a*c*(b^2 - 4*a*c)*e^2*(2*c*d - b*e))/2 + ((b^2 - 4*a*c)*e*(c*d - 3*b*e)*(b*c*d - b^2*e + 2*a*c*e))/2 + c*((5*c*(b^2 - 4*a*c)*e^2*(b*d - 2*a*e))/2 + ((b^2 - 4*a*c)*e*(c*d - 3*b*e)*(2*c*d - b*e))/2)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) - (2*((Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]*((c*(b^2 - 4*a*c)*e^2*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e)))/4 - (-1/4*(c*(b^2 - 4*a*c)*e^2*(-2*c*d + b*e)*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))) + 2*c*(-1/4*(c*(b^2 - 4*a*c)*d*e^2*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))) + ((b^2 - 4*a*c)*e^2*(4*c^3*d^3 + 3*b^3*e^3 - c^2*d*e*(5*b*d - 16*a*e) - b*c*e^2*(2*b*d + 13*a*e)))/4))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e + Sqrt[b^2 - 4*a*c]*e)) + (Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]*((c*(b^2 - 4*a*c)*e^2*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e)))/4 + (-1/4*(c*(b^2 - 4*a*c)*e^2*(-2*c*d + b*e)*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))) + 2*c*(-1/4*(c*(b^2 - 4*a*c)*d*e^2*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))) + ((b^2 - 4*a*c)*e^2*(4*c^3*d^3 + 3*b^3*e^3 - c^2*d*e*(5*b*d - 16*a*e) - b*c*e^2*(2*b*d + 13*a*e)))/4))/(Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]])/(Sqrt[2]*Sqrt[c]*(-2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e))))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2))","A",1
1628,1,833,576,12.578292,"\int (b+2 c x) \sqrt{d+e x} \sqrt{a+b x+c x^2} \, dx","Integrate[(b + 2*c*x)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2],x]","\frac{\frac{4 (2 c d-b e) \left(4 c^2 d^2-b^2 e^2+4 c e (2 a e-b d)\right) (a+x (b+c x)) e^2}{\sqrt{d+e x}}-2 c \sqrt{d+e x} (a+x (b+c x)) \left(\left(8 d^2-6 e x d-30 e^2 x^2\right) c^2-e (11 b d+20 a e+27 b e x) c+b^2 e^2\right) e^2-\frac{i (d+e x) \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{4 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+2} \left((b e-2 c d) \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(-4 c^2 d^2+b^2 e^2+4 c e (b d-2 a e)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(b^4 e^4-b^3 \left(\sqrt{\left(b^2-4 a c\right) e^2}-c d\right) e^3-b^2 c \left(c d^2+2 \sqrt{\left(b^2-4 a c\right) e^2} d+9 a e^2\right) e^2+4 b c \left(3 c \sqrt{\left(b^2-4 a c\right) e^2} d^2+a e^2 \left(2 \sqrt{\left(b^2-4 a c\right) e^2}-c d\right)\right) e+4 c^2 \left(5 a^2 e^4+a d \left(c d-4 \sqrt{\left(b^2-4 a c\right) e^2}\right) e^2-2 c d^3 \sqrt{\left(b^2-4 a c\right) e^2}\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{\sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}}{105 c^2 e^4 \sqrt{a+x (b+c 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}",1,"((4*e^2*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 + 4*c*e*(-(b*d) + 2*a*e))*(a + x*(b + c*x)))/Sqrt[d + e*x] - 2*c*e^2*Sqrt[d + e*x]*(a + x*(b + c*x))*(b^2*e^2 - c*e*(11*b*d + 20*a*e + 27*b*e*x) + c^2*(8*d^2 - 6*d*e*x - 30*e^2*x^2)) - (I*(d + e*x)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[2 + (4*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((-2*c*d + b*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(-4*c^2*d^2 + b^2*e^2 + 4*c*e*(b*d - 2*a*e))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (b^4*e^4 - b^3*e^3*(-(c*d) + Sqrt[(b^2 - 4*a*c)*e^2]) - b^2*c*e^2*(c*d^2 + 9*a*e^2 + 2*d*Sqrt[(b^2 - 4*a*c)*e^2]) + 4*c^2*(5*a^2*e^4 - 2*c*d^3*Sqrt[(b^2 - 4*a*c)*e^2] + a*d*e^2*(c*d - 4*Sqrt[(b^2 - 4*a*c)*e^2])) + 4*b*c*e*(3*c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] + a*e^2*(-(c*d) + 2*Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/(105*c^2*e^4*Sqrt[a + x*(b + c*x)])","C",1
1629,1,709,487,3.7277433,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{\sqrt{d+e x}} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/Sqrt[d + e*x],x]","\frac{\frac{4 e^2 (a+x (b+c x)) \left(4 c e (3 a e-4 b d)+b^2 e^2+16 c^2 d^2\right)}{c \sqrt{d+e x}}-\frac{i (d+e x) \sqrt{1-\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{4 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}+2} \left(\left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right) \left(4 c e (3 a e-4 b d)+b^2 e^2+16 c^2 d^2\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)-\left(4 c \left(4 c d^2 \sqrt{e^2 \left(b^2-4 a c\right)}+a e^2 \left(3 \sqrt{e^2 \left(b^2-4 a c\right)}-2 c d\right)\right)+b^2 e^2 \left(\sqrt{e^2 \left(b^2-4 a c\right)}+2 c d\right)+4 b \left(a c e^3-4 c d e \sqrt{e^2 \left(b^2-4 a c\right)}\right)-b^3 e^3\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{c \sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}+4 e^2 \sqrt{d+e x} (a+x (b+c x)) (7 b e-8 c d+6 c e x)}{30 e^4 \sqrt{a+x (b+c 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}",1,"((4*e^2*(16*c^2*d^2 + b^2*e^2 + 4*c*e*(-4*b*d + 3*a*e))*(a + x*(b + c*x)))/(c*Sqrt[d + e*x]) + 4*e^2*Sqrt[d + e*x]*(-8*c*d + 7*b*e + 6*c*e*x)*(a + x*(b + c*x)) - (I*(d + e*x)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[2 + (4*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(16*c^2*d^2 + b^2*e^2 + 4*c*e*(-4*b*d + 3*a*e))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] - (-(b^3*e^3) + b^2*e^2*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + 4*b*(a*c*e^3 - 4*c*d*e*Sqrt[(b^2 - 4*a*c)*e^2]) + 4*c*(4*c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] + a*e^2*(-2*c*d + 3*Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(c*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]))/(30*e^4*Sqrt[a + x*(b + c*x)])","C",1
1630,1,955,469,4.1977379,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^{3/2}} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^(3/2),x]","\frac{\sqrt{d+e x} \left(\frac{2 (8 c d-3 b e+2 c e x) (a+x (b+c x))}{e^2 (d+e x)}-\frac{(d+e x) \left(-\frac{16 (b e-2 c d) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} (a+x (b+c x)) e^2}{(d+e x)^2}-\frac{4 i \sqrt{2} (2 c d-b e) \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}+\frac{i \sqrt{2} \left(b^2 e^2-4 a c e^2-4 b \sqrt{\left(b^2-4 a c\right) e^2} e+8 c d \sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{e^4 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}\right)}{3 \sqrt{a+x (b+c 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,"(Sqrt[d + e*x]*((2*(8*c*d - 3*b*e + 2*c*e*x)*(a + x*(b + c*x)))/(e^2*(d + e*x)) - ((d + e*x)*((-16*e^2*(-2*c*d + b*e)*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x)))/(d + e*x)^2 - ((4*I)*Sqrt[2]*(2*c*d - b*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] + (I*Sqrt[2]*(b^2*e^2 - 4*a*c*e^2 + 8*c*d*Sqrt[(b^2 - 4*a*c)*e^2] - 4*b*e*Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/(e^4*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])))/(3*Sqrt[a + x*(b + c*x)])","C",1
1631,1,1343,548,6.3267451,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^{5/2}} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^(5/2),x]","\sqrt{d+e x} \sqrt{a+x (b+c x)} \left(-\frac{2 (b e-2 c d)}{3 e^2 (d+e x)^2}-\frac{2 \left(10 c^2 d^2-10 b c e d+b^2 e^2+6 a c e^2\right)}{3 e^2 \left(c d^2-b e d+a e^2\right) (d+e x)}\right)-\frac{(d+e x)^{3/2} \sqrt{a+x (b+c x)} \left(-4 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \left(16 d^2 \left(\frac{d}{d+e x}-1\right)^2 c^3+4 e \left(a e \left(\frac{7 d^2}{(d+e x)^2}-\frac{6 d}{d+e x}+3\right)-4 b d \left(\frac{2 d^2}{(d+e x)^2}-\frac{3 d}{d+e x}+1\right)\right) c^2+e^2 \left(\left(\frac{17 d^2}{(d+e x)^2}-\frac{18 d}{d+e x}+1\right) b^2-\frac{4 a e \left(\frac{7 d}{d+e x}-3\right) b}{d+e x}+\frac{12 a^2 e^2}{(d+e x)^2}\right) c+\frac{b^2 e^3 \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)+\frac{i \sqrt{2} \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(16 c^2 d^2+b^2 e^2+4 c e (3 a e-4 b d)\right) \sqrt{\frac{-\frac{2 a e^2}{d+e x}+b \left(\frac{2 d}{d+e x}-1\right) e-2 c d \left(\frac{d}{d+e x}-1\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{\frac{\frac{2 a e^2}{d+e x}+2 c d \left(\frac{d}{d+e x}-1\right)+b \left(e-\frac{2 d e}{d+e x}\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}-\frac{i \sqrt{2} \left(-b^3 e^3+b^2 \left(2 c d+\sqrt{\left(b^2-4 a c\right) e^2}\right) e^2+4 b \left(a c e^3-4 c d e \sqrt{\left(b^2-4 a c\right) e^2}\right)+4 c \left(4 c \sqrt{\left(b^2-4 a c\right) e^2} d^2+a e^2 \left(3 \sqrt{\left(b^2-4 a c\right) e^2}-2 c d\right)\right)\right) \sqrt{\frac{-\frac{2 a e^2}{d+e x}+b \left(\frac{2 d}{d+e x}-1\right) e-2 c d \left(\frac{d}{d+e x}-1\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{\frac{\frac{2 a e^2}{d+e x}+2 c d \left(\frac{d}{d+e x}-1\right)+b \left(e-\frac{2 d e}{d+e x}\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{6 e^4 \left(c d^2-b e d+a e^2\right) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{c x^2+b x+a} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{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)}{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{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{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,"Sqrt[d + e*x]*Sqrt[a + x*(b + c*x)]*((-2*(-2*c*d + b*e))/(3*e^2*(d + e*x)^2) - (2*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2 + 6*a*c*e^2))/(3*e^2*(c*d^2 - b*d*e + a*e^2)*(d + e*x))) - ((d + e*x)^(3/2)*Sqrt[a + x*(b + c*x)]*(-4*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(16*c^3*d^2*(-1 + d/(d + e*x))^2 + (b^2*e^3*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x) + 4*c^2*e*(a*e*(3 + (7*d^2)/(d + e*x)^2 - (6*d)/(d + e*x)) - 4*b*d*(1 + (2*d^2)/(d + e*x)^2 - (3*d)/(d + e*x))) + c*e^2*((12*a^2*e^2)/(d + e*x)^2 + b^2*(1 + (17*d^2)/(d + e*x)^2 - (18*d)/(d + e*x)) - (4*a*b*e*(-3 + (7*d)/(d + e*x)))/(d + e*x))) + (I*Sqrt[2]*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(16*c^2*d^2 + b^2*e^2 + 4*c*e*(-4*b*d + 3*a*e))*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] - (2*a*e^2)/(d + e*x) - 2*c*d*(-1 + d/(d + e*x)) + b*e*(-1 + (2*d)/(d + e*x)))/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] + (2*a*e^2)/(d + e*x) + 2*c*d*(-1 + d/(d + e*x)) + b*(e - (2*d*e)/(d + e*x)))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] - (I*Sqrt[2]*(-(b^3*e^3) + b^2*e^2*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + 4*b*(a*c*e^3 - 4*c*d*e*Sqrt[(b^2 - 4*a*c)*e^2]) + 4*c*(4*c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] + a*e^2*(-2*c*d + 3*Sqrt[(b^2 - 4*a*c)*e^2])))*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] - (2*a*e^2)/(d + e*x) - 2*c*d*(-1 + d/(d + e*x)) + b*e*(-1 + (2*d)/(d + e*x)))/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] + (2*a*e^2)/(d + e*x) + 2*c*d*(-1 + d/(d + e*x)) + b*(e - (2*d*e)/(d + e*x)))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/(6*e^4*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[a + b*x + c*x^2]*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
1632,1,5427,691,6.5701532,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^{7/2}} \, dx","Integrate[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^(7/2),x]","\text{Result too large to show}","\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{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{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)}",1,"Result too large to show","C",1
1633,1,7917,688,6.5839309,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/Sqrt[d + e*x],x]","\text{Result too large to show}","\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{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} \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{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,"Result too large to show","C",0
1634,1,5373,592,6.7235186,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^(3/2),x]","\text{Result too large to show}","\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 \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{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,"Result too large to show","C",0
1635,1,8929,573,6.7812195,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^(5/2),x]","\text{Result too large to show}","-\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 \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 \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,"Result too large to show","C",0
1636,1,5450,701,6.9857276,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Integrate[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^(7/2),x]","\text{Result too large to show}","\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 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{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)}",1,"Result too large to show","C",0
1637,1,834,600,12.635177,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(5/2))/Sqrt[a + b*x + c*x^2],x]","\frac{4 c \sqrt{d+e x} \left(6 \left(3 d^2+3 e x d+e^2 x^2\right) c^2-e (9 b d+10 a e+3 b e x) c+4 b^2 e^2\right) (a+x (b+c x))+\frac{4 (2 c d-b e) \left(3 c^2 d^2+8 b^2 e^2-c e (3 b d+29 a e)\right) (a+x (b+c x))}{\sqrt{d+e x}}+\frac{i (d+e x) \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{4 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+2} \left((b e-2 c d) \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(3 c^2 d^2+8 b^2 e^2-c e (3 b d+29 a e)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(8 b^4 e^4-b^3 \left(27 c d+8 \sqrt{\left(b^2-4 a c\right) e^2}\right) e^3+b^2 c \left(27 c d^2+19 \sqrt{\left(b^2-4 a c\right) e^2} d-37 a e^2\right) e^2+b c \left(a e^2 \left(108 c d+29 \sqrt{\left(b^2-4 a c\right) e^2}\right)-9 c d^2 \sqrt{\left(b^2-4 a c\right) e^2}\right) e+2 c^2 \left(10 a^2 e^4-a d \left(54 c d+29 \sqrt{\left(b^2-4 a c\right) e^2}\right) e^2+3 c d^3 \sqrt{\left(b^2-4 a c\right) e^2}\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{e^2 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}}{42 c^3 \sqrt{a+x (b+c 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}",1,"((4*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*(a + x*(b + c*x)))/Sqrt[d + e*x] + 4*c*Sqrt[d + e*x]*(a + x*(b + c*x))*(4*b^2*e^2 - c*e*(9*b*d + 10*a*e + 3*b*e*x) + 6*c^2*(3*d^2 + 3*d*e*x + e^2*x^2)) + (I*(d + e*x)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[2 + (4*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((-2*c*d + b*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (8*b^4*e^4 - b^3*e^3*(27*c*d + 8*Sqrt[(b^2 - 4*a*c)*e^2]) + b^2*c*e^2*(27*c*d^2 - 37*a*e^2 + 19*d*Sqrt[(b^2 - 4*a*c)*e^2]) + 2*c^2*(10*a^2*e^4 + 3*c*d^3*Sqrt[(b^2 - 4*a*c)*e^2] - a*d*e^2*(54*c*d + 29*Sqrt[(b^2 - 4*a*c)*e^2])) + b*c*e*(-9*c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] + a*e^2*(108*c*d + 29*Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]))/(42*c^3*Sqrt[a + x*(b + c*x)])","C",1
1638,1,693,507,10.271742,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(3/2))/Sqrt[a + b*x + c*x^2],x]","\frac{\frac{4 (a+x (b+c x)) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\sqrt{d+e x}}-\frac{i (d+e x) \sqrt{1-\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{4 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}+2} \left(\left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(c \left(a e^2 \left(3 \sqrt{e^2 \left(b^2-4 a c\right)}+8 c d\right)-c d^2 \sqrt{e^2 \left(b^2-4 a c\right)}\right)-b^2 e^2 \left(\sqrt{e^2 \left(b^2-4 a c\right)}+2 c d\right)+b c e \left(d \sqrt{e^2 \left(b^2-4 a c\right)}-4 a e^2\right)+b^3 e^3\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{e^2 \sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}+2 c \sqrt{d+e x} (a+x (b+c x)) (-b e+4 c d+2 c e x)}{5 c^2 \sqrt{a+x (b+c 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}",1,"((4*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*(a + x*(b + c*x)))/Sqrt[d + e*x] + 2*c*Sqrt[d + e*x]*(4*c*d - b*e + 2*c*e*x)*(a + x*(b + c*x)) - (I*(d + e*x)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[2 + (4*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (b^3*e^3 - b^2*e^2*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + b*c*e*(-4*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2]) + c*(-(c*d^2*Sqrt[(b^2 - 4*a*c)*e^2]) + a*e^2*(8*c*d + 3*Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]))/(5*c^2*Sqrt[a + x*(b + c*x)])","C",1
1639,1,933,441,7.7261926,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((b + 2*c*x)*Sqrt[d + e*x])/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{d+e x} \left(8 (a+x (b+c x))+\frac{(d+e x) \left(-\frac{4 (b e-2 c d) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} (a+x (b+c x)) e^2}{(d+e x)^2}-\frac{i \sqrt{2} (2 c d-b e) \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}+\frac{i \sqrt{2} \left(b^2 e^2-4 a c e^2-b \sqrt{\left(b^2-4 a c\right) e^2} e+2 c d \sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{c e^2 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}\right)}{6 \sqrt{a+x (b+c 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}",1,"(Sqrt[d + e*x]*(8*(a + x*(b + c*x)) + ((d + e*x)*((-4*e^2*(-2*c*d + b*e)*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x)))/(d + e*x)^2 - (I*Sqrt[2]*(2*c*d - b*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] + (I*Sqrt[2]*(b^2*e^2 - 4*a*c*e^2 + 2*c*d*Sqrt[(b^2 - 4*a*c)*e^2] - b*e*Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/(c*e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])))/(6*Sqrt[a + x*(b + c*x)])","C",1
1640,1,793,391,1.9839564,"\int \frac{b+2 c x}{\sqrt{d+e x} \sqrt{a+b x+c x^2}} \, dx","Integrate[(b + 2*c*x)/(Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{(d+e x)^{3/2} \left(\frac{4 e^2 (a+x (b+c x)) \sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}{(d+e x)^2}+\frac{i \sqrt{2} \sqrt{e^2 \left(b^2-4 a c\right)} \sqrt{\frac{(d+e x) \sqrt{e^2 \left(b^2-4 a c\right)}-2 a e^2+b e (d-e x)+2 c d e x}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{(d+e x) \sqrt{e^2 \left(b^2-4 a c\right)}+2 a e^2+b e (e x-d)-2 c d e x}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}-\frac{i \sqrt{2} \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right) \sqrt{\frac{(d+e x) \sqrt{e^2 \left(b^2-4 a c\right)}-2 a e^2+b e (d-e x)+2 c d e x}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{(d+e x) \sqrt{e^2 \left(b^2-4 a c\right)}+2 a e^2+b e (e x-d)-2 c d e x}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{e^2 \sqrt{a+x (b+c x)} \sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}","\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,"((d + e*x)^(3/2)*((4*e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x)))/(d + e*x)^2 - (I*Sqrt[2]*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + 2*c*d*e*x + b*e*(d - e*x) + Sqrt[(b^2 - 4*a*c)*e^2]*(d + e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 - 2*c*d*e*x + b*e*(-d + e*x) + Sqrt[(b^2 - 4*a*c)*e^2]*(d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] + (I*Sqrt[2]*Sqrt[(b^2 - 4*a*c)*e^2]*Sqrt[(-2*a*e^2 + 2*c*d*e*x + b*e*(d - e*x) + Sqrt[(b^2 - 4*a*c)*e^2]*(d + e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 - 2*c*d*e*x + b*e*(-d + e*x) + Sqrt[(b^2 - 4*a*c)*e^2]*(d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/(e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[a + x*(b + c*x)])","C",1
1641,1,625,458,0.7436084,"\int \frac{b+2 c x}{(d+e x)^{3/2} \sqrt{a+b x+c x^2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{i (d+e x) \sqrt{\frac{d \sqrt{e^2 \left(b^2-4 a c\right)}+e x \sqrt{e^2 \left(b^2-4 a c\right)}-2 a e^2+b e (d-e x)+2 c d e x}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{d \sqrt{e^2 \left(b^2-4 a c\right)}+e x \sqrt{e^2 \left(b^2-4 a c\right)}+2 a e^2+b e (e x-d)-2 c d e x}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}} \left(\left(-2 c d \sqrt{e^2 \left(b^2-4 a c\right)}+b e \sqrt{e^2 \left(b^2-4 a c\right)}+4 a c e^2-b^2 e^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)-(b e-2 c d) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{\sqrt{2} e^2 \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right) \sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}","-\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,"(I*(d + e*x)*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*(-((-2*c*d + b*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]) + (-(b^2*e^2) + 4*a*c*e^2 - 2*c*d*Sqrt[(b^2 - 4*a*c)*e^2] + b*e*Sqrt[(b^2 - 4*a*c)*e^2])*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*e^2*(c*d^2 + e*(-(b*d) + a*e))*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[a + x*(b + c*x)])","C",1
1642,1,807,581,5.5134701,"\int \frac{b+2 c x}{(d+e x)^{5/2} \sqrt{a+b x+c x^2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^(5/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 (a+x (b+c x)) \left((2 c d-b e) \left(c d^2+e (a e-b d)\right)+2 \left(c^2 d^2+b^2 e^2-c e (b d+3 a e)\right) (d+e x)\right)-\frac{(d+e x) \left(4 e^2 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \left(c^2 d^2+b^2 e^2-c e (b d+3 a e)\right) (a+x (b+c x))-i (d+e x)^{3/2} \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{4 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+2} \left(\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(c^2 d^2+b^2 e^2-c e (b d+3 a e)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(b^3 e^3-b^2 \left(2 c d+\sqrt{\left(b^2-4 a c\right) e^2}\right) e^2+b c \left(d \sqrt{\left(b^2-4 a c\right) e^2}-4 a e^2\right) e+c \left(a e^2 \left(8 c d+3 \sqrt{\left(b^2-4 a c\right) e^2}\right)-c d^2 \sqrt{\left(b^2-4 a c\right) e^2}\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)\right)}{e^2 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}}{3 \left(c d^2+e (a e-b d)\right)^2 (d+e x)^{3/2} \sqrt{a+x (b+c 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)}",1,"(2*(a + x*(b + c*x))*((2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e)) + 2*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*(d + e*x)) - ((d + e*x)*(4*e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*(a + x*(b + c*x)) - I*(d + e*x)^(3/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[2 + (4*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (b^3*e^3 - b^2*e^2*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + b*c*e*(-4*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2]) + c*(-(c*d^2*Sqrt[(b^2 - 4*a*c)*e^2]) + a*e^2*(8*c*d + 3*Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])))/(e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]))/(3*(c*d^2 + e*(-(b*d) + a*e))^2*(d + e*x)^(3/2)*Sqrt[a + x*(b + c*x)])","C",1
1643,1,943,540,8.9284178,"\int \frac{(b+2 c x) (d+e x)^{7/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(7/2))/(a + b*x + c*x^2)^(3/2),x]","\frac{\sqrt{d+e x} \left(\frac{4 x e^3}{5 c}+\frac{2 (32 c d-13 b e) e^2}{15 c^2}-\frac{2 \left(c^2 d^3+3 c^2 e x d^2-3 a c e^2 d-3 b c e^2 x d+a b e^3+b^2 e^3 x-a c e^3 x\right)}{c^2 \left(c x^2+b x+a\right)}\right) \left(c x^2+b x+a\right)^2}{(a+x (b+c x))^{3/2}}+\frac{14 (d+e x)^{3/2} \left(\left(23 c^2 d^2+8 b^2 e^2-c e (23 b d+9 a e)\right) \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)-\frac{i \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+1} \left(\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(23 c^2 d^2+8 b^2 e^2-c e (23 b d+9 a e)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(-30 c^3 d^3-c^2 \left(-34 a e^2-45 b d e+23 d \sqrt{\left(b^2-4 a c\right) e^2}\right) d+8 b^2 e^2 \left(b e-\sqrt{\left(b^2-4 a c\right) e^2}\right)+c e \left(-31 d e b^2-17 a e^2 b+23 d \sqrt{\left(b^2-4 a c\right) e^2} b+9 a e \sqrt{\left(b^2-4 a c\right) e^2}\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{2 \sqrt{2} \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{d+e x}}\right) \left(c x^2+b x+a\right)^{3/2}}{15 c^3 (a+x (b+c x))^{3/2} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^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,"(Sqrt[d + e*x]*(a + b*x + c*x^2)^2*((2*e^2*(32*c*d - 13*b*e))/(15*c^2) + (4*e^3*x)/(5*c) - (2*(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + 3*c^2*d^2*e*x - 3*b*c*d*e^2*x + b^2*e^3*x - a*c*e^3*x))/(c^2*(a + b*x + c*x^2))))/(a + x*(b + c*x))^(3/2) + (14*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)*((23*c^2*d^2 + 8*b^2*e^2 - c*e*(23*b*d + 9*a*e))*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)) - ((I/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(23*c^2*d^2 + 8*b^2*e^2 - c*e*(23*b*d + 9*a*e))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (-30*c^3*d^3 + 8*b^2*e^2*(b*e - Sqrt[(b^2 - 4*a*c)*e^2]) - c^2*d*(-45*b*d*e - 34*a*e^2 + 23*d*Sqrt[(b^2 - 4*a*c)*e^2]) + c*e*(-31*b^2*d*e - 17*a*b*e^2 + 23*b*d*Sqrt[(b^2 - 4*a*c)*e^2] + 9*a*e*Sqrt[(b^2 - 4*a*c)*e^2]))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[d + e*x])))/(15*c^3*(a + x*(b + c*x))^(3/2)*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
1644,1,627,468,4.2239419,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^(3/2),x]","\frac{\sqrt{d+e x} \left(2 \left(\frac{e^2 (5 a+x (5 b+2 c x))}{c}-3 d^2-6 d e x\right)+\frac{10 (d+e x) \left(\frac{2 e^2 (a+x (b+c x)) (2 c d-b e)}{(d+e x)^2}+\frac{i \sqrt{1-\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}+1} \left(\left(c \left(2 d \sqrt{e^2 \left(b^2-4 a c\right)}-a e^2-3 b d e\right)+b e \left(b e-\sqrt{e^2 \left(b^2-4 a c\right)}\right)+3 c^2 d^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+(b e-2 c d) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{\sqrt{2} \sqrt{d+e x} \sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}\right)}{c^2}\right)}{3 \sqrt{a+x (b+c 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}}",1,"(Sqrt[d + e*x]*(2*(-3*d^2 - 6*d*e*x + (e^2*(5*a + x*(5*b + 2*c*x)))/c) + (10*(d + e*x)*((2*e^2*(2*c*d - b*e)*(a + x*(b + c*x)))/(d + e*x)^2 + (I*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((-2*c*d + b*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (3*c^2*d^2 + b*e*(b*e - Sqrt[(b^2 - 4*a*c)*e^2]) + c*(-3*b*d*e - a*e^2 + 2*d*Sqrt[(b^2 - 4*a*c)*e^2]))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[d + e*x])))/c^2))/(3*Sqrt[a + x*(b + c*x)])","C",1
1645,1,378,216,0.7796108,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^(3/2),x]","\frac{-4 (d+e x)^{3/2}+\frac{3 i \sqrt{2} \left(e \left(\sqrt{b^2-4 a c}-b\right)+2 c d\right) \sqrt{\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{e \left(\sqrt{b^2-4 a c}+b\right)-2 c d}} \sqrt{1-\frac{2 c (d+e x)}{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}} \left(E\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{c}{\left(b+\sqrt{b^2-4 a c}\right) e-2 c d}} \sqrt{d+e x}\right)|\frac{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}{2 c d+\left(\sqrt{b^2-4 a c}-b\right) e}\right)-F\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{c}{\left(b+\sqrt{b^2-4 a c}\right) e-2 c d}} \sqrt{d+e x}\right)|\frac{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}{2 c d+\left(\sqrt{b^2-4 a c}-b\right) e}\right)\right)}{c \sqrt{\frac{c}{e \left(\sqrt{b^2-4 a c}+b\right)-2 c d}}}}{2 \sqrt{a+x (b+c 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}}",1,"(-4*(d + e*x)^(3/2) + ((3*I)*Sqrt[2]*(2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e)*Sqrt[(e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e)]*(EllipticE[I*ArcSinh[Sqrt[2]*Sqrt[c/(-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[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)] - EllipticF[I*ArcSinh[Sqrt[2]*Sqrt[c/(-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[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)]))/(c*Sqrt[c/(-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)]))/(2*Sqrt[a + x*(b + c*x)])","C",1
1646,1,318,216,2.3004165,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^(3/2),x]","\frac{-2 \sqrt{d+e x}+\frac{i (d+e x) \sqrt{2-\frac{4 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}+1} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}}{\sqrt{a+x (b+c 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}}",1,"(-2*Sqrt[d + e*x] + (I*(d + e*x)*Sqrt[2 - (4*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[a + x*(b + c*x)]","C",1
1647,1,405,290,1.0976204,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2)),x]","\frac{4 \sqrt{d+e x} (b e-c d+c e x)-\frac{i \sqrt{2} \left(e \left(\sqrt{b^2-4 a c}-b\right)+2 c d\right) \sqrt{\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{e \left(\sqrt{b^2-4 a c}+b\right)-2 c d}} \sqrt{1-\frac{2 c (d+e x)}{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}} \left(E\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{c}{\left(b+\sqrt{b^2-4 a c}\right) e-2 c d}} \sqrt{d+e x}\right)|\frac{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}{2 c d+\left(\sqrt{b^2-4 a c}-b\right) e}\right)-F\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{c}{\left(b+\sqrt{b^2-4 a c}\right) e-2 c d}} \sqrt{d+e x}\right)|\frac{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}{2 c d+\left(\sqrt{b^2-4 a c}-b\right) e}\right)\right)}{\sqrt{\frac{c}{e \left(\sqrt{b^2-4 a c}+b\right)-2 c d}}}}{2 \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\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,"(4*Sqrt[d + e*x]*(-(c*d) + b*e + c*e*x) - (I*Sqrt[2]*(2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e)*Sqrt[(e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e)]*(EllipticE[I*ArcSinh[Sqrt[2]*Sqrt[c/(-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[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)] - EllipticF[I*ArcSinh[Sqrt[2]*Sqrt[c/(-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[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)]))/Sqrt[c/(-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)])/(2*(c*d^2 + e*(-(b*d) + a*e))*Sqrt[a + x*(b + c*x)])","C",1
1648,1,672,559,4.6021691,"\int \frac{b+2 c x}{(d+e x)^{3/2} \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(b + 2*c*x)/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)),x]","\frac{-\frac{i \sqrt{2} (d+e x)^{3/2} \sqrt{1-\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}+1} \left(\left(c \left(2 d \sqrt{e^2 \left(b^2-4 a c\right)}-a e^2-3 b d e\right)+b e \left(b e-\sqrt{e^2 \left(b^2-4 a c\right)}\right)+3 c^2 d^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+(b e-2 c d) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{\sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}+4 e^2 (a+x (b+c x)) (b e-2 c d)-2 a b e^3+2 a c e^2 (3 d+e x)-2 b^2 e^2 (d+2 e x)+2 b c e \left(2 d^2+3 d e x-2 e^2 x^2\right)+2 c^2 d \left(-d^2+d e x+4 e^2 x^2\right)}{\sqrt{d+e x} \sqrt{a+x (b+c x)} \left(e (a e-b d)+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*a*b*e^3 + 2*a*c*e^2*(3*d + e*x) - 2*b^2*e^2*(d + 2*e*x) + 2*b*c*e*(2*d^2 + 3*d*e*x - 2*e^2*x^2) + 2*c^2*d*(-d^2 + d*e*x + 4*e^2*x^2) + 4*e^2*(-2*c*d + b*e)*(a + x*(b + c*x)) - (I*Sqrt[2]*(d + e*x)^(3/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((-2*c*d + b*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (3*c^2*d^2 + b*e*(b*e - Sqrt[(b^2 - 4*a*c)*e^2]) + c*(-3*b*d*e - a*e^2 + 2*d*Sqrt[(b^2 - 4*a*c)*e^2]))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/((c*d^2 + e*(-(b*d) + a*e))^2*Sqrt[d + e*x]*Sqrt[a + x*(b + c*x)])","C",1
1649,1,1454,573,13.4273616,"\int \frac{(b+2 c x) (d+e x)^{7/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(7/2))/(a + b*x + c*x^2)^(5/2),x]","\frac{\sqrt{d+e x} \left(c x^2+b x+a\right)^3 \left(\frac{2 \left(14 d^2 e x c^3-40 a d e^2 c^2+7 b d^2 e c^2-18 a e^3 x c^2-14 b d e^2 x c^2+11 a b e^3 c+3 b^2 d e^2 c+8 b^2 e^3 x c-b^3 e^3\right)}{3 c^2 \left(4 a c-b^2\right) \left(c x^2+b x+a\right)}-\frac{2 \left(c^2 d^3+3 c^2 e x d^2-3 a c e^2 d-3 b c e^2 x d+a b e^3+b^2 e^3 x-a c e^3 x\right)}{3 c^2 \left(c x^2+b x+a\right)^2}\right)}{(a+x (b+c x))^{5/2}}-\frac{7 (d+e x)^{3/2} \left(c x^2+b x+a\right)^{5/2} \left(4 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \left(d^2 \left(\frac{d}{d+e x}-1\right)^2 c^3-e \left(a e \left(\frac{2 d^2}{(d+e x)^2}-\frac{6 d}{d+e x}+3\right)+b d \left(\frac{2 d^2}{(d+e x)^2}-\frac{3 d}{d+e x}+1\right)\right) c^2+e^2 \left(\left(\frac{2 d^2}{(d+e x)^2}-\frac{3 d}{d+e x}+1\right) b^2+\frac{a e \left(\frac{2 d}{d+e x}-3\right) b}{d+e x}-\frac{3 a^2 e^2}{(d+e x)^2}\right) c+\frac{b^2 e^3 \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)-\frac{i \sqrt{2} \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(c^2 d^2+b^2 e^2-c e (b d+3 a e)\right) \sqrt{\frac{-\frac{2 a e^2}{d+e x}+b \left(\frac{2 d}{d+e x}-1\right) e-2 c d \left(\frac{d}{d+e x}-1\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{\frac{\frac{2 a e^2}{d+e x}+2 c d \left(\frac{d}{d+e x}-1\right)+b \left(e-\frac{2 d e}{d+e x}\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}+\frac{i \sqrt{2} \left(-b^3 e^3+b^2 \left(2 c d+\sqrt{\left(b^2-4 a c\right) e^2}\right) e^2+b c \left(4 a e^2-d \sqrt{\left(b^2-4 a c\right) e^2}\right) e+c \left(c d^2 \sqrt{\left(b^2-4 a c\right) e^2}-a e^2 \left(8 c d+3 \sqrt{\left(b^2-4 a c\right) e^2}\right)\right)\right) \sqrt{\frac{-\frac{2 a e^2}{d+e x}+b \left(\frac{2 d}{d+e x}-1\right) e-2 c d \left(\frac{d}{d+e x}-1\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{\frac{\frac{2 a e^2}{d+e x}+2 c d \left(\frac{d}{d+e x}-1\right)+b \left(e-\frac{2 d e}{d+e x}\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{3 c^2 \left(4 a c-b^2\right) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} (a+x (b+c x))^{5/2} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^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,"(Sqrt[d + e*x]*(a + b*x + c*x^2)^3*((-2*(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + 3*c^2*d^2*e*x - 3*b*c*d*e^2*x + b^2*e^3*x - a*c*e^3*x))/(3*c^2*(a + b*x + c*x^2)^2) + (2*(7*b*c^2*d^2*e + 3*b^2*c*d*e^2 - 40*a*c^2*d*e^2 - b^3*e^3 + 11*a*b*c*e^3 + 14*c^3*d^2*e*x - 14*b*c^2*d*e^2*x + 8*b^2*c*e^3*x - 18*a*c^2*e^3*x))/(3*c^2*(-b^2 + 4*a*c)*(a + b*x + c*x^2))))/(a + x*(b + c*x))^(5/2) - (7*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(5/2)*(4*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(c^3*d^2*(-1 + d/(d + e*x))^2 + (b^2*e^3*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x) - c^2*e*(a*e*(3 + (2*d^2)/(d + e*x)^2 - (6*d)/(d + e*x)) + b*d*(1 + (2*d^2)/(d + e*x)^2 - (3*d)/(d + e*x))) + c*e^2*((-3*a^2*e^2)/(d + e*x)^2 + b^2*(1 + (2*d^2)/(d + e*x)^2 - (3*d)/(d + e*x)) + (a*b*e*(-3 + (2*d)/(d + e*x)))/(d + e*x))) - (I*Sqrt[2]*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] - (2*a*e^2)/(d + e*x) - 2*c*d*(-1 + d/(d + e*x)) + b*e*(-1 + (2*d)/(d + e*x)))/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] + (2*a*e^2)/(d + e*x) + 2*c*d*(-1 + d/(d + e*x)) + b*(e - (2*d*e)/(d + e*x)))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] + (I*Sqrt[2]*(-(b^3*e^3) + b^2*e^2*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + b*c*e*(4*a*e^2 - d*Sqrt[(b^2 - 4*a*c)*e^2]) + c*(c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] - a*e^2*(8*c*d + 3*Sqrt[(b^2 - 4*a*c)*e^2])))*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] - (2*a*e^2)/(d + e*x) - 2*c*d*(-1 + d/(d + e*x)) + b*e*(-1 + (2*d)/(d + e*x)))/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] + (2*a*e^2)/(d + e*x) + 2*c*d*(-1 + d/(d + e*x)) + b*(e - (2*d*e)/(d + e*x)))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/(3*c^2*(-b^2 + 4*a*c)*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x))^(5/2)*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
1650,1,1150,494,10.0048415,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^(5/2),x]","\frac{\sqrt{d+e x} \left(\frac{2 \left(10 d e x c^2-14 a e^2 c+5 b d e c-5 b e^2 x c+b^2 e^2\right)}{3 c \left(4 a c-b^2\right) \left(c x^2+b x+a\right)}-\frac{2 \left(c d^2+2 c e x d-a e^2-b e^2 x\right)}{3 c \left(c x^2+b x+a\right)^2}\right) \left(c x^2+b x+a\right)^3}{(a+x (b+c x))^{5/2}}+\frac{5 (d+e x)^{3/2} \left(-4 (b e-2 c d) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)+\frac{i \sqrt{2} (b e-2 c d) \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-\frac{2 a e^2}{d+e x}+b \left(\frac{2 d}{d+e x}-1\right) e-2 c d \left(\frac{d}{d+e x}-1\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{\frac{\frac{2 a e^2}{d+e x}+2 c d \left(\frac{d}{d+e x}-1\right)+b \left(e-\frac{2 d e}{d+e x}\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}-\frac{i \sqrt{2} \left(-b^2 e^2+4 a c e^2+b \sqrt{\left(b^2-4 a c\right) e^2} e-2 c d \sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-\frac{2 a e^2}{d+e x}+b \left(\frac{2 d}{d+e x}-1\right) e-2 c d \left(\frac{d}{d+e x}-1\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{\frac{\frac{2 a e^2}{d+e x}+2 c d \left(\frac{d}{d+e x}-1\right)+b \left(e-\frac{2 d e}{d+e x}\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right) \left(c x^2+b x+a\right)^{5/2}}{6 c \left(b^2-4 a c\right) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} (a+x (b+c x))^{5/2} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^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,"(Sqrt[d + e*x]*(a + b*x + c*x^2)^3*((-2*(c*d^2 - a*e^2 + 2*c*d*e*x - b*e^2*x))/(3*c*(a + b*x + c*x^2)^2) + (2*(5*b*c*d*e + b^2*e^2 - 14*a*c*e^2 + 10*c^2*d*e*x - 5*b*c*e^2*x))/(3*c*(-b^2 + 4*a*c)*(a + b*x + c*x^2))))/(a + x*(b + c*x))^(5/2) + (5*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(5/2)*(-4*(-2*c*d + b*e)*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)) + (I*Sqrt[2]*(-2*c*d + b*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] - (2*a*e^2)/(d + e*x) - 2*c*d*(-1 + d/(d + e*x)) + b*e*(-1 + (2*d)/(d + e*x)))/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] + (2*a*e^2)/(d + e*x) + 2*c*d*(-1 + d/(d + e*x)) + b*(e - (2*d*e)/(d + e*x)))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] - (I*Sqrt[2]*(-(b^2*e^2) + 4*a*c*e^2 - 2*c*d*Sqrt[(b^2 - 4*a*c)*e^2] + b*e*Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] - (2*a*e^2)/(d + e*x) - 2*c*d*(-1 + d/(d + e*x)) + b*e*(-1 + (2*d)/(d + e*x)))/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] + (2*a*e^2)/(d + e*x) + 2*c*d*(-1 + d/(d + e*x)) + b*(e - (2*d*e)/(d + e*x)))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/(6*c*(b^2 - 4*a*c)*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x))^(5/2)*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
1651,1,928,456,6.6565007,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^(5/2),x]","\frac{\sqrt{d+e x} \left((a+x (b+c x)) \left(-\frac{2 e (b+2 c x)}{\left(b^2-4 a c\right) (a+x (b+c x))}-\frac{2 (d+e x)}{3 (a+x (b+c x))^2}\right)+\frac{(d+e x) \left(\frac{4 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} (a+x (b+c x)) e^2}{(d+e x)^2}-\frac{i \sqrt{2} \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}+\frac{i \sqrt{2} \sqrt{\left(b^2-4 a c\right) e^2} \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{\left(b^2-4 a c\right) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}\right)}{\sqrt{a+x (b+c 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}}",1,"(Sqrt[d + e*x]*((a + x*(b + c*x))*((-2*(d + e*x))/(3*(a + x*(b + c*x))^2) - (2*e*(b + 2*c*x))/((b^2 - 4*a*c)*(a + x*(b + c*x)))) + ((d + e*x)*((4*e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x)))/(d + e*x)^2 - (I*Sqrt[2]*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] + (I*Sqrt[2]*Sqrt[(b^2 - 4*a*c)*e^2]*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/((b^2 - 4*a*c)*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])))/Sqrt[a + x*(b + c*x)]","C",1
1652,1,1016,517,7.378999,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^(5/2),x]","\frac{\sqrt{d+e x} \left(-\frac{4 e \left(e b^2+c (e x-d) b-2 c (a e+c d x)\right)}{\left(b^2-4 a c\right) \left(e (b d-a e)-c d^2\right)}+\frac{(d+e x) \left(-\frac{4 (b e-2 c d) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} (a+x (b+c x)) e^2}{(d+e x)^2}-\frac{i \sqrt{2} (2 c d-b e) \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}+\frac{i \sqrt{2} \left(b^2 e^2-4 a c e^2-b \sqrt{\left(b^2-4 a c\right) e^2} e+2 c d \sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{\left(b^2-4 a c\right) \left(c d^2+e (a e-b d)\right) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}-\frac{4}{a+x (b+c x)}\right)}{6 \sqrt{a+x (b+c 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}}",1,"(Sqrt[d + e*x]*(-4/(a + x*(b + c*x)) - (4*e*(b^2*e - 2*c*(a*e + c*d*x) + b*c*(-d + e*x)))/((b^2 - 4*a*c)*(-(c*d^2) + e*(b*d - a*e))) + ((d + e*x)*((-4*e^2*(-2*c*d + b*e)*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x)))/(d + e*x)^2 - (I*Sqrt[2]*(2*c*d - b*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] + (I*Sqrt[2]*(b^2*e^2 - 4*a*c*e^2 + 2*c*d*Sqrt[(b^2 - 4*a*c)*e^2] - b*e*Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/((b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e))*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])))/(6*Sqrt[a + x*(b + c*x)])","C",1
1653,1,1450,665,12.1853801,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^(5/2)),x]","\frac{\sqrt{d+e x} \left(c x^2+b x+a\right)^3 \left(\frac{2 (-c d+b e+c e x)}{3 \left(c d^2-b e d+a e^2\right) \left(c x^2+b x+a\right)^2}+\frac{2 \left(2 d^2 e x c^3+8 a d e^2 c^2+b d^2 e c^2-6 a e^3 x c^2-2 b d e^2 x c^2-7 a b e^3 c-3 b^2 d e^2 c+2 b^2 e^3 x c+2 b^3 e^3\right)}{3 \left(b^2-4 a c\right) \left(-c d^2+b e d-a e^2\right)^2 \left(c x^2+b x+a\right)}\right)}{(a+x (b+c x))^{5/2}}-\frac{(d+e x)^{3/2} \left(c x^2+b x+a\right)^{5/2} \left(4 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \left(d^2 \left(\frac{d}{d+e x}-1\right)^2 c^3-e \left(a e \left(\frac{2 d^2}{(d+e x)^2}-\frac{6 d}{d+e x}+3\right)+b d \left(\frac{2 d^2}{(d+e x)^2}-\frac{3 d}{d+e x}+1\right)\right) c^2+e^2 \left(\left(\frac{2 d^2}{(d+e x)^2}-\frac{3 d}{d+e x}+1\right) b^2+\frac{a e \left(\frac{2 d}{d+e x}-3\right) b}{d+e x}-\frac{3 a^2 e^2}{(d+e x)^2}\right) c+\frac{b^2 e^3 \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)-\frac{i \sqrt{2} \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(c^2 d^2+b^2 e^2-c e (b d+3 a e)\right) \sqrt{\frac{-\frac{2 a e^2}{d+e x}+b \left(\frac{2 d}{d+e x}-1\right) e-2 c d \left(\frac{d}{d+e x}-1\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{\frac{\frac{2 a e^2}{d+e x}+2 c d \left(\frac{d}{d+e x}-1\right)+b \left(e-\frac{2 d e}{d+e x}\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}+\frac{i \sqrt{2} \left(-b^3 e^3+b^2 \left(2 c d+\sqrt{\left(b^2-4 a c\right) e^2}\right) e^2+b c \left(4 a e^2-d \sqrt{\left(b^2-4 a c\right) e^2}\right) e+c \left(c d^2 \sqrt{\left(b^2-4 a c\right) e^2}-a e^2 \left(8 c d+3 \sqrt{\left(b^2-4 a c\right) e^2}\right)\right)\right) \sqrt{\frac{-\frac{2 a e^2}{d+e x}+b \left(\frac{2 d}{d+e x}-1\right) e-2 c d \left(\frac{d}{d+e x}-1\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{\frac{\frac{2 a e^2}{d+e x}+2 c d \left(\frac{d}{d+e x}-1\right)+b \left(e-\frac{2 d e}{d+e x}\right)+\sqrt{\left(b^2-4 a c\right) e^2}}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{3 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)^2 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} (a+x (b+c x))^{5/2} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^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-2 b^3 e^2+3 b^2 c d e\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}",1,"(Sqrt[d + e*x]*(a + b*x + c*x^2)^3*((2*(-(c*d) + b*e + c*e*x))/(3*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) + (2*(b*c^2*d^2*e - 3*b^2*c*d*e^2 + 8*a*c^2*d*e^2 + 2*b^3*e^3 - 7*a*b*c*e^3 + 2*c^3*d^2*e*x - 2*b*c^2*d*e^2*x + 2*b^2*c*e^3*x - 6*a*c^2*e^3*x))/(3*(b^2 - 4*a*c)*(-(c*d^2) + b*d*e - a*e^2)^2*(a + b*x + c*x^2))))/(a + x*(b + c*x))^(5/2) - ((d + e*x)^(3/2)*(a + b*x + c*x^2)^(5/2)*(4*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(c^3*d^2*(-1 + d/(d + e*x))^2 + (b^2*e^3*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x) - c^2*e*(a*e*(3 + (2*d^2)/(d + e*x)^2 - (6*d)/(d + e*x)) + b*d*(1 + (2*d^2)/(d + e*x)^2 - (3*d)/(d + e*x))) + c*e^2*((-3*a^2*e^2)/(d + e*x)^2 + b^2*(1 + (2*d^2)/(d + e*x)^2 - (3*d)/(d + e*x)) + (a*b*e*(-3 + (2*d)/(d + e*x)))/(d + e*x))) - (I*Sqrt[2]*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] - (2*a*e^2)/(d + e*x) - 2*c*d*(-1 + d/(d + e*x)) + b*e*(-1 + (2*d)/(d + e*x)))/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] + (2*a*e^2)/(d + e*x) + 2*c*d*(-1 + d/(d + e*x)) + b*(e - (2*d*e)/(d + e*x)))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] + (I*Sqrt[2]*(-(b^3*e^3) + b^2*e^2*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + b*c*e*(4*a*e^2 - d*Sqrt[(b^2 - 4*a*c)*e^2]) + c*(c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] - a*e^2*(8*c*d + 3*Sqrt[(b^2 - 4*a*c)*e^2])))*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] - (2*a*e^2)/(d + e*x) - 2*c*d*(-1 + d/(d + e*x)) + b*e*(-1 + (2*d)/(d + e*x)))/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[(Sqrt[(b^2 - 4*a*c)*e^2] + (2*a*e^2)/(d + e*x) + 2*c*d*(-1 + d/(d + e*x)) + b*(e - (2*d*e)/(d + e*x)))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x))^(5/2)*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
1654,1,1226,449,3.365093,"\int (b+2 c x) (d+e x)^m \left(a+b x+c x^2\right)^3 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^m*(a + b*x + c*x^2)^3,x]","\frac{(d+e x)^{m+1} \left(\frac{3 \left(c e^4 (m+1) (m+2) (m+3) (m+4) (a+x (b+c x))^2 \left(-28 d^2 (5 d-e (m+5) x) c^3+2 e \left(7 b d (d (m+20)-2 e (m+5) x)+2 a e \left(d \left(m^2+m-35\right)+e \left(m^2+12 m+35\right) x\right)\right) c^2-b e^2 \left(-2 a e (11 m+70)+b d \left(m^2+15 m+140\right)+b e m (m+5) x\right) c-2 b^3 e^3 m\right)-2 \left((m+1) (m+2) \left(c e (m+4) \left(c e (b d-2 a e) (m+6) \left(-d e (m+14) b^2+14 \left(c d^2+a e^2\right) b+4 a c d e m\right)-(b d (5 c d-2 b e)+a e (2 c d m-b e (m+1))) \left(28 c^2 d^2-b^2 e^2 m+4 c e (a e (m+7)-7 b d)\right)\right)-(3 c d-b e) \left(c e (2 c d-b e) (m+6) \left(-d e (m+14) b^2+14 \left(c d^2+a e^2\right) b+4 a c d e m\right)-\left(10 c^2 d^2-b^2 e^2 (m+3)+c e (b d (m-4)+2 a e (m+5))\right) \left(28 c^2 d^2-b^2 e^2 m+4 c e (a e (m+7)-7 b d)\right)\right)+c e (m+3) \left(c e (2 c d-b e) (m+6) \left(-d e (m+14) b^2+14 \left(c d^2+a e^2\right) b+4 a c d e m\right)-\left(10 c^2 d^2-b^2 e^2 (m+3)+c e (b d (m-4)+2 a e (m+5))\right) \left(28 c^2 d^2-b^2 e^2 m+4 c e (a e (m+7)-7 b d)\right)\right) x\right) (a+x (b+c x)) e^2+(2 c d-b e) (m+2) \left(840 c^5 d^6-40 c^4 e \left(63 b d+a e \left(2 m^2+2 m-63\right)\right) d^4+4 c^3 e^2 \left(5 b^2 \left(m^2+m+126\right) d^2+20 a b e \left(2 m^2+2 m-63\right) d-2 a^2 e^2 \left(2 m^3+28 m^2+26 m-315\right)\right) d^2+b^4 e^5 (b d-a e) m \left(m^2+4 m+3\right)-b^2 c e^4 m (m+1) \left(b^2 (m-17) d^2+8 a b e (m+8) d-4 a^2 e^2 (2 m+11)\right)-8 c^2 e^3 \left(5 b^3 \left(m^2+m+21\right) d^3+a b^2 e \left(-m^3+m^2+2 m-315\right) d^2-a^2 b e^2 \left(2 m^3+28 m^2+26 m-315\right) d+a^3 e^3 \left(2 m^3+18 m^2+16 m-105\right)\right)\right)+(m+1) \left(-1680 c^6 d^6+80 c^5 e \left(63 b d+a e \left(2 m^2-5 m-63\right)\right) d^4-4 c^4 e^2 \left(5 b^2 \left(2 m^2-5 m+252\right) d^2+40 a b e \left(2 m^2-5 m-63\right) d-12 a^2 e^2 \left(m^3+5 m^2-24 m-105\right)\right) d^2+b^6 e^6 m \left(m^2+5 m+6\right)-b^4 c e^5 m (m+2) (b d (3 m-11)+a e (9 m+47))+b^2 c^2 e^4 m \left(3 b^2 \left(m^2-15 m+26\right) d^2+8 a b e \left(3 m^2+5 m-47\right) d+12 a^2 e^2 \left(2 m^2+20 m+47\right)\right)-8 c^3 e^3 \left(-5 b^3 \left(2 m^2-5 m+42\right) d^3+3 a b^2 e \left(m^3-5 m^2+m+210\right) d^2+6 a^2 b e^2 \left(m^3+5 m^2-24 m-105\right) d+2 a^3 e^3 \left(m^3+15 m^2+71 m+105\right)\right)\right) (d+e x)\right)\right)}{e^6 (m+1) (m+2) (m+3) (m+4) (m+5) (m+6)}-c^2 (14 c d-b e (m+14)-2 c e (m+7) x) (a+x (b+c x))^3\right)}{c^2 e^2 (m+7) (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,"((d + e*x)^(1 + m)*(-(c^2*(14*c*d - b*e*(14 + m) - 2*c*e*(7 + m)*x)*(a + x*(b + c*x))^3) + (3*(-2*((2*c*d - b*e)*(2 + m)*(840*c^5*d^6 + b^4*e^5*(b*d - a*e)*m*(3 + 4*m + m^2) - b^2*c*e^4*m*(1 + m)*(b^2*d^2*(-17 + m) + 8*a*b*d*e*(8 + m) - 4*a^2*e^2*(11 + 2*m)) - 40*c^4*d^4*e*(63*b*d + a*e*(-63 + 2*m + 2*m^2)) + 4*c^3*d^2*e^2*(5*b^2*d^2*(126 + m + m^2) + 20*a*b*d*e*(-63 + 2*m + 2*m^2) - 2*a^2*e^2*(-315 + 26*m + 28*m^2 + 2*m^3)) - 8*c^2*e^3*(5*b^3*d^3*(21 + m + m^2) + a*b^2*d^2*e*(-315 + 2*m + m^2 - m^3) + a^3*e^3*(-105 + 16*m + 18*m^2 + 2*m^3) - a^2*b*d*e^2*(-315 + 26*m + 28*m^2 + 2*m^3))) + (1 + m)*(-1680*c^6*d^6 + b^6*e^6*m*(6 + 5*m + m^2) - b^4*c*e^5*m*(2 + m)*(b*d*(-11 + 3*m) + a*e*(47 + 9*m)) + 80*c^5*d^4*e*(63*b*d + a*e*(-63 - 5*m + 2*m^2)) + b^2*c^2*e^4*m*(3*b^2*d^2*(26 - 15*m + m^2) + 12*a^2*e^2*(47 + 20*m + 2*m^2) + 8*a*b*d*e*(-47 + 5*m + 3*m^2)) - 4*c^4*d^2*e^2*(40*a*b*d*e*(-63 - 5*m + 2*m^2) + 5*b^2*d^2*(252 - 5*m + 2*m^2) - 12*a^2*e^2*(-105 - 24*m + 5*m^2 + m^3)) - 8*c^3*e^3*(-5*b^3*d^3*(42 - 5*m + 2*m^2) + 3*a*b^2*d^2*e*(210 + m - 5*m^2 + m^3) + 6*a^2*b*d*e^2*(-105 - 24*m + 5*m^2 + m^3) + 2*a^3*e^3*(105 + 71*m + 15*m^2 + m^3)))*(d + e*x) + e^2*(1 + m)*(2 + m)*(c*e*(4 + m)*(c*e*(b*d - 2*a*e)*(6 + m)*(14*b*(c*d^2 + a*e^2) + 4*a*c*d*e*m - b^2*d*e*(14 + m)) - (b*d*(5*c*d - 2*b*e) + a*e*(2*c*d*m - b*e*(1 + m)))*(28*c^2*d^2 - b^2*e^2*m + 4*c*e*(-7*b*d + a*e*(7 + m)))) - (3*c*d - b*e)*(c*e*(2*c*d - b*e)*(6 + m)*(14*b*(c*d^2 + a*e^2) + 4*a*c*d*e*m - b^2*d*e*(14 + m)) - (10*c^2*d^2 - b^2*e^2*(3 + m) + c*e*(b*d*(-4 + m) + 2*a*e*(5 + m)))*(28*c^2*d^2 - b^2*e^2*m + 4*c*e*(-7*b*d + a*e*(7 + m)))) + c*e*(3 + m)*(c*e*(2*c*d - b*e)*(6 + m)*(14*b*(c*d^2 + a*e^2) + 4*a*c*d*e*m - b^2*d*e*(14 + m)) - (10*c^2*d^2 - b^2*e^2*(3 + m) + c*e*(b*d*(-4 + m) + 2*a*e*(5 + m)))*(28*c^2*d^2 - b^2*e^2*m + 4*c*e*(-7*b*d + a*e*(7 + m))))*x)*(a + x*(b + c*x))) + c*e^4*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(a + x*(b + c*x))^2*(-2*b^3*e^3*m - 28*c^3*d^2*(5*d - e*(5 + m)*x) - b*c*e^2*(-2*a*e*(70 + 11*m) + b*d*(140 + 15*m + m^2) + b*e*m*(5 + m)*x) + 2*c^2*e*(7*b*d*(d*(20 + m) - 2*e*(5 + m)*x) + 2*a*e*(d*(-35 + m + m^2) + e*(35 + 12*m + m^2)*x)))))/(e^6*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m))))/(c^2*e^2*(7 + m)*(8 + m))","B",1
1655,1,408,270,1.0783185,"\int (b+2 c x) (d+e x)^m \left(a+b x+c x^2\right)^2 \, dx","Integrate[(b + 2*c*x)*(d + e*x)^m*(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(\frac{2 \left(\frac{(d+e x) \left(2 c^2 e^2 \left(4 a^2 e^2 \left(m^2+8 m+15\right)+4 a b d e \left(m^2-4 m-30\right)+b^2 d^2 \left(m^2-4 m+60\right)\right)-2 b^2 c e^3 m (3 a e (m+4)+b d (m-4))-8 c^3 d^2 e \left(a e \left(m^2-4 m-30\right)+30 b d\right)+b^4 e^4 m (m+2)+120 c^4 d^4\right)}{e^2 (m+2)}-(a+x (b+c x)) \left(-2 c^2 e \left(2 a e \left(d \left(m^2+m-15\right)+e \left(m^2+8 m+15\right) x\right)+5 b d (d (m+12)-2 e (m+3) x)\right)+b c e^2 \left(-2 a e (7 m+30)+b d \left(m^2+11 m+60\right)+b e m (m+3) x\right)+b^3 e^3 m+20 c^3 d^2 (3 d-e (m+3) x)\right)-\frac{(2 c d-b e) \left(e (a e-b d)+c d^2\right) \left(-4 c e \left(a e \left(m^2+m-15\right)+15 b d\right)+b^2 e^2 m (m+1)+60 c^2 d^2\right)}{e^2 (m+1)}\right)}{e^2 (m+3) (m+4)}+c (a+x (b+c x))^2 (b e (m+10)+2 c (e (m+5) x-5 d))\right)}{c e^2 (m+5) (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,"((d + e*x)^(1 + m)*(c*(a + x*(b + c*x))^2*(b*e*(10 + m) + 2*c*(-5*d + e*(5 + m)*x)) + (2*(-(((2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))*(60*c^2*d^2 + b^2*e^2*m*(1 + m) - 4*c*e*(15*b*d + a*e*(-15 + m + m^2))))/(e^2*(1 + m))) + ((120*c^4*d^4 + b^4*e^4*m*(2 + m) - 2*b^2*c*e^3*m*(b*d*(-4 + m) + 3*a*e*(4 + m)) - 8*c^3*d^2*e*(30*b*d + a*e*(-30 - 4*m + m^2)) + 2*c^2*e^2*(4*a*b*d*e*(-30 - 4*m + m^2) + b^2*d^2*(60 - 4*m + m^2) + 4*a^2*e^2*(15 + 8*m + m^2)))*(d + e*x))/(e^2*(2 + m)) - (a + x*(b + c*x))*(b^3*e^3*m + 20*c^3*d^2*(3*d - e*(3 + m)*x) + b*c*e^2*(-2*a*e*(30 + 7*m) + b*d*(60 + 11*m + m^2) + b*e*m*(3 + m)*x) - 2*c^2*e*(5*b*d*(d*(12 + m) - 2*e*(3 + m)*x) + 2*a*e*(d*(-15 + m + m^2) + e*(15 + 8*m + m^2)*x)))))/(e^2*(3 + m)*(4 + m))))/(c*e^2*(5 + m)*(6 + m))","A",1
1656,1,134,143,0.2037232,"\int (b+2 c x) (d+e x)^m \left(a+b x+c x^2\right) \, dx","Integrate[(b + 2*c*x)*(d + e*x)^m*(a + b*x + c*x^2),x]","\frac{(d+e x)^{m+1} \left(\frac{(d+e x) \left(4 c e (a e (m+3)-3 b d)-b^2 e^2 m+12 c^2 d^2\right)}{e^2 (m+2)}+\frac{6 (b e-2 c d) \left(e (a e-b d)+c d^2\right)}{e^2 (m+1)}+(a+x (b+c x)) (b e (m+6)-6 c d+2 c e (m+3) x)\right)}{e^2 (m+3) (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,"((d + e*x)^(1 + m)*((6*(-2*c*d + b*e)*(c*d^2 + e*(-(b*d) + a*e)))/(e^2*(1 + m)) + ((12*c^2*d^2 - b^2*e^2*m + 4*c*e*(-3*b*d + a*e*(3 + m)))*(d + e*x))/(e^2*(2 + m)) + (-6*c*d + b*e*(6 + m) + 2*c*e*(3 + m)*x)*(a + x*(b + c*x))))/(e^2*(3 + m)*(4 + m))","A",1
1657,1,152,167,0.2421103,"\int \frac{(b+2 c x) (d+e x)^m}{a+b x+c x^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^m)/(a + b*x + c*x^2),x]","\frac{2 c (d+e x)^{m+1} \left(-\frac{\, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d+\left(\sqrt{b^2-4 a c}-b\right) e}\right)}{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}-\frac{\, _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)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)}{m+1}","-\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)) - 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",1
1658,1,287,358,0.5930592,"\int \frac{(b+2 c x) (d+e x)^m}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((b + 2*c*x)*(d + e*x)^m)/(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(\frac{c e m \sqrt{b^2-4 a c} \left(e \left(\sqrt{b^2-4 a c}+b\right)-2 c d\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d+\left(\sqrt{b^2-4 a c}-b\right) e}\right)}{(m+1) \left(e \left(\sqrt{b^2-4 a c}-b\right)+2 c d\right)}-\frac{c e m \sqrt{b^2-4 a c} \left(e \left(\sqrt{b^2-4 a c}-b\right)+2 c 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(e \left(\sqrt{b^2-4 a c}+b\right)-2 c d\right)}+\frac{\left(b^2-4 a c\right) (b e-c d+c e x)}{a+x (b+c x)}\right)}{\left(b^2-4 a c\right) \left(e (a e-b d)+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*e*x))/(a + x*(b + c*x)) + (c*Sqrt[b^2 - 4*a*c]*e*(-2*c*d + (b + Sqrt[b^2 - 4*a*c])*e)*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)) - (c*Sqrt[b^2 - 4*a*c]*e*(2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e)*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^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e)))","A",1
1659,1,330,120,0.1136189,"\int (A+B x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{6} e^2 x^6 \left(a^2 e^2 (A e+5 B d)+10 a b d e (A e+2 B d)+10 b^2 d^2 (A e+B d)\right)+d e x^5 \left(a^2 e^2 (A e+2 B d)+4 a b d e (A e+B d)+b^2 d^2 (2 A e+B d)\right)+\frac{1}{4} d^2 x^4 \left(10 a^2 e^2 (A e+B d)+10 a b d e (2 A e+B d)+b^2 d^2 (5 A e+B d)\right)+\frac{1}{3} d^3 x^3 \left(A \left(10 a^2 e^2+10 a b d e+b^2 d^2\right)+a B d (5 a e+2 b d)\right)+\frac{1}{7} e^3 x^7 \left(a^2 B e^2+2 a b e (A e+5 B d)+5 b^2 d (A e+2 B d)\right)+a^2 A d^5 x+\frac{1}{2} a d^4 x^2 (5 a A e+a B d+2 A b d)+\frac{1}{8} b e^4 x^8 (2 a B e+A b e+5 b B d)+\frac{1}{9} b^2 B e^5 x^9","-\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,"a^2*A*d^5*x + (a*d^4*(2*A*b*d + a*B*d + 5*a*A*e)*x^2)/2 + (d^3*(a*B*d*(2*b*d + 5*a*e) + A*(b^2*d^2 + 10*a*b*d*e + 10*a^2*e^2))*x^3)/3 + (d^2*(10*a^2*e^2*(B*d + A*e) + 10*a*b*d*e*(B*d + 2*A*e) + b^2*d^2*(B*d + 5*A*e))*x^4)/4 + d*e*(4*a*b*d*e*(B*d + A*e) + a^2*e^2*(2*B*d + A*e) + b^2*d^2*(B*d + 2*A*e))*x^5 + (e^2*(10*b^2*d^2*(B*d + A*e) + 10*a*b*d*e*(2*B*d + A*e) + a^2*e^2*(5*B*d + A*e))*x^6)/6 + (e^3*(a^2*B*e^2 + 5*b^2*d*(2*B*d + A*e) + 2*a*b*e*(5*B*d + A*e))*x^7)/7 + (b*e^4*(5*b*B*d + A*b*e + 2*a*B*e)*x^8)/8 + (b^2*B*e^5*x^9)/9","B",1
1660,1,283,120,0.0967094,"\int (A+B x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{5} e x^5 \left(a^2 e^2 (A e+4 B d)+4 a b d e (2 A e+3 B d)+2 b^2 d^2 (3 A e+2 B d)\right)+\frac{1}{4} d x^4 \left(2 a^2 e^2 (2 A e+3 B d)+4 a b d e (3 A e+2 B d)+b^2 d^2 (4 A e+B d)\right)+\frac{1}{3} d^2 x^3 \left(A \left(6 a^2 e^2+8 a b d e+b^2 d^2\right)+2 a B d (2 a e+b d)\right)+\frac{1}{6} e^2 x^6 \left(a^2 B e^2+2 a b e (A e+4 B d)+2 b^2 d (2 A e+3 B d)\right)+a^2 A d^4 x+\frac{1}{2} a d^3 x^2 (4 a A e+a B d+2 A b d)+\frac{1}{7} b e^3 x^7 (2 a B e+A b e+4 b B d)+\frac{1}{8} b^2 B e^4 x^8","-\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,"a^2*A*d^4*x + (a*d^3*(2*A*b*d + a*B*d + 4*a*A*e)*x^2)/2 + (d^2*(2*a*B*d*(b*d + 2*a*e) + A*(b^2*d^2 + 8*a*b*d*e + 6*a^2*e^2))*x^3)/3 + (d*(2*a^2*e^2*(3*B*d + 2*A*e) + 4*a*b*d*e*(2*B*d + 3*A*e) + b^2*d^2*(B*d + 4*A*e))*x^4)/4 + (e*(a^2*e^2*(4*B*d + A*e) + 4*a*b*d*e*(3*B*d + 2*A*e) + 2*b^2*d^2*(2*B*d + 3*A*e))*x^5)/5 + (e^2*(a^2*B*e^2 + 2*a*b*e*(4*B*d + A*e) + 2*b^2*d*(3*B*d + 2*A*e))*x^6)/6 + (b*e^3*(4*b*B*d + A*b*e + 2*a*B*e)*x^7)/7 + (b^2*B*e^4*x^8)/8","B",1
1661,1,216,120,0.0739871,"\int (A+B x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{4} x^4 \left(a^2 e^2 (A e+3 B d)+6 a b d e (A e+B d)+b^2 d^2 (3 A e+B d)\right)+\frac{1}{3} d x^3 \left(A \left(3 a^2 e^2+6 a b d e+b^2 d^2\right)+a B d (3 a e+2 b d)\right)+\frac{1}{5} e x^5 \left(a^2 B e^2+2 a b e (A e+3 B d)+3 b^2 d (A e+B d)\right)+a^2 A d^3 x+\frac{1}{2} a d^2 x^2 (3 a A e+a B d+2 A b d)+\frac{1}{6} b e^2 x^6 (2 a B e+A b e+3 b B d)+\frac{1}{7} b^2 B e^3 x^7","-\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,"a^2*A*d^3*x + (a*d^2*(2*A*b*d + a*B*d + 3*a*A*e)*x^2)/2 + (d*(a*B*d*(2*b*d + 3*a*e) + A*(b^2*d^2 + 6*a*b*d*e + 3*a^2*e^2))*x^3)/3 + ((6*a*b*d*e*(B*d + A*e) + a^2*e^2*(3*B*d + A*e) + b^2*d^2*(B*d + 3*A*e))*x^4)/4 + (e*(a^2*B*e^2 + 3*b^2*d*(B*d + A*e) + 2*a*b*e*(3*B*d + A*e))*x^5)/5 + (b*e^2*(3*b*B*d + A*b*e + 2*a*B*e)*x^6)/6 + (b^2*B*e^3*x^7)/7","A",1
1662,1,157,118,0.0539637,"\int (A+B x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{3} x^3 \left(A \left(a^2 e^2+4 a b d e+b^2 d^2\right)+2 a B d (a e+b d)\right)+\frac{1}{4} x^4 \left(a^2 B e^2+2 a b e (A e+2 B d)+b^2 d (2 A e+B d)\right)+a^2 A d^2 x+\frac{1}{5} b e x^5 (2 a B e+A b e+2 b B d)+\frac{1}{2} a d x^2 (2 A (a e+b d)+a B d)+\frac{1}{6} b^2 B e^2 x^6","\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^2*A*d^2*x + (a*d*(a*B*d + 2*A*(b*d + a*e))*x^2)/2 + ((2*a*B*d*(b*d + a*e) + A*(b^2*d^2 + 4*a*b*d*e + a^2*e^2))*x^3)/3 + ((a^2*B*e^2 + 2*a*b*e*(2*B*d + A*e) + b^2*d*(B*d + 2*A*e))*x^4)/4 + (b*e*(2*b*B*d + A*b*e + 2*a*B*e)*x^5)/5 + (b^2*B*e^2*x^6)/6","A",1
1663,1,96,75,0.0277627,"\int (A+B x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{3} x^3 \left(a^2 B e+2 a A b e+2 a b B d+A b^2 d\right)+a^2 A d x+\frac{1}{4} b x^4 (2 a B e+A b e+b B d)+\frac{1}{2} a x^2 (a A e+a B d+2 A b d)+\frac{1}{5} b^2 B e x^5","\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^2*A*d*x + (a*(2*A*b*d + a*B*d + a*A*e)*x^2)/2 + ((A*b^2*d + 2*a*b*B*d + 2*a*A*b*e + a^2*B*e)*x^3)/3 + (b*(b*B*d + A*b*e + 2*a*B*e)*x^4)/4 + (b^2*B*e*x^5)/5","A",1
1664,1,46,38,0.0100993,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{12} x \left(6 a^2 (2 A+B x)+4 a b x (3 A+2 B x)+b^2 x^2 (4 A+3 B x)\right)","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}",1,"(x*(6*a^2*(2*A + B*x) + 4*a*b*x*(3*A + 2*B*x) + b^2*x^2*(4*A + 3*B*x)))/12","A",1
1665,1,102,92,0.0580865,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{d+e x} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x),x]","\frac{e x \left(6 a^2 B e^2+6 a b e (2 A e-2 B d+B e x)+b^2 \left(3 A e (e x-2 d)+B \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)\right)-6 (b d-a e)^2 (B d-A e) \log (d+e x)}{6 e^4}","-\frac{(b d-a e)^2 (B d-A e) \log (d+e x)}{e^4}+\frac{b x (b d-a e) (B d-A e)}{e^3}-\frac{(a+b x)^2 (B d-A e)}{2 e^2}+\frac{B (a+b x)^3}{3 b e}",1,"(e*x*(6*a^2*B*e^2 + 6*a*b*e*(-2*B*d + 2*A*e + B*e*x) + b^2*(3*A*e*(-2*d + e*x) + B*(6*d^2 - 3*d*e*x + 2*e^2*x^2))) - 6*(b*d - a*e)^2*(B*d - A*e)*Log[d + e*x])/(6*e^4)","A",1
1666,1,98,101,0.1033331,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^2,x]","\frac{\frac{2 (b d-a e)^2 (B d-A e)}{d+e x}+2 b e x (2 a B e+A b e-2 b B d)+2 (b d-a e) \log (d+e x) (-a B e-2 A b e+3 b B d)+b^2 B e^2 x^2}{2 e^4}","\frac{(b d-a e)^2 (B d-A e)}{e^4 (d+e x)}+\frac{(b d-a e) \log (d+e x) (-a B e-2 A b e+3 b B d)}{e^4}-\frac{b x (-2 a B e-A b e+2 b B d)}{e^3}+\frac{b^2 B x^2}{2 e^2}",1,"(2*b*e*(-2*b*B*d + A*b*e + 2*a*B*e)*x + b^2*B*e^2*x^2 + (2*(b*d - a*e)^2*(B*d - A*e))/(d + e*x) + 2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*Log[d + e*x])/(2*e^4)","A",1
1667,1,143,106,0.0779423,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^3,x]","-\frac{a^2 e^2 (A e+B (d+2 e x))+2 a b e (A e (d+2 e x)-B d (3 d+4 e x))+2 b (d+e x)^2 \log (d+e x) (-2 a B e-A b e+3 b B d)-\left(b^2 \left(A d e (3 d+4 e x)+B \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)\right)\right)}{2 e^4 (d+e x)^2}","-\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,"-1/2*(a^2*e^2*(A*e + B*(d + 2*e*x)) + 2*a*b*e*(A*e*(d + 2*e*x) - B*d*(3*d + 4*e*x)) - b^2*(A*d*e*(3*d + 4*e*x) + B*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3)) + 2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2*Log[d + e*x])/(e^4*(d + e*x)^2)","A",1
1668,1,138,101,0.0629615,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^4,x]","\frac{-a^2 e^2 (2 A e+B (d+3 e x))-2 a b e \left(A e (d+3 e x)+2 B \left(d^2+3 d e x+3 e^2 x^2\right)\right)+b^2 \left(B d \left(11 d^2+27 d e x+18 e^2 x^2\right)-2 A e \left(d^2+3 d e x+3 e^2 x^2\right)\right)+6 b^2 B (d+e x)^3 \log (d+e x)}{6 e^4 (d+e x)^3}","-\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,"(-(a^2*e^2*(2*A*e + B*(d + 3*e*x))) - 2*a*b*e*(A*e*(d + 3*e*x) + 2*B*(d^2 + 3*d*e*x + 3*e^2*x^2)) + b^2*(-2*A*e*(d^2 + 3*d*e*x + 3*e^2*x^2) + B*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) + 6*b^2*B*(d + e*x)^3*Log[d + e*x])/(6*e^4*(d + e*x)^3)","A",1
1669,1,125,86,0.0548071,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^5,x]","-\frac{a^2 e^2 (3 A e+B (d+4 e x))+2 a b e \left(A e (d+4 e x)+B \left(d^2+4 d e x+6 e^2 x^2\right)\right)+b^2 \left(A e \left(d^2+4 d e x+6 e^2 x^2\right)+3 B \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)}{12 e^4 (d+e x)^4}","\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,"-1/12*(a^2*e^2*(3*A*e + B*(d + 4*e*x)) + 2*a*b*e*(A*e*(d + 4*e*x) + B*(d^2 + 4*d*e*x + 6*e^2*x^2)) + b^2*(A*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*B*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)))/(e^4*(d + e*x)^4)","A",1
1670,1,129,120,0.05679,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^6,x]","-\frac{3 a^2 e^2 (4 A e+B (d+5 e x))+2 a b e \left(3 A e (d+5 e x)+2 B \left(d^2+5 d e x+10 e^2 x^2\right)\right)+b^2 \left(2 A e \left(d^2+5 d e x+10 e^2 x^2\right)+3 B \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)}{60 e^4 (d+e x)^5}","\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,"-1/60*(3*a^2*e^2*(4*A*e + B*(d + 5*e*x)) + 2*a*b*e*(3*A*e*(d + 5*e*x) + 2*B*(d^2 + 5*d*e*x + 10*e^2*x^2)) + b^2*(2*A*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*B*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)))/(e^4*(d + e*x)^5)","A",1
1671,1,126,120,0.0627633,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^7,x]","-\frac{2 a^2 e^2 (5 A e+B (d+6 e x))+2 a b e \left(2 A e (d+6 e x)+B \left(d^2+6 d e x+15 e^2 x^2\right)\right)+b^2 \left(A e \left(d^2+6 d e x+15 e^2 x^2\right)+B \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)}{60 e^4 (d+e x)^6}","\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,"-1/60*(2*a^2*e^2*(5*A*e + B*(d + 6*e*x)) + 2*a*b*e*(2*A*e*(d + 6*e*x) + B*(d^2 + 6*d*e*x + 15*e^2*x^2)) + b^2*(A*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + B*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)))/(e^4*(d + e*x)^6)","A",1
1672,1,129,120,0.0572958,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^8,x]","-\frac{10 a^2 e^2 (6 A e+B (d+7 e x))+4 a b e \left(5 A e (d+7 e x)+2 B \left(d^2+7 d e x+21 e^2 x^2\right)\right)+b^2 \left(4 A e \left(d^2+7 d e x+21 e^2 x^2\right)+3 B \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)\right)}{420 e^4 (d+e x)^7}","\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,"-1/420*(10*a^2*e^2*(6*A*e + B*(d + 7*e*x)) + 4*a*b*e*(5*A*e*(d + 7*e*x) + 2*B*(d^2 + 7*d*e*x + 21*e^2*x^2)) + b^2*(4*A*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*B*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3)))/(e^4*(d + e*x)^7)","A",1
1673,1,823,206,0.2810393,"\int (A+B x) (d+e x)^7 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{1}{13} b^4 B e^7 x^{13}+\frac{1}{12} b^3 e^6 (7 b B d+A b e+4 a B e) x^{12}+\frac{1}{11} b^2 e^5 \left(7 d (3 B d+A e) b^2+4 a e (7 B d+A e) b+6 a^2 B e^2\right) x^{11}+\frac{1}{10} b e^4 \left(7 d^2 (5 B d+3 A e) b^3+28 a d e (3 B d+A e) b^2+6 a^2 e^2 (7 B d+A e) b+4 a^3 B e^3\right) x^{10}+\frac{1}{9} e^3 \left(35 d^3 (B d+A e) b^4+28 a d^2 e (5 B d+3 A e) b^3+42 a^2 d e^2 (3 B d+A e) b^2+4 a^3 e^3 (7 B d+A e) b+a^4 B e^4\right) x^9+\frac{1}{8} e^2 \left(7 b^4 (3 B d+5 A e) d^4+140 a b^3 e (B d+A e) d^3+42 a^2 b^2 e^2 (5 B d+3 A e) d^2+28 a^3 b e^3 (3 B d+A e) d+a^4 e^4 (7 B d+A e)\right) x^8+d e \left(b^4 (B d+3 A e) d^4+4 a b^3 e (3 B d+5 A e) d^3+30 a^2 b^2 e^2 (B d+A e) d^2+4 a^3 b e^3 (5 B d+3 A e) d+a^4 e^4 (3 B d+A e)\right) x^7+\frac{1}{6} d^2 \left(b^4 (B d+7 A e) d^4+28 a b^3 e (B d+3 A e) d^3+42 a^2 b^2 e^2 (3 B d+5 A e) d^2+140 a^3 b e^3 (B d+A e) d+7 a^4 e^4 (5 B d+3 A e)\right) x^6+\frac{1}{5} d^3 \left(a B d \left(4 b^3 d^3+42 a b^2 e d^2+84 a^2 b e^2 d+35 a^3 e^3\right)+A \left(b^4 d^4+28 a b^3 e d^3+126 a^2 b^2 e^2 d^2+140 a^3 b e^3 d+35 a^4 e^4\right)\right) x^5+\frac{1}{4} a d^4 \left(a B d \left(6 b^2 d^2+28 a b e d+21 a^2 e^2\right)+A \left(4 b^3 d^3+42 a b^2 e d^2+84 a^2 b e^2 d+35 a^3 e^3\right)\right) x^4+\frac{1}{3} a^2 d^5 \left(a B d (4 b d+7 a e)+A \left(6 b^2 d^2+28 a b e d+21 a^2 e^2\right)\right) x^3+\frac{1}{2} a^3 d^6 (4 A b d+a B d+7 a A e) x^2+a^4 A d^7 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}",1,"a^4*A*d^7*x + (a^3*d^6*(4*A*b*d + a*B*d + 7*a*A*e)*x^2)/2 + (a^2*d^5*(a*B*d*(4*b*d + 7*a*e) + A*(6*b^2*d^2 + 28*a*b*d*e + 21*a^2*e^2))*x^3)/3 + (a*d^4*(a*B*d*(6*b^2*d^2 + 28*a*b*d*e + 21*a^2*e^2) + A*(4*b^3*d^3 + 42*a*b^2*d^2*e + 84*a^2*b*d*e^2 + 35*a^3*e^3))*x^4)/4 + (d^3*(a*B*d*(4*b^3*d^3 + 42*a*b^2*d^2*e + 84*a^2*b*d*e^2 + 35*a^3*e^3) + A*(b^4*d^4 + 28*a*b^3*d^3*e + 126*a^2*b^2*d^2*e^2 + 140*a^3*b*d*e^3 + 35*a^4*e^4))*x^5)/5 + (d^2*(140*a^3*b*d*e^3*(B*d + A*e) + 28*a*b^3*d^3*e*(B*d + 3*A*e) + 7*a^4*e^4*(5*B*d + 3*A*e) + 42*a^2*b^2*d^2*e^2*(3*B*d + 5*A*e) + b^4*d^4*(B*d + 7*A*e))*x^6)/6 + d*e*(30*a^2*b^2*d^2*e^2*(B*d + A*e) + a^4*e^4*(3*B*d + A*e) + b^4*d^4*(B*d + 3*A*e) + 4*a^3*b*d*e^3*(5*B*d + 3*A*e) + 4*a*b^3*d^3*e*(3*B*d + 5*A*e))*x^7 + (e^2*(140*a*b^3*d^3*e*(B*d + A*e) + 28*a^3*b*d*e^3*(3*B*d + A*e) + a^4*e^4*(7*B*d + A*e) + 42*a^2*b^2*d^2*e^2*(5*B*d + 3*A*e) + 7*b^4*d^4*(3*B*d + 5*A*e))*x^8)/8 + (e^3*(a^4*B*e^4 + 35*b^4*d^3*(B*d + A*e) + 42*a^2*b^2*d*e^2*(3*B*d + A*e) + 4*a^3*b*e^3*(7*B*d + A*e) + 28*a*b^3*d^2*e*(5*B*d + 3*A*e))*x^9)/9 + (b*e^4*(4*a^3*B*e^3 + 28*a*b^2*d*e*(3*B*d + A*e) + 6*a^2*b*e^2*(7*B*d + A*e) + 7*b^3*d^2*(5*B*d + 3*A*e))*x^10)/10 + (b^2*e^5*(6*a^2*B*e^2 + 7*b^2*d*(3*B*d + A*e) + 4*a*b*e*(7*B*d + A*e))*x^11)/11 + (b^3*e^6*(7*b*B*d + A*b*e + 4*a*B*e)*x^12)/12 + (b^4*B*e^7*x^13)/13","B",1
1674,1,737,206,0.2469107,"\int (A+B x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^4 A d^6 x+\frac{1}{2} a^3 d^5 x^2 (6 a A e+a B d+4 A b d)+\frac{1}{3} a^2 d^4 x^3 \left(3 A \left(5 a^2 e^2+8 a b d e+2 b^2 d^2\right)+2 a B d (3 a e+2 b d)\right)+\frac{1}{10} b^2 e^4 x^{10} \left(6 a^2 B e^2+4 a b e (A e+6 B d)+3 b^2 d (2 A e+5 B d)\right)+\frac{1}{9} b e^3 x^9 \left(4 a^3 B e^3+6 a^2 b e^2 (A e+6 B d)+12 a b^2 d e (2 A e+5 B d)+5 b^3 d^2 (3 A e+4 B d)\right)+\frac{1}{4} a d^3 x^4 \left(3 a B d \left(5 a^2 e^2+8 a b d e+2 b^2 d^2\right)+4 A \left(5 a^3 e^3+15 a^2 b d e^2+9 a b^2 d^2 e+b^3 d^3\right)\right)+\frac{1}{8} e^2 x^8 \left(a^4 B e^4+4 a^3 b e^3 (A e+6 B d)+18 a^2 b^2 d e^2 (2 A e+5 B d)+20 a b^3 d^2 e (3 A e+4 B d)+5 b^4 d^3 (4 A e+3 B d)\right)+\frac{1}{7} e x^7 \left(a^4 e^4 (A e+6 B d)+12 a^3 b d e^3 (2 A e+5 B d)+30 a^2 b^2 d^2 e^2 (3 A e+4 B d)+20 a b^3 d^3 e (4 A e+3 B d)+3 b^4 d^4 (5 A e+2 B d)\right)+\frac{1}{6} d x^6 \left(3 a^4 e^4 (2 A e+5 B d)+20 a^3 b d e^3 (3 A e+4 B d)+30 a^2 b^2 d^2 e^2 (4 A e+3 B d)+12 a b^3 d^3 e (5 A e+2 B d)+b^4 d^4 (6 A e+B d)\right)+\frac{1}{5} d^2 x^5 \left(4 a B d \left(5 a^3 e^3+15 a^2 b d e^2+9 a b^2 d^2 e+b^3 d^3\right)+A \left(15 a^4 e^4+80 a^3 b d e^3+90 a^2 b^2 d^2 e^2+24 a b^3 d^3 e+b^4 d^4\right)\right)+\frac{1}{11} b^3 e^5 x^{11} (4 a B e+A b e+6 b B d)+\frac{1}{12} b^4 B e^6 x^{12}","-\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,"a^4*A*d^6*x + (a^3*d^5*(4*A*b*d + a*B*d + 6*a*A*e)*x^2)/2 + (a^2*d^4*(2*a*B*d*(2*b*d + 3*a*e) + 3*A*(2*b^2*d^2 + 8*a*b*d*e + 5*a^2*e^2))*x^3)/3 + (a*d^3*(3*a*B*d*(2*b^2*d^2 + 8*a*b*d*e + 5*a^2*e^2) + 4*A*(b^3*d^3 + 9*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 5*a^3*e^3))*x^4)/4 + (d^2*(4*a*B*d*(b^3*d^3 + 9*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 5*a^3*e^3) + A*(b^4*d^4 + 24*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 80*a^3*b*d*e^3 + 15*a^4*e^4))*x^5)/5 + (d*(3*a^4*e^4*(5*B*d + 2*A*e) + 20*a^3*b*d*e^3*(4*B*d + 3*A*e) + 30*a^2*b^2*d^2*e^2*(3*B*d + 4*A*e) + 12*a*b^3*d^3*e*(2*B*d + 5*A*e) + b^4*d^4*(B*d + 6*A*e))*x^6)/6 + (e*(a^4*e^4*(6*B*d + A*e) + 12*a^3*b*d*e^3*(5*B*d + 2*A*e) + 30*a^2*b^2*d^2*e^2*(4*B*d + 3*A*e) + 20*a*b^3*d^3*e*(3*B*d + 4*A*e) + 3*b^4*d^4*(2*B*d + 5*A*e))*x^7)/7 + (e^2*(a^4*B*e^4 + 4*a^3*b*e^3*(6*B*d + A*e) + 18*a^2*b^2*d*e^2*(5*B*d + 2*A*e) + 20*a*b^3*d^2*e*(4*B*d + 3*A*e) + 5*b^4*d^3*(3*B*d + 4*A*e))*x^8)/8 + (b*e^3*(4*a^3*B*e^3 + 6*a^2*b*e^2*(6*B*d + A*e) + 12*a*b^2*d*e*(5*B*d + 2*A*e) + 5*b^3*d^2*(4*B*d + 3*A*e))*x^9)/9 + (b^2*e^4*(6*a^2*B*e^2 + 4*a*b*e*(6*B*d + A*e) + 3*b^2*d*(5*B*d + 2*A*e))*x^10)/10 + (b^3*e^5*(6*b*B*d + A*b*e + 4*a*B*e)*x^11)/11 + (b^4*B*e^6*x^12)/12","B",1
1675,1,615,206,0.2025311,"\int (A+B x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^4 A d^5 x+\frac{1}{2} a^3 d^4 x^2 (5 a A e+a B d+4 A b d)+\frac{1}{3} a^2 d^3 x^3 \left(2 A \left(5 a^2 e^2+10 a b d e+3 b^2 d^2\right)+a B d (5 a e+4 b d)\right)+\frac{1}{9} b^2 e^3 x^9 \left(6 a^2 B e^2+4 a b e (A e+5 B d)+5 b^2 d (A e+2 B d)\right)+\frac{1}{4} b e^2 x^8 \left(2 a^3 B e^3+3 a^2 b e^2 (A e+5 B d)+10 a b^2 d e (A e+2 B d)+5 b^3 d^2 (A e+B d)\right)+\frac{1}{2} a d^2 x^4 \left(a B d \left(5 a^2 e^2+10 a b d e+3 b^2 d^2\right)+A \left(5 a^3 e^3+20 a^2 b d e^2+15 a b^2 d^2 e+2 b^3 d^3\right)\right)+\frac{1}{7} e x^7 \left(a^4 B e^4+4 a^3 b e^3 (A e+5 B d)+30 a^2 b^2 d e^2 (A e+2 B d)+40 a b^3 d^2 e (A e+B d)+5 b^4 d^3 (2 A e+B d)\right)+\frac{1}{6} x^6 \left(a^4 e^4 (A e+5 B d)+20 a^3 b d e^3 (A e+2 B d)+60 a^2 b^2 d^2 e^2 (A e+B d)+20 a b^3 d^3 e (2 A e+B d)+b^4 d^4 (5 A e+B d)\right)+\frac{1}{5} d x^5 \left(2 a B d \left(5 a^3 e^3+20 a^2 b d e^2+15 a b^2 d^2 e+2 b^3 d^3\right)+A \left(5 a^4 e^4+40 a^3 b d e^3+60 a^2 b^2 d^2 e^2+20 a b^3 d^3 e+b^4 d^4\right)\right)+\frac{1}{10} b^3 e^4 x^{10} (4 a B e+A b e+5 b B d)+\frac{1}{11} b^4 B e^5 x^{11}","-\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,"a^4*A*d^5*x + (a^3*d^4*(4*A*b*d + a*B*d + 5*a*A*e)*x^2)/2 + (a^2*d^3*(a*B*d*(4*b*d + 5*a*e) + 2*A*(3*b^2*d^2 + 10*a*b*d*e + 5*a^2*e^2))*x^3)/3 + (a*d^2*(a*B*d*(3*b^2*d^2 + 10*a*b*d*e + 5*a^2*e^2) + A*(2*b^3*d^3 + 15*a*b^2*d^2*e + 20*a^2*b*d*e^2 + 5*a^3*e^3))*x^4)/2 + (d*(2*a*B*d*(2*b^3*d^3 + 15*a*b^2*d^2*e + 20*a^2*b*d*e^2 + 5*a^3*e^3) + A*(b^4*d^4 + 20*a*b^3*d^3*e + 60*a^2*b^2*d^2*e^2 + 40*a^3*b*d*e^3 + 5*a^4*e^4))*x^5)/5 + ((60*a^2*b^2*d^2*e^2*(B*d + A*e) + 20*a^3*b*d*e^3*(2*B*d + A*e) + a^4*e^4*(5*B*d + A*e) + 20*a*b^3*d^3*e*(B*d + 2*A*e) + b^4*d^4*(B*d + 5*A*e))*x^6)/6 + (e*(a^4*B*e^4 + 40*a*b^3*d^2*e*(B*d + A*e) + 30*a^2*b^2*d*e^2*(2*B*d + A*e) + 4*a^3*b*e^3*(5*B*d + A*e) + 5*b^4*d^3*(B*d + 2*A*e))*x^7)/7 + (b*e^2*(2*a^3*B*e^3 + 5*b^3*d^2*(B*d + A*e) + 10*a*b^2*d*e*(2*B*d + A*e) + 3*a^2*b*e^2*(5*B*d + A*e))*x^8)/4 + (b^2*e^3*(6*a^2*B*e^2 + 5*b^2*d*(2*B*d + A*e) + 4*a*b*e*(5*B*d + A*e))*x^9)/9 + (b^3*e^4*(5*b*B*d + A*b*e + 4*a*B*e)*x^10)/10 + (b^4*B*e^5*x^11)/11","B",1
1676,1,512,204,0.1616716,"\int (A+B x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^4 A d^4 x+\frac{1}{2} a^3 d^3 x^2 (4 A (a e+b d)+a B d)+\frac{2}{3} a^2 d^2 x^3 \left(A \left(3 a^2 e^2+8 a b d e+3 b^2 d^2\right)+2 a B d (a e+b d)\right)+\frac{1}{4} b^2 e^2 x^8 \left(3 a^2 B e^2+2 a b e (A e+4 B d)+b^2 d (2 A e+3 B d)\right)+\frac{2}{7} b e x^7 \left(2 a^3 B e^3+3 a^2 b e^2 (A e+4 B d)+4 a b^2 d e (2 A e+3 B d)+b^3 d^2 (3 A e+2 B d)\right)+\frac{1}{2} a d x^4 \left(a B d \left(3 a^2 e^2+8 a b d e+3 b^2 d^2\right)+2 A \left(a^3 e^3+6 a^2 b d e^2+6 a b^2 d^2 e+b^3 d^3\right)\right)+\frac{1}{6} x^6 \left(a^4 B e^4+4 a^3 b e^3 (A e+4 B d)+12 a^2 b^2 d e^2 (2 A e+3 B d)+8 a b^3 d^2 e (3 A e+2 B d)+b^4 d^3 (4 A e+B d)\right)+\frac{1}{5} x^5 \left(4 a B d \left(a^3 e^3+6 a^2 b d e^2+6 a b^2 d^2 e+b^3 d^3\right)+A \left(a^4 e^4+16 a^3 b d e^3+36 a^2 b^2 d^2 e^2+16 a b^3 d^3 e+b^4 d^4\right)\right)+\frac{1}{9} b^3 e^3 x^9 (4 a B e+A b e+4 b B d)+\frac{1}{10} b^4 B e^4 x^{10}","\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^4*A*d^4*x + (a^3*d^3*(a*B*d + 4*A*(b*d + a*e))*x^2)/2 + (2*a^2*d^2*(2*a*B*d*(b*d + a*e) + A*(3*b^2*d^2 + 8*a*b*d*e + 3*a^2*e^2))*x^3)/3 + (a*d*(a*B*d*(3*b^2*d^2 + 8*a*b*d*e + 3*a^2*e^2) + 2*A*(b^3*d^3 + 6*a*b^2*d^2*e + 6*a^2*b*d*e^2 + a^3*e^3))*x^4)/2 + ((4*a*B*d*(b^3*d^3 + 6*a*b^2*d^2*e + 6*a^2*b*d*e^2 + a^3*e^3) + A*(b^4*d^4 + 16*a*b^3*d^3*e + 36*a^2*b^2*d^2*e^2 + 16*a^3*b*d*e^3 + a^4*e^4))*x^5)/5 + ((a^4*B*e^4 + 4*a^3*b*e^3*(4*B*d + A*e) + 12*a^2*b^2*d*e^2*(3*B*d + 2*A*e) + 8*a*b^3*d^2*e*(2*B*d + 3*A*e) + b^4*d^3*(B*d + 4*A*e))*x^6)/6 + (2*b*e*(2*a^3*B*e^3 + 3*a^2*b*e^2*(4*B*d + A*e) + 4*a*b^2*d*e*(3*B*d + 2*A*e) + b^3*d^2*(2*B*d + 3*A*e))*x^7)/7 + (b^2*e^2*(3*a^2*B*e^2 + 2*a*b*e*(4*B*d + A*e) + b^2*d*(3*B*d + 2*A*e))*x^8)/4 + (b^3*e^3*(4*b*B*d + A*b*e + 4*a*B*e)*x^9)/9 + (b^4*B*e^4*x^10)/10","B",1
1677,1,402,159,0.1369572,"\int (A+B x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^4 A d^3 x+\frac{1}{2} a^3 d^2 x^2 (3 a A e+a B d+4 A b d)+\frac{1}{3} a^2 d x^3 \left(3 A \left(a^2 e^2+4 a b d e+2 b^2 d^2\right)+a B d (3 a e+4 b d)\right)+\frac{1}{7} b^2 e x^7 \left(6 a^2 B e^2+4 a b e (A e+3 B d)+3 b^2 d (A e+B d)\right)+\frac{1}{6} b x^6 \left(4 a^3 B e^3+6 a^2 b e^2 (A e+3 B d)+12 a b^2 d e (A e+B d)+b^3 d^2 (3 A e+B d)\right)+\frac{1}{5} x^5 \left(A b \left(4 a^3 e^3+18 a^2 b d e^2+12 a b^2 d^2 e+b^3 d^3\right)+a B \left(a^3 e^3+12 a^2 b d e^2+18 a b^2 d^2 e+4 b^3 d^3\right)\right)+\frac{1}{4} a x^4 \left(3 a B d \left(a^2 e^2+4 a b d e+2 b^2 d^2\right)+A \left(a^3 e^3+12 a^2 b d e^2+18 a b^2 d^2 e+4 b^3 d^3\right)\right)+\frac{1}{8} b^3 e^2 x^8 (4 a B e+A b e+3 b B d)+\frac{1}{9} b^4 B e^3 x^9","\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^4*A*d^3*x + (a^3*d^2*(4*A*b*d + a*B*d + 3*a*A*e)*x^2)/2 + (a^2*d*(a*B*d*(4*b*d + 3*a*e) + 3*A*(2*b^2*d^2 + 4*a*b*d*e + a^2*e^2))*x^3)/3 + (a*(3*a*B*d*(2*b^2*d^2 + 4*a*b*d*e + a^2*e^2) + A*(4*b^3*d^3 + 18*a*b^2*d^2*e + 12*a^2*b*d*e^2 + a^3*e^3))*x^4)/4 + ((a*B*(4*b^3*d^3 + 18*a*b^2*d^2*e + 12*a^2*b*d*e^2 + a^3*e^3) + A*b*(b^3*d^3 + 12*a*b^2*d^2*e + 18*a^2*b*d*e^2 + 4*a^3*e^3))*x^5)/5 + (b*(4*a^3*B*e^3 + 12*a*b^2*d*e*(B*d + A*e) + 6*a^2*b*e^2*(3*B*d + A*e) + b^3*d^2*(B*d + 3*A*e))*x^6)/6 + (b^2*e*(6*a^2*B*e^2 + 3*b^2*d*(B*d + A*e) + 4*a*b*e*(3*B*d + A*e))*x^7)/7 + (b^3*e^2*(3*b*B*d + A*b*e + 4*a*B*e)*x^8)/8 + (b^4*B*e^3*x^9)/9","B",1
1678,1,288,118,0.0918725,"\int (A+B x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^4 A d^2 x+\frac{1}{2} a^3 d x^2 (2 a A e+a B d+4 A b d)+\frac{1}{5} b x^5 \left(A b \left(6 a^2 e^2+8 a b d e+b^2 d^2\right)+4 a B \left(a^2 e^2+3 a b d e+b^2 d^2\right)\right)+\frac{1}{4} a x^4 \left(4 A b \left(a^2 e^2+3 a b d e+b^2 d^2\right)+a B \left(a^2 e^2+8 a b d e+6 b^2 d^2\right)\right)+\frac{1}{3} a^2 x^3 \left(A \left(a^2 e^2+8 a b d e+6 b^2 d^2\right)+2 a B d (a e+2 b d)\right)+\frac{1}{6} b^2 x^6 \left(6 a^2 B e^2+4 a b e (A e+2 B d)+b^2 d (2 A e+B d)\right)+\frac{1}{7} b^3 e x^7 (4 a B e+A b e+2 b B d)+\frac{1}{8} b^4 B e^2 x^8","\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^4*A*d^2*x + (a^3*d*(4*A*b*d + a*B*d + 2*a*A*e)*x^2)/2 + (a^2*(2*a*B*d*(2*b*d + a*e) + A*(6*b^2*d^2 + 8*a*b*d*e + a^2*e^2))*x^3)/3 + (a*(4*A*b*(b^2*d^2 + 3*a*b*d*e + a^2*e^2) + a*B*(6*b^2*d^2 + 8*a*b*d*e + a^2*e^2))*x^4)/4 + (b*(4*a*B*(b^2*d^2 + 3*a*b*d*e + a^2*e^2) + A*b*(b^2*d^2 + 8*a*b*d*e + 6*a^2*e^2))*x^5)/5 + (b^2*(6*a^2*B*e^2 + 4*a*b*e*(2*B*d + A*e) + b^2*d*(B*d + 2*A*e))*x^6)/6 + (b^3*e*(2*b*B*d + A*b*e + 4*a*B*e)*x^7)/7 + (b^4*B*e^2*x^8)/8","B",1
1679,1,172,75,0.0539628,"\int (A+B x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^4 A d x+\frac{1}{2} a^3 x^2 (a A e+a B d+4 A b d)+\frac{1}{3} a^2 x^3 (2 A b (2 a e+3 b d)+a B (a e+4 b d))+\frac{1}{6} b^3 x^6 (4 a B e+A b e+b B d)+\frac{1}{5} b^2 x^5 (A b (4 a e+b d)+2 a B (3 a e+2 b d))+\frac{1}{2} a b x^4 (A b (3 a e+2 b d)+a B (2 a e+3 b d))+\frac{1}{7} b^4 B e x^7","\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^4*A*d*x + (a^3*(4*A*b*d + a*B*d + a*A*e)*x^2)/2 + (a^2*(a*B*(4*b*d + a*e) + 2*A*b*(3*b*d + 2*a*e))*x^3)/3 + (a*b*(a*B*(3*b*d + 2*a*e) + A*b*(2*b*d + 3*a*e))*x^4)/2 + (b^2*(2*a*B*(2*b*d + 3*a*e) + A*b*(b*d + 4*a*e))*x^5)/5 + (b^3*(b*B*d + A*b*e + 4*a*B*e)*x^6)/6 + (b^4*B*e*x^7)/7","B",1
1680,1,84,38,0.0168897,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{1}{30} x \left(15 a^4 (2 A+B x)+20 a^3 b x (3 A+2 B x)+15 a^2 b^2 x^2 (4 A+3 B x)+6 a b^3 x^3 (5 A+4 B x)+b^4 x^4 (6 A+5 B x)\right)","\frac{(a+b x)^5 (A b-a B)}{5 b^2}+\frac{B (a+b x)^6}{6 b^2}",1,"(x*(15*a^4*(2*A + B*x) + 20*a^3*b*x*(3*A + 2*B*x) + 15*a^2*b^2*x^2*(4*A + 3*B*x) + 6*a*b^3*x^3*(5*A + 4*B*x) + b^4*x^4*(6*A + 5*B*x)))/30","B",1
1681,1,258,156,0.1341909,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{d+e x} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x),x]","\frac{e x \left(60 a^4 B e^4+120 a^3 b e^3 (2 A e-2 B d+B e x)+60 a^2 b^2 e^2 \left(3 A e (e x-2 d)+B \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+20 a b^3 e \left(2 A e \left(6 d^2-3 d e x+2 e^2 x^2\right)+B \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)+b^4 \left(5 A e \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+B \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)\right)-60 (b d-a e)^4 (B d-A e) \log (d+e x)}{60 e^6}","-\frac{(b d-a e)^4 (B d-A e) \log (d+e x)}{e^6}+\frac{b x (b d-a e)^3 (B d-A e)}{e^5}-\frac{(a+b x)^2 (b d-a e)^2 (B d-A e)}{2 e^4}+\frac{(a+b x)^3 (b d-a e) (B d-A e)}{3 e^3}-\frac{(a+b x)^4 (B d-A e)}{4 e^2}+\frac{B (a+b x)^5}{5 b e}",1,"(e*x*(60*a^4*B*e^4 + 120*a^3*b*e^3*(-2*B*d + 2*A*e + B*e*x) + 60*a^2*b^2*e^2*(3*A*e*(-2*d + e*x) + B*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + 20*a*b^3*e*(2*A*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + B*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)) + b^4*(5*A*e*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + B*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4))) - 60*(b*d - a*e)^4*(B*d - A*e)*Log[d + e*x])/(60*e^6)","A",1
1682,1,354,188,0.1477394,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^2,x]","\frac{12 a^4 e^4 (B d-A e)+48 a^3 b e^3 \left(A d e+B \left(-d^2+d e x+e^2 x^2\right)\right)+36 a^2 b^2 e^2 \left(2 A e \left(-d^2+d e x+e^2 x^2\right)+B \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)\right)+8 a b^3 e \left(3 A e \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+2 B \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)\right)+12 (d+e x) (b d-a e)^3 \log (d+e x) (-a B e-4 A b e+5 b B d)+b^4 \left(4 A e \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)+B \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)\right)}{12 e^6 (d+e x)}","-\frac{b^3 (d+e x)^3 (-4 a B e-A b e+5 b B d)}{3 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 d-a e)^4 (B d-A e)}{e^6 (d+e x)}+\frac{(b d-a e)^3 \log (d+e x) (-a B e-4 A b e+5 b B d)}{e^6}-\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^4 B (d+e x)^4}{4 e^6}",1,"(12*a^4*e^4*(B*d - A*e) + 48*a^3*b*e^3*(A*d*e + B*(-d^2 + d*e*x + e^2*x^2)) + 36*a^2*b^2*e^2*(2*A*e*(-d^2 + d*e*x + e^2*x^2) + B*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3)) + 8*a*b^3*e*(3*A*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 2*B*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4)) + b^4*(4*A*e*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + B*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5)) + 12*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)*Log[d + e*x])/(12*e^6*(d + e*x))","A",1
1683,1,187,193,0.101125,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^3,x]","\frac{-6 b^2 e x \left(-6 a^2 B e^2-4 a b e (A e-3 B d)+3 b^2 d (A e-2 B d)\right)+3 b^3 e^2 x^2 (4 a B e+A b e-3 b B d)-\frac{6 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{d+e x}+\frac{3 (b d-a e)^4 (B d-A e)}{(d+e x)^2}-12 b (b d-a e)^2 \log (d+e x) (-2 a B e-3 A b e+5 b B d)+2 b^4 B e^3 x^3}{6 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,"(-6*b^2*e*(-6*a^2*B*e^2 - 4*a*b*e*(-3*B*d + A*e) + 3*b^2*d*(-2*B*d + A*e))*x + 3*b^3*e^2*(-3*b*B*d + A*b*e + 4*a*B*e)*x^2 + 2*b^4*B*e^3*x^3 + (3*(b*d - a*e)^4*(B*d - A*e))/(d + e*x)^2 - (6*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e))/(d + e*x) - 12*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*Log[d + e*x])/(6*e^6)","A",1
1684,1,351,189,0.1632496,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^4,x]","\frac{-a^4 e^4 (2 A e+B (d+3 e x))-4 a^3 b e^3 \left(A e (d+3 e x)+2 B \left(d^2+3 d e x+3 e^2 x^2\right)\right)+6 a^2 b^2 e^2 \left(B d \left(11 d^2+27 d e x+18 e^2 x^2\right)-2 A e \left(d^2+3 d e x+3 e^2 x^2\right)\right)+4 a b^3 e \left(A d e \left(11 d^2+27 d e x+18 e^2 x^2\right)-2 B \left(13 d^4+27 d^3 e x+9 d^2 e^2 x^2-9 d e^3 x^3-3 e^4 x^4\right)\right)+12 b^2 (d+e x)^3 (b d-a e) \log (d+e x) (-3 a B e-2 A b e+5 b B d)+b^4 \left(2 A e \left(-13 d^4-27 d^3 e x-9 d^2 e^2 x^2+9 d e^3 x^3+3 e^4 x^4\right)+B \left(47 d^5+81 d^4 e x-9 d^3 e^2 x^2-63 d^2 e^3 x^3-15 d e^4 x^4+3 e^5 x^5\right)\right)}{6 e^6 (d+e x)^3}","-\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,"(-(a^4*e^4*(2*A*e + B*(d + 3*e*x))) - 4*a^3*b*e^3*(A*e*(d + 3*e*x) + 2*B*(d^2 + 3*d*e*x + 3*e^2*x^2)) + 6*a^2*b^2*e^2*(-2*A*e*(d^2 + 3*d*e*x + 3*e^2*x^2) + B*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) + 4*a*b^3*e*(A*d*e*(11*d^2 + 27*d*e*x + 18*e^2*x^2) - 2*B*(13*d^4 + 27*d^3*e*x + 9*d^2*e^2*x^2 - 9*d*e^3*x^3 - 3*e^4*x^4)) + b^4*(2*A*e*(-13*d^4 - 27*d^3*e*x - 9*d^2*e^2*x^2 + 9*d*e^3*x^3 + 3*e^4*x^4) + B*(47*d^5 + 81*d^4*e*x - 9*d^3*e^2*x^2 - 63*d^2*e^3*x^3 - 15*d*e^4*x^4 + 3*e^5*x^5)) + 12*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3*Log[d + e*x])/(6*e^6*(d + e*x)^3)","A",1
1685,1,338,189,0.1665243,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^5,x]","-\frac{a^4 e^4 (3 A e+B (d+4 e x))+4 a^3 b e^3 \left(A e (d+4 e x)+B \left(d^2+4 d e x+6 e^2 x^2\right)\right)+6 a^2 b^2 e^2 \left(A e \left(d^2+4 d e x+6 e^2 x^2\right)+3 B \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)-4 a b^3 e \left(B d \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)-3 A e \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+12 b^3 (d+e x)^4 \log (d+e x) (-4 a B e-A b e+5 b B d)-\left(b^4 \left(A d e \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)-B \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)\right)\right)}{12 e^6 (d+e x)^4}","-\frac{b^3 \log (d+e x) (-4 a B e-A b e+5 b B d)}{e^6}-\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 (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,"-1/12*(a^4*e^4*(3*A*e + B*(d + 4*e*x)) + 4*a^3*b*e^3*(A*e*(d + 4*e*x) + B*(d^2 + 4*d*e*x + 6*e^2*x^2)) + 6*a^2*b^2*e^2*(A*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*B*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)) - 4*a*b^3*e*(-3*A*e*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) + B*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) - b^4*(A*d*e*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3) - B*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5)) + 12*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4*Log[d + e*x])/(e^6*(d + e*x)^4)","A",1
1686,1,332,155,0.147677,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^6,x]","\frac{-3 a^4 e^4 (4 A e+B (d+5 e x))-4 a^3 b e^3 \left(3 A e (d+5 e x)+2 B \left(d^2+5 d e x+10 e^2 x^2\right)\right)-6 a^2 b^2 e^2 \left(2 A e \left(d^2+5 d e x+10 e^2 x^2\right)+3 B \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)-12 a b^3 e \left(A e \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+4 B \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)+b^4 \left(B d \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)-12 A e \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)+60 b^4 B (d+e x)^5 \log (d+e x)}{60 e^6 (d+e x)^5}","-\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,"(-3*a^4*e^4*(4*A*e + B*(d + 5*e*x)) - 4*a^3*b*e^3*(3*A*e*(d + 5*e*x) + 2*B*(d^2 + 5*d*e*x + 10*e^2*x^2)) - 6*a^2*b^2*e^2*(2*A*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*B*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)) - 12*a*b^3*e*(A*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 4*B*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4)) + b^4*(-12*A*e*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4) + B*d*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4)) + 60*b^4*B*(d + e*x)^5*Log[d + e*x])/(60*e^6*(d + e*x)^5)","B",1
1687,1,317,86,0.1323106,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^7,x]","-\frac{a^4 e^4 (5 A e+B (d+6 e x))+2 a^3 b e^3 \left(2 A e (d+6 e x)+B \left(d^2+6 d e x+15 e^2 x^2\right)\right)+3 a^2 b^2 e^2 \left(A e \left(d^2+6 d e x+15 e^2 x^2\right)+B \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)+2 a b^3 e \left(A e \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+2 B \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)+b^4 \left(A e \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)+5 B \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right)\right)}{30 e^6 (d+e x)^6}","\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,"-1/30*(a^4*e^4*(5*A*e + B*(d + 6*e*x)) + 2*a^3*b*e^3*(2*A*e*(d + 6*e*x) + B*(d^2 + 6*d*e*x + 15*e^2*x^2)) + 3*a^2*b^2*e^2*(A*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + B*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)) + 2*a*b^3*e*(A*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 2*B*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)) + b^4*(A*e*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4) + 5*B*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5)))/(e^6*(d + e*x)^6)","B",1
1688,1,323,135,0.1310458,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^8,x]","-\frac{5 a^4 e^4 (6 A e+B (d+7 e x))+4 a^3 b e^3 \left(5 A e (d+7 e x)+2 B \left(d^2+7 d e x+21 e^2 x^2\right)\right)+3 a^2 b^2 e^2 \left(4 A e \left(d^2+7 d e x+21 e^2 x^2\right)+3 B \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)\right)+2 a b^3 e \left(3 A e \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+4 B \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)+b^4 \left(2 A e \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)+5 B \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)\right)}{210 e^6 (d+e x)^7}","\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,"-1/210*(5*a^4*e^4*(6*A*e + B*(d + 7*e*x)) + 4*a^3*b*e^3*(5*A*e*(d + 7*e*x) + 2*B*(d^2 + 7*d*e*x + 21*e^2*x^2)) + 3*a^2*b^2*e^2*(4*A*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*B*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3)) + 2*a*b^3*e*(3*A*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 4*B*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)) + b^4*(2*A*e*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4) + 5*B*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5)))/(e^6*(d + e*x)^7)","B",1
1689,1,320,185,0.134392,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^9} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^9,x]","-\frac{15 a^4 e^4 (7 A e+B (d+8 e x))+20 a^3 b e^3 \left(3 A e (d+8 e x)+B \left(d^2+8 d e x+28 e^2 x^2\right)\right)+6 a^2 b^2 e^2 \left(5 A e \left(d^2+8 d e x+28 e^2 x^2\right)+3 B \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)\right)+12 a b^3 e \left(A e \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+B \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)\right)+b^4 \left(3 A e \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)+5 B \left(d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right)\right)}{840 e^6 (d+e x)^8}","\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,"-1/840*(15*a^4*e^4*(7*A*e + B*(d + 8*e*x)) + 20*a^3*b*e^3*(3*A*e*(d + 8*e*x) + B*(d^2 + 8*d*e*x + 28*e^2*x^2)) + 6*a^2*b^2*e^2*(5*A*e*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*B*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3)) + 12*a*b^3*e*(A*e*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + B*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4)) + b^4*(3*A*e*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4) + 5*B*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5)))/(e^6*(d + e*x)^8)","A",1
1690,1,322,206,0.1355462,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{10}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^10,x]","-\frac{35 a^4 e^4 (8 A e+B (d+9 e x))+20 a^3 b e^3 \left(7 A e (d+9 e x)+2 B \left(d^2+9 d e x+36 e^2 x^2\right)\right)+30 a^2 b^2 e^2 \left(2 A e \left(d^2+9 d e x+36 e^2 x^2\right)+B \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)\right)+4 a b^3 e \left(5 A e \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)+4 B \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)\right)+b^4 \left(4 A e \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)+5 B \left(d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right)\right)}{2520 e^6 (d+e x)^9}","\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,"-1/2520*(35*a^4*e^4*(8*A*e + B*(d + 9*e*x)) + 20*a^3*b*e^3*(7*A*e*(d + 9*e*x) + 2*B*(d^2 + 9*d*e*x + 36*e^2*x^2)) + 30*a^2*b^2*e^2*(2*A*e*(d^2 + 9*d*e*x + 36*e^2*x^2) + B*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3)) + 4*a*b^3*e*(5*A*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 4*B*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4)) + b^4*(4*A*e*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4) + 5*B*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5)))/(e^6*(d + e*x)^9)","A",1
1691,1,320,206,0.1458655,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{11}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^11,x]","-\frac{14 a^4 e^4 (9 A e+B (d+10 e x))+14 a^3 b e^3 \left(4 A e (d+10 e x)+B \left(d^2+10 d e x+45 e^2 x^2\right)\right)+3 a^2 b^2 e^2 \left(7 A e \left(d^2+10 d e x+45 e^2 x^2\right)+3 B \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)\right)+2 a b^3 e \left(3 A e \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)+2 B \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)\right)+b^4 \left(A e \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)+B \left(d^5+10 d^4 e x+45 d^3 e^2 x^2+120 d^2 e^3 x^3+210 d e^4 x^4+252 e^5 x^5\right)\right)}{1260 e^6 (d+e x)^{10}}","\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,"-1/1260*(14*a^4*e^4*(9*A*e + B*(d + 10*e*x)) + 14*a^3*b*e^3*(4*A*e*(d + 10*e*x) + B*(d^2 + 10*d*e*x + 45*e^2*x^2)) + 3*a^2*b^2*e^2*(7*A*e*(d^2 + 10*d*e*x + 45*e^2*x^2) + 3*B*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3)) + 2*a*b^3*e*(3*A*e*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 2*B*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4)) + b^4*(A*e*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4) + B*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5)))/(e^6*(d + e*x)^10)","A",1
1692,1,323,206,0.138047,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{12}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^12,x]","-\frac{126 a^4 e^4 (10 A e+B (d+11 e x))+56 a^3 b e^3 \left(9 A e (d+11 e x)+2 B \left(d^2+11 d e x+55 e^2 x^2\right)\right)+21 a^2 b^2 e^2 \left(8 A e \left(d^2+11 d e x+55 e^2 x^2\right)+3 B \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)\right)+6 a b^3 e \left(7 A e \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)+4 B \left(d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right)\right)+b^4 \left(6 A e \left(d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right)+5 B \left(d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right)\right)}{13860 e^6 (d+e x)^{11}}","\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,"-1/13860*(126*a^4*e^4*(10*A*e + B*(d + 11*e*x)) + 56*a^3*b*e^3*(9*A*e*(d + 11*e*x) + 2*B*(d^2 + 11*d*e*x + 55*e^2*x^2)) + 21*a^2*b^2*e^2*(8*A*e*(d^2 + 11*d*e*x + 55*e^2*x^2) + 3*B*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3)) + 6*a*b^3*e*(7*A*e*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3) + 4*B*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4)) + b^4*(6*A*e*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4) + 5*B*(d^5 + 11*d^4*e*x + 55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*e^5*x^5)))/(e^6*(d + e*x)^11)","A",1
1693,1,365,187,0.1652982,"\int \frac{(A+B x) (d+e x)^4}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{-4 A b \left(3 a^4 e^4-3 a^3 b e^3 (4 d+3 e x)+6 a^2 b^2 e^2 \left(3 d^2+4 d e x-e^2 x^2\right)+2 a b^3 e \left(-6 d^3-9 d^2 e x+9 d e^2 x^2+e^3 x^3\right)+b^4 \left(3 d^4-18 d^2 e^2 x^2-6 d e^3 x^3-e^4 x^4\right)\right)+B \left(12 a^5 e^4-48 a^4 b e^3 (d+e x)+6 a^3 b^2 e^2 \left(12 d^2+24 d e x-5 e^2 x^2\right)+2 a^2 b^3 e \left(-24 d^3-72 d^2 e x+48 d e^2 x^2+5 e^3 x^3\right)+a b^4 \left(12 d^4+48 d^3 e x-108 d^2 e^2 x^2-32 d e^3 x^3-5 e^4 x^4\right)+b^5 e x^2 \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)\right)+12 (a+b x) (b d-a e)^3 \log (a+b x) (-5 a B e+4 A b e+b B d)}{12 b^6 (a+b x)}","\frac{e^3 (a+b x)^3 (-5 a B e+A b e+4 b B d)}{3 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{(A b-a B) (b d-a e)^4}{b^6 (a+b x)}+\frac{(b d-a e)^3 \log (a+b x) (-5 a B e+4 A b e+b B d)}{b^6}+\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 e^4 (a+b x)^4}{4 b^6}",1,"(B*(12*a^5*e^4 - 48*a^4*b*e^3*(d + e*x) + 6*a^3*b^2*e^2*(12*d^2 + 24*d*e*x - 5*e^2*x^2) + b^5*e*x^2*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3) + 2*a^2*b^3*e*(-24*d^3 - 72*d^2*e*x + 48*d*e^2*x^2 + 5*e^3*x^3) + a*b^4*(12*d^4 + 48*d^3*e*x - 108*d^2*e^2*x^2 - 32*d*e^3*x^3 - 5*e^4*x^4)) - 4*A*b*(3*a^4*e^4 - 3*a^3*b*e^3*(4*d + 3*e*x) + 6*a^2*b^2*e^2*(3*d^2 + 4*d*e*x - e^2*x^2) + 2*a*b^3*e*(-6*d^3 - 9*d^2*e*x + 9*d*e^2*x^2 + e^3*x^3) + b^4*(3*d^4 - 18*d^2*e^2*x^2 - 6*d*e^3*x^3 - e^4*x^4)) + 12*(b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e)*(a + b*x)*Log[a + b*x])/(12*b^6*(a + b*x))","A",1
1694,1,250,145,0.1190086,"\int \frac{(A+B x) (d+e x)^3}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{-3 A b \left(-2 a^3 e^3+2 a^2 b e^2 (3 d+2 e x)+3 a b^2 e \left(-2 d^2-2 d e x+e^2 x^2\right)+b^3 \left(2 d^3-6 d e^2 x^2-e^3 x^3\right)\right)+B \left(-6 a^4 e^3+18 a^3 b e^2 (d+e x)+6 a^2 b^2 e \left(-3 d^2-6 d e x+2 e^2 x^2\right)+a b^3 \left(6 d^3+18 d^2 e x-27 d e^2 x^2-4 e^3 x^3\right)+b^4 e x^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+6 (a+b x) (b d-a e)^2 \log (a+b x) (-4 a B e+3 A b e+b B d)}{6 b^5 (a+b 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{(b d-a e)^2 \log (a+b x) (-4 a B e+3 A b e+b B d)}{b^5}+\frac{3 e x (b d-a e) (-2 a B e+A b e+b B d)}{b^4}+\frac{B e^3 (a+b x)^3}{3 b^5}",1,"(B*(-6*a^4*e^3 + 18*a^3*b*e^2*(d + e*x) + 6*a^2*b^2*e*(-3*d^2 - 6*d*e*x + 2*e^2*x^2) + b^4*e*x^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2) + a*b^3*(6*d^3 + 18*d^2*e*x - 27*d*e^2*x^2 - 4*e^3*x^3)) - 3*A*b*(-2*a^3*e^3 + 2*a^2*b*e^2*(3*d + 2*e*x) + 3*a*b^2*e*(-2*d^2 - 2*d*e*x + e^2*x^2) + b^3*(2*d^3 - 6*d*e^2*x^2 - e^3*x^3)) + 6*(b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*(a + b*x)*Log[a + b*x])/(6*b^5*(a + b*x))","A",1
1695,1,153,99,0.0712343,"\int \frac{(A+B x) (d+e x)^2}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\log (a+b x) \left(3 a^2 B e^2-2 a A b e^2-4 a b B d e+2 A b^2 d e+b^2 B d^2\right)}{b^4}+\frac{a^3 B e^2-a^2 A b e^2-2 a^2 b B d e+2 a A b^2 d e+a b^2 B d^2-A b^3 d^2}{b^4 (a+b x)}+\frac{e x (-2 a B e+A b e+2 b B d)}{b^3}+\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{(b d-a e) \log (a+b x) (-3 a B e+2 A b e+b B d)}{b^4}+\frac{e x (-2 a B e+A b e+2 b B d)}{b^3}+\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^3*d^2) + a*b^2*B*d^2 + 2*a*A*b^2*d*e - 2*a^2*b*B*d*e - a^2*A*b*e^2 + a^3*B*e^2)/(b^4*(a + b*x)) + ((b^2*B*d^2 + 2*A*b^2*d*e - 4*a*b*B*d*e - 2*a*A*b*e^2 + 3*a^2*B*e^2)*Log[a + b*x])/b^4","A",1
1696,1,56,60,0.0455622,"\int \frac{(A+B x) (d+e x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((A + B*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{-\frac{(A b-a B) (b d-a e)}{a+b x}+\log (a+b x) (-2 a B e+A b e+b B d)+b B e x}{b^3}","-\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*B*e*x - ((A*b - a*B)*(b*d - a*e))/(a + b*x) + (b*B*d + A*b*e - 2*a*B*e)*Log[a + b*x])/b^3","A",1
1697,1,31,32,0.0105956,"\int \frac{A+B x}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{a B-A b}{b^2 (a+b x)}+\frac{B \log (a+b x)}{b^2}","\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",1
1698,1,69,82,0.0592332,"\int \frac{A+B x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{\frac{(a B-A b) (b d-a e)}{b (a+b x)}+\log (a+b x) (B d-A e)+(A e-B d) \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*d - a*e))/(b*(a + b*x)) + (B*d - A*e)*Log[a + b*x] + (-(B*d) + A*e)*Log[d + e*x])/(b*d - a*e)^2","A",1
1699,1,103,117,0.1116886,"\int \frac{A+B x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{\frac{(a B-A b) (b d-a e)}{a+b x}+\frac{(b d-a e) (B d-A e)}{d+e x}+\log (a+b x) (a B e-2 A b e+b B d)-\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))/(a + b*x) + ((b*d - a*e)*(B*d - A*e))/(d + e*x) + (b*B*d - 2*A*b*e + a*B*e)*Log[a + b*x] - (b*B*d - 2*A*b*e + a*B*e)*Log[d + e*x])/(b*d - a*e)^3","A",1
1700,1,146,157,0.1189865,"\int \frac{A+B x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{\frac{(b d-a e)^2 (B d-A e)}{(d+e x)^2}-\frac{2 b (A b-a B) (b d-a e)}{a+b x}+\frac{2 (b d-a e) (a B e-2 A b e+b B d)}{d+e x}+2 b \log (a+b x) (2 a B e-3 A b e+b B d)-2 b \log (d+e x) (2 a B e-3 A b e+b B d)}{2 (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,"((-2*b*(A*b - a*B)*(b*d - a*e))/(a + b*x) + ((b*d - a*e)^2*(B*d - A*e))/(d + e*x)^2 + (2*(b*d - a*e)*(b*B*d - 2*A*b*e + a*B*e))/(d + e*x) + 2*b*(b*B*d - 3*A*b*e + 2*a*B*e)*Log[a + b*x] - 2*b*(b*B*d - 3*A*b*e + 2*a*B*e)*Log[d + e*x])/(2*(b*d - a*e)^4)","A",1
1701,1,362,186,0.1906803,"\int \frac{(A+B x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{-2 A b \left(13 a^4 e^4+a^3 b e^3 (27 e x-22 d)+3 a^2 b^2 e^2 \left(2 d^2-18 d e x+3 e^2 x^2\right)+a b^3 e \left(2 d^3+18 d^2 e x-36 d e^2 x^2-9 e^3 x^3\right)+b^4 \left(d^4+6 d^3 e x+18 d^2 e^2 x^2-3 e^4 x^4\right)\right)+B \left(47 a^5 e^4+a^4 b e^3 (81 e x-104 d)-3 a^3 b^2 e^2 \left(-22 d^2+72 d e x+3 e^2 x^2\right)-a^2 b^3 e \left(8 d^3-162 d^2 e x+72 d e^2 x^2+63 e^3 x^3\right)-a b^4 \left(d^4+24 d^3 e x-108 d^2 e^2 x^2-72 d e^3 x^3+15 e^4 x^4\right)+3 b^5 x \left(-d^4-8 d^3 e x+8 d e^3 x^3+e^4 x^4\right)\right)+12 e^2 (a+b x)^3 (b d-a e) \log (a+b x) (-5 a B e+2 A b e+3 b B d)}{6 b^6 (a+b x)^3}","\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{e^3 x (-4 a B e+A b e+4 b B d)}{b^5}+\frac{B e^4 x^2}{2 b^4}",1,"(-2*A*b*(13*a^4*e^4 + a^3*b*e^3*(-22*d + 27*e*x) + 3*a^2*b^2*e^2*(2*d^2 - 18*d*e*x + 3*e^2*x^2) + a*b^3*e*(2*d^3 + 18*d^2*e*x - 36*d*e^2*x^2 - 9*e^3*x^3) + b^4*(d^4 + 6*d^3*e*x + 18*d^2*e^2*x^2 - 3*e^4*x^4)) + B*(47*a^5*e^4 + a^4*b*e^3*(-104*d + 81*e*x) - 3*a^3*b^2*e^2*(-22*d^2 + 72*d*e*x + 3*e^2*x^2) - a^2*b^3*e*(8*d^3 - 162*d^2*e*x + 72*d*e^2*x^2 + 63*e^3*x^3) + 3*b^5*x*(-d^4 - 8*d^3*e*x + 8*d*e^3*x^3 + e^4*x^4) - a*b^4*(d^4 + 24*d^3*e*x - 108*d^2*e^2*x^2 - 72*d*e^3*x^3 + 15*e^4*x^4)) + 12*e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)^3*Log[a + b*x])/(6*b^6*(a + b*x)^3)","A",1
1702,1,217,144,0.1211369,"\int \frac{(A+B x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{A b (b d-a e) \left(11 a^2 e^2+a b e (5 d+27 e x)+b^2 \left(2 d^2+9 d e x+18 e^2 x^2\right)\right)+B \left(26 a^4 e^3+3 a^3 b e^2 (18 e x-11 d)+3 a^2 b^2 e \left(2 d^2-27 d e x+6 e^2 x^2\right)+a b^3 \left(d^3+18 d^2 e x-54 d e^2 x^2-18 e^3 x^3\right)+3 b^4 x \left(d^3+6 d^2 e x-2 e^3 x^3\right)\right)-6 e^2 (a+b x)^3 \log (a+b x) (-4 a B e+A b e+3 b B d)}{6 b^5 (a+b x)^3}","\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,"-1/6*(A*b*(b*d - a*e)*(11*a^2*e^2 + a*b*e*(5*d + 27*e*x) + b^2*(2*d^2 + 9*d*e*x + 18*e^2*x^2)) + B*(26*a^4*e^3 + 3*a^3*b*e^2*(-11*d + 18*e*x) + 3*a^2*b^2*e*(2*d^2 - 27*d*e*x + 6*e^2*x^2) + a*b^3*(d^3 + 18*d^2*e*x - 54*d*e^2*x^2 - 18*e^3*x^3) + 3*b^4*x*(d^3 + 6*d^2*e*x - 2*e^3*x^3)) - 6*e^2*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^3*Log[a + b*x])/(b^5*(a + b*x)^3)","A",1
1703,1,138,101,0.0676859,"\int \frac{(A+B x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{-2 A b \left(a^2 e^2+a b e (d+3 e x)+b^2 \left(d^2+3 d e x+3 e^2 x^2\right)\right)+B \left(11 a^3 e^2+a^2 b e (27 e x-4 d)-a b^2 \left(d^2+12 d e x-18 e^2 x^2\right)-3 b^3 d x (d+4 e x)\right)+6 B e^2 (a+b x)^3 \log (a+b x)}{6 b^4 (a+b x)^3}","-\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*(11*a^3*e^2 - 3*b^3*d*x*(d + 4*e*x) + a^2*b*e*(-4*d + 27*e*x) - a*b^2*(d^2 + 12*d*e*x - 18*e^2*x^2)) - 2*A*b*(a^2*e^2 + a*b*e*(d + 3*e*x) + b^2*(d^2 + 3*d*e*x + 3*e^2*x^2)) + 6*B*e^2*(a + b*x)^3*Log[a + b*x])/(6*b^4*(a + b*x)^3)","A",1
1704,1,61,73,0.0290557,"\int \frac{(A+B x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{B \left(2 a^2 e+a b (d+6 e x)+3 b^2 x (d+2 e x)\right)+A b (a e+2 b d+3 b e x)}{6 b^3 (a+b x)^3}","-\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,"-1/6*(A*b*(2*b*d + a*e + 3*b*e*x) + B*(2*a^2*e + 3*b^2*x*(d + 2*e*x) + a*b*(d + 6*e*x)))/(b^3*(a + b*x)^3)","A",1
1705,1,27,38,0.0097296,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{B (a+3 b x)+2 A b}{6 b^2 (a+b x)^3}","-\frac{A b-a B}{3 b^2 (a+b x)^3}-\frac{B}{2 b^2 (a+b x)^2}",1,"-1/6*(2*A*b + B*(a + 3*b*x))/(b^2*(a + b*x)^3)","A",1
1706,1,136,146,0.0877008,"\int \frac{A+B x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{6 e^2 \log (a+b x) (B d-A e)+\frac{2 (a B-A b) (b d-a e)^3}{b (a+b x)^3}+\frac{3 (b d-a e)^2 (A e-B d)}{(a+b x)^2}+\frac{6 e (a e-b d) (A e-B d)}{a+b x}+6 e^2 (A e-B d) \log (d+e x)}{6 (b d-a e)^4}","\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,"((2*(-(A*b) + a*B)*(b*d - a*e)^3)/(b*(a + b*x)^3) + (3*(b*d - a*e)^2*(-(B*d) + A*e))/(a + b*x)^2 + (6*e*(-(b*d) + a*e)*(-(B*d) + A*e))/(a + b*x) + 6*e^2*(B*d - A*e)*Log[a + b*x] + 6*e^2*(-(B*d) + A*e)*Log[d + e*x])/(6*(b*d - a*e)^4)","A",1
1707,1,189,199,0.1296537,"\int \frac{A+B x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{6 e^2 (a e-b d) (A e-B d)}{d+e x}+6 e^2 \log (a+b x) (a B e-4 A b e+3 b B d)-6 e^2 \log (d+e x) (a B e-4 A b e+3 b B d)+\frac{2 (a B-A b) (b d-a e)^3}{(a+b x)^3}-\frac{3 (b d-a e)^2 (a B e-2 A b e+b B d)}{(a+b x)^2}+\frac{6 e (a e-b d) (-a B e+3 A b e-2 b B d)}{a+b x}}{6 (b d-a e)^5}","\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,"((2*(-(A*b) + a*B)*(b*d - a*e)^3)/(a + b*x)^3 - (3*(b*d - a*e)^2*(b*B*d - 2*A*b*e + a*B*e))/(a + b*x)^2 + (6*e*(-(b*d) + a*e)*(-2*b*B*d + 3*A*b*e - a*B*e))/(a + b*x) + (6*e^2*(-(b*d) + a*e)*(-(B*d) + A*e))/(d + e*x) + 6*e^2*(3*b*B*d - 4*A*b*e + a*B*e)*Log[a + b*x] - 6*e^2*(3*b*B*d - 4*A*b*e + a*B*e)*Log[d + e*x])/(6*(b*d - a*e)^5)","A",1
1708,1,208,158,0.0792741,"\int (A+B x) (d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} \left(7 a \left(6 A \left(5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right)+B x \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)\right)+b x \left(7 A \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)+2 B x \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)\right)\right)}{210 (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,"(x*Sqrt[(a + b*x)^2]*(7*a*(6*A*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4) + B*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4)) + b*x*(7*A*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4) + 2*B*x*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4))))/(210*(a + b*x))","A",1
1709,1,163,158,0.0647187,"\int (A+B x) (d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} \left(3 a \left(5 A \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+B x \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)\right)+b x \left(3 A \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)+B x \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)\right)\right)}{60 (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,"(x*Sqrt[(a + b*x)^2]*(3*a*(5*A*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) + B*x*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3)) + b*x*(3*A*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3) + B*x*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3))))/(60*(a + b*x))","A",1
1710,1,120,158,0.0448527,"\int (A+B x) (d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} \left(5 a \left(4 A \left(3 d^2+3 d e x+e^2 x^2\right)+B x \left(6 d^2+8 d e x+3 e^2 x^2\right)\right)+b x \left(5 A \left(6 d^2+8 d e x+3 e^2 x^2\right)+2 B x \left(10 d^2+15 d e x+6 e^2 x^2\right)\right)\right)}{60 (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,"(x*Sqrt[(a + b*x)^2]*(5*a*(4*A*(3*d^2 + 3*d*e*x + e^2*x^2) + B*x*(6*d^2 + 8*d*e*x + 3*e^2*x^2)) + b*x*(5*A*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + 2*B*x*(10*d^2 + 15*d*e*x + 6*e^2*x^2))))/(60*(a + b*x))","A",1
1711,1,74,164,0.0355025,"\int (A+B x) (d+e x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} (2 a (3 A (2 d+e x)+B x (3 d+2 e x))+b x (A (6 d+4 e x)+B x (4 d+3 e x)))}{12 (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{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{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,"(x*Sqrt[(a + b*x)^2]*(2*a*(3*A*(2*d + e*x) + B*x*(3*d + 2*e*x)) + b*x*(B*x*(4*d + 3*e*x) + A*(6*d + 4*e*x))))/(12*(a + b*x))","A",1
1712,1,45,69,0.0147051,"\int (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} (3 a (2 A+B x)+b x (3 A+2 B x))}{6 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(3*a*(2*A + B*x) + b*x*(3*A + 2*B*x)))/(6*(a + b*x))","A",1
1713,1,74,132,0.0414466,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{d+e x} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x),x]","\frac{\sqrt{(a+b x)^2} (e x (2 a B e+b (2 A e-2 B d+B e x))+2 (b d-a e) (B d-A e) \log (d+e x))}{2 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) \log (d+e x)}{e^3 (a+b 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{B (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 b e}",1,"(Sqrt[(a + b*x)^2]*(e*x*(2*a*B*e + b*(-2*B*d + 2*A*e + B*e*x)) + 2*(b*d - a*e)*(B*d - A*e)*Log[d + e*x]))/(2*e^3*(a + b*x))","A",1
1714,1,96,144,0.0455143,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^2} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^2,x]","\frac{\sqrt{(a+b x)^2} \left(-(d+e x) \log (d+e x) (-a B e-A b e+2 b B d)+a e (B d-A e)+b \left(A d e-B d^2+B d e x+B e^2 x^2\right)\right)}{e^3 (a+b x) (d+e 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,"(Sqrt[(a + b*x)^2]*(a*e*(B*d - A*e) + b*(-(B*d^2) + A*d*e + B*d*e*x + B*e^2*x^2) - (2*b*B*d - A*b*e - a*B*e)*(d + e*x)*Log[d + e*x]))/(e^3*(a + b*x)*(d + e*x))","A",1
1715,1,89,151,0.047575,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^3} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^3,x]","-\frac{\sqrt{(a+b x)^2} \left(a e (A e+B (d+2 e x))+b (A e (d+2 e x)-B d (3 d+4 e x))-2 b B (d+e x)^2 \log (d+e x)\right)}{2 e^3 (a+b x) (d+e x)^2}","-\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,"-1/2*(Sqrt[(a + b*x)^2]*(a*e*(A*e + B*(d + 2*e*x)) + b*(A*e*(d + 2*e*x) - B*d*(3*d + 4*e*x)) - 2*b*B*(d + e*x)^2*Log[d + e*x]))/(e^3*(a + b*x)*(d + e*x)^2)","A",1
1716,1,81,104,0.0369396,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^4} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^4,x]","-\frac{\sqrt{(a+b x)^2} \left(a e (2 A e+B (d+3 e x))+b \left(A e (d+3 e x)+2 B \left(d^2+3 d e x+3 e^2 x^2\right)\right)\right)}{6 e^3 (a+b x) (d+e x)^3}","\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,"-1/6*(Sqrt[(a + b*x)^2]*(a*e*(2*A*e + B*(d + 3*e*x)) + b*(A*e*(d + 3*e*x) + 2*B*(d^2 + 3*d*e*x + 3*e^2*x^2))))/(e^3*(a + b*x)*(d + e*x)^3)","A",1
1717,1,80,158,0.0353536,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^5} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^5,x]","-\frac{\sqrt{(a+b x)^2} \left(a e (3 A e+B (d+4 e x))+b \left(A e (d+4 e x)+B \left(d^2+4 d e x+6 e^2 x^2\right)\right)\right)}{12 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)}{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,"-1/12*(Sqrt[(a + b*x)^2]*(a*e*(3*A*e + B*(d + 4*e*x)) + b*(A*e*(d + 4*e*x) + B*(d^2 + 4*d*e*x + 6*e^2*x^2))))/(e^3*(a + b*x)*(d + e*x)^4)","A",1
1718,1,83,158,0.037875,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^6} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^6,x]","-\frac{\sqrt{(a+b x)^2} \left(3 a e (4 A e+B (d+5 e x))+b \left(3 A e (d+5 e x)+2 B \left(d^2+5 d e x+10 e^2 x^2\right)\right)\right)}{60 e^3 (a+b x) (d+e x)^5}","\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,"-1/60*(Sqrt[(a + b*x)^2]*(3*a*e*(4*A*e + B*(d + 5*e*x)) + b*(3*A*e*(d + 5*e*x) + 2*B*(d^2 + 5*d*e*x + 10*e^2*x^2))))/(e^3*(a + b*x)*(d + e*x)^5)","A",1
1719,1,82,158,0.0392905,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^7} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^7,x]","-\frac{\sqrt{(a+b x)^2} \left(2 a e (5 A e+B (d+6 e x))+b \left(2 A e (d+6 e x)+B \left(d^2+6 d e x+15 e^2 x^2\right)\right)\right)}{60 e^3 (a+b x) (d+e x)^6}","\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,"-1/60*(Sqrt[(a + b*x)^2]*(2*a*e*(5*A*e + B*(d + 6*e*x)) + b*(2*A*e*(d + 6*e*x) + B*(d^2 + 6*d*e*x + 15*e^2*x^2))))/(e^3*(a + b*x)*(d + e*x)^6)","A",1
1720,1,496,298,0.2048094,"\int (A+B x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(60 a^3 \left(7 A \left(6 d^5+15 d^4 e x+20 d^3 e^2 x^2+15 d^2 e^3 x^3+6 d e^4 x^4+e^5 x^5\right)+B x \left(21 d^5+70 d^4 e x+105 d^3 e^2 x^2+84 d^2 e^3 x^3+35 d e^4 x^4+6 e^5 x^5\right)\right)+45 a^2 b x \left(4 A \left(21 d^5+70 d^4 e x+105 d^3 e^2 x^2+84 d^2 e^3 x^3+35 d e^4 x^4+6 e^5 x^5\right)+B x \left(56 d^5+210 d^4 e x+336 d^3 e^2 x^2+280 d^2 e^3 x^3+120 d e^4 x^4+21 e^5 x^5\right)\right)+15 a b^2 x^2 \left(3 A \left(56 d^5+210 d^4 e x+336 d^3 e^2 x^2+280 d^2 e^3 x^3+120 d e^4 x^4+21 e^5 x^5\right)+B x \left(126 d^5+504 d^4 e x+840 d^3 e^2 x^2+720 d^2 e^3 x^3+315 d e^4 x^4+56 e^5 x^5\right)\right)+b^3 x^3 \left(5 A \left(126 d^5+504 d^4 e x+840 d^3 e^2 x^2+720 d^2 e^3 x^3+315 d e^4 x^4+56 e^5 x^5\right)+2 B x \left(252 d^5+1050 d^4 e x+1800 d^3 e^2 x^2+1575 d^2 e^3 x^3+700 d e^4 x^4+126 e^5 x^5\right)\right)\right)}{2520 (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,"(x*Sqrt[(a + b*x)^2]*(60*a^3*(7*A*(6*d^5 + 15*d^4*e*x + 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 + 6*d*e^4*x^4 + e^5*x^5) + B*x*(21*d^5 + 70*d^4*e*x + 105*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 35*d*e^4*x^4 + 6*e^5*x^5)) + 45*a^2*b*x*(4*A*(21*d^5 + 70*d^4*e*x + 105*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 35*d*e^4*x^4 + 6*e^5*x^5) + B*x*(56*d^5 + 210*d^4*e*x + 336*d^3*e^2*x^2 + 280*d^2*e^3*x^3 + 120*d*e^4*x^4 + 21*e^5*x^5)) + 15*a*b^2*x^2*(3*A*(56*d^5 + 210*d^4*e*x + 336*d^3*e^2*x^2 + 280*d^2*e^3*x^3 + 120*d*e^4*x^4 + 21*e^5*x^5) + B*x*(126*d^5 + 504*d^4*e*x + 840*d^3*e^2*x^2 + 720*d^2*e^3*x^3 + 315*d*e^4*x^4 + 56*e^5*x^5)) + b^3*x^3*(5*A*(126*d^5 + 504*d^4*e*x + 840*d^3*e^2*x^2 + 720*d^2*e^3*x^3 + 315*d*e^4*x^4 + 56*e^5*x^5) + 2*B*x*(252*d^5 + 1050*d^4*e*x + 1800*d^3*e^2*x^2 + 1575*d^2*e^3*x^3 + 700*d*e^4*x^4 + 126*e^5*x^5))))/(2520*(a + b*x))","A",1
1721,1,410,298,0.1566874,"\int (A+B x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(84 a^3 \left(6 A \left(5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right)+B x \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)\right)+36 a^2 b x \left(7 A \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)+2 B x \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)\right)+9 a b^2 x^2 \left(8 A \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)+3 B x \left(70 d^4+224 d^3 e x+280 d^2 e^2 x^2+160 d e^3 x^3+35 e^4 x^4\right)\right)+b^3 x^3 \left(9 A \left(70 d^4+224 d^3 e x+280 d^2 e^2 x^2+160 d e^3 x^3+35 e^4 x^4\right)+4 B x \left(126 d^4+420 d^3 e x+540 d^2 e^2 x^2+315 d e^3 x^3+70 e^4 x^4\right)\right)\right)}{2520 (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,"(x*Sqrt[(a + b*x)^2]*(84*a^3*(6*A*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4) + B*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4)) + 36*a^2*b*x*(7*A*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4) + 2*B*x*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4)) + 9*a*b^2*x^2*(8*A*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4) + 3*B*x*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4)) + b^3*x^3*(9*A*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4) + 4*B*x*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4))))/(2520*(a + b*x))","A",1
1722,1,320,259,0.1411591,"\int (A+B x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(14 a^3 \left(5 A \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+B x \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)\right)+14 a^2 b x \left(3 A \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)+B x \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)\right)+2 a b^2 x^2 \left(7 A \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)+3 B x \left(35 d^3+84 d^2 e x+70 d e^2 x^2+20 e^3 x^3\right)\right)+b^3 x^3 \left(2 A \left(35 d^3+84 d^2 e x+70 d e^2 x^2+20 e^3 x^3\right)+B x \left(56 d^3+140 d^2 e x+120 d e^2 x^2+35 e^3 x^3\right)\right)\right)}{280 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(14*a^3*(5*A*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) + B*x*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3)) + 14*a^2*b*x*(3*A*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3) + B*x*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3)) + 2*a*b^2*x^2*(7*A*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3) + 3*B*x*(35*d^3 + 84*d^2*e*x + 70*d*e^2*x^2 + 20*e^3*x^3)) + b^3*x^3*(2*A*(35*d^3 + 84*d^2*e*x + 70*d*e^2*x^2 + 20*e^3*x^3) + B*x*(56*d^3 + 140*d^2*e*x + 120*d*e^2*x^2 + 35*e^3*x^3))))/(280*(a + b*x))","A",1
1723,1,233,198,0.0903574,"\int (A+B x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(35 a^3 \left(4 A \left(3 d^2+3 d e x+e^2 x^2\right)+B x \left(6 d^2+8 d e x+3 e^2 x^2\right)\right)+21 a^2 b x \left(5 A \left(6 d^2+8 d e x+3 e^2 x^2\right)+2 B x \left(10 d^2+15 d e x+6 e^2 x^2\right)\right)+21 a b^2 x^2 \left(2 A \left(10 d^2+15 d e x+6 e^2 x^2\right)+B x \left(15 d^2+24 d e x+10 e^2 x^2\right)\right)+b^3 x^3 \left(7 A \left(15 d^2+24 d e x+10 e^2 x^2\right)+4 B x \left(21 d^2+35 d e x+15 e^2 x^2\right)\right)\right)}{420 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(35*a^3*(4*A*(3*d^2 + 3*d*e*x + e^2*x^2) + B*x*(6*d^2 + 8*d*e*x + 3*e^2*x^2)) + 21*a^2*b*x*(5*A*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + 2*B*x*(10*d^2 + 15*d*e*x + 6*e^2*x^2)) + 21*a*b^2*x^2*(2*A*(10*d^2 + 15*d*e*x + 6*e^2*x^2) + B*x*(15*d^2 + 24*d*e*x + 10*e^2*x^2)) + b^3*x^3*(7*A*(15*d^2 + 24*d*e*x + 10*e^2*x^2) + 4*B*x*(21*d^2 + 35*d*e*x + 15*e^2*x^2))))/(420*(a + b*x))","A",1
1724,1,144,135,0.0861734,"\int (A+B x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(10 a^3 (3 A (2 d+e x)+B x (3 d+2 e x))+15 a^2 b x (A (6 d+4 e x)+B x (4 d+3 e x))+3 a b^2 x^2 (5 A (4 d+3 e x)+3 B x (5 d+4 e x))+b^3 x^3 (3 A (5 d+4 e x)+2 B x (6 d+5 e x))\right)}{60 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(10*a^3*(3*A*(2*d + e*x) + B*x*(3*d + 2*e*x)) + 3*a*b^2*x^2*(5*A*(4*d + 3*e*x) + 3*B*x*(5*d + 4*e*x)) + 15*a^2*b*x*(B*x*(4*d + 3*e*x) + A*(6*d + 4*e*x)) + b^3*x^3*(3*A*(5*d + 4*e*x) + 2*B*x*(6*d + 5*e*x))))/(60*(a + b*x))","A",1
1725,1,83,69,0.0282176,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(10 a^3 (2 A+B x)+10 a^2 b x (3 A+2 B x)+5 a b^2 x^2 (4 A+3 B x)+b^3 x^3 (5 A+4 B x)\right)}{20 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(10*a^3*(2*A + B*x) + 10*a^2*b*x*(3*A + 2*B*x) + 5*a*b^2*x^2*(4*A + 3*B*x) + b^3*x^3*(5*A + 4*B*x)))/(20*(a + b*x))","A",1
1726,1,187,236,0.1154828,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{d+e x} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x),x]","\frac{\sqrt{(a+b x)^2} \left(e x \left(12 a^3 B e^3+18 a^2 b e^2 (2 A e-2 B d+B e x)+6 a b^2 e \left(3 A e (e x-2 d)+B \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+b^3 \left(2 A e \left(6 d^2-3 d e x+2 e^2 x^2\right)+B \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)\right)+12 (b d-a e)^3 (B d-A e) \log (d+e x)\right)}{12 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) \log (d+e x)}{e^5 (a+b 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{B (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 b e}",1,"(Sqrt[(a + b*x)^2]*(e*x*(12*a^3*B*e^3 + 18*a^2*b*e^2*(-2*B*d + 2*A*e + B*e*x) + 6*a*b^2*e*(3*A*e*(-2*d + e*x) + B*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + b^3*(2*A*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + B*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3))) + 12*(b*d - a*e)^3*(B*d - A*e)*Log[d + e*x]))/(12*e^5*(a + b*x))","A",1
1727,1,262,285,0.1408162,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^2,x]","\frac{\sqrt{(a+b x)^2} \left(6 a^3 e^3 (B d-A e)+18 a^2 b e^2 \left(A d e+B \left(-d^2+d e x+e^2 x^2\right)\right)+9 a b^2 e \left(2 A e \left(-d^2+d e x+e^2 x^2\right)+B \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)\right)-6 (d+e x) (b d-a e)^2 \log (d+e x) (-a B e-3 A b e+4 b B d)+b^3 \left(3 A e \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+2 B \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)\right)\right)}{6 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)}{e^5 (a+b x) (d+e 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{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^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^5 (a+b x)}",1,"(Sqrt[(a + b*x)^2]*(6*a^3*e^3*(B*d - A*e) + 18*a^2*b*e^2*(A*d*e + B*(-d^2 + d*e*x + e^2*x^2)) + 9*a*b^2*e*(2*A*e*(-d^2 + d*e*x + e^2*x^2) + B*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3)) + b^3*(3*A*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 2*B*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4)) - 6*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)*Log[d + e*x]))/(6*e^5*(a + b*x)*(d + e*x))","A",1
1728,1,256,280,0.1480636,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^3,x]","\frac{\sqrt{(a+b x)^2} \left(-a^3 e^3 (A e+B (d+2 e x))-3 a^2 b e^2 (A e (d+2 e x)-B d (3 d+4 e x))+3 a b^2 e \left(A d e (3 d+4 e x)+B \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)\right)+6 b (d+e x)^2 (b d-a e) \log (d+e x) (-a B e-A b e+2 b B d)+b^3 \left(A e \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)+B \left(7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right)\right)\right)}{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)^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^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{b^3 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^3 (a+b x)}",1,"(Sqrt[(a + b*x)^2]*(-(a^3*e^3*(A*e + B*(d + 2*e*x))) - 3*a^2*b*e^2*(A*e*(d + 2*e*x) - B*d*(3*d + 4*e*x)) + 3*a*b^2*e*(A*d*e*(3*d + 4*e*x) + B*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3)) + b^3*(A*e*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + B*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4)) + 6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2*Log[d + e*x]))/(2*e^5*(a + b*x)*(d + e*x)^2)","A",1
1729,1,251,284,0.1458507,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^4,x]","-\frac{\sqrt{(a+b x)^2} \left(a^3 e^3 (2 A e+B (d+3 e x))+3 a^2 b e^2 \left(A e (d+3 e x)+2 B \left(d^2+3 d e x+3 e^2 x^2\right)\right)+3 a b^2 e \left(2 A e \left(d^2+3 d e x+3 e^2 x^2\right)-B d \left(11 d^2+27 d e x+18 e^2 x^2\right)\right)+6 b^2 (d+e x)^3 \log (d+e x) (-3 a B e-A b e+4 b B d)+b^3 \left(2 B \left(13 d^4+27 d^3 e x+9 d^2 e^2 x^2-9 d e^3 x^3-3 e^4 x^4\right)-A d e \left(11 d^2+27 d e x+18 e^2 x^2\right)\right)\right)}{6 e^5 (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) (-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,"-1/6*(Sqrt[(a + b*x)^2]*(a^3*e^3*(2*A*e + B*(d + 3*e*x)) + 3*a^2*b*e^2*(A*e*(d + 3*e*x) + 2*B*(d^2 + 3*d*e*x + 3*e^2*x^2)) + 3*a*b^2*e*(2*A*e*(d^2 + 3*d*e*x + 3*e^2*x^2) - B*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) + b^3*(-(A*d*e*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) + 2*B*(13*d^4 + 27*d^3*e*x + 9*d^2*e^2*x^2 - 9*d*e^3*x^3 - 3*e^4*x^4)) + 6*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3*Log[d + e*x]))/(e^5*(a + b*x)*(d + e*x)^3)","A",1
1730,1,240,257,0.1383284,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^5,x]","-\frac{\sqrt{(a+b x)^2} \left(a^3 e^3 (3 A e+B (d+4 e x))+3 a^2 b e^2 \left(A e (d+4 e x)+B \left(d^2+4 d e x+6 e^2 x^2\right)\right)+3 a b^2 e \left(A e \left(d^2+4 d e x+6 e^2 x^2\right)+3 B \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+b^3 \left(3 A e \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)-B d \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)\right)-12 b^3 B (d+e x)^4 \log (d+e x)\right)}{12 e^5 (a+b x) (d+e x)^4}","-\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,"-1/12*(Sqrt[(a + b*x)^2]*(a^3*e^3*(3*A*e + B*(d + 4*e*x)) + 3*a^2*b*e^2*(A*e*(d + 4*e*x) + B*(d^2 + 4*d*e*x + 6*e^2*x^2)) + 3*a*b^2*e*(A*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*B*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)) + b^3*(3*A*e*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) - B*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) - 12*b^3*B*(d + e*x)^4*Log[d + e*x]))/(e^5*(a + b*x)*(d + e*x)^4)","A",1
1731,1,229,106,0.103625,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^6,x]","-\frac{\sqrt{(a+b x)^2} \left(a^3 e^3 (4 A e+B (d+5 e x))+a^2 b e^2 \left(3 A e (d+5 e x)+2 B \left(d^2+5 d e x+10 e^2 x^2\right)\right)+a b^2 e \left(2 A e \left(d^2+5 d e x+10 e^2 x^2\right)+3 B \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)+b^3 \left(A e \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+4 B \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)\right)}{20 e^5 (a+b x) (d+e x)^5}","\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,"-1/20*(Sqrt[(a + b*x)^2]*(a^3*e^3*(4*A*e + B*(d + 5*e*x)) + a^2*b*e^2*(3*A*e*(d + 5*e*x) + 2*B*(d^2 + 5*d*e*x + 10*e^2*x^2)) + a*b^2*e*(2*A*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*B*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)) + b^3*(A*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 4*B*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4))))/(e^5*(a + b*x)*(d + e*x)^5)","B",1
1732,1,229,193,0.1012848,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^7,x]","-\frac{\sqrt{(a+b x)^2} \left(2 a^3 e^3 (5 A e+B (d+6 e x))+3 a^2 b e^2 \left(2 A e (d+6 e x)+B \left(d^2+6 d e x+15 e^2 x^2\right)\right)+3 a b^2 e \left(A e \left(d^2+6 d e x+15 e^2 x^2\right)+B \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)+b^3 \left(A e \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+2 B \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)\right)}{60 e^5 (a+b x) (d+e x)^6}","\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,"-1/60*(Sqrt[(a + b*x)^2]*(2*a^3*e^3*(5*A*e + B*(d + 6*e*x)) + 3*a^2*b*e^2*(2*A*e*(d + 6*e*x) + B*(d^2 + 6*d*e*x + 15*e^2*x^2)) + 3*a*b^2*e*(A*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + B*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)) + b^3*(A*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 2*B*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4))))/(e^5*(a + b*x)*(d + e*x)^6)","A",1
1733,1,233,298,0.1013125,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^8,x]","-\frac{\sqrt{(a+b x)^2} \left(10 a^3 e^3 (6 A e+B (d+7 e x))+6 a^2 b e^2 \left(5 A e (d+7 e x)+2 B \left(d^2+7 d e x+21 e^2 x^2\right)\right)+3 a b^2 e \left(4 A e \left(d^2+7 d e x+21 e^2 x^2\right)+3 B \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)\right)+b^3 \left(3 A e \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+4 B \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)\right)}{420 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)}{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,"-1/420*(Sqrt[(a + b*x)^2]*(10*a^3*e^3*(6*A*e + B*(d + 7*e*x)) + 6*a^2*b*e^2*(5*A*e*(d + 7*e*x) + 2*B*(d^2 + 7*d*e*x + 21*e^2*x^2)) + 3*a*b^2*e*(4*A*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*B*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3)) + b^3*(3*A*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 4*B*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4))))/(e^5*(a + b*x)*(d + e*x)^7)","A",1
1734,1,229,298,0.1054601,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^9} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^9,x]","-\frac{\sqrt{(a+b x)^2} \left(5 a^3 e^3 (7 A e+B (d+8 e x))+5 a^2 b e^2 \left(3 A e (d+8 e x)+B \left(d^2+8 d e x+28 e^2 x^2\right)\right)+a b^2 e \left(5 A e \left(d^2+8 d e x+28 e^2 x^2\right)+3 B \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)\right)+b^3 \left(A e \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+B \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)\right)\right)}{280 e^5 (a+b x) (d+e x)^8}","\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,"-1/280*(Sqrt[(a + b*x)^2]*(5*a^3*e^3*(7*A*e + B*(d + 8*e*x)) + 5*a^2*b*e^2*(3*A*e*(d + 8*e*x) + B*(d^2 + 8*d*e*x + 28*e^2*x^2)) + a*b^2*e*(5*A*e*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*B*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3)) + b^3*(A*e*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + B*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4))))/(e^5*(a + b*x)*(d + e*x)^8)","A",1
1735,1,232,298,0.1081886,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{10}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^10,x]","-\frac{\sqrt{(a+b x)^2} \left(35 a^3 e^3 (8 A e+B (d+9 e x))+15 a^2 b e^2 \left(7 A e (d+9 e x)+2 B \left(d^2+9 d e x+36 e^2 x^2\right)\right)+15 a b^2 e \left(2 A e \left(d^2+9 d e x+36 e^2 x^2\right)+B \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)\right)+b^3 \left(5 A e \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)+4 B \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)\right)\right)}{2520 e^5 (a+b x) (d+e x)^9}","\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,"-1/2520*(Sqrt[(a + b*x)^2]*(35*a^3*e^3*(8*A*e + B*(d + 9*e*x)) + 15*a^2*b*e^2*(7*A*e*(d + 9*e*x) + 2*B*(d^2 + 9*d*e*x + 36*e^2*x^2)) + 15*a*b^2*e*(2*A*e*(d^2 + 9*d*e*x + 36*e^2*x^2) + B*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3)) + b^3*(5*A*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 4*B*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4))))/(e^5*(a + b*x)*(d + e*x)^9)","A",1
1736,1,232,298,0.1007247,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{11}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^11,x]","-\frac{\sqrt{(a+b x)^2} \left(28 a^3 e^3 (9 A e+B (d+10 e x))+21 a^2 b e^2 \left(4 A e (d+10 e x)+B \left(d^2+10 d e x+45 e^2 x^2\right)\right)+3 a b^2 e \left(7 A e \left(d^2+10 d e x+45 e^2 x^2\right)+3 B \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)\right)+b^3 \left(3 A e \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)+2 B \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)\right)\right)}{2520 e^5 (a+b x) (d+e x)^{10}}","\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,"-1/2520*(Sqrt[(a + b*x)^2]*(28*a^3*e^3*(9*A*e + B*(d + 10*e*x)) + 21*a^2*b*e^2*(4*A*e*(d + 10*e*x) + B*(d^2 + 10*d*e*x + 45*e^2*x^2)) + 3*a*b^2*e*(7*A*e*(d^2 + 10*d*e*x + 45*e^2*x^2) + 3*B*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3)) + b^3*(3*A*e*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 2*B*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4))))/(e^5*(a + b*x)*(d + e*x)^10)","A",1
1737,1,233,298,0.1115493,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{12}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^12,x]","-\frac{\sqrt{(a+b x)^2} \left(84 a^3 e^3 (10 A e+B (d+11 e x))+28 a^2 b e^2 \left(9 A e (d+11 e x)+2 B \left(d^2+11 d e x+55 e^2 x^2\right)\right)+7 a b^2 e \left(8 A e \left(d^2+11 d e x+55 e^2 x^2\right)+3 B \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)\right)+b^3 \left(7 A e \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)+4 B \left(d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right)\right)\right)}{9240 e^5 (a+b x) (d+e x)^{11}}","\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,"-1/9240*(Sqrt[(a + b*x)^2]*(84*a^3*e^3*(10*A*e + B*(d + 11*e*x)) + 28*a^2*b*e^2*(9*A*e*(d + 11*e*x) + 2*B*(d^2 + 11*d*e*x + 55*e^2*x^2)) + 7*a*b^2*e*(8*A*e*(d^2 + 11*d*e*x + 55*e^2*x^2) + 3*B*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3)) + b^3*(7*A*e*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3) + 4*B*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4))))/(e^5*(a + b*x)*(d + e*x)^11)","A",1
1738,1,876,436,0.3650661,"\int (A+B x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(1287 \left(8 A \left(7 d^6+21 e x d^5+35 e^2 x^2 d^4+35 e^3 x^3 d^3+21 e^4 x^4 d^2+7 e^5 x^5 d+e^6 x^6\right)+B x \left(28 d^6+112 e x d^5+210 e^2 x^2 d^4+224 e^3 x^3 d^3+140 e^4 x^4 d^2+48 e^5 x^5 d+7 e^6 x^6\right)\right) a^5+715 b x \left(9 A \left(28 d^6+112 e x d^5+210 e^2 x^2 d^4+224 e^3 x^3 d^3+140 e^4 x^4 d^2+48 e^5 x^5 d+7 e^6 x^6\right)+2 B x \left(84 d^6+378 e x d^5+756 e^2 x^2 d^4+840 e^3 x^3 d^3+540 e^4 x^4 d^2+189 e^5 x^5 d+28 e^6 x^6\right)\right) a^4+286 b^2 x^2 \left(10 A \left(84 d^6+378 e x d^5+756 e^2 x^2 d^4+840 e^3 x^3 d^3+540 e^4 x^4 d^2+189 e^5 x^5 d+28 e^6 x^6\right)+3 B x \left(210 d^6+1008 e x d^5+2100 e^2 x^2 d^4+2400 e^3 x^3 d^3+1575 e^4 x^4 d^2+560 e^5 x^5 d+84 e^6 x^6\right)\right) a^3+78 b^3 x^3 \left(11 A \left(210 d^6+1008 e x d^5+2100 e^2 x^2 d^4+2400 e^3 x^3 d^3+1575 e^4 x^4 d^2+560 e^5 x^5 d+84 e^6 x^6\right)+4 B x \left(462 d^6+2310 e x d^5+4950 e^2 x^2 d^4+5775 e^3 x^3 d^3+3850 e^4 x^4 d^2+1386 e^5 x^5 d+210 e^6 x^6\right)\right) a^2+13 b^4 x^4 \left(12 A \left(462 d^6+2310 e x d^5+4950 e^2 x^2 d^4+5775 e^3 x^3 d^3+3850 e^4 x^4 d^2+1386 e^5 x^5 d+210 e^6 x^6\right)+5 B x \left(924 d^6+4752 e x d^5+10395 e^2 x^2 d^4+12320 e^3 x^3 d^3+8316 e^4 x^4 d^2+3024 e^5 x^5 d+462 e^6 x^6\right)\right) a+b^5 x^5 \left(13 A \left(924 d^6+4752 e x d^5+10395 e^2 x^2 d^4+12320 e^3 x^3 d^3+8316 e^4 x^4 d^2+3024 e^5 x^5 d+462 e^6 x^6\right)+6 B x \left(1716 d^6+9009 e x d^5+20020 e^2 x^2 d^4+24024 e^3 x^3 d^3+16380 e^4 x^4 d^2+6006 e^5 x^5 d+924 e^6 x^6\right)\right)\right)}{72072 (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^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^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13}}{13 e^7 (a+b x)}",1,"(x*Sqrt[(a + b*x)^2]*(1287*a^5*(8*A*(7*d^6 + 21*d^5*e*x + 35*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 21*d^2*e^4*x^4 + 7*d*e^5*x^5 + e^6*x^6) + B*x*(28*d^6 + 112*d^5*e*x + 210*d^4*e^2*x^2 + 224*d^3*e^3*x^3 + 140*d^2*e^4*x^4 + 48*d*e^5*x^5 + 7*e^6*x^6)) + 715*a^4*b*x*(9*A*(28*d^6 + 112*d^5*e*x + 210*d^4*e^2*x^2 + 224*d^3*e^3*x^3 + 140*d^2*e^4*x^4 + 48*d*e^5*x^5 + 7*e^6*x^6) + 2*B*x*(84*d^6 + 378*d^5*e*x + 756*d^4*e^2*x^2 + 840*d^3*e^3*x^3 + 540*d^2*e^4*x^4 + 189*d*e^5*x^5 + 28*e^6*x^6)) + 286*a^3*b^2*x^2*(10*A*(84*d^6 + 378*d^5*e*x + 756*d^4*e^2*x^2 + 840*d^3*e^3*x^3 + 540*d^2*e^4*x^4 + 189*d*e^5*x^5 + 28*e^6*x^6) + 3*B*x*(210*d^6 + 1008*d^5*e*x + 2100*d^4*e^2*x^2 + 2400*d^3*e^3*x^3 + 1575*d^2*e^4*x^4 + 560*d*e^5*x^5 + 84*e^6*x^6)) + 78*a^2*b^3*x^3*(11*A*(210*d^6 + 1008*d^5*e*x + 2100*d^4*e^2*x^2 + 2400*d^3*e^3*x^3 + 1575*d^2*e^4*x^4 + 560*d*e^5*x^5 + 84*e^6*x^6) + 4*B*x*(462*d^6 + 2310*d^5*e*x + 4950*d^4*e^2*x^2 + 5775*d^3*e^3*x^3 + 3850*d^2*e^4*x^4 + 1386*d*e^5*x^5 + 210*e^6*x^6)) + 13*a*b^4*x^4*(12*A*(462*d^6 + 2310*d^5*e*x + 4950*d^4*e^2*x^2 + 5775*d^3*e^3*x^3 + 3850*d^2*e^4*x^4 + 1386*d*e^5*x^5 + 210*e^6*x^6) + 5*B*x*(924*d^6 + 4752*d^5*e*x + 10395*d^4*e^2*x^2 + 12320*d^3*e^3*x^3 + 8316*d^2*e^4*x^4 + 3024*d*e^5*x^5 + 462*e^6*x^6)) + b^5*x^5*(13*A*(924*d^6 + 4752*d^5*e*x + 10395*d^4*e^2*x^2 + 12320*d^3*e^3*x^3 + 8316*d^2*e^4*x^4 + 3024*d*e^5*x^5 + 462*e^6*x^6) + 6*B*x*(1716*d^6 + 9009*d^5*e*x + 20020*d^4*e^2*x^2 + 24024*d^3*e^3*x^3 + 16380*d^2*e^4*x^4 + 6006*d*e^5*x^5 + 924*e^6*x^6))))/(72072*(a + b*x))","B",1
1739,1,740,383,0.3148634,"\int (A+B x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(132 a^5 \left(7 A \left(6 d^5+15 d^4 e x+20 d^3 e^2 x^2+15 d^2 e^3 x^3+6 d e^4 x^4+e^5 x^5\right)+B x \left(21 d^5+70 d^4 e x+105 d^3 e^2 x^2+84 d^2 e^3 x^3+35 d e^4 x^4+6 e^5 x^5\right)\right)+165 a^4 b x \left(4 A \left(21 d^5+70 d^4 e x+105 d^3 e^2 x^2+84 d^2 e^3 x^3+35 d e^4 x^4+6 e^5 x^5\right)+B x \left(56 d^5+210 d^4 e x+336 d^3 e^2 x^2+280 d^2 e^3 x^3+120 d e^4 x^4+21 e^5 x^5\right)\right)+110 a^3 b^2 x^2 \left(3 A \left(56 d^5+210 d^4 e x+336 d^3 e^2 x^2+280 d^2 e^3 x^3+120 d e^4 x^4+21 e^5 x^5\right)+B x \left(126 d^5+504 d^4 e x+840 d^3 e^2 x^2+720 d^2 e^3 x^3+315 d e^4 x^4+56 e^5 x^5\right)\right)+22 a^2 b^3 x^3 \left(5 A \left(126 d^5+504 d^4 e x+840 d^3 e^2 x^2+720 d^2 e^3 x^3+315 d e^4 x^4+56 e^5 x^5\right)+2 B x \left(252 d^5+1050 d^4 e x+1800 d^3 e^2 x^2+1575 d^2 e^3 x^3+700 d e^4 x^4+126 e^5 x^5\right)\right)+2 a b^4 x^4 \left(11 A \left(252 d^5+1050 d^4 e x+1800 d^3 e^2 x^2+1575 d^2 e^3 x^3+700 d e^4 x^4+126 e^5 x^5\right)+5 B x \left(462 d^5+1980 d^4 e x+3465 d^3 e^2 x^2+3080 d^2 e^3 x^3+1386 d e^4 x^4+252 e^5 x^5\right)\right)+b^5 x^5 \left(A \left(924 d^5+3960 d^4 e x+6930 d^3 e^2 x^2+6160 d^2 e^3 x^3+2772 d e^4 x^4+504 e^5 x^5\right)+B x \left(792 d^5+3465 d^4 e x+6160 d^3 e^2 x^2+5544 d^2 e^3 x^3+2520 d e^4 x^4+462 e^5 x^5\right)\right)\right)}{5544 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(132*a^5*(7*A*(6*d^5 + 15*d^4*e*x + 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 + 6*d*e^4*x^4 + e^5*x^5) + B*x*(21*d^5 + 70*d^4*e*x + 105*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 35*d*e^4*x^4 + 6*e^5*x^5)) + 165*a^4*b*x*(4*A*(21*d^5 + 70*d^4*e*x + 105*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 35*d*e^4*x^4 + 6*e^5*x^5) + B*x*(56*d^5 + 210*d^4*e*x + 336*d^3*e^2*x^2 + 280*d^2*e^3*x^3 + 120*d*e^4*x^4 + 21*e^5*x^5)) + 110*a^3*b^2*x^2*(3*A*(56*d^5 + 210*d^4*e*x + 336*d^3*e^2*x^2 + 280*d^2*e^3*x^3 + 120*d*e^4*x^4 + 21*e^5*x^5) + B*x*(126*d^5 + 504*d^4*e*x + 840*d^3*e^2*x^2 + 720*d^2*e^3*x^3 + 315*d*e^4*x^4 + 56*e^5*x^5)) + 22*a^2*b^3*x^3*(5*A*(126*d^5 + 504*d^4*e*x + 840*d^3*e^2*x^2 + 720*d^2*e^3*x^3 + 315*d*e^4*x^4 + 56*e^5*x^5) + 2*B*x*(252*d^5 + 1050*d^4*e*x + 1800*d^3*e^2*x^2 + 1575*d^2*e^3*x^3 + 700*d*e^4*x^4 + 126*e^5*x^5)) + 2*a*b^4*x^4*(11*A*(252*d^5 + 1050*d^4*e*x + 1800*d^3*e^2*x^2 + 1575*d^2*e^3*x^3 + 700*d*e^4*x^4 + 126*e^5*x^5) + 5*B*x*(462*d^5 + 1980*d^4*e*x + 3465*d^3*e^2*x^2 + 3080*d^2*e^3*x^3 + 1386*d*e^4*x^4 + 252*e^5*x^5)) + b^5*x^5*(B*x*(792*d^5 + 3465*d^4*e*x + 6160*d^3*e^2*x^2 + 5544*d^2*e^3*x^3 + 2520*d*e^4*x^4 + 462*e^5*x^5) + A*(924*d^5 + 3960*d^4*e*x + 6930*d^3*e^2*x^2 + 6160*d^2*e^3*x^3 + 2772*d*e^4*x^4 + 504*e^5*x^5))))/(5544*(a + b*x))","A",1
1740,1,611,324,0.2361918,"\int (A+B x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(462 a^5 \left(6 A \left(5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right)+B x \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)\right)+330 a^4 b x \left(7 A \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)+2 B x \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)\right)+165 a^3 b^2 x^2 \left(8 A \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)+3 B x \left(70 d^4+224 d^3 e x+280 d^2 e^2 x^2+160 d e^3 x^3+35 e^4 x^4\right)\right)+55 a^2 b^3 x^3 \left(9 A \left(70 d^4+224 d^3 e x+280 d^2 e^2 x^2+160 d e^3 x^3+35 e^4 x^4\right)+4 B x \left(126 d^4+420 d^3 e x+540 d^2 e^2 x^2+315 d e^3 x^3+70 e^4 x^4\right)\right)+55 a b^4 x^4 \left(2 A \left(126 d^4+420 d^3 e x+540 d^2 e^2 x^2+315 d e^3 x^3+70 e^4 x^4\right)+B x \left(210 d^4+720 d^3 e x+945 d^2 e^2 x^2+560 d e^3 x^3+126 e^4 x^4\right)\right)+b^5 x^5 \left(11 A \left(210 d^4+720 d^3 e x+945 d^2 e^2 x^2+560 d e^3 x^3+126 e^4 x^4\right)+6 B x \left(330 d^4+1155 d^3 e x+1540 d^2 e^2 x^2+924 d e^3 x^3+210 e^4 x^4\right)\right)\right)}{13860 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(462*a^5*(6*A*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4) + B*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4)) + 330*a^4*b*x*(7*A*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4) + 2*B*x*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4)) + 165*a^3*b^2*x^2*(8*A*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4) + 3*B*x*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4)) + 55*a^2*b^3*x^3*(9*A*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4) + 4*B*x*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4)) + 55*a*b^4*x^4*(2*A*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4) + B*x*(210*d^4 + 720*d^3*e*x + 945*d^2*e^2*x^2 + 560*d*e^3*x^3 + 126*e^4*x^4)) + b^5*x^5*(11*A*(210*d^4 + 720*d^3*e*x + 945*d^2*e^2*x^2 + 560*d*e^3*x^3 + 126*e^4*x^4) + 6*B*x*(330*d^4 + 1155*d^3*e*x + 1540*d^2*e^2*x^2 + 924*d*e^3*x^3 + 210*e^4*x^4))))/(13860*(a + b*x))","A",1
1741,1,478,259,0.196164,"\int (A+B x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(126 a^5 \left(5 A \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+B x \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)\right)+210 a^4 b x \left(3 A \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)+B x \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)\right)+60 a^3 b^2 x^2 \left(7 A \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)+3 B x \left(35 d^3+84 d^2 e x+70 d e^2 x^2+20 e^3 x^3\right)\right)+90 a^2 b^3 x^3 \left(2 A \left(35 d^3+84 d^2 e x+70 d e^2 x^2+20 e^3 x^3\right)+B x \left(56 d^3+140 d^2 e x+120 d e^2 x^2+35 e^3 x^3\right)\right)+5 a b^4 x^4 \left(9 A \left(56 d^3+140 d^2 e x+120 d e^2 x^2+35 e^3 x^3\right)+5 B x \left(84 d^3+216 d^2 e x+189 d e^2 x^2+56 e^3 x^3\right)\right)+b^5 x^5 \left(5 A \left(84 d^3+216 d^2 e x+189 d e^2 x^2+56 e^3 x^3\right)+3 B x \left(120 d^3+315 d^2 e x+280 d e^2 x^2+84 e^3 x^3\right)\right)\right)}{2520 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(126*a^5*(5*A*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) + B*x*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3)) + 210*a^4*b*x*(3*A*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3) + B*x*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3)) + 60*a^3*b^2*x^2*(7*A*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3) + 3*B*x*(35*d^3 + 84*d^2*e*x + 70*d*e^2*x^2 + 20*e^3*x^3)) + 90*a^2*b^3*x^3*(2*A*(35*d^3 + 84*d^2*e*x + 70*d*e^2*x^2 + 20*e^3*x^3) + B*x*(56*d^3 + 140*d^2*e*x + 120*d*e^2*x^2 + 35*e^3*x^3)) + 5*a*b^4*x^4*(9*A*(56*d^3 + 140*d^2*e*x + 120*d*e^2*x^2 + 35*e^3*x^3) + 5*B*x*(84*d^3 + 216*d^2*e*x + 189*d*e^2*x^2 + 56*e^3*x^3)) + b^5*x^5*(5*A*(84*d^3 + 216*d^2*e*x + 189*d*e^2*x^2 + 56*e^3*x^3) + 3*B*x*(120*d^3 + 315*d^2*e*x + 280*d*e^2*x^2 + 84*e^3*x^3))))/(2520*(a + b*x))","A",1
1742,1,347,198,0.1446134,"\int (A+B x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(42 a^5 \left(4 A \left(3 d^2+3 d e x+e^2 x^2\right)+B x \left(6 d^2+8 d e x+3 e^2 x^2\right)\right)+42 a^4 b x \left(5 A \left(6 d^2+8 d e x+3 e^2 x^2\right)+2 B x \left(10 d^2+15 d e x+6 e^2 x^2\right)\right)+84 a^3 b^2 x^2 \left(2 A \left(10 d^2+15 d e x+6 e^2 x^2\right)+B x \left(15 d^2+24 d e x+10 e^2 x^2\right)\right)+12 a^2 b^3 x^3 \left(7 A \left(15 d^2+24 d e x+10 e^2 x^2\right)+4 B x \left(21 d^2+35 d e x+15 e^2 x^2\right)\right)+3 a b^4 x^4 \left(8 A \left(21 d^2+35 d e x+15 e^2 x^2\right)+5 B x \left(28 d^2+48 d e x+21 e^2 x^2\right)\right)+b^5 x^5 \left(3 A \left(28 d^2+48 d e x+21 e^2 x^2\right)+2 B x \left(36 d^2+63 d e x+28 e^2 x^2\right)\right)\right)}{504 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(42*a^5*(4*A*(3*d^2 + 3*d*e*x + e^2*x^2) + B*x*(6*d^2 + 8*d*e*x + 3*e^2*x^2)) + 42*a^4*b*x*(5*A*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + 2*B*x*(10*d^2 + 15*d*e*x + 6*e^2*x^2)) + 84*a^3*b^2*x^2*(2*A*(10*d^2 + 15*d*e*x + 6*e^2*x^2) + B*x*(15*d^2 + 24*d*e*x + 10*e^2*x^2)) + 12*a^2*b^3*x^3*(7*A*(15*d^2 + 24*d*e*x + 10*e^2*x^2) + 4*B*x*(21*d^2 + 35*d*e*x + 15*e^2*x^2)) + 3*a*b^4*x^4*(8*A*(21*d^2 + 35*d*e*x + 15*e^2*x^2) + 5*B*x*(28*d^2 + 48*d*e*x + 21*e^2*x^2)) + b^5*x^5*(3*A*(28*d^2 + 48*d*e*x + 21*e^2*x^2) + 2*B*x*(36*d^2 + 63*d*e*x + 28*e^2*x^2))))/(504*(a + b*x))","A",1
1743,1,214,135,0.0981982,"\int (A+B x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(28 a^5 (3 A (2 d+e x)+B x (3 d+2 e x))+70 a^4 b x (A (6 d+4 e x)+B x (4 d+3 e x))+28 a^3 b^2 x^2 (5 A (4 d+3 e x)+3 B x (5 d+4 e x))+28 a^2 b^3 x^3 (3 A (5 d+4 e x)+2 B x (6 d+5 e x))+4 a b^4 x^4 (7 A (6 d+5 e x)+5 B x (7 d+6 e x))+b^5 x^5 (4 A (7 d+6 e x)+3 B x (8 d+7 e x))\right)}{168 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(28*a^5*(3*A*(2*d + e*x) + B*x*(3*d + 2*e*x)) + 28*a^3*b^2*x^2*(5*A*(4*d + 3*e*x) + 3*B*x*(5*d + 4*e*x)) + 70*a^4*b*x*(B*x*(4*d + 3*e*x) + A*(6*d + 4*e*x)) + 28*a^2*b^3*x^3*(3*A*(5*d + 4*e*x) + 2*B*x*(6*d + 5*e*x)) + 4*a*b^4*x^4*(7*A*(6*d + 5*e*x) + 5*B*x*(7*d + 6*e*x)) + b^5*x^5*(4*A*(7*d + 6*e*x) + 3*B*x*(8*d + 7*e*x))))/(168*(a + b*x))","A",1
1744,1,121,69,0.0437829,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(21 a^5 (2 A+B x)+35 a^4 b x (3 A+2 B x)+35 a^3 b^2 x^2 (4 A+3 B x)+21 a^2 b^3 x^3 (5 A+4 B x)+7 a b^4 x^4 (6 A+5 B x)+b^5 x^5 (7 A+6 B x)\right)}{42 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(21*a^5*(2*A + B*x) + 35*a^4*b*x*(3*A + 2*B*x) + 35*a^3*b^2*x^2*(4*A + 3*B*x) + 21*a^2*b^3*x^3*(5*A + 4*B*x) + 7*a*b^4*x^4*(6*A + 5*B*x) + b^5*x^5*(7*A + 6*B*x)))/(42*(a + b*x))","A",1
1745,1,386,340,0.2351243,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{d+e x} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x),x]","\frac{\sqrt{(a+b x)^2} \left(e x \left(60 a^5 B e^5+150 a^4 b e^4 (2 A e-2 B d+B e x)+100 a^3 b^2 e^3 \left(3 A e (e x-2 d)+B \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+50 a^2 b^3 e^2 \left(2 A e \left(6 d^2-3 d e x+2 e^2 x^2\right)+B \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)+5 a b^4 e \left(5 A e \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+B \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)+b^5 \left(A e \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)+B \left(-60 d^5+30 d^4 e x-20 d^3 e^2 x^2+15 d^2 e^3 x^3-12 d e^4 x^4+10 e^5 x^5\right)\right)\right)+60 (b d-a e)^5 (B d-A e) \log (d+e x)\right)}{60 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) \log (d+e x)}{e^7 (a+b 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{B (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 b e}",1,"(Sqrt[(a + b*x)^2]*(e*x*(60*a^5*B*e^5 + 150*a^4*b*e^4*(-2*B*d + 2*A*e + B*e*x) + 100*a^3*b^2*e^3*(3*A*e*(-2*d + e*x) + B*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + 50*a^2*b^3*e^2*(2*A*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + B*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)) + 5*a*b^4*e*(5*A*e*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + B*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4)) + b^5*(A*e*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + B*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5))) + 60*(b*d - a*e)^5*(B*d - A*e)*Log[d + e*x]))/(60*e^7*(a + b*x))","A",1
1746,1,506,423,0.3082486,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^2,x]","\frac{\sqrt{(a+b x)^2} \left(60 a^5 e^5 (B d-A e)+300 a^4 b e^4 \left(A d e+B \left(-d^2+d e x+e^2 x^2\right)\right)+300 a^3 b^2 e^3 \left(2 A e \left(-d^2+d e x+e^2 x^2\right)+B \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)\right)+100 a^2 b^3 e^2 \left(3 A e \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+2 B \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)\right)+25 a b^4 e \left(4 A e \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)+B \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)\right)-60 (d+e x) (b d-a e)^4 \log (d+e x) (-a B e-5 A b e+6 b B d)+b^5 \left(5 A e \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)-6 B \left(10 d^6-50 d^5 e x-30 d^4 e^2 x^2+10 d^3 e^3 x^3-5 d^2 e^4 x^4+3 d e^5 x^5-2 e^6 x^6\right)\right)\right)}{60 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)}{e^7 (a+b x) (d+e 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{\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{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{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{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^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5}{5 e^7 (a+b x)}",1,"(Sqrt[(a + b*x)^2]*(60*a^5*e^5*(B*d - A*e) + 300*a^4*b*e^4*(A*d*e + B*(-d^2 + d*e*x + e^2*x^2)) + 300*a^3*b^2*e^3*(2*A*e*(-d^2 + d*e*x + e^2*x^2) + B*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3)) + 100*a^2*b^3*e^2*(3*A*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 2*B*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4)) + 25*a*b^4*e*(4*A*e*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + B*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5)) + b^5*(5*A*e*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5) - 6*B*(10*d^6 - 50*d^5*e*x - 30*d^4*e^2*x^2 + 10*d^3*e^3*x^3 - 5*d^2*e^4*x^4 + 3*d*e^5*x^5 - 2*e^6*x^6)) - 60*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x)*Log[d + e*x]))/(60*e^7*(a + b*x)*(d + e*x))","A",1
1747,1,501,424,0.2883017,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^3,x]","\frac{\sqrt{(a+b x)^2} \left(-6 a^5 e^5 (A e+B (d+2 e x))-30 a^4 b e^4 (A e (d+2 e x)-B d (3 d+4 e x))+60 a^3 b^2 e^3 \left(A d e (3 d+4 e x)+B \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)\right)+60 a^2 b^3 e^2 \left(A e \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)+B \left(7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right)\right)+10 a b^4 e \left(3 A e \left(7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right)+B \left(-27 d^5+6 d^4 e x+63 d^3 e^2 x^2+20 d^2 e^3 x^3-5 d e^4 x^4+2 e^5 x^5\right)\right)+60 b (d+e x)^2 (b d-a e)^3 \log (d+e x) (-a B e-2 A b e+3 b B d)+b^5 \left(2 A e \left(-27 d^5+6 d^4 e x+63 d^3 e^2 x^2+20 d^2 e^3 x^3-5 d e^4 x^4+2 e^5 x^5\right)+3 B \left(22 d^6-16 d^5 e x-68 d^4 e^2 x^2-20 d^3 e^3 x^3+5 d^2 e^4 x^4-2 d e^5 x^5+e^6 x^6\right)\right)\right)}{12 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)}{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{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{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{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,"(Sqrt[(a + b*x)^2]*(-6*a^5*e^5*(A*e + B*(d + 2*e*x)) - 30*a^4*b*e^4*(A*e*(d + 2*e*x) - B*d*(3*d + 4*e*x)) + 60*a^3*b^2*e^3*(A*d*e*(3*d + 4*e*x) + B*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3)) + 60*a^2*b^3*e^2*(A*e*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + B*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4)) + 10*a*b^4*e*(3*A*e*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4) + B*(-27*d^5 + 6*d^4*e*x + 63*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5)) + b^5*(2*A*e*(-27*d^5 + 6*d^4*e*x + 63*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5) + 3*B*(22*d^6 - 16*d^5*e*x - 68*d^4*e^2*x^2 - 20*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 2*d*e^5*x^5 + e^6*x^6)) + 60*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2*Log[d + e*x]))/(12*e^7*(a + b*x)*(d + e*x)^2)","A",1
1748,1,504,425,0.3193189,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^4,x]","-\frac{\sqrt{(a+b x)^2} \left(a^5 e^5 (2 A e+B (d+3 e x))+5 a^4 b e^4 \left(A e (d+3 e x)+2 B \left(d^2+3 d e x+3 e^2 x^2\right)\right)+10 a^3 b^2 e^3 \left(2 A e \left(d^2+3 d e x+3 e^2 x^2\right)-B d \left(11 d^2+27 d e x+18 e^2 x^2\right)\right)-10 a^2 b^3 e^2 \left(A d e \left(11 d^2+27 d e x+18 e^2 x^2\right)-2 B \left(13 d^4+27 d^3 e x+9 d^2 e^2 x^2-9 d e^3 x^3-3 e^4 x^4\right)\right)-5 a b^4 e \left(2 A e \left(-13 d^4-27 d^3 e x-9 d^2 e^2 x^2+9 d e^3 x^3+3 e^4 x^4\right)+B \left(47 d^5+81 d^4 e x-9 d^3 e^2 x^2-63 d^2 e^3 x^3-15 d e^4 x^4+3 e^5 x^5\right)\right)+60 b^2 (d+e x)^3 (b d-a e)^2 \log (d+e x) (-a B e-A b e+2 b B d)+b^5 \left(A e \left(-47 d^5-81 d^4 e x+9 d^3 e^2 x^2+63 d^2 e^3 x^3+15 d e^4 x^4-3 e^5 x^5\right)+2 B \left(37 d^6+51 d^5 e x-39 d^4 e^2 x^2-73 d^3 e^3 x^3-15 d^2 e^4 x^4+3 d e^5 x^5-e^6 x^6\right)\right)\right)}{6 e^7 (a+b x) (d+e x)^3}","-\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^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{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,"-1/6*(Sqrt[(a + b*x)^2]*(a^5*e^5*(2*A*e + B*(d + 3*e*x)) + 5*a^4*b*e^4*(A*e*(d + 3*e*x) + 2*B*(d^2 + 3*d*e*x + 3*e^2*x^2)) + 10*a^3*b^2*e^3*(2*A*e*(d^2 + 3*d*e*x + 3*e^2*x^2) - B*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) - 10*a^2*b^3*e^2*(A*d*e*(11*d^2 + 27*d*e*x + 18*e^2*x^2) - 2*B*(13*d^4 + 27*d^3*e*x + 9*d^2*e^2*x^2 - 9*d*e^3*x^3 - 3*e^4*x^4)) - 5*a*b^4*e*(2*A*e*(-13*d^4 - 27*d^3*e*x - 9*d^2*e^2*x^2 + 9*d*e^3*x^3 + 3*e^4*x^4) + B*(47*d^5 + 81*d^4*e*x - 9*d^3*e^2*x^2 - 63*d^2*e^3*x^3 - 15*d*e^4*x^4 + 3*e^5*x^5)) + b^5*(A*e*(-47*d^5 - 81*d^4*e*x + 9*d^3*e^2*x^2 + 63*d^2*e^3*x^3 + 15*d*e^4*x^4 - 3*e^5*x^5) + 2*B*(37*d^6 + 51*d^5*e*x - 39*d^4*e^2*x^2 - 73*d^3*e^3*x^3 - 15*d^2*e^4*x^4 + 3*d*e^5*x^5 - e^6*x^6)) + 60*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3*Log[d + e*x]))/(e^7*(a + b*x)*(d + e*x)^3)","A",1
1749,1,497,421,0.299328,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^5,x]","-\frac{\sqrt{(a+b x)^2} \left(a^5 e^5 (3 A e+B (d+4 e x))+5 a^4 b e^4 \left(A e (d+4 e x)+B \left(d^2+4 d e x+6 e^2 x^2\right)\right)+10 a^3 b^2 e^3 \left(A e \left(d^2+4 d e x+6 e^2 x^2\right)+3 B \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+10 a^2 b^3 e^2 \left(3 A e \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)-B d \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)\right)-5 a b^4 e \left(A d e \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)-B \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)\right)-60 b^3 (d+e x)^4 (b d-a e) \log (d+e x) (-2 a B e-A b e+3 b B d)+b^5 \left(A e \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)-3 B \left(57 d^6+168 d^5 e x+132 d^4 e^2 x^2-32 d^3 e^3 x^3-68 d^2 e^4 x^4-12 d e^5 x^5+2 e^6 x^6\right)\right)\right)}{12 e^7 (a+b x) (d+e x)^4}","\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{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{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,"-1/12*(Sqrt[(a + b*x)^2]*(a^5*e^5*(3*A*e + B*(d + 4*e*x)) + 5*a^4*b*e^4*(A*e*(d + 4*e*x) + B*(d^2 + 4*d*e*x + 6*e^2*x^2)) + 10*a^3*b^2*e^3*(A*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*B*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)) + 10*a^2*b^3*e^2*(3*A*e*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) - B*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) - 5*a*b^4*e*(A*d*e*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3) - B*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5)) + b^5*(A*e*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5) - 3*B*(57*d^6 + 168*d^5*e*x + 132*d^4*e^2*x^2 - 32*d^3*e^3*x^3 - 68*d^2*e^4*x^4 - 12*d*e^5*x^5 + 2*e^6*x^6)) - 60*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4*Log[d + e*x]))/(e^7*(a + b*x)*(d + e*x)^4)","A",1
1750,1,490,422,0.2867954,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^6,x]","-\frac{\sqrt{(a+b x)^2} \left(3 a^5 e^5 (4 A e+B (d+5 e x))+5 a^4 b e^4 \left(3 A e (d+5 e x)+2 B \left(d^2+5 d e x+10 e^2 x^2\right)\right)+10 a^3 b^2 e^3 \left(2 A e \left(d^2+5 d e x+10 e^2 x^2\right)+3 B \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)+30 a^2 b^3 e^2 \left(A e \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+4 B \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)+5 a b^4 e \left(12 A e \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)-B d \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)\right)+60 b^4 (d+e x)^5 \log (d+e x) (-5 a B e-A b e+6 b B d)+b^5 \left(6 B \left(87 d^6+375 d^5 e x+600 d^4 e^2 x^2+400 d^3 e^3 x^3+50 d^2 e^4 x^4-50 d e^5 x^5-10 e^6 x^6\right)-A d e \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)\right)\right)}{60 e^7 (a+b x) (d+e x)^5}","\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{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{b^5 B x \sqrt{a^2+2 a b x+b^2 x^2}}{e^6 (a+b x)}",1,"-1/60*(Sqrt[(a + b*x)^2]*(3*a^5*e^5*(4*A*e + B*(d + 5*e*x)) + 5*a^4*b*e^4*(3*A*e*(d + 5*e*x) + 2*B*(d^2 + 5*d*e*x + 10*e^2*x^2)) + 10*a^3*b^2*e^3*(2*A*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*B*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)) + 30*a^2*b^3*e^2*(A*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 4*B*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4)) + 5*a*b^4*e*(12*A*e*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4) - B*d*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4)) + b^5*(-(A*d*e*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4)) + 6*B*(87*d^6 + 375*d^5*e*x + 600*d^4*e^2*x^2 + 400*d^3*e^3*x^3 + 50*d^2*e^4*x^4 - 50*d*e^5*x^5 - 10*e^6*x^6)) + 60*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5*Log[d + e*x]))/(e^7*(a + b*x)*(d + e*x)^5)","A",1
1751,1,477,365,0.2865895,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^7,x]","-\frac{\sqrt{(a+b x)^2} \left(2 a^5 e^5 (5 A e+B (d+6 e x))+5 a^4 b e^4 \left(2 A e (d+6 e x)+B \left(d^2+6 d e x+15 e^2 x^2\right)\right)+10 a^3 b^2 e^3 \left(A e \left(d^2+6 d e x+15 e^2 x^2\right)+B \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)+10 a^2 b^3 e^2 \left(A e \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+2 B \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)+10 a b^4 e \left(A e \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)+5 B \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right)\right)+b^5 \left(10 A e \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right)-B d \left(147 d^5+822 d^4 e x+1875 d^3 e^2 x^2+2200 d^2 e^3 x^3+1350 d e^4 x^4+360 e^5 x^5\right)\right)-60 b^5 B (d+e x)^6 \log (d+e x)\right)}{60 e^7 (a+b x) (d+e x)^6}","-\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{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{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}",1,"-1/60*(Sqrt[(a + b*x)^2]*(2*a^5*e^5*(5*A*e + B*(d + 6*e*x)) + 5*a^4*b*e^4*(2*A*e*(d + 6*e*x) + B*(d^2 + 6*d*e*x + 15*e^2*x^2)) + 10*a^3*b^2*e^3*(A*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + B*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)) + 10*a^2*b^3*e^2*(A*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 2*B*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)) + 10*a*b^4*e*(A*e*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4) + 5*B*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5)) + b^5*(10*A*e*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5) - B*d*(147*d^5 + 822*d^4*e*x + 1875*d^3*e^2*x^2 + 2200*d^2*e^3*x^3 + 1350*d*e^4*x^4 + 360*e^5*x^5)) - 60*b^5*B*(d + e*x)^6*Log[d + e*x]))/(e^7*(a + b*x)*(d + e*x)^6)","A",1
1752,1,465,106,0.2038028,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^8,x]","-\frac{\sqrt{(a+b x)^2} \left(a^5 e^5 (6 A e+B (d+7 e x))+a^4 b e^4 \left(5 A e (d+7 e x)+2 B \left(d^2+7 d e x+21 e^2 x^2\right)\right)+a^3 b^2 e^3 \left(4 A e \left(d^2+7 d e x+21 e^2 x^2\right)+3 B \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)\right)+a^2 b^3 e^2 \left(3 A e \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+4 B \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)+a b^4 e \left(2 A e \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)+5 B \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)\right)+b^5 \left(A e \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)+6 B \left(d^6+7 d^5 e x+21 d^4 e^2 x^2+35 d^3 e^3 x^3+35 d^2 e^4 x^4+21 d e^5 x^5+7 e^6 x^6\right)\right)\right)}{42 e^7 (a+b x) (d+e x)^7}","\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,"-1/42*(Sqrt[(a + b*x)^2]*(a^5*e^5*(6*A*e + B*(d + 7*e*x)) + a^4*b*e^4*(5*A*e*(d + 7*e*x) + 2*B*(d^2 + 7*d*e*x + 21*e^2*x^2)) + a^3*b^2*e^3*(4*A*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*B*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3)) + a^2*b^3*e^2*(3*A*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 4*B*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)) + a*b^4*e*(2*A*e*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4) + 5*B*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5)) + b^5*(A*e*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5) + 6*B*(d^6 + 7*d^5*e*x + 21*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 35*d^2*e^4*x^4 + 21*d*e^5*x^5 + 7*e^6*x^6))))/(e^7*(a + b*x)*(d + e*x)^7)","B",1
1753,1,466,193,0.2129721,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^9} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^9,x]","-\frac{\sqrt{(a+b x)^2} \left(3 a^5 e^5 (7 A e+B (d+8 e x))+5 a^4 b e^4 \left(3 A e (d+8 e x)+B \left(d^2+8 d e x+28 e^2 x^2\right)\right)+2 a^3 b^2 e^3 \left(5 A e \left(d^2+8 d e x+28 e^2 x^2\right)+3 B \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)\right)+6 a^2 b^3 e^2 \left(A e \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+B \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)\right)+a b^4 e \left(3 A e \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)+5 B \left(d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right)\right)+b^5 \left(A e \left(d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right)+3 B \left(d^6+8 d^5 e x+28 d^4 e^2 x^2+56 d^3 e^3 x^3+70 d^2 e^4 x^4+56 d e^5 x^5+28 e^6 x^6\right)\right)\right)}{168 e^7 (a+b x) (d+e x)^8}","\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,"-1/168*(Sqrt[(a + b*x)^2]*(3*a^5*e^5*(7*A*e + B*(d + 8*e*x)) + 5*a^4*b*e^4*(3*A*e*(d + 8*e*x) + B*(d^2 + 8*d*e*x + 28*e^2*x^2)) + 2*a^3*b^2*e^3*(5*A*e*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*B*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3)) + 6*a^2*b^3*e^2*(A*e*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + B*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4)) + a*b^4*e*(3*A*e*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4) + 5*B*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5)) + b^5*(A*e*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5) + 3*B*(d^6 + 8*d^5*e*x + 28*d^4*e^2*x^2 + 56*d^3*e^3*x^3 + 70*d^2*e^4*x^4 + 56*d*e^5*x^5 + 28*e^6*x^6))))/(e^7*(a + b*x)*(d + e*x)^8)","B",1
1754,1,468,262,0.213136,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{10}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^10,x]","-\frac{\sqrt{(a+b x)^2} \left(7 a^5 e^5 (8 A e+B (d+9 e x))+5 a^4 b e^4 \left(7 A e (d+9 e x)+2 B \left(d^2+9 d e x+36 e^2 x^2\right)\right)+10 a^3 b^2 e^3 \left(2 A e \left(d^2+9 d e x+36 e^2 x^2\right)+B \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)\right)+2 a^2 b^3 e^2 \left(5 A e \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)+4 B \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)\right)+a b^4 e \left(4 A e \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)+5 B \left(d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right)\right)+b^5 \left(A e \left(d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right)+2 B \left(d^6+9 d^5 e x+36 d^4 e^2 x^2+84 d^3 e^3 x^3+126 d^2 e^4 x^4+126 d e^5 x^5+84 e^6 x^6\right)\right)\right)}{504 e^7 (a+b x) (d+e x)^9}","\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,"-1/504*(Sqrt[(a + b*x)^2]*(7*a^5*e^5*(8*A*e + B*(d + 9*e*x)) + 5*a^4*b*e^4*(7*A*e*(d + 9*e*x) + 2*B*(d^2 + 9*d*e*x + 36*e^2*x^2)) + 10*a^3*b^2*e^3*(2*A*e*(d^2 + 9*d*e*x + 36*e^2*x^2) + B*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3)) + 2*a^2*b^3*e^2*(5*A*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 4*B*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4)) + a*b^4*e*(4*A*e*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4) + 5*B*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5)) + b^5*(A*e*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5) + 2*B*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6))))/(e^7*(a + b*x)*(d + e*x)^9)","A",1
1755,1,468,438,0.2147649,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{11}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^11,x]","-\frac{\sqrt{(a+b x)^2} \left(28 a^5 e^5 (9 A e+B (d+10 e x))+35 a^4 b e^4 \left(4 A e (d+10 e x)+B \left(d^2+10 d e x+45 e^2 x^2\right)\right)+10 a^3 b^2 e^3 \left(7 A e \left(d^2+10 d e x+45 e^2 x^2\right)+3 B \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)\right)+10 a^2 b^3 e^2 \left(3 A e \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)+2 B \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)\right)+10 a b^4 e \left(A e \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)+B \left(d^5+10 d^4 e x+45 d^3 e^2 x^2+120 d^2 e^3 x^3+210 d e^4 x^4+252 e^5 x^5\right)\right)+b^5 \left(2 A e \left(d^5+10 d^4 e x+45 d^3 e^2 x^2+120 d^2 e^3 x^3+210 d e^4 x^4+252 e^5 x^5\right)+3 B \left(d^6+10 d^5 e x+45 d^4 e^2 x^2+120 d^3 e^3 x^3+210 d^2 e^4 x^4+252 d e^5 x^5+210 e^6 x^6\right)\right)\right)}{2520 e^7 (a+b x) (d+e x)^{10}}","\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^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{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,"-1/2520*(Sqrt[(a + b*x)^2]*(28*a^5*e^5*(9*A*e + B*(d + 10*e*x)) + 35*a^4*b*e^4*(4*A*e*(d + 10*e*x) + B*(d^2 + 10*d*e*x + 45*e^2*x^2)) + 10*a^3*b^2*e^3*(7*A*e*(d^2 + 10*d*e*x + 45*e^2*x^2) + 3*B*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3)) + 10*a^2*b^3*e^2*(3*A*e*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 2*B*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4)) + 10*a*b^4*e*(A*e*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4) + B*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5)) + b^5*(2*A*e*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5) + 3*B*(d^6 + 10*d^5*e*x + 45*d^4*e^2*x^2 + 120*d^3*e^3*x^3 + 210*d^2*e^4*x^4 + 252*d*e^5*x^5 + 210*e^6*x^6))))/(e^7*(a + b*x)*(d + e*x)^10)","A",1
1756,1,471,438,0.2281438,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{12}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^12,x]","-\frac{\sqrt{(a+b x)^2} \left(126 a^5 e^5 (10 A e+B (d+11 e x))+70 a^4 b e^4 \left(9 A e (d+11 e x)+2 B \left(d^2+11 d e x+55 e^2 x^2\right)\right)+35 a^3 b^2 e^3 \left(8 A e \left(d^2+11 d e x+55 e^2 x^2\right)+3 B \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)\right)+15 a^2 b^3 e^2 \left(7 A e \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)+4 B \left(d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right)\right)+5 a b^4 e \left(6 A e \left(d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right)+5 B \left(d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right)\right)+b^5 \left(5 A e \left(d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right)+6 B \left(d^6+11 d^5 e x+55 d^4 e^2 x^2+165 d^3 e^3 x^3+330 d^2 e^4 x^4+462 d e^5 x^5+462 e^6 x^6\right)\right)\right)}{13860 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)^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^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{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,"-1/13860*(Sqrt[(a + b*x)^2]*(126*a^5*e^5*(10*A*e + B*(d + 11*e*x)) + 70*a^4*b*e^4*(9*A*e*(d + 11*e*x) + 2*B*(d^2 + 11*d*e*x + 55*e^2*x^2)) + 35*a^3*b^2*e^3*(8*A*e*(d^2 + 11*d*e*x + 55*e^2*x^2) + 3*B*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3)) + 15*a^2*b^3*e^2*(7*A*e*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3) + 4*B*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4)) + 5*a*b^4*e*(6*A*e*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4) + 5*B*(d^5 + 11*d^4*e*x + 55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*e^5*x^5)) + b^5*(5*A*e*(d^5 + 11*d^4*e*x + 55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*e^5*x^5) + 6*B*(d^6 + 11*d^5*e*x + 55*d^4*e^2*x^2 + 165*d^3*e^3*x^3 + 330*d^2*e^4*x^4 + 462*d*e^5*x^5 + 462*e^6*x^6))))/(e^7*(a + b*x)*(d + e*x)^11)","A",1
1757,1,465,438,0.2095347,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{13}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^13,x]","-\frac{\sqrt{(a+b x)^2} \left(42 a^5 e^5 (11 A e+B (d+12 e x))+42 a^4 b e^4 \left(5 A e (d+12 e x)+B \left(d^2+12 d e x+66 e^2 x^2\right)\right)+28 a^3 b^2 e^3 \left(3 A e \left(d^2+12 d e x+66 e^2 x^2\right)+B \left(d^3+12 d^2 e x+66 d e^2 x^2+220 e^3 x^3\right)\right)+14 a^2 b^3 e^2 \left(2 A e \left(d^3+12 d^2 e x+66 d e^2 x^2+220 e^3 x^3\right)+B \left(d^4+12 d^3 e x+66 d^2 e^2 x^2+220 d e^3 x^3+495 e^4 x^4\right)\right)+a b^4 e \left(7 A e \left(d^4+12 d^3 e x+66 d^2 e^2 x^2+220 d e^3 x^3+495 e^4 x^4\right)+5 B \left(d^5+12 d^4 e x+66 d^3 e^2 x^2+220 d^2 e^3 x^3+495 d e^4 x^4+792 e^5 x^5\right)\right)+b^5 \left(A e \left(d^5+12 d^4 e x+66 d^3 e^2 x^2+220 d^2 e^3 x^3+495 d e^4 x^4+792 e^5 x^5\right)+B \left(d^6+12 d^5 e x+66 d^4 e^2 x^2+220 d^3 e^3 x^3+495 d^2 e^4 x^4+792 d e^5 x^5+924 e^6 x^6\right)\right)\right)}{5544 e^7 (a+b x) (d+e x)^{12}}","\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^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{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,"-1/5544*(Sqrt[(a + b*x)^2]*(42*a^5*e^5*(11*A*e + B*(d + 12*e*x)) + 42*a^4*b*e^4*(5*A*e*(d + 12*e*x) + B*(d^2 + 12*d*e*x + 66*e^2*x^2)) + 28*a^3*b^2*e^3*(3*A*e*(d^2 + 12*d*e*x + 66*e^2*x^2) + B*(d^3 + 12*d^2*e*x + 66*d*e^2*x^2 + 220*e^3*x^3)) + 14*a^2*b^3*e^2*(2*A*e*(d^3 + 12*d^2*e*x + 66*d*e^2*x^2 + 220*e^3*x^3) + B*(d^4 + 12*d^3*e*x + 66*d^2*e^2*x^2 + 220*d*e^3*x^3 + 495*e^4*x^4)) + a*b^4*e*(7*A*e*(d^4 + 12*d^3*e*x + 66*d^2*e^2*x^2 + 220*d*e^3*x^3 + 495*e^4*x^4) + 5*B*(d^5 + 12*d^4*e*x + 66*d^3*e^2*x^2 + 220*d^2*e^3*x^3 + 495*d*e^4*x^4 + 792*e^5*x^5)) + b^5*(A*e*(d^5 + 12*d^4*e*x + 66*d^3*e^2*x^2 + 220*d^2*e^3*x^3 + 495*d*e^4*x^4 + 792*e^5*x^5) + B*(d^6 + 12*d^5*e*x + 66*d^4*e^2*x^2 + 220*d^3*e^3*x^3 + 495*d^2*e^4*x^4 + 792*d*e^5*x^5 + 924*e^6*x^6))))/(e^7*(a + b*x)*(d + e*x)^12)","A",1
1758,1,471,435,0.2141827,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{14}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^14,x]","-\frac{\sqrt{(a+b x)^2} \left(462 a^5 e^5 (12 A e+B (d+13 e x))+210 a^4 b e^4 \left(11 A e (d+13 e x)+2 B \left(d^2+13 d e x+78 e^2 x^2\right)\right)+84 a^3 b^2 e^3 \left(10 A e \left(d^2+13 d e x+78 e^2 x^2\right)+3 B \left(d^3+13 d^2 e x+78 d e^2 x^2+286 e^3 x^3\right)\right)+28 a^2 b^3 e^2 \left(9 A e \left(d^3+13 d^2 e x+78 d e^2 x^2+286 e^3 x^3\right)+4 B \left(d^4+13 d^3 e x+78 d^2 e^2 x^2+286 d e^3 x^3+715 e^4 x^4\right)\right)+7 a b^4 e \left(8 A e \left(d^4+13 d^3 e x+78 d^2 e^2 x^2+286 d e^3 x^3+715 e^4 x^4\right)+5 B \left(d^5+13 d^4 e x+78 d^3 e^2 x^2+286 d^2 e^3 x^3+715 d e^4 x^4+1287 e^5 x^5\right)\right)+b^5 \left(7 A e \left(d^5+13 d^4 e x+78 d^3 e^2 x^2+286 d^2 e^3 x^3+715 d e^4 x^4+1287 e^5 x^5\right)+6 B \left(d^6+13 d^5 e x+78 d^4 e^2 x^2+286 d^3 e^3 x^3+715 d^2 e^4 x^4+1287 d e^5 x^5+1716 e^6 x^6\right)\right)\right)}{72072 e^7 (a+b x) (d+e x)^{13}}","\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^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^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 e^7 (a+b x) (d+e x)^7}",1,"-1/72072*(Sqrt[(a + b*x)^2]*(462*a^5*e^5*(12*A*e + B*(d + 13*e*x)) + 210*a^4*b*e^4*(11*A*e*(d + 13*e*x) + 2*B*(d^2 + 13*d*e*x + 78*e^2*x^2)) + 84*a^3*b^2*e^3*(10*A*e*(d^2 + 13*d*e*x + 78*e^2*x^2) + 3*B*(d^3 + 13*d^2*e*x + 78*d*e^2*x^2 + 286*e^3*x^3)) + 28*a^2*b^3*e^2*(9*A*e*(d^3 + 13*d^2*e*x + 78*d*e^2*x^2 + 286*e^3*x^3) + 4*B*(d^4 + 13*d^3*e*x + 78*d^2*e^2*x^2 + 286*d*e^3*x^3 + 715*e^4*x^4)) + 7*a*b^4*e*(8*A*e*(d^4 + 13*d^3*e*x + 78*d^2*e^2*x^2 + 286*d*e^3*x^3 + 715*e^4*x^4) + 5*B*(d^5 + 13*d^4*e*x + 78*d^3*e^2*x^2 + 286*d^2*e^3*x^3 + 715*d*e^4*x^4 + 1287*e^5*x^5)) + b^5*(7*A*e*(d^5 + 13*d^4*e*x + 78*d^3*e^2*x^2 + 286*d^2*e^3*x^3 + 715*d*e^4*x^4 + 1287*e^5*x^5) + 6*B*(d^6 + 13*d^5*e*x + 78*d^4*e^2*x^2 + 286*d^3*e^3*x^3 + 715*d^2*e^4*x^4 + 1287*d*e^5*x^5 + 1716*e^6*x^6))))/(e^7*(a + b*x)*(d + e*x)^13)","A",1
1759,1,185,248,0.125566,"\int \frac{(A+B x) (d+e x)^3}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \left(b x \left(-12 a^3 B e^3+6 a^2 b e^2 (2 A e+6 B d+B e x)-2 a b^2 e \left(3 A e (6 d+e x)+B \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+b^3 \left(2 A e \left(18 d^2+9 d e x+2 e^2 x^2\right)+3 B \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)\right)\right)+12 (A b-a B) (b d-a e)^3 \log (a+b x)\right)}{12 b^5 \sqrt{(a+b 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) (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{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) (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{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*x)*(b*x*(-12*a^3*B*e^3 + 6*a^2*b*e^2*(6*B*d + 2*A*e + B*e*x) - 2*a*b^2*e*(3*A*e*(6*d + e*x) + B*(18*d^2 + 9*d*e*x + 2*e^2*x^2)) + b^3*(2*A*e*(18*d^2 + 9*d*e*x + 2*e^2*x^2) + 3*B*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3))) + 12*(A*b - a*B)*(b*d - a*e)^3*Log[a + b*x]))/(12*b^5*Sqrt[(a + b*x)^2])","A",1
1760,1,118,191,0.0829842,"\int \frac{(A+B x) (d+e x)^2}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \left(b x \left(6 a^2 B e^2-3 a b e (2 A e+4 B d+B e x)+b^2 \left(3 A e (4 d+e x)+2 B \left(3 d^2+3 d e x+e^2 x^2\right)\right)\right)+6 (A b-a B) (b d-a e)^2 \log (a+b x)\right)}{6 b^4 \sqrt{(a+b 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{(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{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{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*x)*(b*x*(6*a^2*B*e^2 - 3*a*b*e*(4*B*d + 2*A*e + B*e*x) + b^2*(3*A*e*(4*d + e*x) + 2*B*(3*d^2 + 3*d*e*x + e^2*x^2))) + 6*(A*b - a*B)*(b*d - a*e)^2*Log[a + b*x]))/(6*b^4*Sqrt[(a + b*x)^2])","A",1
1761,1,72,134,0.0407386,"\int \frac{(A+B x) (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((A + B*x)*(d + e*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (b x (b (2 A e+2 B d+B e x)-2 a B e)+2 (A b-a B) (b d-a e) \log (a+b x))}{2 b^3 \sqrt{(a+b 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{(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{B x (a+b x) (b d-a e)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*(b*x*(-2*a*B*e + b*(2*B*d + 2*A*e + B*e*x)) + 2*(A*b - a*B)*(b*d - a*e)*Log[a + b*x]))/(2*b^3*Sqrt[(a + b*x)^2])","A",1
1762,1,40,69,0.0168405,"\int \frac{A+B x}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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 B x)}{b^2 \sqrt{(a+b x)^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,"((a + b*x)*(b*B*x + (A*b - a*B)*Log[a + b*x]))/(b^2*Sqrt[(a + b*x)^2])","A",1
1763,1,66,107,0.0391343,"\int \frac{A+B x}{(d+e x) \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) (e (A b-a B) \log (a+b x)+b (B d-A e) \log (d+e x))}{b e \sqrt{(a+b 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*x)*((A*b - a*B)*e*Log[a + b*x] + b*(B*d - A*e)*Log[d + e*x]))/(b*e*(b*d - a*e)*Sqrt[(a + b*x)^2])","A",1
1764,1,97,148,0.1236633,"\int \frac{A+B x}{(d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) \left(\frac{B d-A e}{e (d+e x) (a e-b d)}+\frac{(A b-a B) \log (a+b x)}{(b d-a e)^2}+\frac{(a B-A b) \log (d+e x)}{(b d-a e)^2}\right)}{\sqrt{(a+b x)^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,"((a + b*x)*((B*d - A*e)/(e*(-(b*d) + a*e)*(d + e*x)) + ((A*b - a*B)*Log[a + b*x])/(b*d - a*e)^2 + ((-(A*b) + a*B)*Log[d + e*x])/(b*d - a*e)^2))/Sqrt[(a + b*x)^2]","A",1
1765,1,131,212,0.1536532,"\int \frac{A+B x}{(d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) \left(\frac{2 (A b-a B)}{(d+e x) (b d-a e)^2}+\frac{B d-A e}{e (d+e x)^2 (a e-b d)}+\frac{2 b (A b-a B) \log (a+b x)}{(b d-a e)^3}-\frac{2 b (A b-a B) \log (d+e x)}{(b d-a e)^3}\right)}{2 \sqrt{(a+b x)^2}}","\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,"((a + b*x)*((B*d - A*e)/(e*(-(b*d) + a*e)*(d + e*x)^2) + (2*(A*b - a*B))/((b*d - a*e)^2*(d + e*x)) + (2*b*(A*b - a*B)*Log[a + b*x])/(b*d - a*e)^3 - (2*b*(A*b - a*B)*Log[d + e*x])/(b*d - a*e)^3))/(2*Sqrt[(a + b*x)^2])","A",1
1766,1,168,271,0.1596399,"\int \frac{A+B x}{(d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) \left(6 b^2 e (d+e x)^3 (A b-a B) \log (a+b x)-6 b^2 e (d+e x)^3 (A b-a B) \log (d+e x)+3 e (d+e x) (A b-a B) (b d-a e)^2+6 b e (d+e x)^2 (A b-a B) (b d-a e)-2 (b d-a e)^3 (B d-A e)\right)}{6 e \sqrt{(a+b x)^2} (d+e x)^3 (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,"((a + b*x)*(-2*(b*d - a*e)^3*(B*d - A*e) + 3*(A*b - a*B)*e*(b*d - a*e)^2*(d + e*x) + 6*b*(A*b - a*B)*e*(b*d - a*e)*(d + e*x)^2 + 6*b^2*(A*b - a*B)*e*(d + e*x)^3*Log[a + b*x] - 6*b^2*(A*b - a*B)*e*(d + e*x)^3*Log[d + e*x]))/(6*e*(b*d - a*e)^4*Sqrt[(a + b*x)^2]*(d + e*x)^3)","A",1
1767,1,373,329,0.2282227,"\int \frac{(A+B x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{-3 A b \left(-7 a^4 e^4-2 a^3 b e^3 (e x-10 d)+a^2 b^2 e^2 \left(-18 d^2+16 d e x+11 e^2 x^2\right)+4 a b^3 e \left(d^3-6 d^2 e x-4 d e^2 x^2+e^3 x^3\right)+b^4 \left(d^4+8 d^3 e x-8 d e^3 x^3-e^4 x^4\right)\right)+B \left(-27 a^5 e^4+6 a^4 b e^3 (14 d+e x)+3 a^3 b^2 e^2 \left(-30 d^2+8 d e x+21 e^2 x^2\right)+4 a^2 b^3 e \left(9 d^3-18 d^2 e x-33 d e^2 x^2+5 e^3 x^3\right)+a b^4 \left(-3 d^4+48 d^3 e x+72 d^2 e^2 x^2-48 d e^3 x^3-5 e^4 x^4\right)+2 b^5 x \left(-3 d^4+18 d^2 e^2 x^2+6 d e^3 x^3+e^4 x^4\right)\right)+12 e (a+b x)^2 (b d-a e)^2 \log (a+b x) (-5 a B e+3 A b e+2 b B d)}{6 b^6 (a+b x) \sqrt{(a+b 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{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{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{B e^4 x^3 (a+b x)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-3*A*b*(-7*a^4*e^4 - 2*a^3*b*e^3*(-10*d + e*x) + a^2*b^2*e^2*(-18*d^2 + 16*d*e*x + 11*e^2*x^2) + 4*a*b^3*e*(d^3 - 6*d^2*e*x - 4*d*e^2*x^2 + e^3*x^3) + b^4*(d^4 + 8*d^3*e*x - 8*d*e^3*x^3 - e^4*x^4)) + B*(-27*a^5*e^4 + 6*a^4*b*e^3*(14*d + e*x) + 3*a^3*b^2*e^2*(-30*d^2 + 8*d*e*x + 21*e^2*x^2) + 4*a^2*b^3*e*(9*d^3 - 18*d^2*e*x - 33*d*e^2*x^2 + 5*e^3*x^3) + a*b^4*(-3*d^4 + 48*d^3*e*x + 72*d^2*e^2*x^2 - 48*d*e^3*x^3 - 5*e^4*x^4) + 2*b^5*x*(-3*d^4 + 18*d^2*e^2*x^2 + 6*d*e^3*x^3 + e^4*x^4)) + 12*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*(a + b*x)^2*Log[a + b*x])/(6*b^6*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
1768,1,256,249,0.159351,"\int \frac{(A+B x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{-A b \left(5 a^3 e^3+a^2 b e^2 (4 e x-9 d)+a b^2 e \left(3 d^2-12 d e x-4 e^2 x^2\right)+b^3 \left(d^3+6 d^2 e x-2 e^3 x^3\right)\right)+B \left(7 a^4 e^3+a^3 b e^2 (2 e x-15 d)+a^2 b^2 e \left(9 d^2-12 d e x-11 e^2 x^2\right)-a b^3 \left(d^3-12 d^2 e x-12 d e^2 x^2+4 e^3 x^3\right)+b^4 x \left(-2 d^3+6 d e^2 x^2+e^3 x^3\right)\right)+6 e (a+b x)^2 (b d-a e) \log (a+b x) (-2 a B e+A b e+b B d)}{2 b^5 (a+b x) \sqrt{(a+b 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{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 e^3 x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-(A*b*(5*a^3*e^3 + a^2*b*e^2*(-9*d + 4*e*x) + a*b^2*e*(3*d^2 - 12*d*e*x - 4*e^2*x^2) + b^3*(d^3 + 6*d^2*e*x - 2*e^3*x^3))) + B*(7*a^4*e^3 + a^3*b*e^2*(-15*d + 2*e*x) + a^2*b^2*e*(9*d^2 - 12*d*e*x - 11*e^2*x^2) + b^4*x*(-2*d^3 + 6*d*e^2*x^2 + e^3*x^3) - a*b^3*(d^3 - 12*d^2*e*x - 12*d*e^2*x^2 + 4*e^3*x^3)) + 6*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^2*Log[a + b*x])/(2*b^5*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
1769,1,151,186,0.0927398,"\int \frac{(A+B x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{B \left(-5 a^3 e^2+2 a^2 b e (3 d-2 e x)+a b^2 \left(-d^2+8 d e x+4 e^2 x^2\right)+2 b^3 x \left(e^2 x^2-d^2\right)\right)+2 e (a+b x)^2 \log (a+b x) (-3 a B e+A b e+2 b B d)-A b (b d-a e) (3 a e+b (d+4 e x))}{2 b^4 (a+b x) \sqrt{(a+b 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,"(-(A*b*(b*d - a*e)*(3*a*e + b*(d + 4*e*x))) + B*(-5*a^3*e^2 + 2*a^2*b*e*(3*d - 2*e*x) + 2*b^3*x*(-d^2 + e^2*x^2) + a*b^2*(-d^2 + 8*d*e*x + 4*e^2*x^2)) + 2*e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^2*Log[a + b*x])/(2*b^4*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
1770,1,86,127,0.0482887,"\int \frac{(A+B x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{B \left(3 a^2 e-a b d+4 a b e x-2 b^2 d x\right)-A b (a e+b d+2 b e x)+2 B e (a+b x)^2 \log (a+b x)}{2 b^3 (a+b x) \sqrt{(a+b 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,"(-(A*b*(b*d + a*e + 2*b*e*x)) + B*(-(a*b*d) + 3*a^2*e - 2*b^2*d*x + 4*a*b*e*x) + 2*B*e*(a + b*x)^2*Log[a + b*x])/(2*b^3*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
1771,1,39,69,0.0163914,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{-B (a+2 b x)-A b}{2 b^2 (a+b x) \sqrt{(a+b 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,"(-(A*b) - B*(a + 2*b*x))/(2*b^2*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
1772,1,132,196,0.1113283,"\int \frac{A+B x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{-(b d-a e) \left(B \left(a^2 e+a b d+2 b^2 d x\right)+A b (b (d-2 e x)-3 a e)\right)+2 b e (a+b x)^2 \log (a+b x) (A e-B d)+2 b e (a+b x)^2 (B d-A e) \log (d+e x)}{2 b (a+b x) \sqrt{(a+b 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*(a*b*d + a^2*e + 2*b^2*d*x) + A*b*(-3*a*e + b*(d - 2*e*x)))) + 2*b*e*(-(B*d) + A*e)*(a + b*x)^2*Log[a + b*x] + 2*b*e*(B*d - A*e)*(a + b*x)^2*Log[d + e*x])/(2*b*(b*d - a*e)^3*(a + b*x)*Sqrt[(a + b*x)^2])","A",1
1773,1,174,266,0.1848752,"\int \frac{A+B x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{(a+b x) \left(-2 (a+b x) (b d-a e) (a B e-2 A b e+b B d)+\frac{2 e (a+b x)^2 (b d-a e) (A e-B d)}{d+e x}-2 e (a+b x)^2 \log (a+b x) (a B e-3 A b e+2 b B d)+2 e (a+b x)^2 \log (d+e x) (a B e-3 A b e+2 b B d)+(a B-A b) (b d-a e)^2\right)}{2 \left((a+b x)^2\right)^{3/2} (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,"((a + b*x)*((-(A*b) + a*B)*(b*d - a*e)^2 - 2*(b*d - a*e)*(b*B*d - 2*A*b*e + a*B*e)*(a + b*x) + (2*e*(b*d - a*e)*(-(B*d) + A*e)*(a + b*x)^2)/(d + e*x) - 2*e*(2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)^2*Log[a + b*x] + 2*e*(2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)^2*Log[d + e*x]))/(2*(b*d - a*e)^4*((a + b*x)^2)^(3/2))","A",1
1774,1,220,332,0.272175,"\int \frac{A+B x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{(a+b x) \left(\frac{e (a+b x)^2 (b d-a e)^2 (A e-B d)}{(d+e x)^2}-2 b (a+b x) (b d-a e) (2 a B e-3 A b e+b B d)+\frac{2 e (a+b x)^2 (b d-a e) (-a B e+3 A b e-2 b B d)}{d+e x}-6 b e (a+b x)^2 \log (a+b x) (a B e-2 A b e+b B d)+6 b e (a+b x)^2 \log (d+e x) (a B e-2 A b e+b B d)-b (A b-a B) (b d-a e)^2\right)}{2 \left((a+b x)^2\right)^{3/2} (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,"((a + b*x)*(-(b*(A*b - a*B)*(b*d - a*e)^2) - 2*b*(b*d - a*e)*(b*B*d - 3*A*b*e + 2*a*B*e)*(a + b*x) + (e*(b*d - a*e)^2*(-(B*d) + A*e)*(a + b*x)^2)/(d + e*x)^2 + (2*e*(b*d - a*e)*(-2*b*B*d + 3*A*b*e - a*B*e)*(a + b*x)^2)/(d + e*x) - 6*b*e*(b*B*d - 2*A*b*e + a*B*e)*(a + b*x)^2*Log[a + b*x] + 6*b*e*(b*B*d - 2*A*b*e + a*B*e)*(a + b*x)^2*Log[d + e*x]))/(2*(b*d - a*e)^5*((a + b*x)^2)^(3/2))","A",1
1775,1,513,373,0.3249898,"\int \frac{(A+B x) (d+e x)^5}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^5)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-A b \left(77 a^5 e^5+a^4 b e^4 (248 e x-125 d)+2 a^3 b^2 e^3 \left(15 d^2-220 d e x+126 e^2 x^2\right)+2 a^2 b^3 e^2 \left(5 d^3+60 d^2 e x-270 d e^2 x^2+24 e^3 x^3\right)+a b^4 e \left(5 d^4+40 d^3 e x+180 d^2 e^2 x^2-240 d e^3 x^3-48 e^4 x^4\right)+b^5 \left(3 d^5+20 d^4 e x+60 d^3 e^2 x^2+120 d^2 e^3 x^3-12 e^5 x^5\right)\right)+B \left(171 a^6 e^5+7 a^5 b e^4 (72 e x-55 d)+2 a^4 b^2 e^3 \left(125 d^2-620 d e x+198 e^2 x^2\right)-2 a^3 b^3 e^2 \left(15 d^3-440 d^2 e x+630 d e^2 x^2+48 e^3 x^3\right)-a^2 b^4 e \left(5 d^4+120 d^3 e x-1080 d^2 e^2 x^2+240 d e^3 x^3+204 e^4 x^4\right)-a b^5 \left(d^5+20 d^4 e x+180 d^3 e^2 x^2-480 d^2 e^3 x^3-240 d e^4 x^4+36 e^5 x^5\right)+2 b^6 x \left(-2 d^5-15 d^4 e x-60 d^3 e^2 x^2+30 d e^4 x^4+3 e^5 x^5\right)\right)+60 e^3 (a+b x)^4 (b d-a e) \log (a+b x) (-3 a B e+A b e+2 b B d)}{12 b^7 (a+b x)^3 \sqrt{(a+b 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{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 (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{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{B e^5 x^2 (a+b x)}{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-(A*b*(77*a^5*e^5 + a^4*b*e^4*(-125*d + 248*e*x) + 2*a^3*b^2*e^3*(15*d^2 - 220*d*e*x + 126*e^2*x^2) + 2*a^2*b^3*e^2*(5*d^3 + 60*d^2*e*x - 270*d*e^2*x^2 + 24*e^3*x^3) + a*b^4*e*(5*d^4 + 40*d^3*e*x + 180*d^2*e^2*x^2 - 240*d*e^3*x^3 - 48*e^4*x^4) + b^5*(3*d^5 + 20*d^4*e*x + 60*d^3*e^2*x^2 + 120*d^2*e^3*x^3 - 12*e^5*x^5))) + B*(171*a^6*e^5 + 7*a^5*b*e^4*(-55*d + 72*e*x) + 2*a^4*b^2*e^3*(125*d^2 - 620*d*e*x + 198*e^2*x^2) - 2*a^3*b^3*e^2*(15*d^3 - 440*d^2*e*x + 630*d*e^2*x^2 + 48*e^3*x^3) - a^2*b^4*e*(5*d^4 + 120*d^3*e*x - 1080*d^2*e^2*x^2 + 240*d*e^3*x^3 + 204*e^4*x^4) + 2*b^6*x*(-2*d^5 - 15*d^4*e*x - 60*d^3*e^2*x^2 + 30*d*e^4*x^4 + 3*e^5*x^5) - a*b^5*(d^5 + 20*d^4*e*x + 180*d^3*e^2*x^2 - 480*d^2*e^3*x^3 - 240*d*e^4*x^4 + 36*e^5*x^5)) + 60*e^3*(b*d - a*e)*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^4*Log[a + b*x])/(12*b^7*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
1776,1,331,310,0.2179225,"\int \frac{(A+B x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-A b (b d-a e) \left(25 a^3 e^3+a^2 b e^2 (13 d+88 e x)+a b^2 e \left(7 d^2+40 d e x+108 e^2 x^2\right)+b^3 \left(3 d^3+16 d^2 e x+36 d e^2 x^2+48 e^3 x^3\right)\right)-B \left(77 a^5 e^4+4 a^4 b e^3 (62 e x-25 d)+2 a^3 b^2 e^2 \left(9 d^2-176 d e x+126 e^2 x^2\right)+4 a^2 b^3 e \left(d^3+18 d^2 e x-108 d e^2 x^2+12 e^3 x^3\right)+a b^4 \left(d^4+16 d^3 e x+108 d^2 e^2 x^2-192 d e^3 x^3-48 e^4 x^4\right)+4 b^5 x \left(d^4+6 d^3 e x+18 d^2 e^2 x^2-3 e^4 x^4\right)\right)+12 e^3 (a+b x)^4 \log (a+b x) (-5 a B e+A b e+4 b B d)}{12 b^6 (a+b x)^3 \sqrt{(a+b 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{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 (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,"(-(A*b*(b*d - a*e)*(25*a^3*e^3 + a^2*b*e^2*(13*d + 88*e*x) + a*b^2*e*(7*d^2 + 40*d*e*x + 108*e^2*x^2) + b^3*(3*d^3 + 16*d^2*e*x + 36*d*e^2*x^2 + 48*e^3*x^3))) - B*(77*a^5*e^4 + 4*a^4*b*e^3*(-25*d + 62*e*x) + 2*a^3*b^2*e^2*(9*d^2 - 176*d*e*x + 126*e^2*x^2) + 4*a^2*b^3*e*(d^3 + 18*d^2*e*x - 108*d*e^2*x^2 + 12*e^3*x^3) + a*b^4*(d^4 + 16*d^3*e*x + 108*d^2*e^2*x^2 - 192*d*e^3*x^3 - 48*e^4*x^4) + 4*b^5*x*(d^4 + 6*d^3*e*x + 18*d^2*e^2*x^2 - 3*e^4*x^4)) + 12*e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^4*Log[a + b*x])/(12*b^6*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
1777,1,239,227,0.1349094,"\int \frac{(A+B x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-3 A b \left(a^3 e^3+a^2 b e^2 (d+4 e x)+a b^2 e \left(d^2+4 d e x+6 e^2 x^2\right)+b^3 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+B \left(25 a^4 e^3+a^3 b e^2 (88 e x-9 d)-3 a^2 b^2 e \left(d^2+12 d e x-36 e^2 x^2\right)-a b^3 \left(d^3+12 d^2 e x+54 d e^2 x^2-48 e^3 x^3\right)-2 b^4 d x \left(2 d^2+9 d e x+18 e^2 x^2\right)\right)+12 B e^3 (a+b x)^4 \log (a+b x)}{12 b^5 (a+b x)^3 \sqrt{(a+b 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,"(B*(25*a^4*e^3 + a^3*b*e^2*(-9*d + 88*e*x) - 3*a^2*b^2*e*(d^2 + 12*d*e*x - 36*e^2*x^2) - 2*b^4*d*x*(2*d^2 + 9*d*e*x + 18*e^2*x^2) - a*b^3*(d^3 + 12*d^2*e*x + 54*d*e^2*x^2 - 48*e^3*x^3)) - 3*A*b*(a^3*e^3 + a^2*b*e^2*(d + 4*e*x) + a*b^2*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + b^3*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)) + 12*B*e^3*(a + b*x)^4*Log[a + b*x])/(12*b^5*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
1778,1,142,106,0.0754859,"\int \frac{(A+B x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-A b \left(a^2 e^2+2 a b e (d+2 e x)+b^2 \left(3 d^2+8 d e x+6 e^2 x^2\right)\right)-B \left(3 a^3 e^2+2 a^2 b e (d+6 e x)+a b^2 \left(d^2+8 d e x+18 e^2 x^2\right)+4 b^3 x \left(d^2+3 d e x+3 e^2 x^2\right)\right)}{12 b^4 (a+b x)^3 \sqrt{(a+b x)^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,"(-(A*b*(a^2*e^2 + 2*a*b*e*(d + 2*e*x) + b^2*(3*d^2 + 8*d*e*x + 6*e^2*x^2))) - B*(3*a^3*e^2 + 2*a^2*b*e*(d + 6*e*x) + 4*b^3*x*(d^2 + 3*d*e*x + 3*e^2*x^2) + a*b^2*(d^2 + 8*d*e*x + 18*e^2*x^2)))/(12*b^4*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
1779,1,75,135,0.0436828,"\int \frac{(A+B x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-B \left(a^2 e+a b (d+4 e x)+2 b^2 x (2 d+3 e x)\right)-A b (a e+3 b d+4 b e x)}{12 b^3 (a+b x)^3 \sqrt{(a+b 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*(3*b*d + a*e + 4*b*e*x)) - B*(a^2*e + 2*b^2*x*(2*d + 3*e*x) + a*b*(d + 4*e*x)))/(12*b^3*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
1780,1,39,71,0.0182465,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-B (a+4 b x)-3 A b}{12 b^2 (a+b x)^3 \sqrt{(a+b x)^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,"(-3*A*b - B*(a + 4*b*x))/(12*b^2*(a + b*x)^3*Sqrt[(a + b*x)^2])","A",1
1781,1,182,302,0.149891,"\int \frac{A+B x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{12 e^3 (a+b x)^3 \log (a+b x) (A e-B d)+12 e^3 (a+b x)^3 (B d-A e) \log (d+e x)+12 e^2 (a+b x)^2 (b d-a e) (A e-B d)+\frac{3 (a B-A b) (b d-a e)^4}{b (a+b x)}-6 e (a+b x) (b d-a e)^2 (A e-B d)+4 (b d-a e)^3 (A e-B d)}{12 \left((a+b x)^2\right)^{3/2} (b d-a e)^5}","-\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^2 (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\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,"(4*(b*d - a*e)^3*(-(B*d) + A*e) + (3*(-(A*b) + a*B)*(b*d - a*e)^4)/(b*(a + b*x)) - 6*e*(b*d - a*e)^2*(-(B*d) + A*e)*(a + b*x) + 12*e^2*(b*d - a*e)*(-(B*d) + A*e)*(a + b*x)^2 + 12*e^3*(-(B*d) + A*e)*(a + b*x)^3*Log[a + b*x] + 12*e^3*(B*d - A*e)*(a + b*x)^3*Log[d + e*x])/(12*(b*d - a*e)^5*((a + b*x)^2)^(3/2))","A",1
1782,1,250,388,0.2743906,"\int \frac{A+B x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{\frac{12 e^3 (a+b x)^3 (b d-a e) (A e-B d)}{d+e x}-12 e^3 (a+b x)^3 \log (a+b x) (a B e-5 A b e+4 b B d)+12 e^3 (a+b x)^3 \log (d+e x) (a B e-5 A b e+4 b B d)+12 e^2 (a+b x)^2 (b d-a e) (-a B e+4 A b e-3 b B d)+\frac{3 (a B-A b) (b d-a e)^4}{a+b x}-6 e (a+b x) (b d-a e)^2 (-a B e+3 A b e-2 b B d)-4 (b d-a e)^3 (a B e-2 A b e+b B d)}{12 \left((a+b x)^2\right)^{3/2} (b d-a e)^6}","-\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^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^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 (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,"(-4*(b*d - a*e)^3*(b*B*d - 2*A*b*e + a*B*e) + (3*(-(A*b) + a*B)*(b*d - a*e)^4)/(a + b*x) - 6*e*(b*d - a*e)^2*(-2*b*B*d + 3*A*b*e - a*B*e)*(a + b*x) + 12*e^2*(b*d - a*e)*(-3*b*B*d + 4*A*b*e - a*B*e)*(a + b*x)^2 + (12*e^3*(b*d - a*e)*(-(B*d) + A*e)*(a + b*x)^3)/(d + e*x) - 12*e^3*(4*b*B*d - 5*A*b*e + a*B*e)*(a + b*x)^3*Log[a + b*x] + 12*e^3*(4*b*B*d - 5*A*b*e + a*B*e)*(a + b*x)^3*Log[d + e*x])/(12*(b*d - a*e)^6*((a + b*x)^2)^(3/2))","A",1
1783,1,302,460,0.3882821,"\int \frac{A+B x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{\frac{6 e^3 (a+b x)^3 (b d-a e)^2 (A e-B d)}{(d+e x)^2}+\frac{12 e^3 (a+b x)^3 (b d-a e) (-a B e+5 A b e-4 b B d)}{d+e x}-60 b e^3 (a+b x)^3 \log (a+b x) (a B e-3 A b e+2 b B d)+60 b e^3 (a+b x)^3 \log (d+e x) (a B e-3 A b e+2 b B d)+24 b e^2 (a+b x)^2 (b d-a e) (-2 a B e+5 A b e-3 b B d)-\frac{3 b (A b-a B) (b d-a e)^4}{a+b x}-18 b e (a+b x) (b d-a e)^2 (-a B e+2 A b e-b B d)-4 b (b d-a e)^3 (2 a B e-3 A b e+b B d)}{12 \left((a+b x)^2\right)^{3/2} (b d-a e)^7}","-\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{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{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{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,"(-4*b*(b*d - a*e)^3*(b*B*d - 3*A*b*e + 2*a*B*e) - (3*b*(A*b - a*B)*(b*d - a*e)^4)/(a + b*x) - 18*b*e*(b*d - a*e)^2*(-(b*B*d) + 2*A*b*e - a*B*e)*(a + b*x) + 24*b*e^2*(b*d - a*e)*(-3*b*B*d + 5*A*b*e - 2*a*B*e)*(a + b*x)^2 + (6*e^3*(b*d - a*e)^2*(-(B*d) + A*e)*(a + b*x)^3)/(d + e*x)^2 + (12*e^3*(b*d - a*e)*(-4*b*B*d + 5*A*b*e - a*B*e)*(a + b*x)^3)/(d + e*x) - 60*b*e^3*(2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)^3*Log[a + b*x] + 60*b*e^3*(2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)^3*Log[d + e*x])/(12*(b*d - a*e)^7*((a + b*x)^2)^(3/2))","A",1
1784,1,107,128,0.1515093,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (d+e x)^{9/2} \left(-495 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+585 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-715 (b d-a e)^2 (B d-A e)+429 b^2 B (d+e x)^3\right)}{6435 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*(d + e*x)^(9/2)*(-715*(b*d - a*e)^2*(B*d - A*e) + 585*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 495*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 429*b^2*B*(d + e*x)^3))/(6435*e^4)","A",1
1785,1,107,128,0.1211383,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (d+e x)^{7/2} \left(-819 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+1001 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-1287 (b d-a e)^2 (B d-A e)+693 b^2 B (d+e x)^3\right)}{9009 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*(d + e*x)^(7/2)*(-1287*(b*d - a*e)^2*(B*d - A*e) + 1001*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 819*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 693*b^2*B*(d + e*x)^3))/(9009*e^4)","A",1
1786,1,107,128,0.1091881,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (d+e x)^{5/2} \left(-385 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+495 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-693 (b d-a e)^2 (B d-A e)+315 b^2 B (d+e x)^3\right)}{3465 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*(d + e*x)^(5/2)*(-693*(b*d - a*e)^2*(B*d - A*e) + 495*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 385*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 315*b^2*B*(d + e*x)^3))/(3465*e^4)","A",1
1787,1,107,128,0.0978242,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (d+e x)^{3/2} \left(-45 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+63 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-105 (b d-a e)^2 (B d-A e)+35 b^2 B (d+e x)^3\right)}{315 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*(d + e*x)^(3/2)*(-105*(b*d - a*e)^2*(B*d - A*e) + 63*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 45*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 35*b^2*B*(d + e*x)^3))/(315*e^4)","A",1
1788,1,107,126,0.0846654,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-21 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+35 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-105 (b d-a e)^2 (B d-A e)+15 b^2 B (d+e x)^3\right)}{105 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*Sqrt[d + e*x]*(-105*(b*d - a*e)^2*(B*d - A*e) + 35*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 21*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 15*b^2*B*(d + e*x)^3))/(105*e^4)","A",1
1789,1,107,124,0.086075,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(3/2),x]","\frac{2 \left(-5 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+15 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)+15 (b d-a e)^2 (B d-A e)+3 b^2 B (d+e x)^3\right)}{15 e^4 \sqrt{d+e 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}",1,"(2*(15*(b*d - a*e)^2*(B*d - A*e) + 15*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 5*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 3*b^2*B*(d + e*x)^3))/(15*e^4*Sqrt[d + e*x])","A",1
1790,1,105,124,0.0934773,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(5/2),x]","\frac{2 \left(-3 b (d+e x)^2 (-2 a B e-A b e+3 b B d)-3 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)+(b d-a e)^2 (B d-A e)+b^2 B (d+e x)^3\right)}{3 e^4 (d+e x)^{3/2}}","-\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*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 3*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + b^2*B*(d + e*x)^3))/(3*e^4*(d + e*x)^(3/2))","A",1
1791,1,107,124,0.0893118,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(7/2),x]","\frac{2 \left(15 b (d+e x)^2 (-2 a B e-A b e+3 b B d)-5 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)+3 (b d-a e)^2 (B d-A e)+15 b^2 B (d+e x)^3\right)}{15 e^4 (d+e x)^{5/2}}","\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*(3*(b*d - a*e)^2*(B*d - A*e) - 5*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) + 15*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 15*b^2*B*(d + e*x)^3))/(15*e^4*(d + e*x)^(5/2))","A",1
1792,1,183,218,0.2028243,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 (d+e x)^{9/2} \left(-122265 b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)+277134 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)-319770 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)+188955 (d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)-230945 (b d-a e)^4 (B d-A e)+109395 b^4 B (d+e x)^5\right)}{2078505 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*(d + e*x)^(9/2)*(-230945*(b*d - a*e)^4*(B*d - A*e) + 188955*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x) - 319770*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2 + 277134*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3 - 122265*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4 + 109395*b^4*B*(d + e*x)^5))/(2078505*e^6)","A",1
1793,1,183,218,0.1705815,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 (d+e x)^{7/2} \left(-51051 b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)+117810 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)-139230 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)+85085 (d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)-109395 (b d-a e)^4 (B d-A e)+45045 b^4 B (d+e x)^5\right)}{765765 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*(d + e*x)^(7/2)*(-109395*(b*d - a*e)^4*(B*d - A*e) + 85085*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x) - 139230*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2 + 117810*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3 - 51051*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4 + 45045*b^4*B*(d + e*x)^5))/(765765*e^6)","A",1
1794,1,183,218,0.1578256,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 (d+e x)^{5/2} \left(-3465 b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)+8190 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)-10010 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)+6435 (d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)-9009 (b d-a e)^4 (B d-A e)+3003 b^4 B (d+e x)^5\right)}{45045 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*(d + e*x)^(5/2)*(-9009*(b*d - a*e)^4*(B*d - A*e) + 6435*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x) - 10010*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2 + 8190*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3 - 3465*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4 + 3003*b^4*B*(d + e*x)^5))/(45045*e^6)","A",1
1795,1,183,218,0.1376384,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 (d+e x)^{3/2} \left(-4095 b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)+10010 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)-12870 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)+9009 (d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)-15015 (b d-a e)^4 (B d-A e)+3465 b^4 B (d+e x)^5\right)}{45045 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*(d + e*x)^(3/2)*(-15015*(b*d - a*e)^4*(B*d - A*e) + 9009*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x) - 12870*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2 + 10010*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3 - 4095*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4 + 3465*b^4*B*(d + e*x)^5))/(45045*e^6)","A",1
1796,1,183,216,0.1198278,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-385 b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)+990 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)-1386 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)+1155 (d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)-3465 (b d-a e)^4 (B d-A e)+315 b^4 B (d+e x)^5\right)}{3465 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*Sqrt[d + e*x]*(-3465*(b*d - a*e)^4*(B*d - A*e) + 1155*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x) - 1386*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2 + 990*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3 - 385*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4 + 315*b^4*B*(d + e*x)^5))/(3465*e^6)","A",1
1797,1,183,214,0.1212842,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(3/2),x]","\frac{2 \left(-45 b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)+126 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)-210 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)+315 (d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)+315 (b d-a e)^4 (B d-A e)+35 b^4 B (d+e x)^5\right)}{315 e^6 \sqrt{d+e 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}",1,"(2*(315*(b*d - a*e)^4*(B*d - A*e) + 315*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x) - 210*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2 + 126*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3 - 45*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4 + 35*b^4*B*(d + e*x)^5))/(315*e^6*Sqrt[d + e*x])","A",1
1798,1,183,214,0.1059817,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(5/2),x]","\frac{2 \left(-21 b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)+70 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)-210 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)-105 (d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)+35 (b d-a e)^4 (B d-A e)+15 b^4 B (d+e x)^5\right)}{105 e^6 (d+e x)^{3/2}}","-\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*(35*(b*d - a*e)^4*(B*d - A*e) - 105*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x) - 210*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2 + 70*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3 - 21*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4 + 15*b^4*B*(d + e*x)^5))/(105*e^6*(d + e*x)^(3/2))","A",1
1799,1,183,214,0.1101045,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(7/2),x]","\frac{2 \left(-5 b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)+30 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)+30 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)-5 (d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)+3 (b d-a e)^4 (B d-A e)+3 b^4 B (d+e x)^5\right)}{15 e^6 (d+e x)^{5/2}}","-\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*(3*(b*d - a*e)^4*(B*d - A*e) - 5*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x) + 30*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2 + 30*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3 - 5*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4 + 3*b^4*B*(d + e*x)^5))/(15*e^6*(d + e*x)^(5/2))","A",1
1800,1,259,308,0.3493254,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 (d+e x)^{9/2} \left(-3187041 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+10567557 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-19684665 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+22309287 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)-15444891 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)+6084351 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)-7436429 (b d-a e)^6 (B d-A e)+2909907 b^6 B (d+e x)^7\right)}{66927861 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*(d + e*x)^(9/2)*(-7436429*(b*d - a*e)^6*(B*d - A*e) + 6084351*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x) - 15444891*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^2 + 22309287*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^3 - 19684665*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^4 + 10567557*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5 - 3187041*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^6 + 2909907*b^6*B*(d + e*x)^7))/(66927861*e^8)","A",1
1801,1,259,308,0.2619645,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 (d+e x)^{7/2} \left(-153153 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+513513 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-969969 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+1119195 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)-793611 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)+323323 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)-415701 (b d-a e)^6 (B d-A e)+138567 b^6 B (d+e x)^7\right)}{2909907 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*(d + e*x)^(7/2)*(-415701*(b*d - a*e)^6*(B*d - A*e) + 323323*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x) - 793611*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^2 + 1119195*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^3 - 969969*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^4 + 513513*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5 - 153153*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^6 + 138567*b^6*B*(d + e*x)^7))/(2909907*e^8)","A",1
1802,1,259,308,0.2392937,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 (d+e x)^{5/2} \left(-285285 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+969969 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-1865325 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+2204475 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)-1616615 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)+692835 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)-969969 (b d-a e)^6 (B d-A e)+255255 b^6 B (d+e x)^7\right)}{4849845 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*(d + e*x)^(5/2)*(-969969*(b*d - a*e)^6*(B*d - A*e) + 692835*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x) - 1616615*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^2 + 2204475*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^3 - 1865325*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^4 + 969969*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5 - 285285*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^6 + 255255*b^6*B*(d + e*x)^7))/(4849845*e^8)","A",1
1803,1,259,308,0.2438175,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 (d+e x)^{3/2} \left(-51051 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+176715 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-348075 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+425425 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)-328185 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)+153153 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)-255255 (b d-a e)^6 (B d-A e)+45045 b^6 B (d+e x)^7\right)}{765765 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*(d + e*x)^(3/2)*(-255255*(b*d - a*e)^6*(B*d - A*e) + 153153*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x) - 328185*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^2 + 425425*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^3 - 348075*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^4 + 176715*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5 - 51051*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^6 + 45045*b^6*B*(d + e*x)^7))/(765765*e^8)","A",1
1804,1,259,306,0.1951831,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-3465 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+12285 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-25025 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+32175 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)-27027 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)+15015 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)-45045 (b d-a e)^6 (B d-A e)+3003 b^6 B (d+e x)^7\right)}{45045 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*Sqrt[d + e*x]*(-45045*(b*d - a*e)^6*(B*d - A*e) + 15015*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x) - 27027*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^2 + 32175*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^3 - 25025*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^4 + 12285*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5 - 3465*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^6 + 3003*b^6*B*(d + e*x)^7))/(45045*e^8)","A",1
1805,1,259,300,0.2009193,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(3/2),x]","\frac{2 \left(-273 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+1001 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-2145 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+3003 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)-3003 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)+3003 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)+3003 (b d-a e)^6 (B d-A e)+231 b^6 B (d+e x)^7\right)}{3003 e^8 \sqrt{d+e 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}",1,"(2*(3003*(b*d - a*e)^6*(B*d - A*e) + 3003*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x) - 3003*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^2 + 3003*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^3 - 2145*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^4 + 1001*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5 - 273*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^6 + 231*b^6*B*(d + e*x)^7))/(3003*e^8*Sqrt[d + e*x])","A",1
1806,1,259,302,0.1899159,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(5/2),x]","\frac{2 \left(-77 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+297 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-693 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+1155 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)-2079 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)-693 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)+231 (b d-a e)^6 (B d-A e)+63 b^6 B (d+e x)^7\right)}{693 e^8 (d+e x)^{3/2}}","-\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*(231*(b*d - a*e)^6*(B*d - A*e) - 693*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x) - 2079*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^2 + 1155*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^3 - 693*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^4 + 297*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5 - 77*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^6 + 63*b^6*B*(d + e*x)^7))/(693*e^8*(d + e*x)^(3/2))","A",1
1807,1,259,304,0.1921407,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(7/2),x]","\frac{2 \left(-45 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+189 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-525 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+1575 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)+945 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)-105 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)+63 (b d-a e)^6 (B d-A e)+35 b^6 B (d+e x)^7\right)}{315 e^8 (d+e x)^{5/2}}","-\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*(63*(b*d - a*e)^6*(B*d - A*e) - 105*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x) + 945*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^2 + 1575*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^3 - 525*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^4 + 189*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5 - 45*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^6 + 35*b^6*B*(d + e*x)^7))/(315*e^8*(d + e*x)^(5/2))","A",1
1808,1,193,256,0.6371988,"\int \frac{(A+B x) (d+e x)^{7/2}}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\frac{2 \left(-\frac{9 a B e}{2}+\frac{7 A b e}{2}+b B d\right) \left(7 (b d-a e) \left(5 (b d-a e) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)+3 b^{5/2} (d+e x)^{5/2}\right)+15 b^{7/2} (d+e x)^{7/2}\right)}{105 b^{9/2}}+\frac{(d+e x)^{9/2} (a B-A b)}{a+b x}}{b (b d-a e)}","-\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{\sqrt{d+e x} (b d-a e)^2 (-9 a B e+7 A b e+2 b B d)}{b^5}+\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{(d+e x)^{5/2} (-9 a B e+7 A b e+2 b B d)}{5 b^3}+\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)^{9/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"(((-(A*b) + a*B)*(d + e*x)^(9/2))/(a + b*x) + (2*(b*B*d + (7*A*b*e)/2 - (9*a*B*e)/2)*(15*b^(7/2)*(d + e*x)^(7/2) + 7*(b*d - a*e)*(3*b^(5/2)*(d + e*x)^(5/2) + 5*(b*d - a*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))))/(105*b^(9/2)))/(b*(b*d - a*e))","A",1
1809,1,166,214,0.3581026,"\int \frac{(A+B x) (d+e x)^{5/2}}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\frac{2 \left(-\frac{7 a B e}{2}+\frac{5 A b e}{2}+b B d\right) \left(5 (b d-a e) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)+3 b^{5/2} (d+e x)^{5/2}\right)}{15 b^{7/2}}+\frac{(d+e x)^{7/2} (a B-A b)}{a+b x}}{b (b d-a e)}","-\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{\sqrt{d+e x} (b d-a e) (-7 a B e+5 A b e+2 b B d)}{b^4}+\frac{(d+e x)^{3/2} (-7 a B e+5 A b e+2 b B d)}{3 b^3}+\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)^{7/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"(((-(A*b) + a*B)*(d + e*x)^(7/2))/(a + b*x) + (2*(b*B*d + (5*A*b*e)/2 - (7*a*B*e)/2)*(3*b^(5/2)*(d + e*x)^(5/2) + 5*(b*d - a*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])))/(15*b^(7/2)))/(b*(b*d - a*e))","A",1
1810,1,136,174,0.2253458,"\int \frac{(A+B x) (d+e x)^{3/2}}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\frac{(-5 a B e+3 A b e+2 b B d) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)}{3 b^{5/2}}+\frac{(d+e x)^{5/2} (a B-A b)}{a+b x}}{b (b d-a e)}","-\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{\sqrt{d+e x} (-5 a B e+3 A b e+2 b B d)}{b^3}+\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{(d+e x)^{5/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"(((-(A*b) + a*B)*(d + e*x)^(5/2))/(a + b*x) + ((2*b*B*d + 3*A*b*e - 5*a*B*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/(3*b^(5/2)))/(b*(b*d - a*e))","A",1
1811,1,119,140,0.1376736,"\int \frac{(A+B x) \sqrt{d+e x}}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\frac{(-3 a B e+A b e+2 b B d) \left(\sqrt{b} \sqrt{d+e x}-\sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)}{b^{3/2}}+\frac{(d+e x)^{3/2} (a B-A b)}{a+b x}}{b (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{\sqrt{d+e x} (-3 a B e+A b e+2 b B d)}{b^2 (b d-a e)}-\frac{(d+e x)^{3/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"(((-(A*b) + a*B)*(d + e*x)^(3/2))/(a + b*x) + ((2*b*B*d + A*b*e - 3*a*B*e)*(Sqrt[b]*Sqrt[d + e*x] - Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/b^(3/2))/(b*(b*d - a*e))","A",1
1812,1,102,103,0.0766718,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)),x]","\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{(-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",1
1813,1,95,140,0.0395769,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{(a+b x) (a B e-3 A b e+2 b B d) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)-(A b-a B) (b d-a e)}{b (a+b x) \sqrt{d+e x} (b d-a e)^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,"(-((A*b - a*B)*(b*d - a*e)) + (2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)*Hypergeometric2F1[-1/2, 1, 1/2, (b*(d + e*x))/(b*d - a*e)])/(b*(b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x])","C",1
1814,1,94,181,0.0367446,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{(3 a B e-5 A b e+2 b B d) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)-\frac{3 (A b-a B) (b d-a e)}{a+b x}}{3 b (d+e x)^{3/2} (b d-a e)^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,"((-3*(A*b - a*B)*(b*d - a*e))/(a + b*x) + (2*b*B*d - 5*A*b*e + 3*a*B*e)*Hypergeometric2F1[-3/2, 1, -1/2, (b*(d + e*x))/(b*d - a*e)])/(3*b*(b*d - a*e)^2*(d + e*x)^(3/2))","C",1
1815,1,94,221,0.0393864,"\int \frac{A+B x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{(5 a B e-7 A b e+2 b B d) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)-\frac{5 (A b-a B) (b d-a e)}{a+b x}}{5 b (d+e x)^{5/2} (b d-a e)^2}","-\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,"((-5*(A*b - a*B)*(b*d - a*e))/(a + b*x) + (2*b*B*d - 7*A*b*e + 5*a*B*e)*Hypergeometric2F1[-5/2, 1, -3/2, (b*(d + e*x))/(b*d - a*e)])/(5*b*(b*d - a*e)^2*(d + e*x)^(5/2))","C",1
1816,1,100,332,0.1060211,"\int \frac{(A+B x) (d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(d+e x)^{11/2} \left(\frac{11 (a B-A b)}{(a+b x)^3}-\frac{e^2 (-11 a B e+5 A b e+6 b B d) \, _2F_1\left(3,\frac{11}{2};\frac{13}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^3}\right)}{33 b (b d-a e)}","-\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{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{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 (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{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)^{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{(d+e x)^{11/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"((d + e*x)^(11/2)*((11*(-(A*b) + a*B))/(a + b*x)^3 - (e^2*(6*b*B*d + 5*A*b*e - 11*a*B*e)*Hypergeometric2F1[3, 11/2, 13/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^3))/(33*b*(b*d - a*e))","C",1
1817,1,99,284,0.0880921,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(d+e x)^{9/2} \left(\frac{9 a B-9 A b}{(a+b x)^3}-\frac{3 e^2 (-3 a B e+A b e+2 b B d) \, _2F_1\left(3,\frac{9}{2};\frac{11}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^3}\right)}{27 b (b d-a e)}","-\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{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 (d+e x)^{3/2} (-3 a B e+A b e+2 b B d)}{24 b^4 (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)^{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{(d+e x)^{9/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"((d + e*x)^(9/2)*((-9*A*b + 9*a*B)/(a + b*x)^3 - (3*e^2*(2*b*B*d + A*b*e - 3*a*B*e)*Hypergeometric2F1[3, 9/2, 11/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^3))/(27*b*(b*d - a*e))","C",1
1818,1,99,250,0.0793673,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(d+e x)^{7/2} \left(\frac{7 a B-7 A b}{(a+b x)^3}-\frac{e^2 (-7 a B e+A b e+6 b B d) \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^3}\right)}{21 b (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{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 (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)^{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{(d+e x)^{7/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"((d + e*x)^(7/2)*((-7*A*b + 7*a*B)/(a + b*x)^3 - (e^2*(6*b*B*d + A*b*e - 7*a*B*e)*Hypergeometric2F1[3, 7/2, 9/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^3))/(21*b*(b*d - a*e))","C",1
1819,1,177,209,0.4477839,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{\frac{(a+b x) (-5 a B e-A b e+6 b B d) \left(3 \sqrt{b} e^2 (a+b x)^2 \sqrt{d+e x} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)-b (d+e x) \sqrt{a e-b d} (3 a e+2 b d+5 b e x)\right)}{\sqrt{a e-b d}}-8 b^3 (d+e x)^3 (A b-a B)}{24 b^4 (a+b x)^3 \sqrt{d+e x} (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{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)^{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{(d+e x)^{5/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"(-8*b^3*(A*b - a*B)*(d + e*x)^3 + ((6*b*B*d - A*b*e - 5*a*B*e)*(a + b*x)*(-(b*Sqrt[-(b*d) + a*e]*(d + e*x)*(2*b*d + 3*a*e + 5*b*e*x)) + 3*Sqrt[b]*e^2*(a + b*x)^2*Sqrt[d + e*x]*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]]))/Sqrt[-(b*d) + a*e])/(24*b^4*(b*d - a*e)*(a + b*x)^3*Sqrt[d + e*x])","A",1
1820,1,98,209,0.064553,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(d+e x)^{3/2} \left(\frac{3 e^2 (a B e+A b e-2 b B d) \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^3}+\frac{3 a B-3 A b}{(a+b x)^3}\right)}{9 b (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,"((d + e*x)^(3/2)*((-3*A*b + 3*a*B)/(a + b*x)^3 + (3*e^2*(-2*b*B*d + A*b*e + a*B*e)*Hypergeometric2F1[3/2, 3, 5/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^3))/(9*b*(b*d - a*e))","C",1
1821,1,97,209,0.0531689,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\sqrt{d+e x} \left(\frac{e^2 (a B e+5 A b e-6 b B d) \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^3}+\frac{a B-A b}{(a+b x)^3}\right)}{3 b (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,"(Sqrt[d + e*x]*((-(A*b) + a*B)/(a + b*x)^3 + (e^2*(-6*b*B*d + 5*A*b*e + a*B*e)*Hypergeometric2F1[1/2, 3, 3/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^3))/(3*b*(b*d - a*e))","C",1
1822,1,99,250,0.0558554,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{a B-A b}{(a+b x)^3}-\frac{e^2 (-a B e+7 A b e-6 b B d) \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^3}}{3 b \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,"((-(A*b) + a*B)/(a + b*x)^3 - (e^2*(-6*b*B*d + 7*A*b*e - a*B*e)*Hypergeometric2F1[-1/2, 3, 1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^3)/(3*b*(b*d - a*e)*Sqrt[d + e*x])","C",1
1823,1,100,291,0.0619328,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{3 a B-3 A b}{(a+b x)^3}-\frac{3 e^2 (-a B e+3 A b e-2 b B d) \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^3}}{9 b (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,"((-3*A*b + 3*a*B)/(a + b*x)^3 - (3*e^2*(-2*b*B*d + 3*A*b*e - a*B*e)*Hypergeometric2F1[-3/2, 3, -1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^3)/(9*b*(b*d - a*e)*(d + e*x)^(3/2))","C",1
1824,1,100,339,0.0697873,"\int \frac{A+B x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{5 a B-5 A b}{(a+b x)^3}-\frac{e^2 (-5 a B e+11 A b e-6 b B d) \, _2F_1\left(-\frac{5}{2},3;-\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^3}}{15 b (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,"((-5*A*b + 5*a*B)/(a + b*x)^3 - (e^2*(-6*b*B*d + 11*A*b*e - 5*a*B*e)*Hypergeometric2F1[-5/2, 3, -3/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^3)/(15*b*(b*d - a*e)*(d + e*x)^(5/2))","C",1
1825,1,100,393,0.0799657,"\int \frac{(A+B x) (d+e x)^{11/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(11/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(d+e x)^{13/2} \left(\frac{13 (a B-A b)}{(a+b x)^5}-\frac{e^4 (-13 a B e+3 A b e+10 b B d) \, _2F_1\left(5,\frac{13}{2};\frac{15}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^5}\right)}{65 b (b d-a e)}","-\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{231 e^4 \sqrt{d+e x} (-13 a B e+3 A b e+10 b B d)}{128 b^7}+\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^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{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{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)^{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{(d+e x)^{13/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"((d + e*x)^(13/2)*((13*(-(A*b) + a*B))/(a + b*x)^5 - (e^4*(10*b*B*d + 3*A*b*e - 13*a*B*e)*Hypergeometric2F1[5, 13/2, 15/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^5))/(65*b*(b*d - a*e))","C",1
1826,1,99,352,0.0705688,"\int \frac{(A+B x) (d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(d+e x)^{11/2} \left(\frac{11 (a B-A b)}{(a+b x)^5}-\frac{e^4 (-11 a B e+A b e+10 b B d) \, _2F_1\left(5,\frac{11}{2};\frac{13}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^5}\right)}{55 b (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{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{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{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{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)^{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{(d+e x)^{11/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"((d + e*x)^(11/2)*((11*(-(A*b) + a*B))/(a + b*x)^5 - (e^4*(10*b*B*d + A*b*e - 11*a*B*e)*Hypergeometric2F1[5, 11/2, 13/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^5))/(55*b*(b*d - a*e))","C",1
1827,1,260,313,0.9464253,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{\frac{(a+b x) (9 a B e+A b e-10 b B d) \left(48 b^4 (d+e x)^4 \sqrt{a e-b d}+56 b^3 e (a+b x) (d+e x)^3 \sqrt{a e-b d}+70 b^2 e^2 (a+b x)^2 (d+e x)^2 \sqrt{a e-b d}-105 \sqrt{b} e^4 (a+b x)^4 \sqrt{d+e x} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)+105 b e^3 (a+b x)^3 (d+e x) \sqrt{a e-b d}\right)}{\sqrt{a e-b d}}-384 b^5 (d+e x)^5 (A b-a B)}{1920 b^6 (a+b x)^5 \sqrt{d+e 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{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^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 (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)^{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{(d+e x)^{9/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"(-384*b^5*(A*b - a*B)*(d + e*x)^5 + ((-10*b*B*d + A*b*e + 9*a*B*e)*(a + b*x)*(105*b*e^3*Sqrt[-(b*d) + a*e]*(a + b*x)^3*(d + e*x) + 70*b^2*e^2*Sqrt[-(b*d) + a*e]*(a + b*x)^2*(d + e*x)^2 + 56*b^3*e*Sqrt[-(b*d) + a*e]*(a + b*x)*(d + e*x)^3 + 48*b^4*Sqrt[-(b*d) + a*e]*(d + e*x)^4 - 105*Sqrt[b]*e^4*(a + b*x)^4*Sqrt[d + e*x]*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]]))/Sqrt[-(b*d) + a*e])/(1920*b^6*(b*d - a*e)*(a + b*x)^5*Sqrt[d + e*x])","A",1
1828,1,99,313,0.0620401,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(d+e x)^{7/2} \left(\frac{e^4 (7 a B e+3 A b e-10 b B d) \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^5}+\frac{7 a B-7 A b}{(a+b x)^5}\right)}{35 b (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^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 (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,"((d + e*x)^(7/2)*((-7*A*b + 7*a*B)/(a + b*x)^5 + (e^4*(-10*b*B*d + 3*A*b*e + 7*a*B*e)*Hypergeometric2F1[7/2, 5, 9/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^5))/(35*b*(b*d - a*e))","C",1
1829,1,98,313,0.0608141,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(d+e x)^{5/2} \left(\frac{5 e^4 (a B e+A b e-2 b B d) \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^5}+\frac{5 a B-5 A b}{(a+b x)^5}\right)}{25 b (b d-a e)}","-\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{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{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,"((d + e*x)^(5/2)*((-5*A*b + 5*a*B)/(a + b*x)^5 + (5*e^4*(-2*b*B*d + A*b*e + a*B*e)*Hypergeometric2F1[5/2, 5, 7/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^5))/(25*b*(b*d - a*e))","C",1
1830,1,99,313,0.0585679,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(d+e x)^{3/2} \left(\frac{e^4 (3 a B e+7 A b e-10 b B d) \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^5}+\frac{3 a B-3 A b}{(a+b x)^5}\right)}{15 b (b d-a e)}","\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^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 \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,"((d + e*x)^(3/2)*((-3*A*b + 3*a*B)/(a + b*x)^5 + (e^4*(-10*b*B*d + 7*A*b*e + 3*a*B*e)*Hypergeometric2F1[3/2, 5, 5/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^5))/(15*b*(b*d - a*e))","C",1
1831,1,97,313,0.0529181,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\sqrt{d+e x} \left(\frac{e^4 (a B e+9 A b e-10 b B d) \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^5}+\frac{a B-A b}{(a+b x)^5}\right)}{5 b (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,"(Sqrt[d + e*x]*((-(A*b) + a*B)/(a + b*x)^5 + (e^4*(-10*b*B*d + 9*A*b*e + a*B*e)*Hypergeometric2F1[1/2, 5, 3/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^5))/(5*b*(b*d - a*e))","C",1
1832,1,97,352,0.0721143,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{e^4 (a B e-11 A b e+10 b B d) \, _2F_1\left(-\frac{1}{2},5;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^5}+\frac{a B-A b}{(a+b x)^5}}{5 b \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{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{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{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,"((-(A*b) + a*B)/(a + b*x)^5 + (e^4*(10*b*B*d - 11*A*b*e + a*B*e)*Hypergeometric2F1[-1/2, 5, 1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^5)/(5*b*(b*d - a*e)*Sqrt[d + e*x])","C",1
1833,1,99,400,0.0760082,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{e^4 (3 a B e-13 A b e+10 b B d) \, _2F_1\left(-\frac{3}{2},5;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^5}+\frac{3 a B-3 A b}{(a+b x)^5}}{15 b (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 \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{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{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,"((-3*A*b + 3*a*B)/(a + b*x)^5 + (e^4*(10*b*B*d - 13*A*b*e + 3*a*B*e)*Hypergeometric2F1[-3/2, 5, -1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^5)/(15*b*(b*d - a*e)*(d + e*x)^(3/2))","C",1
1834,1,100,435,0.0688292,"\int \frac{A+B x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{5 a B-5 A b}{(a+b x)^5}-\frac{5 e^4 (-a B e+3 A b e-2 b B d) \, _2F_1\left(-\frac{5}{2},5;-\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^5}}{25 b (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,"((-5*A*b + 5*a*B)/(a + b*x)^5 - (5*e^4*(-2*b*B*d + 3*A*b*e - a*B*e)*Hypergeometric2F1[-5/2, 5, -3/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^5)/(25*b*(b*d - a*e)*(d + e*x)^(5/2))","C",1
1835,1,88,164,0.0841152,"\int (A+B x) (d+e x)^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{9/2} \left(13 a e (11 A e-2 B d+9 B e x)+13 A b e (9 e x-2 d)+b B \left(8 d^2-36 d e x+99 e^2 x^2\right)\right)}{1287 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*Sqrt[(a + b*x)^2]*(d + e*x)^(9/2)*(13*A*b*e*(-2*d + 9*e*x) + 13*a*e*(-2*B*d + 11*A*e + 9*B*e*x) + b*B*(8*d^2 - 36*d*e*x + 99*e^2*x^2)))/(1287*e^3*(a + b*x))","A",1
1836,1,88,164,0.0811285,"\int (A+B x) (d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{7/2} \left(11 a e (9 A e-2 B d+7 B e x)+11 A b e (7 e x-2 d)+b B \left(8 d^2-28 d e x+63 e^2 x^2\right)\right)}{693 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*Sqrt[(a + b*x)^2]*(d + e*x)^(7/2)*(11*A*b*e*(-2*d + 7*e*x) + 11*a*e*(-2*B*d + 9*A*e + 7*B*e*x) + b*B*(8*d^2 - 28*d*e*x + 63*e^2*x^2)))/(693*e^3*(a + b*x))","A",1
1837,1,88,164,0.0668749,"\int (A+B x) (d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{5/2} \left(9 a e (7 A e-2 B d+5 B e x)+9 A b e (5 e x-2 d)+b B \left(8 d^2-20 d e x+35 e^2 x^2\right)\right)}{315 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*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2)*(9*A*b*e*(-2*d + 5*e*x) + 9*a*e*(-2*B*d + 7*A*e + 5*B*e*x) + b*B*(8*d^2 - 20*d*e*x + 35*e^2*x^2)))/(315*e^3*(a + b*x))","A",1
1838,1,88,164,0.0594839,"\int (A+B x) \sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{3/2} \left(7 a e (5 A e-2 B d+3 B e x)+7 A b e (3 e x-2 d)+b B \left(8 d^2-12 d e x+15 e^2 x^2\right)\right)}{105 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*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2)*(7*A*b*e*(-2*d + 3*e*x) + 7*a*e*(-2*B*d + 5*A*e + 3*B*e*x) + b*B*(8*d^2 - 12*d*e*x + 15*e^2*x^2)))/(105*e^3*(a + b*x))","A",1
1839,1,86,162,0.0680881,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/Sqrt[d + e*x],x]","\frac{2 \sqrt{(a+b x)^2} \sqrt{d+e x} \left(5 a e (3 A e-2 B d+B e x)+5 A b e (e x-2 d)+b B \left(8 d^2-4 d e x+3 e^2 x^2\right)\right)}{15 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*Sqrt[(a + b*x)^2]*Sqrt[d + e*x]*(5*A*b*e*(-2*d + e*x) + 5*a*e*(-2*B*d + 3*A*e + B*e*x) + b*B*(8*d^2 - 4*d*e*x + 3*e^2*x^2)))/(15*e^3*(a + b*x))","A",1
1840,1,85,160,0.0595223,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(3 a e (-A e+2 B d+B e x)+3 A b e (2 d+e x)+b B \left(-8 d^2-4 d e x+e^2 x^2\right)\right)}{3 e^3 (a+b x) \sqrt{d+e 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*Sqrt[(a + b*x)^2]*(3*A*b*e*(2*d + e*x) + 3*a*e*(2*B*d - A*e + B*e*x) + b*B*(-8*d^2 - 4*d*e*x + e^2*x^2)))/(3*e^3*(a + b*x)*Sqrt[d + e*x])","A",1
1841,1,86,160,0.0666068,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(5/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(a e (A e+2 B d+3 B e x)+A b e (2 d+3 e x)-b B \left(8 d^2+12 d e x+3 e^2 x^2\right)\right)}{3 e^3 (a+b x) (d+e x)^{3/2}}","\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*Sqrt[(a + b*x)^2]*(A*b*e*(2*d + 3*e*x) + a*e*(2*B*d + A*e + 3*B*e*x) - b*B*(8*d^2 + 12*d*e*x + 3*e^2*x^2)))/(3*e^3*(a + b*x)*(d + e*x)^(3/2))","A",1
1842,1,86,162,0.0637966,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{7/2}} \, dx","Integrate[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(a e (3 A e+2 B d+5 B e x)+A b e (2 d+5 e x)+b B \left(8 d^2+20 d e x+15 e^2 x^2\right)\right)}{15 e^3 (a+b x) (d+e x)^{5/2}}","\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*Sqrt[(a + b*x)^2]*(A*b*e*(2*d + 5*e*x) + a*e*(2*B*d + 3*A*e + 5*B*e*x) + b*B*(8*d^2 + 20*d*e*x + 15*e^2*x^2)))/(15*e^3*(a + b*x)*(d + e*x)^(5/2))","A",1
1843,1,163,308,0.2502123,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 \left((a+b x)^2\right)^{3/2} (d+e x)^{9/2} \left(-7293 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+25245 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-9945 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+12155 (b d-a e)^3 (B d-A e)+6435 b^3 B (d+e x)^4\right)}{109395 e^5 (a+b x)^3}","-\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*((a + b*x)^2)^(3/2)*(d + e*x)^(9/2)*(12155*(b*d - a*e)^3*(B*d - A*e) - 9945*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 25245*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 7293*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 6435*b^3*B*(d + e*x)^4))/(109395*e^5*(a + b*x)^3)","A",1
1844,1,163,308,0.1965972,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 \left((a+b x)^2\right)^{3/2} (d+e x)^{7/2} \left(-3465 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+12285 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-5005 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+6435 (b d-a e)^3 (B d-A e)+3003 b^3 B (d+e x)^4\right)}{45045 e^5 (a+b x)^3}","-\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*((a + b*x)^2)^(3/2)*(d + e*x)^(7/2)*(6435*(b*d - a*e)^3*(B*d - A*e) - 5005*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 12285*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 3465*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 3003*b^3*B*(d + e*x)^4))/(45045*e^5*(a + b*x)^3)","A",1
1845,1,163,308,0.1757942,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 \left((a+b x)^2\right)^{3/2} (d+e x)^{5/2} \left(-1365 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+5005 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-2145 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+3003 (b d-a e)^3 (B d-A e)+1155 b^3 B (d+e x)^4\right)}{15015 e^5 (a+b x)^3}","-\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*((a + b*x)^2)^(3/2)*(d + e*x)^(5/2)*(3003*(b*d - a*e)^3*(B*d - A*e) - 2145*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 5005*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 1365*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 1155*b^3*B*(d + e*x)^4))/(15015*e^5*(a + b*x)^3)","A",1
1846,1,163,308,0.1704963,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 \left((a+b x)^2\right)^{3/2} (d+e x)^{3/2} \left(-385 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+1485 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-693 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+1155 (b d-a e)^3 (B d-A e)+315 b^3 B (d+e x)^4\right)}{3465 e^5 (a+b x)^3}","-\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*((a + b*x)^2)^(3/2)*(d + e*x)^(3/2)*(1155*(b*d - a*e)^3*(B*d - A*e) - 693*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 1485*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 385*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 315*b^3*B*(d + e*x)^4))/(3465*e^5*(a + b*x)^3)","A",1
1847,1,163,306,0.0996187,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/Sqrt[d + e*x],x]","\frac{2 \left((a+b x)^2\right)^{3/2} \sqrt{d+e x} \left(-45 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+189 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-105 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+315 (b d-a e)^3 (B d-A e)+35 b^3 B (d+e x)^4\right)}{315 e^5 (a+b x)^3}","-\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*((a + b*x)^2)^(3/2)*Sqrt[d + e*x]*(315*(b*d - a*e)^3*(B*d - A*e) - 105*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 189*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 45*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 35*b^3*B*(d + e*x)^4))/(315*e^5*(a + b*x)^3)","A",1
1848,1,240,302,0.1382527,"\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","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(35 a^3 e^3 (-A e+2 B d+B e x)+35 a^2 b e^2 \left(3 A e (2 d+e x)+B \left(-8 d^2-4 d e x+e^2 x^2\right)\right)+7 a b^2 e \left(5 A e \left(-8 d^2-4 d e x+e^2 x^2\right)+3 B \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)\right)+b^3 \left(7 A e \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)+B \left(-128 d^4-64 d^3 e x+16 d^2 e^2 x^2-8 d e^3 x^3+5 e^4 x^4\right)\right)\right)}{35 e^5 (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)^{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*Sqrt[(a + b*x)^2]*(35*a^3*e^3*(2*B*d - A*e + B*e*x) + 35*a^2*b*e^2*(3*A*e*(2*d + e*x) + B*(-8*d^2 - 4*d*e*x + e^2*x^2)) + 7*a*b^2*e*(5*A*e*(-8*d^2 - 4*d*e*x + e^2*x^2) + 3*B*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3)) + b^3*(7*A*e*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) + B*(-128*d^4 - 64*d^3*e*x + 16*d^2*e^2*x^2 - 8*d*e^3*x^3 + 5*e^4*x^4))))/(35*e^5*(a + b*x)*Sqrt[d + e*x])","A",1
1849,1,241,304,0.1754928,"\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","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-5 a^3 e^3 (A e+2 B d+3 B e x)+15 a^2 b e^2 \left(B \left(8 d^2+12 d e x+3 e^2 x^2\right)-A e (2 d+3 e x)\right)+15 a b^2 e \left(A e \left(8 d^2+12 d e x+3 e^2 x^2\right)+B \left(-16 d^3-24 d^2 e x-6 d e^2 x^2+e^3 x^3\right)\right)+b^3 \left(5 A e \left(-16 d^3-24 d^2 e x-6 d e^2 x^2+e^3 x^3\right)+B \left(128 d^4+192 d^3 e x+48 d^2 e^2 x^2-8 d e^3 x^3+3 e^4 x^4\right)\right)\right)}{15 e^5 (a+b x) (d+e x)^{3/2}}","-\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*Sqrt[(a + b*x)^2]*(-5*a^3*e^3*(2*B*d + A*e + 3*B*e*x) + 15*a^2*b*e^2*(-(A*e*(2*d + 3*e*x)) + B*(8*d^2 + 12*d*e*x + 3*e^2*x^2)) + 15*a*b^2*e*(A*e*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + B*(-16*d^3 - 24*d^2*e*x - 6*d*e^2*x^2 + e^3*x^3)) + b^3*(5*A*e*(-16*d^3 - 24*d^2*e*x - 6*d*e^2*x^2 + e^3*x^3) + B*(128*d^4 + 192*d^3*e*x + 48*d^2*e^2*x^2 - 8*d*e^3*x^3 + 3*e^4*x^4))))/(15*e^5*(a + b*x)*(d + e*x)^(3/2))","A",1
1850,1,244,304,0.1525841,"\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","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(a^3 e^3 (3 A e+2 B d+5 B e x)+3 a^2 b e^2 \left(A e (2 d+5 e x)+B \left(8 d^2+20 d e x+15 e^2 x^2\right)\right)-3 a b^2 e \left(3 B \left(16 d^3+40 d^2 e x+30 d e^2 x^2+5 e^3 x^3\right)-A e \left(8 d^2+20 d e x+15 e^2 x^2\right)\right)+b^3 \left(B \left(128 d^4+320 d^3 e x+240 d^2 e^2 x^2+40 d e^3 x^3-5 e^4 x^4\right)-3 A e \left(16 d^3+40 d^2 e x+30 d e^2 x^2+5 e^3 x^3\right)\right)\right)}{15 e^5 (a+b x) (d+e x)^{5/2}}","-\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*Sqrt[(a + b*x)^2]*(a^3*e^3*(2*B*d + 3*A*e + 5*B*e*x) + 3*a^2*b*e^2*(A*e*(2*d + 5*e*x) + B*(8*d^2 + 20*d*e*x + 15*e^2*x^2)) - 3*a*b^2*e*(-(A*e*(8*d^2 + 20*d*e*x + 15*e^2*x^2)) + 3*B*(16*d^3 + 40*d^2*e*x + 30*d*e^2*x^2 + 5*e^3*x^3)) + b^3*(-3*A*e*(16*d^3 + 40*d^2*e*x + 30*d*e^2*x^2 + 5*e^3*x^3) + B*(128*d^4 + 320*d^3*e*x + 240*d^2*e^2*x^2 + 40*d*e^3*x^3 - 5*e^4*x^4))))/(15*e^5*(a + b*x)*(d + e*x)^(5/2))","A",1
1851,1,239,452,0.308693,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{9/2} \left(-153153 b^4 (d+e x)^5 (-5 a B e-A b e+6 b B d)+855855 b^3 (d+e x)^4 (b d-a e) (-2 a B e-A b e+3 b B d)-1939938 b^2 (d+e x)^3 (b d-a e)^2 (-a B e-A b e+2 b B d)+1119195 b (d+e x)^2 (b d-a e)^3 (-a B e-2 A b e+3 b B d)-264537 (d+e x) (b d-a e)^4 (-a B e-5 A b e+6 b B d)+323323 (b d-a e)^5 (B d-A e)+138567 b^5 B (d+e x)^6\right)}{2909907 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^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{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*Sqrt[(a + b*x)^2]*(d + e*x)^(9/2)*(323323*(b*d - a*e)^5*(B*d - A*e) - 264537*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x) + 1119195*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2 - 1939938*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3 + 855855*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4 - 153153*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5 + 138567*b^5*B*(d + e*x)^6))/(2909907*e^7*(a + b*x))","A",1
1852,1,239,452,0.2405458,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{7/2} \left(-171171 b^4 (d+e x)^5 (-5 a B e-A b e+6 b B d)+969969 b^3 (d+e x)^4 (b d-a e) (-2 a B e-A b e+3 b B d)-2238390 b^2 (d+e x)^3 (b d-a e)^2 (-a B e-A b e+2 b B d)+1322685 b (d+e x)^2 (b d-a e)^3 (-a B e-2 A b e+3 b B d)-323323 (d+e x) (b d-a e)^4 (-a B e-5 A b e+6 b B d)+415701 (b d-a e)^5 (B d-A e)+153153 b^5 B (d+e x)^6\right)}{2909907 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^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{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*Sqrt[(a + b*x)^2]*(d + e*x)^(7/2)*(415701*(b*d - a*e)^5*(B*d - A*e) - 323323*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x) + 1322685*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2 - 2238390*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3 + 969969*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4 - 171171*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5 + 153153*b^5*B*(d + e*x)^6))/(2909907*e^7*(a + b*x))","A",1
1853,1,239,452,0.2210057,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{5/2} \left(-51051 b^4 (d+e x)^5 (-5 a B e-A b e+6 b B d)+294525 b^3 (d+e x)^4 (b d-a e) (-2 a B e-A b e+3 b B d)-696150 b^2 (d+e x)^3 (b d-a e)^2 (-a B e-A b e+2 b B d)+425425 b (d+e x)^2 (b d-a e)^3 (-a B e-2 A b e+3 b B d)-109395 (d+e x) (b d-a e)^4 (-a B e-5 A b e+6 b B d)+153153 (b d-a e)^5 (B d-A e)+45045 b^5 B (d+e x)^6\right)}{765765 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^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{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*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2)*(153153*(b*d - a*e)^5*(B*d - A*e) - 109395*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x) + 425425*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2 - 696150*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3 + 294525*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4 - 51051*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5 + 45045*b^5*B*(d + e*x)^6))/(765765*e^7*(a + b*x))","A",1
1854,1,239,452,0.2026806,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{3/2} \left(-3465 b^4 (d+e x)^5 (-5 a B e-A b e+6 b B d)+20475 b^3 (d+e x)^4 (b d-a e) (-2 a B e-A b e+3 b B d)-50050 b^2 (d+e x)^3 (b d-a e)^2 (-a B e-A b e+2 b B d)+32175 b (d+e x)^2 (b d-a e)^3 (-a B e-2 A b e+3 b B d)-9009 (d+e x) (b d-a e)^4 (-a B e-5 A b e+6 b B d)+15015 (b d-a e)^5 (B d-A e)+3003 b^5 B (d+e x)^6\right)}{45045 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^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{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*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2)*(15015*(b*d - a*e)^5*(B*d - A*e) - 9009*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x) + 32175*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2 - 50050*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3 + 20475*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4 - 3465*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5 + 3003*b^5*B*(d + e*x)^6))/(45045*e^7*(a + b*x))","A",1
1855,1,239,448,0.1929252,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{(a+b x)^2} \sqrt{d+e x} \left(-819 b^4 (d+e x)^5 (-5 a B e-A b e+6 b B d)+5005 b^3 (d+e x)^4 (b d-a e) (-2 a B e-A b e+3 b B d)-12870 b^2 (d+e x)^3 (b d-a e)^2 (-a B e-A b e+2 b B d)+9009 b (d+e x)^2 (b d-a e)^3 (-a B e-2 A b e+3 b B d)-3003 (d+e x) (b d-a e)^4 (-a B e-5 A b e+6 b B d)+9009 (b d-a e)^5 (B d-A e)+693 b^5 B (d+e x)^6\right)}{9009 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^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{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*Sqrt[(a + b*x)^2]*Sqrt[d + e*x]*(9009*(b*d - a*e)^5*(B*d - A*e) - 3003*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x) + 9009*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2 - 12870*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3 + 5005*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4 - 819*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5 + 693*b^5*B*(d + e*x)^6))/(9009*e^7*(a + b*x))","A",1
1856,1,239,446,0.1962064,"\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","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-77 b^4 (d+e x)^5 (-5 a B e-A b e+6 b B d)+495 b^3 (d+e x)^4 (b d-a e) (-2 a B e-A b e+3 b B d)-1386 b^2 (d+e x)^3 (b d-a e)^2 (-a B e-A b e+2 b B d)+1155 b (d+e x)^2 (b d-a e)^3 (-a B e-2 A b e+3 b B d)-693 (d+e x) (b d-a e)^4 (-a B e-5 A b e+6 b B d)-693 (b d-a e)^5 (B d-A e)+63 b^5 B (d+e x)^6\right)}{693 e^7 (a+b x) \sqrt{d+e 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^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{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*Sqrt[(a + b*x)^2]*(-693*(b*d - a*e)^5*(B*d - A*e) - 693*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x) + 1155*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2 - 1386*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3 + 495*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4 - 77*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5 + 63*b^5*B*(d + e*x)^6))/(693*e^7*(a + b*x)*Sqrt[d + e*x])","A",1
1857,1,239,446,0.2901177,"\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","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-9 b^4 (d+e x)^5 (-5 a B e-A b e+6 b B d)+63 b^3 (d+e x)^4 (b d-a e) (-2 a B e-A b e+3 b B d)-210 b^2 (d+e x)^3 (b d-a e)^2 (-a B e-A b e+2 b B d)+315 b (d+e x)^2 (b d-a e)^3 (-a B e-2 A b e+3 b B d)+63 (d+e x) (b d-a e)^4 (-a B e-5 A b e+6 b B d)-21 (b d-a e)^5 (B d-A e)+7 b^5 B (d+e x)^6\right)}{63 e^7 (a+b x) (d+e x)^{3/2}}","-\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^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{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*Sqrt[(a + b*x)^2]*(-21*(b*d - a*e)^5*(B*d - A*e) + 63*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x) + 315*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2 - 210*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3 + 63*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4 - 9*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5 + 7*b^5*B*(d + e*x)^6))/(63*e^7*(a + b*x)*(d + e*x)^(3/2))","A",1
1858,1,239,448,0.3116755,"\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","Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(7/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-21 b^4 (d+e x)^5 (-5 a B e-A b e+6 b B d)+175 b^3 (d+e x)^4 (b d-a e) (-2 a B e-A b e+3 b B d)-1050 b^2 (d+e x)^3 (b d-a e)^2 (-a B e-A b e+2 b B d)-525 b (d+e x)^2 (b d-a e)^3 (-a B e-2 A b e+3 b B d)+35 (d+e x) (b d-a e)^4 (-a B e-5 A b e+6 b B d)-21 (b d-a e)^5 (B d-A e)+15 b^5 B (d+e x)^6\right)}{105 e^7 (a+b x) (d+e x)^{5/2}}","-\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^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{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*Sqrt[(a + b*x)^2]*(-21*(b*d - a*e)^5*(B*d - A*e) + 35*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x) - 525*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2 - 1050*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3 + 175*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4 - 21*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5 + 15*b^5*B*(d + e*x)^6))/(105*e^7*(a + b*x)*(d + e*x)^(5/2))","A",1
1859,1,154,289,0.3002484,"\int \frac{(A+B x) (d+e x)^{5/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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) \left(\frac{7 e (A b-a B) \left(5 (b d-a e) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)+3 b^{5/2} (d+e x)^{5/2}\right)}{15 b^{7/2}}+B (d+e x)^{7/2}\right)}{7 b e \sqrt{(a+b 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) (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 (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) (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 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*x)*(B*(d + e*x)^(7/2) + (7*(A*b - a*B)*e*(3*b^(5/2)*(d + e*x)^(5/2) + 5*(b*d - a*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])))/(15*b^(7/2))))/(7*b*e*Sqrt[(a + b*x)^2])","A",1
1860,1,127,230,0.1715536,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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) \left(\frac{5 e (A b-a B) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)}{3 b^{5/2}}+B (d+e x)^{5/2}\right)}{5 b e \sqrt{(a+b 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) (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 (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 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*x)*(B*(d + e*x)^(5/2) + (5*(A*b - a*B)*e*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/(3*b^(5/2))))/(5*b*e*Sqrt[(a + b*x)^2])","A",1
1861,1,114,173,0.0887796,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \left(\sqrt{b} \sqrt{d+e x} (-3 a B e+3 A b e+b B (d+e x))+3 e (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)\right)}{3 b^{5/2} e \sqrt{(a+b 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*x)*(Sqrt[b]*Sqrt[d + e*x]*(3*A*b*e - 3*a*B*e + b*B*(d + e*x)) + 3*(-(A*b) + a*B)*e*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/(3*b^(5/2)*e*Sqrt[(a + b*x)^2])","A",1
1862,1,111,124,0.0654543,"\int \frac{A+B x}{\sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 (a+b x) \left(e (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)+\sqrt{b} B \sqrt{d+e x} (b d-a e)\right)}{b^{3/2} e \sqrt{(a+b x)^2} (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*(a + b*x)*(Sqrt[b]*B*(b*d - a*e)*Sqrt[d + e*x] + (-(A*b) + a*B)*e*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/(b^(3/2)*e*(b*d - a*e)*Sqrt[(a + b*x)^2])","A",1
1863,1,128,138,0.0848899,"\int \frac{A+B x}{(d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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) \left(e \sqrt{d+e 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)-\sqrt{b} (b d-a e) (B d-A e)\right)}{\sqrt{b} e \sqrt{(a+b x)^2} \sqrt{d+e x} (b d-a e)^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*(a + b*x)*(-(Sqrt[b]*(b*d - a*e)*(B*d - A*e)) + (-(A*b) + a*B)*e*Sqrt[b*d - a*e]*Sqrt[d + e*x]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/(Sqrt[b]*e*(b*d - a*e)^2*Sqrt[(a + b*x)^2]*Sqrt[d + e*x])","A",1
1864,1,102,194,0.0496802,"\int \frac{A+B x}{(d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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) \left(3 e (d+e x) (A b-a B) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)-(b d-a e) (B d-A e)\right)}{3 e \sqrt{(a+b x)^2} (d+e x)^{3/2} (b d-a e)^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*(a + b*x)*(-((b*d - a*e)*(B*d - A*e)) + 3*(A*b - a*B)*e*(d + e*x)*Hypergeometric2F1[-1/2, 1, 1/2, (b*(d + e*x))/(b*d - a*e)]))/(3*e*(b*d - a*e)^2*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2))","C",1
1865,1,102,251,0.0520881,"\int \frac{A+B x}{(d+e x)^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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) \left(5 e (d+e x) (A b-a B) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)-3 (b d-a e) (B d-A e)\right)}{15 e \sqrt{(a+b x)^2} (d+e x)^{5/2} (b d-a e)^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*(a + b*x)*(-3*(b*d - a*e)*(B*d - A*e) + 5*(A*b - a*B)*e*(d + e*x)*Hypergeometric2F1[-3/2, 1, -1/2, (b*(d + e*x))/(b*d - a*e)]))/(15*e*(b*d - a*e)^2*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2))","C",1
1866,1,111,407,0.1211948,"\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","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) (d+e x)^{9/2} \left(\frac{e (a+b x)^2 (-9 a B e+5 A b e+4 b B d) \, _2F_1\left(2,\frac{9}{2};\frac{11}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+9 a B-9 A b\right)}{18 b \left((a+b x)^2\right)^{3/2} (b d-a e)}","-\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) (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{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) (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) (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)}",1,"((a + b*x)*(d + e*x)^(9/2)*(-9*A*b + 9*a*B + (e*(4*b*B*d + 5*A*b*e - 9*a*B*e)*(a + b*x)^2*Hypergeometric2F1[2, 9/2, 11/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2))/(18*b*(b*d - a*e)*((a + b*x)^2)^(3/2))","C",1
1867,1,111,341,0.1047681,"\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","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) (d+e x)^{7/2} \left(\frac{e (a+b x)^2 (-7 a B e+3 A b e+4 b B d) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+7 a B-7 A b\right)}{14 b \left((a+b x)^2\right)^{3/2} (b d-a e)}","-\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) \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{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) (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)}",1,"((a + b*x)*(d + e*x)^(7/2)*(-7*A*b + 7*a*B + (e*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)^2*Hypergeometric2F1[2, 7/2, 9/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2))/(14*b*(b*d - a*e)*((a + b*x)^2)^(3/2))","C",1
1868,1,110,280,0.0862336,"\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","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) (d+e x)^{5/2} \left(\frac{e (a+b x)^2 (-5 a B e+A b e+4 b B d) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+5 a B-5 A b\right)}{10 b \left((a+b x)^2\right)^{3/2} (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) (-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{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)}",1,"((a + b*x)*(d + e*x)^(5/2)*(-5*A*b + 5*a*B + (e*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^2*Hypergeometric2F1[2, 5/2, 7/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2))/(10*b*(b*d - a*e)*((a + b*x)^2)^(3/2))","C",1
1869,1,167,215,0.3343594,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) \left(\frac{(a+b x) (-3 a B e-A b e+4 b B d) \left(\sqrt{b} e (a+b x) \sqrt{d+e x} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)-b (d+e x) \sqrt{a e-b d}\right)}{\sqrt{a e-b d}}-2 b^2 (d+e x)^2 (A b-a B)\right)}{4 b^3 \left((a+b x)^2\right)^{3/2} \sqrt{d+e x} (b d-a e)}","-\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,"((a + b*x)*(-2*b^2*(A*b - a*B)*(d + e*x)^2 + ((4*b*B*d - A*b*e - 3*a*B*e)*(a + b*x)*(-(b*Sqrt[-(b*d) + a*e]*(d + e*x)) + Sqrt[b]*e*(a + b*x)*Sqrt[d + e*x]*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]]))/Sqrt[-(b*d) + a*e]))/(4*b^3*(b*d - a*e)*((a + b*x)^2)^(3/2)*Sqrt[d + e*x])","A",1
1870,1,170,215,0.2566378,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{(a+b x) \sqrt{d+e x} \left(\frac{(a+b x) (-a B e-3 A b e+4 b B d) \left(\sqrt{b} \sqrt{d+e x} (a e-b d)+e (a+b x) \sqrt{a e-b d} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)\right)}{2 \sqrt{b} \sqrt{d+e x} (b d-a e)^2}+a B-A b\right)}{2 b \left((a+b x)^2\right)^{3/2} (b d-a e)}","-\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,"((a + b*x)*Sqrt[d + e*x]*(-(A*b) + a*B + ((4*b*B*d - 3*A*b*e - a*B*e)*(a + b*x)*(Sqrt[b]*(-(b*d) + a*e)*Sqrt[d + e*x] + e*Sqrt[-(b*d) + a*e]*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]]))/(2*Sqrt[b]*(b*d - a*e)^2*Sqrt[d + e*x])))/(2*b*(b*d - a*e)*((a + b*x)^2)^(3/2))","A",1
1871,1,110,281,0.0681573,"\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","Integrate[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{(a+b x) \left(\frac{e (a+b x)^2 (-a B e+5 A b e-4 b B d) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+a B-A b\right)}{2 b \left((a+b x)^2\right)^{3/2} \sqrt{d+e x} (b d-a e)}","-\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,"((a + b*x)*(-(A*b) + a*B + (e*(-4*b*B*d + 5*A*b*e - a*B*e)*(a + b*x)^2*Hypergeometric2F1[-1/2, 2, 1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2))/(2*b*(b*d - a*e)*((a + b*x)^2)^(3/2)*Sqrt[d + e*x])","C",1
1872,1,111,348,0.0691879,"\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","Integrate[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{(a+b x) \left(\frac{e (a+b x)^2 (-3 a B e+7 A b e-4 b B d) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+3 a B-3 A b\right)}{6 b \left((a+b x)^2\right)^{3/2} (d+e x)^{3/2} (b d-a e)}","-\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,"((a + b*x)*(-3*A*b + 3*a*B + (e*(-4*b*B*d + 7*A*b*e - 3*a*B*e)*(a + b*x)^2*Hypergeometric2F1[-3/2, 2, -1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2))/(6*b*(b*d - a*e)*((a + b*x)^2)^(3/2)*(d + e*x)^(3/2))","C",1
1873,1,111,414,0.0744843,"\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","Integrate[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{(a+b x) \left(\frac{e (a+b x)^2 (-5 a B e+9 A b e-4 b B d) \, _2F_1\left(-\frac{5}{2},2;-\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+5 a B-5 A b\right)}{10 b \left((a+b x)^2\right)^{3/2} (d+e x)^{5/2} (b d-a e)}","-\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,"((a + b*x)*(-5*A*b + 5*a*B + (e*(-4*b*B*d + 9*A*b*e - 5*a*B*e)*(a + b*x)^2*Hypergeometric2F1[-5/2, 2, -3/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2))/(10*b*(b*d - a*e)*((a + b*x)^2)^(3/2)*(d + e*x)^(5/2))","C",1
1874,1,117,557,0.2118349,"\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","Integrate[((A + B*x)*(d + e*x)^(11/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(d+e x)^{13/2} \left(\frac{e^3 (a+b x)^4 (-13 a B e+5 A b e+8 b B d) \, _2F_1\left(4,\frac{13}{2};\frac{15}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^4}+13 (a B-A b)\right)}{52 b (a+b x)^3 \sqrt{(a+b x)^2} (b d-a e)}","-\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{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{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{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) (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{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{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,"((d + e*x)^(13/2)*(13*(-(A*b) + a*B) + (e^3*(8*b*B*d + 5*A*b*e - 13*a*B*e)*(a + b*x)^4*Hypergeometric2F1[4, 13/2, 15/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^4))/(52*b*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
1875,1,117,489,0.1823681,"\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","Integrate[((A + B*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(d+e x)^{11/2} \left(\frac{e^3 (a+b x)^4 (-11 a B e+3 A b e+8 b B d) \, _2F_1\left(4,\frac{11}{2};\frac{13}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^4}+11 (a B-A b)\right)}{44 b (a+b x)^3 \sqrt{(a+b x)^2} (b d-a e)}","-\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{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{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{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{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{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,"((d + e*x)^(11/2)*(11*(-(A*b) + a*B) + (e^3*(8*b*B*d + 3*A*b*e - 11*a*B*e)*(a + b*x)^4*Hypergeometric2F1[4, 11/2, 13/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^4))/(44*b*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
1876,1,114,424,0.1619969,"\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","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(d+e x)^{9/2} \left(\frac{e^3 (a+b x)^4 (-9 a B e+A b e+8 b B d) \, _2F_1\left(4,\frac{9}{2};\frac{11}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^4}+9 a B-9 A b\right)}{36 b (a+b x)^3 \sqrt{(a+b x)^2} (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{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{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^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{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,"((d + e*x)^(9/2)*(-9*A*b + 9*a*B + (e^3*(8*b*B*d + A*b*e - 9*a*B*e)*(a + b*x)^4*Hypergeometric2F1[4, 9/2, 11/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^4))/(36*b*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
1877,1,219,359,1.0005781,"\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","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-\frac{(a+b x) (-7 a B e-A b e+8 b B d) \left(b (d+e x) \sqrt{a e-b d} \left(15 a^2 e^2+10 a b e (d+4 e x)+b^2 \left(8 d^2+26 d e x+33 e^2 x^2\right)\right)-15 \sqrt{b} e^3 (a+b x)^3 \sqrt{d+e x} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)\right)}{3 \sqrt{a e-b d}}-16 b^4 (d+e x)^4 (A b-a B)}{64 b^5 (a+b x)^3 \sqrt{(a+b x)^2} \sqrt{d+e x} (b d-a e)}","-\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^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{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 (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,"(-16*b^4*(A*b - a*B)*(d + e*x)^4 - ((8*b*B*d - A*b*e - 7*a*B*e)*(a + b*x)*(b*Sqrt[-(b*d) + a*e]*(d + e*x)*(15*a^2*e^2 + 10*a*b*e*(d + 4*e*x) + b^2*(8*d^2 + 26*d*e*x + 33*e^2*x^2)) - 15*Sqrt[b]*e^3*(a + b*x)^3*Sqrt[d + e*x]*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]]))/(3*Sqrt[-(b*d) + a*e]))/(64*b^5*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2]*Sqrt[d + e*x])","A",1
1878,1,116,359,0.1204061,"\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","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(d+e x)^{5/2} \left(-\frac{e^3 (a+b x)^4 (5 a B e+3 A b e-8 b B d) \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^4}+5 a B-5 A b\right)}{20 b (a+b x)^3 \sqrt{(a+b 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^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^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 \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)}",1,"((d + e*x)^(5/2)*(-5*A*b + 5*a*B - (e^3*(-8*b*B*d + 3*A*b*e + 5*a*B*e)*(a + b*x)^4*Hypergeometric2F1[5/2, 4, 7/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^4))/(20*b*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
1879,1,116,359,0.1002067,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(d+e x)^{3/2} \left(-\frac{e^3 (a+b x)^4 (3 a B e+5 A b e-8 b B d) \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^4}+3 a B-3 A b\right)}{12 b (a+b x)^3 \sqrt{(a+b 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 \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^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}}",1,"((d + e*x)^(3/2)*(-3*A*b + 3*a*B - (e^3*(-8*b*B*d + 5*A*b*e + 3*a*B*e)*(a + b*x)^4*Hypergeometric2F1[3/2, 4, 5/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^4))/(12*b*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
1880,1,114,359,0.0838679,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{\sqrt{d+e x} \left(-\frac{e^3 (a+b x)^4 (a B e+7 A b e-8 b B d) \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^4}+a B-A b\right)}{4 b (a+b x)^3 \sqrt{(a+b 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 \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^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}}",1,"(Sqrt[d + e*x]*(-(A*b) + a*B - (e^3*(-8*b*B*d + 7*A*b*e + a*B*e)*(a + b*x)^4*Hypergeometric2F1[1/2, 4, 3/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^4))/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2])","C",1
1881,1,114,424,0.0878341,"\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","Integrate[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{\frac{e^3 (a+b x)^4 (-a B e+9 A b e-8 b B d) \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^4}+a B-A b}{4 b (a+b x)^3 \sqrt{(a+b 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^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{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{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,"(-(A*b) + a*B + (e^3*(-8*b*B*d + 9*A*b*e - a*B*e)*(a + b*x)^4*Hypergeometric2F1[-1/2, 4, 1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^4)/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2]*Sqrt[d + e*x])","C",1
1882,1,115,496,0.0940365,"\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","Integrate[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{\frac{e^3 (a+b x)^4 (-3 a B e+11 A b e-8 b B d) \, _2F_1\left(-\frac{3}{2},4;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^4}+3 a B-3 A b}{12 b (a+b x)^3 \sqrt{(a+b 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{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{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{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,"(-3*A*b + 3*a*B + (e^3*(-8*b*B*d + 11*A*b*e - 3*a*B*e)*(a + b*x)^4*Hypergeometric2F1[-3/2, 4, -1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^4)/(12*b*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2))","C",1
1883,1,115,564,0.0996478,"\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","Integrate[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{\frac{e^3 (a+b x)^4 (-5 a B e+13 A b e-8 b B d) \, _2F_1\left(-\frac{5}{2},4;-\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^4}+5 a B-5 A b}{20 b (a+b x)^3 \sqrt{(a+b 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{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^{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}}",1,"(-5*A*b + 5*a*B + (e^3*(-8*b*B*d + 13*A*b*e - 5*a*B*e)*(a + b*x)^4*Hypergeometric2F1[-5/2, 4, -3/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^4)/(20*b*(b*d - a*e)*(a + b*x)^3*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2))","C",1
1884,1,208,234,0.2155869,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(-\frac{b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)}{m+5}+\frac{2 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{m+4}-\frac{2 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{m+3}+\frac{(d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{m+2}-\frac{(b d-a e)^4 (B d-A e)}{m+1}+\frac{b^4 B (d+e x)^5}{m+6}\right)}{e^6}","-\frac{b^3 (d+e x)^{m+5} (-4 a B e-A b e+5 b B d)}{e^6 (m+5)}+\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 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,"((d + e*x)^(1 + m)*(-(((b*d - a*e)^4*(B*d - A*e))/(1 + m)) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x))/(2 + m) - (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2)/(3 + m) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3)/(4 + m) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4)/(5 + m) + (b^4*B*(d + e*x)^5)/(6 + m)))/e^6","A",1
1885,1,122,138,0.1021631,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(d+e x)^{m+1} \left(-\frac{b (d+e x)^2 (-2 a B e-A b e+3 b B d)}{m+3}+\frac{(d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)}{m+2}-\frac{(b d-a e)^2 (B d-A e)}{m+1}+\frac{b^2 B (d+e x)^3}{m+4}\right)}{e^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,"((d + e*x)^(1 + m)*(-(((b*d - a*e)^2*(B*d - A*e))/(1 + m)) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x))/(2 + m) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2)/(3 + m) + (b^2*B*(d + e*x)^3)/(4 + m)))/e^4","A",1
1886,1,99,112,0.0467778,"\int \frac{(A+B x) (d+e x)^m}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(d+e x)^{m+1} \left(\frac{(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)}{m+1}-\frac{(A b-a B) (b d-a e)}{a+b x}\right)}{b (b d-a e)^2}","\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,"((d + e*x)^(1 + m)*(-(((A*b - a*B)*(b*d - a*e))/(a + b*x)) + ((a*B*e*(1 + m) - b*(B*d + A*e*m))*Hypergeometric2F1[1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/(1 + m)))/(b*(b*d - a*e)^2)","A",1
1887,1,109,126,0.0817452,"\int \frac{(A+B x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(\frac{a B-A b}{(a+b x)^3}-\frac{e^2 (-a B e (m+1)+A b e (m-2)+3 b B d) \, _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}\right)}{3 b (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,"((d + e*x)^(1 + m)*((-(A*b) + a*B)/(a + b*x)^3 - (e^2*(3*b*B*d + A*b*e*(-2 + m) - a*B*e*(1 + m))*Hypergeometric2F1[3, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^3*(1 + m))))/(3*b*(b*d - a*e))","A",1
1888,1,269,471,0.3107026,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{(a+b x)^2} (d+e x)^{m+1} \left(-\frac{b^4 (d+e x)^5 (-5 a B e-A b e+6 b B d)}{m+6}+\frac{5 b^3 (d+e x)^4 (b d-a e) (-2 a B e-A b e+3 b B d)}{m+5}-\frac{10 b^2 (d+e x)^3 (b d-a e)^2 (-a B e-A b e+2 b B d)}{m+4}+\frac{5 b (d+e x)^2 (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{m+3}-\frac{(d+e x) (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{m+2}+\frac{(b d-a e)^5 (B d-A e)}{m+1}+\frac{b^5 B (d+e x)^6}{m+7}\right)}{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) (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{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{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^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,"(Sqrt[(a + b*x)^2]*(d + e*x)^(1 + m)*(((b*d - a*e)^5*(B*d - A*e))/(1 + m) - ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x))/(2 + m) + (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^2)/(3 + m) - (10*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^3)/(4 + m) + (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^4)/(5 + m) - (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^5)/(6 + m) + (b^5*B*(d + e*x)^6)/(7 + m)))/(e^7*(a + b*x))","A",1
1889,1,183,321,0.2704443,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\left((a+b x)^2\right)^{3/2} (d+e x)^{m+1} \left(-\frac{b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)}{m+4}+\frac{3 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)}{m+3}-\frac{(d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{m+2}+\frac{(b d-a e)^3 (B d-A e)}{m+1}+\frac{b^3 B (d+e x)^4}{m+5}\right)}{e^5 (a+b x)^3}","\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,"(((a + b*x)^2)^(3/2)*(d + e*x)^(1 + m)*(((b*d - a*e)^3*(B*d - A*e))/(1 + m) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x))/(2 + m) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2)/(3 + m) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3)/(4 + m) + (b^3*B*(d + e*x)^4)/(5 + m)))/(e^5*(a + b*x)^3)","A",1
1890,1,121,171,0.1160153,"\int (A+B x) (d+e x)^m \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(A + B*x)*(d + e*x)^m*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sqrt{(a+b x)^2} (d+e x)^{m+1} \left(a e (m+3) (A e (m+2)-B d+B e (m+1) x)+b \left(A e (m+3) (e (m+1) x-d)+B \left(2 d^2-2 d e (m+1) x+e^2 \left(m^2+3 m+2\right) x^2\right)\right)\right)}{e^3 (m+1) (m+2) (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,"(Sqrt[(a + b*x)^2]*(d + e*x)^(1 + m)*(a*e*(3 + m)*(-(B*d) + A*e*(2 + m) + B*e*(1 + m)*x) + b*(A*e*(3 + m)*(-d + e*(1 + m)*x) + B*(2*d^2 - 2*d*e*(1 + m)*x + e^2*(2 + 3*m + m^2)*x^2))))/(e^3*(1 + m)*(2 + m)*(3 + m)*(a + b*x))","A",1
1891,1,94,135,0.0613923,"\int \frac{(A+B x) (d+e x)^m}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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} \left((a B e-A b e) \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)+B (b d-a e)\right)}{b e (m+1) \sqrt{(a+b 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,"((a + b*x)*(d + e*x)^(1 + m)*(B*(b*d - a*e) + (-(A*b*e) + a*B*e)*Hypergeometric2F1[1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)]))/(b*e*(b*d - a*e)*(1 + m)*Sqrt[(a + b*x)^2])","A",1
1892,1,120,169,0.1487759,"\int \frac{(A+B x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) (d+e x)^{m+1} \left(\frac{e (a+b x)^2 (-a B e (m+1)+A b e (m-1)+2 b B d) \, _2F_1\left(2,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)^2}+a B-A b\right)}{2 b \left((a+b x)^2\right)^{3/2} (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*x)*(d + e*x)^(1 + m)*(-(A*b) + a*B + (e*(2*b*B*d + A*b*e*(-1 + m) - a*B*e*(1 + m))*(a + b*x)^2*Hypergeometric2F1[2, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^2*(1 + m))))/(2*b*(b*d - a*e)*((a + b*x)^2)^(3/2))","A",1
1893,1,125,174,0.1165874,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left((a+b x)^2\right)^p (d+e x)^{m+1} \left(B e (a+b x)-\frac{\left(\frac{e (a+b x)}{a e-b d}\right)^{-2 p} (a B e (m+1)-A b e (m+2 p+2)+b B (2 d p+d)) \, _2F_1\left(m+1,-2 p;m+2;\frac{b (d+e x)}{b d-a e}\right)}{m+1}\right)}{b e^2 (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,"(((a + b*x)^2)^p*(d + e*x)^(1 + m)*(B*e*(a + b*x) - ((a*B*e*(1 + m) - A*b*e*(2 + m + 2*p) + b*B*(d + 2*d*p))*Hypergeometric2F1[1 + m, -2*p, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((1 + m)*((e*(a + b*x))/(-(b*d) + a*e))^(2*p))))/(b*e^2*(2 + m + 2*p))","A",1
1894,1,97,119,0.0769154,"\int (d+e x)^{-3-2 p} (f+g x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Integrate[(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) \left((a+b x)^2\right)^p (d+e x)^{-2 (p+1)} (b (2 d f (p+1)+d g (2 p+1) x+e f x)-a (d g+e (2 f p+f+2 g (p+1) 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,"((a + b*x)*((a + b*x)^2)^p*(b*(2*d*f*(1 + p) + e*f*x + d*g*(1 + 2*p)*x) - a*(d*g + e*(f + 2*f*p + 2*g*(1 + p)*x))))/(2*(b*d - a*e)^2*(1 + p)*(1 + 2*p)*(d + e*x)^(2*(1 + p)))","A",1
1895,1,267,92,0.0345925,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2),x]","a^3 d^5 x+\frac{1}{7} b e^3 x^7 \left(3 a^2 e^2+15 a b d e+10 b^2 d^2\right)+\frac{1}{3} a d^3 x^3 \left(10 a^2 e^2+15 a b d e+3 b^2 d^2\right)+\frac{1}{2} a^2 d^4 x^2 (5 a e+3 b d)+\frac{1}{6} e^2 x^6 \left(a^3 e^3+15 a^2 b d e^2+30 a b^2 d^2 e+10 b^3 d^3\right)+d e x^5 \left(a^3 e^3+6 a^2 b d e^2+6 a b^2 d^2 e+b^3 d^3\right)+\frac{1}{4} d^2 x^4 \left(10 a^3 e^3+30 a^2 b d e^2+15 a b^2 d^2 e+b^3 d^3\right)+\frac{1}{8} b^2 e^4 x^8 (3 a e+5 b d)+\frac{1}{9} b^3 e^5 x^9","-\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,"a^3*d^5*x + (a^2*d^4*(3*b*d + 5*a*e)*x^2)/2 + (a*d^3*(3*b^2*d^2 + 15*a*b*d*e + 10*a^2*e^2)*x^3)/3 + (d^2*(b^3*d^3 + 15*a*b^2*d^2*e + 30*a^2*b*d*e^2 + 10*a^3*e^3)*x^4)/4 + d*e*(b^3*d^3 + 6*a*b^2*d^2*e + 6*a^2*b*d*e^2 + a^3*e^3)*x^5 + (e^2*(10*b^3*d^3 + 30*a*b^2*d^2*e + 15*a^2*b*d*e^2 + a^3*e^3)*x^6)/6 + (b*e^3*(10*b^2*d^2 + 15*a*b*d*e + 3*a^2*e^2)*x^7)/7 + (b^2*e^4*(5*b*d + 3*a*e)*x^8)/8 + (b^3*e^5*x^9)/9","B",1
1896,1,217,92,0.0306028,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2),x]","a^3 d^4 x+\frac{1}{2} b e^2 x^6 \left(a^2 e^2+4 a b d e+2 b^2 d^2\right)+a d^2 x^3 \left(2 a^2 e^2+4 a b d e+b^2 d^2\right)+\frac{1}{2} a^2 d^3 x^2 (4 a e+3 b d)+\frac{1}{5} e x^5 \left(a^3 e^3+12 a^2 b d e^2+18 a b^2 d^2 e+4 b^3 d^3\right)+\frac{1}{4} d x^4 \left(4 a^3 e^3+18 a^2 b d e^2+12 a b^2 d^2 e+b^3 d^3\right)+\frac{1}{7} b^2 e^3 x^7 (3 a e+4 b d)+\frac{1}{8} b^3 e^4 x^8","-\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,"a^3*d^4*x + (a^2*d^3*(3*b*d + 4*a*e)*x^2)/2 + a*d^2*(b^2*d^2 + 4*a*b*d*e + 2*a^2*e^2)*x^3 + (d*(b^3*d^3 + 12*a*b^2*d^2*e + 18*a^2*b*d*e^2 + 4*a^3*e^3)*x^4)/4 + (e*(4*b^3*d^3 + 18*a*b^2*d^2*e + 12*a^2*b*d*e^2 + a^3*e^3)*x^5)/5 + (b*e^2*(2*b^2*d^2 + 4*a*b*d*e + a^2*e^2)*x^6)/2 + (b^2*e^3*(4*b*d + 3*a*e)*x^7)/7 + (b^3*e^4*x^8)/8","B",1
1897,1,161,92,0.0225916,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2),x]","a^3 d^3 x+\frac{3}{5} b e x^5 \left(a^2 e^2+3 a b d e+b^2 d^2\right)+a d x^3 \left(a^2 e^2+3 a b d e+b^2 d^2\right)+\frac{3}{2} a^2 d^2 x^2 (a e+b d)+\frac{1}{4} x^4 \left(a^3 e^3+9 a^2 b d e^2+9 a b^2 d^2 e+b^3 d^3\right)+\frac{1}{2} b^2 e^2 x^6 (a e+b d)+\frac{1}{7} b^3 e^3 x^7","\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,"a^3*d^3*x + (3*a^2*d^2*(b*d + a*e)*x^2)/2 + a*d*(b^2*d^2 + 3*a*b*d*e + a^2*e^2)*x^3 + ((b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e^2 + a^3*e^3)*x^4)/4 + (3*b*e*(b^2*d^2 + 3*a*b*d*e + a^2*e^2)*x^5)/5 + (b^2*e^2*(b*d + a*e)*x^6)/2 + (b^3*e^3*x^7)/7","A",1
1898,1,122,65,0.0183689,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2),x]","a^3 d^2 x+\frac{1}{4} b x^4 \left(3 a^2 e^2+6 a b d e+b^2 d^2\right)+\frac{1}{3} a x^3 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)+\frac{1}{2} a^2 d x^2 (2 a e+3 b d)+\frac{1}{5} b^2 e x^5 (3 a e+2 b d)+\frac{1}{6} b^3 e^2 x^6","\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,"a^3*d^2*x + (a^2*d*(3*b*d + 2*a*e)*x^2)/2 + (a*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2)*x^3)/3 + (b*(b^2*d^2 + 6*a*b*d*e + 3*a^2*e^2)*x^4)/4 + (b^2*e*(2*b*d + 3*a*e)*x^5)/5 + (b^3*e^2*x^6)/6","A",1
1899,1,67,38,0.0102695,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","a^3 d x+\frac{1}{2} a^2 x^2 (a e+3 b d)+\frac{1}{4} b^2 x^4 (3 a e+b d)+a b x^3 (a e+b d)+\frac{1}{5} b^3 e x^5","\frac{(a+b x)^4 (b d-a e)}{4 b^2}+\frac{e (a+b x)^5}{5 b^2}",1,"a^3*d*x + (a^2*(3*b*d + a*e)*x^2)/2 + a*b*(b*d + a*e)*x^3 + (b^2*(b*d + 3*a*e)*x^4)/4 + (b^3*e*x^5)/5","A",1
1900,1,14,14,0.0010939,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(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",1
1901,1,74,74,0.0286483,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{d+e x} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x),x]","\frac{b e x \left(18 a^2 e^2+9 a b e (e x-2 d)+b^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)-6 (b d-a e)^3 \log (d+e x)}{6 e^4}","-\frac{(b d-a e)^3 \log (d+e x)}{e^4}+\frac{b x (b d-a e)^2}{e^3}-\frac{(a+b x)^2 (b d-a e)}{2 e^2}+\frac{(a+b x)^3}{3 e}",1,"(b*e*x*(18*a^2*e^2 + 9*a*b*e*(-2*d + e*x) + b^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) - 6*(b*d - a*e)^3*Log[d + e*x])/(6*e^4)","A",1
1902,1,114,75,0.0353493,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^2} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^2,x]","\frac{3 \left(a^2 b e^2-2 a b^2 d e+b^3 d^2\right) \log (d+e x)}{e^4}+\frac{-a^3 e^3+3 a^2 b d e^2-3 a b^2 d^2 e+b^3 d^3}{e^4 (d+e x)}-\frac{b^2 x (2 b d-3 a e)}{e^3}+\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^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)/(e^4*(d + e*x)) + (3*(b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2)*Log[d + e*x])/e^4","A",1
1903,1,114,78,0.0394692,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^3} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^3,x]","\frac{-a^3 e^3-3 a^2 b e^2 (d+2 e x)+3 a b^2 d e (3 d+4 e x)-6 b^2 (d+e x)^2 (b d-a e) \log (d+e x)+b^3 \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)}{2 e^4 (d+e x)^2}","-\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,"(-(a^3*e^3) - 3*a^2*b*e^2*(d + 2*e*x) + 3*a*b^2*d*e*(3*d + 4*e*x) + b^3*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) - 6*b^2*(b*d - a*e)*(d + e*x)^2*Log[d + e*x])/(2*e^4*(d + e*x)^2)","A",1
1904,1,79,86,0.0386855,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^4} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^4,x]","\frac{\frac{(b d-a e) \left(2 a^2 e^2+a b e (5 d+9 e x)+b^2 \left(11 d^2+27 d e x+18 e^2 x^2\right)\right)}{(d+e x)^3}+6 b^3 \log (d+e x)}{6 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)*(2*a^2*e^2 + a*b*e*(5*d + 9*e*x) + b^2*(11*d^2 + 27*d*e*x + 18*e^2*x^2)))/(d + e*x)^3 + 6*b^3*Log[d + e*x])/(6*e^4)","A",1
1905,1,501,143,0.0683011,"\int (a+b x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^5 d^6 x+\frac{1}{2} a^4 d^5 x^2 (6 a e+5 b d)+\frac{1}{2} b^3 e^4 x^{10} \left(2 a^2 e^2+6 a b d e+3 b^2 d^2\right)+\frac{5}{3} a^3 d^4 x^3 \left(3 a^2 e^2+6 a b d e+2 b^2 d^2\right)+\frac{5}{9} b^2 e^3 x^9 \left(2 a^3 e^3+12 a^2 b d e^2+15 a b^2 d^2 e+4 b^3 d^3\right)+\frac{5}{4} a^2 d^3 x^4 \left(4 a^3 e^3+15 a^2 b d e^2+12 a b^2 d^2 e+2 b^3 d^3\right)+\frac{5}{8} b e^2 x^8 \left(a^4 e^4+12 a^3 b d e^3+30 a^2 b^2 d^2 e^2+20 a b^3 d^3 e+3 b^4 d^4\right)+a d^2 x^5 \left(3 a^4 e^4+20 a^3 b d e^3+30 a^2 b^2 d^2 e^2+12 a b^3 d^3 e+b^4 d^4\right)+\frac{1}{7} e x^7 \left(a^5 e^5+30 a^4 b d e^4+150 a^3 b^2 d^2 e^3+200 a^2 b^3 d^3 e^2+75 a b^4 d^4 e+6 b^5 d^5\right)+\frac{1}{6} d x^6 \left(6 a^5 e^5+75 a^4 b d e^4+200 a^3 b^2 d^2 e^3+150 a^2 b^3 d^3 e^2+30 a b^4 d^4 e+b^5 d^5\right)+\frac{1}{11} b^4 e^5 x^{11} (5 a e+6 b d)+\frac{1}{12} b^5 e^6 x^{12}","-\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,"a^5*d^6*x + (a^4*d^5*(5*b*d + 6*a*e)*x^2)/2 + (5*a^3*d^4*(2*b^2*d^2 + 6*a*b*d*e + 3*a^2*e^2)*x^3)/3 + (5*a^2*d^3*(2*b^3*d^3 + 12*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 4*a^3*e^3)*x^4)/4 + a*d^2*(b^4*d^4 + 12*a*b^3*d^3*e + 30*a^2*b^2*d^2*e^2 + 20*a^3*b*d*e^3 + 3*a^4*e^4)*x^5 + (d*(b^5*d^5 + 30*a*b^4*d^4*e + 150*a^2*b^3*d^3*e^2 + 200*a^3*b^2*d^2*e^3 + 75*a^4*b*d*e^4 + 6*a^5*e^5)*x^6)/6 + (e*(6*b^5*d^5 + 75*a*b^4*d^4*e + 200*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d^2*e^3 + 30*a^4*b*d*e^4 + a^5*e^5)*x^7)/7 + (5*b*e^2*(3*b^4*d^4 + 20*a*b^3*d^3*e + 30*a^2*b^2*d^2*e^2 + 12*a^3*b*d*e^3 + a^4*e^4)*x^8)/8 + (5*b^2*e^3*(4*b^3*d^3 + 15*a*b^2*d^2*e + 12*a^2*b*d*e^2 + 2*a^3*e^3)*x^9)/9 + (b^3*e^4*(3*b^2*d^2 + 6*a*b*d*e + 2*a^2*e^2)*x^10)/2 + (b^4*e^5*(6*b*d + 5*a*e)*x^11)/11 + (b^5*e^6*x^12)/12","B",1
1906,1,413,146,0.0480137,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^5 d^5 x+\frac{5}{2} a^4 d^4 x^2 (a e+b d)+\frac{5}{9} b^3 e^3 x^9 \left(2 a^2 e^2+5 a b d e+2 b^2 d^2\right)+\frac{5}{3} a^3 d^3 x^3 \left(2 a^2 e^2+5 a b d e+2 b^2 d^2\right)+\frac{5}{4} b^2 e^2 x^8 \left(a^3 e^3+5 a^2 b d e^2+5 a b^2 d^2 e+b^3 d^3\right)+\frac{5}{2} a^2 d^2 x^4 \left(a^3 e^3+5 a^2 b d e^2+5 a b^2 d^2 e+b^3 d^3\right)+\frac{5}{7} b e x^7 \left(a^4 e^4+10 a^3 b d e^3+20 a^2 b^2 d^2 e^2+10 a b^3 d^3 e+b^4 d^4\right)+a d x^5 \left(a^4 e^4+10 a^3 b d e^3+20 a^2 b^2 d^2 e^2+10 a b^3 d^3 e+b^4 d^4\right)+\frac{1}{6} x^6 \left(a^5 e^5+25 a^4 b d e^4+100 a^3 b^2 d^2 e^3+100 a^2 b^3 d^3 e^2+25 a b^4 d^4 e+b^5 d^5\right)+\frac{1}{2} b^4 e^4 x^{10} (a e+b d)+\frac{1}{11} b^5 e^5 x^{11}","\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,"a^5*d^5*x + (5*a^4*d^4*(b*d + a*e)*x^2)/2 + (5*a^3*d^3*(2*b^2*d^2 + 5*a*b*d*e + 2*a^2*e^2)*x^3)/3 + (5*a^2*d^2*(b^3*d^3 + 5*a*b^2*d^2*e + 5*a^2*b*d*e^2 + a^3*e^3)*x^4)/2 + a*d*(b^4*d^4 + 10*a*b^3*d^3*e + 20*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 + a^4*e^4)*x^5 + ((b^5*d^5 + 25*a*b^4*d^4*e + 100*a^2*b^3*d^3*e^2 + 100*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + a^5*e^5)*x^6)/6 + (5*b*e*(b^4*d^4 + 10*a*b^3*d^3*e + 20*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 + a^4*e^4)*x^7)/7 + (5*b^2*e^2*(b^3*d^3 + 5*a*b^2*d^2*e + 5*a^2*b*d*e^2 + a^3*e^3)*x^8)/4 + (5*b^3*e^3*(2*b^2*d^2 + 5*a*b*d*e + 2*a^2*e^2)*x^9)/9 + (b^4*e^4*(b*d + a*e)*x^10)/2 + (b^5*e^5*x^11)/11","B",1
1907,1,301,119,0.0848463,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{x \left(252 a^5 \left(5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right)+210 a^4 b x \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)+120 a^3 b^2 x^2 \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)+45 a^2 b^3 x^3 \left(70 d^4+224 d^3 e x+280 d^2 e^2 x^2+160 d e^3 x^3+35 e^4 x^4\right)+10 a b^4 x^4 \left(126 d^4+420 d^3 e x+540 d^2 e^2 x^2+315 d e^3 x^3+70 e^4 x^4\right)+b^5 x^5 \left(210 d^4+720 d^3 e x+945 d^2 e^2 x^2+560 d e^3 x^3+126 e^4 x^4\right)\right)}{1260}","\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,"(x*(252*a^5*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4) + 210*a^4*b*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4) + 120*a^3*b^2*x^2*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4) + 45*a^2*b^3*x^3*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4) + 10*a*b^4*x^4*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4) + b^5*x^5*(210*d^4 + 720*d^3*e*x + 945*d^2*e^2*x^2 + 560*d*e^3*x^3 + 126*e^4*x^4)))/1260","B",1
1908,1,235,92,0.0658366,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{1}{504} x \left(126 a^5 \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+126 a^4 b x \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)+84 a^3 b^2 x^2 \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)+36 a^2 b^3 x^3 \left(35 d^3+84 d^2 e x+70 d e^2 x^2+20 e^3 x^3\right)+9 a b^4 x^4 \left(56 d^3+140 d^2 e x+120 d e^2 x^2+35 e^3 x^3\right)+b^5 x^5 \left(84 d^3+216 d^2 e x+189 d e^2 x^2+56 e^3 x^3\right)\right)","\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,"(x*(126*a^5*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) + 126*a^4*b*x*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3) + 84*a^3*b^2*x^2*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3) + 36*a^2*b^3*x^3*(35*d^3 + 84*d^2*e*x + 70*d*e^2*x^2 + 20*e^3*x^3) + 9*a*b^4*x^4*(56*d^3 + 140*d^2*e*x + 120*d*e^2*x^2 + 35*e^3*x^3) + b^5*x^5*(84*d^3 + 216*d^2*e*x + 189*d*e^2*x^2 + 56*e^3*x^3)))/504","B",1
1909,1,189,65,0.0296523,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^5 d^2 x+\frac{1}{2} a^4 d x^2 (2 a e+5 b d)+a b^2 x^5 \left(2 a^2 e^2+4 a b d e+b^2 d^2\right)+\frac{5}{4} a^2 b x^4 \left(a^2 e^2+4 a b d e+2 b^2 d^2\right)+\frac{1}{6} b^3 x^6 \left(10 a^2 e^2+10 a b d e+b^2 d^2\right)+\frac{1}{3} a^3 x^3 \left(a^2 e^2+10 a b d e+10 b^2 d^2\right)+\frac{1}{7} b^4 e x^7 (5 a e+2 b d)+\frac{1}{8} b^5 e^2 x^8","\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,"a^5*d^2*x + (a^4*d*(5*b*d + 2*a*e)*x^2)/2 + (a^3*(10*b^2*d^2 + 10*a*b*d*e + a^2*e^2)*x^3)/3 + (5*a^2*b*(2*b^2*d^2 + 4*a*b*d*e + a^2*e^2)*x^4)/4 + a*b^2*(b^2*d^2 + 4*a*b*d*e + 2*a^2*e^2)*x^5 + (b^3*(b^2*d^2 + 10*a*b*d*e + 10*a^2*e^2)*x^6)/6 + (b^4*e*(2*b*d + 5*a*e)*x^7)/7 + (b^5*e^2*x^8)/8","B",1
1910,1,109,38,0.0154846,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","a^5 d x+\frac{1}{2} a^4 x^2 (a e+5 b d)+\frac{5}{3} a^3 b x^3 (a e+2 b d)+\frac{5}{2} a^2 b^2 x^4 (a e+b d)+\frac{1}{6} b^4 x^6 (5 a e+b d)+a b^3 x^5 (2 a e+b d)+\frac{1}{7} b^5 e x^7","\frac{(a+b x)^6 (b d-a e)}{6 b^2}+\frac{e (a+b x)^7}{7 b^2}",1,"a^5*d*x + (a^4*(5*b*d + a*e)*x^2)/2 + (5*a^3*b*(2*b*d + a*e)*x^3)/3 + (5*a^2*b^2*(b*d + a*e)*x^4)/2 + a*b^3*(b*d + 2*a*e)*x^5 + (b^4*(b*d + 5*a*e)*x^6)/6 + (b^5*e*x^7)/7","B",1
1911,1,14,14,0.0016417,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(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",1
1912,1,167,122,0.0611507,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{d+e x} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x),x]","\frac{b e x \left(300 a^4 e^4+300 a^3 b e^3 (e x-2 d)+100 a^2 b^2 e^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)+25 a b^3 e \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+b^4 \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)-60 (b d-a e)^5 \log (d+e x)}{60 e^6}","-\frac{(b d-a e)^5 \log (d+e x)}{e^6}+\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{(a+b x)^5}{5 e}",1,"(b*e*x*(300*a^4*e^4 + 300*a^3*b*e^3*(-2*d + e*x) + 100*a^2*b^2*e^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + 25*a*b^3*e*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + b^4*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4)) - 60*(b*d - a*e)^5*Log[d + e*x])/(60*e^6)","A",1
1913,1,228,130,0.0666917,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^2} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^2,x]","\frac{-12 a^5 e^5+60 a^4 b d e^4+120 a^3 b^2 e^3 \left(-d^2+d e x+e^2 x^2\right)+60 a^2 b^3 e^2 \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+20 a b^4 e \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)+60 b (d+e x) (b d-a e)^4 \log (d+e x)+b^5 \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)}{12 e^6 (d+e 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}",1,"(60*a^4*b*d*e^4 - 12*a^5*e^5 + 120*a^3*b^2*e^3*(-d^2 + d*e*x + e^2*x^2) + 60*a^2*b^3*e^2*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 20*a*b^4*e*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + b^5*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5) + 60*b*(b*d - a*e)^4*(d + e*x)*Log[d + e*x])/(12*e^6*(d + e*x))","A",1
1914,1,230,133,0.0736616,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^3} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^3,x]","\frac{-3 a^5 e^5-15 a^4 b e^4 (d+2 e x)+30 a^3 b^2 d e^3 (3 d+4 e x)+30 a^2 b^3 e^2 \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)+15 a b^4 e \left(7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right)-60 b^2 (d+e x)^2 (b d-a e)^3 \log (d+e x)+b^5 \left(-27 d^5+6 d^4 e x+63 d^3 e^2 x^2+20 d^2 e^3 x^3-5 d e^4 x^4+2 e^5 x^5\right)}{6 e^6 (d+e x)^2}","-\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,"(-3*a^5*e^5 - 15*a^4*b*e^4*(d + 2*e*x) + 30*a^3*b^2*d*e^3*(3*d + 4*e*x) + 30*a^2*b^3*e^2*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + 15*a*b^4*e*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4) + b^5*(-27*d^5 + 6*d^4*e*x + 63*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5) - 60*b^2*(b*d - a*e)^3*(d + e*x)^2*Log[d + e*x])/(6*e^6*(d + e*x)^2)","A",1
1915,1,229,130,0.0769046,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^4} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^4,x]","\frac{-2 a^5 e^5-5 a^4 b e^4 (d+3 e x)-20 a^3 b^2 e^3 \left(d^2+3 d e x+3 e^2 x^2\right)+10 a^2 b^3 d e^2 \left(11 d^2+27 d e x+18 e^2 x^2\right)+10 a b^4 e \left(-13 d^4-27 d^3 e x-9 d^2 e^2 x^2+9 d e^3 x^3+3 e^4 x^4\right)+60 b^3 (d+e x)^3 (b d-a e)^2 \log (d+e x)+b^5 \left(47 d^5+81 d^4 e x-9 d^3 e^2 x^2-63 d^2 e^3 x^3-15 d e^4 x^4+3 e^5 x^5\right)}{6 e^6 (d+e x)^3}","-\frac{b^4 x (4 b d-5 a e)}{e^5}+\frac{10 b^3 (b d-a e)^2 \log (d+e x)}{e^6}+\frac{10 b^2 (b d-a e)^3}{e^6 (d+e x)}-\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,"(-2*a^5*e^5 - 5*a^4*b*e^4*(d + 3*e*x) - 20*a^3*b^2*e^3*(d^2 + 3*d*e*x + 3*e^2*x^2) + 10*a^2*b^3*d*e^2*(11*d^2 + 27*d*e*x + 18*e^2*x^2) + 10*a*b^4*e*(-13*d^4 - 27*d^3*e*x - 9*d^2*e^2*x^2 + 9*d*e^3*x^3 + 3*e^4*x^4) + b^5*(47*d^5 + 81*d^4*e*x - 9*d^3*e^2*x^2 - 63*d^2*e^3*x^3 - 15*d*e^4*x^4 + 3*e^5*x^5) + 60*b^3*(b*d - a*e)^2*(d + e*x)^3*Log[d + e*x])/(6*e^6*(d + e*x)^3)","A",1
1916,1,581,173,0.1702784,"\int (a+b x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x \left(3432 a^7 \left(7 d^6+21 d^5 e x+35 d^4 e^2 x^2+35 d^3 e^3 x^3+21 d^2 e^4 x^4+7 d e^5 x^5+e^6 x^6\right)+3003 a^6 b x \left(28 d^6+112 d^5 e x+210 d^4 e^2 x^2+224 d^3 e^3 x^3+140 d^2 e^4 x^4+48 d e^5 x^5+7 e^6 x^6\right)+2002 a^5 b^2 x^2 \left(84 d^6+378 d^5 e x+756 d^4 e^2 x^2+840 d^3 e^3 x^3+540 d^2 e^4 x^4+189 d e^5 x^5+28 e^6 x^6\right)+1001 a^4 b^3 x^3 \left(210 d^6+1008 d^5 e x+2100 d^4 e^2 x^2+2400 d^3 e^3 x^3+1575 d^2 e^4 x^4+560 d e^5 x^5+84 e^6 x^6\right)+364 a^3 b^4 x^4 \left(462 d^6+2310 d^5 e x+4950 d^4 e^2 x^2+5775 d^3 e^3 x^3+3850 d^2 e^4 x^4+1386 d e^5 x^5+210 e^6 x^6\right)+91 a^2 b^5 x^5 \left(924 d^6+4752 d^5 e x+10395 d^4 e^2 x^2+12320 d^3 e^3 x^3+8316 d^2 e^4 x^4+3024 d e^5 x^5+462 e^6 x^6\right)+14 a b^6 x^6 \left(1716 d^6+9009 d^5 e x+20020 d^4 e^2 x^2+24024 d^3 e^3 x^3+16380 d^2 e^4 x^4+6006 d e^5 x^5+924 e^6 x^6\right)+b^7 x^7 \left(3003 d^6+16016 d^5 e x+36036 d^4 e^2 x^2+43680 d^3 e^3 x^3+30030 d^2 e^4 x^4+11088 d e^5 x^5+1716 e^6 x^6\right)\right)}{24024}","\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,"(x*(3432*a^7*(7*d^6 + 21*d^5*e*x + 35*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 21*d^2*e^4*x^4 + 7*d*e^5*x^5 + e^6*x^6) + 3003*a^6*b*x*(28*d^6 + 112*d^5*e*x + 210*d^4*e^2*x^2 + 224*d^3*e^3*x^3 + 140*d^2*e^4*x^4 + 48*d*e^5*x^5 + 7*e^6*x^6) + 2002*a^5*b^2*x^2*(84*d^6 + 378*d^5*e*x + 756*d^4*e^2*x^2 + 840*d^3*e^3*x^3 + 540*d^2*e^4*x^4 + 189*d*e^5*x^5 + 28*e^6*x^6) + 1001*a^4*b^3*x^3*(210*d^6 + 1008*d^5*e*x + 2100*d^4*e^2*x^2 + 2400*d^3*e^3*x^3 + 1575*d^2*e^4*x^4 + 560*d*e^5*x^5 + 84*e^6*x^6) + 364*a^3*b^4*x^4*(462*d^6 + 2310*d^5*e*x + 4950*d^4*e^2*x^2 + 5775*d^3*e^3*x^3 + 3850*d^2*e^4*x^4 + 1386*d*e^5*x^5 + 210*e^6*x^6) + 91*a^2*b^5*x^5*(924*d^6 + 4752*d^5*e*x + 10395*d^4*e^2*x^2 + 12320*d^3*e^3*x^3 + 8316*d^2*e^4*x^4 + 3024*d*e^5*x^5 + 462*e^6*x^6) + 14*a*b^6*x^6*(1716*d^6 + 9009*d^5*e*x + 20020*d^4*e^2*x^2 + 24024*d^3*e^3*x^3 + 16380*d^2*e^4*x^4 + 6006*d*e^5*x^5 + 924*e^6*x^6) + b^7*x^7*(3003*d^6 + 16016*d^5*e*x + 36036*d^4*e^2*x^2 + 43680*d^3*e^3*x^3 + 30030*d^2*e^4*x^4 + 11088*d*e^5*x^5 + 1716*e^6*x^6)))/24024","B",1
1917,1,493,143,0.1403901,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x \left(1716 a^7 \left(6 d^5+15 d^4 e x+20 d^3 e^2 x^2+15 d^2 e^3 x^3+6 d e^4 x^4+e^5 x^5\right)+1716 a^6 b x \left(21 d^5+70 d^4 e x+105 d^3 e^2 x^2+84 d^2 e^3 x^3+35 d e^4 x^4+6 e^5 x^5\right)+1287 a^5 b^2 x^2 \left(56 d^5+210 d^4 e x+336 d^3 e^2 x^2+280 d^2 e^3 x^3+120 d e^4 x^4+21 e^5 x^5\right)+715 a^4 b^3 x^3 \left(126 d^5+504 d^4 e x+840 d^3 e^2 x^2+720 d^2 e^3 x^3+315 d e^4 x^4+56 e^5 x^5\right)+286 a^3 b^4 x^4 \left(252 d^5+1050 d^4 e x+1800 d^3 e^2 x^2+1575 d^2 e^3 x^3+700 d e^4 x^4+126 e^5 x^5\right)+78 a^2 b^5 x^5 \left(462 d^5+1980 d^4 e x+3465 d^3 e^2 x^2+3080 d^2 e^3 x^3+1386 d e^4 x^4+252 e^5 x^5\right)+13 a b^6 x^6 \left(792 d^5+3465 d^4 e x+6160 d^3 e^2 x^2+5544 d^2 e^3 x^3+2520 d e^4 x^4+462 e^5 x^5\right)+b^7 x^7 \left(1287 d^5+5720 d^4 e x+10296 d^3 e^2 x^2+9360 d^2 e^3 x^3+4290 d e^4 x^4+792 e^5 x^5\right)\right)}{10296}","\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,"(x*(1716*a^7*(6*d^5 + 15*d^4*e*x + 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 + 6*d*e^4*x^4 + e^5*x^5) + 1716*a^6*b*x*(21*d^5 + 70*d^4*e*x + 105*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 35*d*e^4*x^4 + 6*e^5*x^5) + 1287*a^5*b^2*x^2*(56*d^5 + 210*d^4*e*x + 336*d^3*e^2*x^2 + 280*d^2*e^3*x^3 + 120*d*e^4*x^4 + 21*e^5*x^5) + 715*a^4*b^3*x^3*(126*d^5 + 504*d^4*e*x + 840*d^3*e^2*x^2 + 720*d^2*e^3*x^3 + 315*d*e^4*x^4 + 56*e^5*x^5) + 286*a^3*b^4*x^4*(252*d^5 + 1050*d^4*e*x + 1800*d^3*e^2*x^2 + 1575*d^2*e^3*x^3 + 700*d*e^4*x^4 + 126*e^5*x^5) + 78*a^2*b^5*x^5*(462*d^5 + 1980*d^4*e*x + 3465*d^3*e^2*x^2 + 3080*d^2*e^3*x^3 + 1386*d*e^4*x^4 + 252*e^5*x^5) + 13*a*b^6*x^6*(792*d^5 + 3465*d^4*e*x + 6160*d^3*e^2*x^2 + 5544*d^2*e^3*x^3 + 2520*d*e^4*x^4 + 462*e^5*x^5) + b^7*x^7*(1287*d^5 + 5720*d^4*e*x + 10296*d^3*e^2*x^2 + 9360*d^2*e^3*x^3 + 4290*d*e^4*x^4 + 792*e^5*x^5)))/10296","B",1
1918,1,405,119,0.1245233,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x \left(792 a^7 \left(5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right)+924 a^6 b x \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)+792 a^5 b^2 x^2 \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)+495 a^4 b^3 x^3 \left(70 d^4+224 d^3 e x+280 d^2 e^2 x^2+160 d e^3 x^3+35 e^4 x^4\right)+220 a^3 b^4 x^4 \left(126 d^4+420 d^3 e x+540 d^2 e^2 x^2+315 d e^3 x^3+70 e^4 x^4\right)+66 a^2 b^5 x^5 \left(210 d^4+720 d^3 e x+945 d^2 e^2 x^2+560 d e^3 x^3+126 e^4 x^4\right)+12 a b^6 x^6 \left(330 d^4+1155 d^3 e x+1540 d^2 e^2 x^2+924 d e^3 x^3+210 e^4 x^4\right)+b^7 x^7 \left(495 d^4+1760 d^3 e x+2376 d^2 e^2 x^2+1440 d e^3 x^3+330 e^4 x^4\right)\right)}{3960}","\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,"(x*(792*a^7*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4) + 924*a^6*b*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4) + 792*a^5*b^2*x^2*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4) + 495*a^4*b^3*x^3*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4) + 220*a^3*b^4*x^4*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4) + 66*a^2*b^5*x^5*(210*d^4 + 720*d^3*e*x + 945*d^2*e^2*x^2 + 560*d*e^3*x^3 + 126*e^4*x^4) + 12*a*b^6*x^6*(330*d^4 + 1155*d^3*e*x + 1540*d^2*e^2*x^2 + 924*d*e^3*x^3 + 210*e^4*x^4) + b^7*x^7*(495*d^4 + 1760*d^3*e*x + 2376*d^2*e^2*x^2 + 1440*d*e^3*x^3 + 330*e^4*x^4)))/3960","B",1
1919,1,360,92,0.0478527,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","a^7 d^3 x+\frac{1}{2} a^6 d^2 x^2 (3 a e+7 b d)+\frac{1}{3} b^5 e x^9 \left(7 a^2 e^2+7 a b d e+b^2 d^2\right)+a^5 d x^3 \left(a^2 e^2+7 a b d e+7 b^2 d^2\right)+a b^3 x^7 \left(5 a^3 e^3+15 a^2 b d e^2+9 a b^2 d^2 e+b^3 d^3\right)+\frac{7}{2} a^2 b^2 x^6 \left(a^3 e^3+5 a^2 b d e^2+5 a b^2 d^2 e+b^3 d^3\right)+\frac{7}{5} a^3 b x^5 \left(a^3 e^3+9 a^2 b d e^2+15 a b^2 d^2 e+5 b^3 d^3\right)+\frac{1}{8} b^4 x^8 \left(35 a^3 e^3+63 a^2 b d e^2+21 a b^2 d^2 e+b^3 d^3\right)+\frac{1}{4} a^4 x^4 \left(a^3 e^3+21 a^2 b d e^2+63 a b^2 d^2 e+35 b^3 d^3\right)+\frac{1}{10} b^6 e^2 x^{10} (7 a e+3 b d)+\frac{1}{11} b^7 e^3 x^{11}","\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,"a^7*d^3*x + (a^6*d^2*(7*b*d + 3*a*e)*x^2)/2 + a^5*d*(7*b^2*d^2 + 7*a*b*d*e + a^2*e^2)*x^3 + (a^4*(35*b^3*d^3 + 63*a*b^2*d^2*e + 21*a^2*b*d*e^2 + a^3*e^3)*x^4)/4 + (7*a^3*b*(5*b^3*d^3 + 15*a*b^2*d^2*e + 9*a^2*b*d*e^2 + a^3*e^3)*x^5)/5 + (7*a^2*b^2*(b^3*d^3 + 5*a*b^2*d^2*e + 5*a^2*b*d*e^2 + a^3*e^3)*x^6)/2 + a*b^3*(b^3*d^3 + 9*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 5*a^3*e^3)*x^7 + (b^4*(b^3*d^3 + 21*a*b^2*d^2*e + 63*a^2*b*d*e^2 + 35*a^3*e^3)*x^8)/8 + (b^5*e*(b^2*d^2 + 7*a*b*d*e + 7*a^2*e^2)*x^9)/3 + (b^6*e^2*(3*b*d + 7*a*e)*x^10)/10 + (b^7*e^3*x^11)/11","B",1
1920,1,229,65,0.0693995,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{1}{360} x \left(120 a^7 \left(3 d^2+3 d e x+e^2 x^2\right)+210 a^6 b x \left(6 d^2+8 d e x+3 e^2 x^2\right)+252 a^5 b^2 x^2 \left(10 d^2+15 d e x+6 e^2 x^2\right)+210 a^4 b^3 x^3 \left(15 d^2+24 d e x+10 e^2 x^2\right)+120 a^3 b^4 x^4 \left(21 d^2+35 d e x+15 e^2 x^2\right)+45 a^2 b^5 x^5 \left(28 d^2+48 d e x+21 e^2 x^2\right)+10 a b^6 x^6 \left(36 d^2+63 d e x+28 e^2 x^2\right)+b^7 x^7 \left(45 d^2+80 d e x+36 e^2 x^2\right)\right)","\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,"(x*(120*a^7*(3*d^2 + 3*d*e*x + e^2*x^2) + 210*a^6*b*x*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + 252*a^5*b^2*x^2*(10*d^2 + 15*d*e*x + 6*e^2*x^2) + 210*a^4*b^3*x^3*(15*d^2 + 24*d*e*x + 10*e^2*x^2) + 120*a^3*b^4*x^4*(21*d^2 + 35*d*e*x + 15*e^2*x^2) + 45*a^2*b^5*x^5*(28*d^2 + 48*d*e*x + 21*e^2*x^2) + 10*a*b^6*x^6*(36*d^2 + 63*d*e*x + 28*e^2*x^2) + b^7*x^7*(45*d^2 + 80*d*e*x + 36*e^2*x^2)))/360","B",1
1921,1,151,38,0.0219381,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","a^7 d x+\frac{1}{2} a^6 x^2 (a e+7 b d)+\frac{7}{3} a^5 b x^3 (a e+3 b d)+\frac{7}{4} a^4 b^2 x^4 (3 a e+5 b d)+7 a^3 b^3 x^5 (a e+b d)+\frac{7}{6} a^2 b^4 x^6 (5 a e+3 b d)+\frac{1}{8} b^6 x^8 (7 a e+b d)+a b^5 x^7 (3 a e+b d)+\frac{1}{9} b^7 e x^9","\frac{(a+b x)^8 (b d-a e)}{8 b^2}+\frac{e (a+b x)^9}{9 b^2}",1,"a^7*d*x + (a^6*(7*b*d + a*e)*x^2)/2 + (7*a^5*b*(3*b*d + a*e)*x^3)/3 + (7*a^4*b^2*(5*b*d + 3*a*e)*x^4)/4 + 7*a^3*b^3*(b*d + a*e)*x^5 + (7*a^2*b^4*(3*b*d + 5*a*e)*x^6)/6 + a*b^5*(b*d + 3*a*e)*x^7 + (b^6*(b*d + 7*a*e)*x^8)/8 + (b^7*e*x^9)/9","B",1
1922,1,14,14,0.001176,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(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",1
1923,1,304,170,0.1076727,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{d+e x} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x),x]","\frac{b e x \left(2940 a^6 e^6+4410 a^5 b e^5 (e x-2 d)+2450 a^4 b^2 e^4 \left(6 d^2-3 d e x+2 e^2 x^2\right)+1225 a^3 b^3 e^3 \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+147 a^2 b^4 e^2 \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)+49 a b^5 e \left(-60 d^5+30 d^4 e x-20 d^3 e^2 x^2+15 d^2 e^3 x^3-12 d e^4 x^4+10 e^5 x^5\right)+b^6 \left(420 d^6-210 d^5 e x+140 d^4 e^2 x^2-105 d^3 e^3 x^3+84 d^2 e^4 x^4-70 d e^5 x^5+60 e^6 x^6\right)\right)-420 (b d-a e)^7 \log (d+e x)}{420 e^8}","-\frac{(b d-a e)^7 \log (d+e x)}{e^8}+\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{(a+b x)^7}{7 e}",1,"(b*e*x*(2940*a^6*e^6 + 4410*a^5*b*e^5*(-2*d + e*x) + 2450*a^4*b^2*e^4*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + 1225*a^3*b^3*e^3*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + 147*a^2*b^4*e^2*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + 49*a*b^5*e*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5) + b^6*(420*d^6 - 210*d^5*e*x + 140*d^4*e^2*x^2 - 105*d^3*e^3*x^3 + 84*d^2*e^4*x^4 - 70*d*e^5*x^5 + 60*e^6*x^6)) - 420*(b*d - a*e)^7*Log[d + e*x])/(420*e^8)","A",1
1924,1,387,186,0.1133604,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^2} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^2,x]","\frac{-60 a^7 e^7+420 a^6 b d e^6+1260 a^5 b^2 e^5 \left(-d^2+d e x+e^2 x^2\right)+1050 a^4 b^3 e^4 \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+700 a^3 b^4 e^3 \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)+105 a^2 b^5 e^2 \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)+42 a b^6 e \left(-10 d^6+50 d^5 e x+30 d^4 e^2 x^2-10 d^3 e^3 x^3+5 d^2 e^4 x^4-3 d e^5 x^5+2 e^6 x^6\right)+420 b (d+e x) (b d-a e)^6 \log (d+e x)+b^7 \left(60 d^7-360 d^6 e x-210 d^5 e^2 x^2+70 d^4 e^3 x^3-35 d^3 e^4 x^4+21 d^2 e^5 x^5-14 d e^6 x^6+10 e^7 x^7\right)}{60 e^8 (d+e 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}",1,"(420*a^6*b*d*e^6 - 60*a^7*e^7 + 1260*a^5*b^2*e^5*(-d^2 + d*e*x + e^2*x^2) + 1050*a^4*b^3*e^4*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 700*a^3*b^4*e^3*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + 105*a^2*b^5*e^2*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5) + 42*a*b^6*e*(-10*d^6 + 50*d^5*e*x + 30*d^4*e^2*x^2 - 10*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 3*d*e^5*x^5 + 2*e^6*x^6) + b^7*(60*d^7 - 360*d^6*e*x - 210*d^5*e^2*x^2 + 70*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 - 14*d*e^6*x^6 + 10*e^7*x^7) + 420*b*(b*d - a*e)^6*(d + e*x)*Log[d + e*x])/(60*e^8*(d + e*x))","B",1
1925,1,388,185,0.1195759,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^3} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^3,x]","\frac{-10 a^7 e^7-70 a^6 b e^6 (d+2 e x)+210 a^5 b^2 d e^5 (3 d+4 e x)+350 a^4 b^3 e^4 \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)+350 a^3 b^4 e^3 \left(7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right)+70 a^2 b^5 e^2 \left(-27 d^5+6 d^4 e x+63 d^3 e^2 x^2+20 d^2 e^3 x^3-5 d e^4 x^4+2 e^5 x^5\right)+35 a b^6 e \left(22 d^6-16 d^5 e x-68 d^4 e^2 x^2-20 d^3 e^3 x^3+5 d^2 e^4 x^4-2 d e^5 x^5+e^6 x^6\right)-420 b^2 (d+e x)^2 (b d-a e)^5 \log (d+e x)+b^7 \left(-130 d^7+160 d^6 e x+500 d^5 e^2 x^2+140 d^4 e^3 x^3-35 d^3 e^4 x^4+14 d^2 e^5 x^5-7 d e^6 x^6+4 e^7 x^7\right)}{20 e^8 (d+e x)^2}","-\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,"(-10*a^7*e^7 - 70*a^6*b*e^6*(d + 2*e*x) + 210*a^5*b^2*d*e^5*(3*d + 4*e*x) + 350*a^4*b^3*e^4*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + 350*a^3*b^4*e^3*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4) + 70*a^2*b^5*e^2*(-27*d^5 + 6*d^4*e*x + 63*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5) + 35*a*b^6*e*(22*d^6 - 16*d^5*e*x - 68*d^4*e^2*x^2 - 20*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 2*d*e^5*x^5 + e^6*x^6) + b^7*(-130*d^7 + 160*d^6*e*x + 500*d^5*e^2*x^2 + 140*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 14*d^2*e^5*x^5 - 7*d*e^6*x^6 + 4*e^7*x^7) - 420*b^2*(b*d - a*e)^5*(d + e*x)^2*Log[d + e*x])/(20*e^8*(d + e*x)^2)","B",1
1926,1,199,187,0.0939201,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^4} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^4,x]","\frac{6 b^5 e^2 x^2 \left(21 a^2 e^2-28 a b d e+10 b^2 d^2\right)-12 b^4 e x \left(-35 a^3 e^3+84 a^2 b d e^2-70 a b^2 d^2 e+20 b^3 d^3\right)-4 b^6 e^3 x^3 (4 b d-7 a e)+420 b^3 (b d-a e)^4 \log (d+e x)+\frac{252 b^2 (b d-a e)^5}{d+e x}-\frac{42 b (b d-a e)^6}{(d+e x)^2}+\frac{4 (b d-a e)^7}{(d+e x)^3}+3 b^7 e^4 x^4}{12 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{35 b^3 (b d-a e)^4 \log (d+e x)}{e^8}+\frac{21 b^2 (b d-a e)^5}{e^8 (d+e x)}-\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,"(-12*b^4*e*(20*b^3*d^3 - 70*a*b^2*d^2*e + 84*a^2*b*d*e^2 - 35*a^3*e^3)*x + 6*b^5*e^2*(10*b^2*d^2 - 28*a*b*d*e + 21*a^2*e^2)*x^2 - 4*b^6*e^3*(4*b*d - 7*a*e)*x^3 + 3*b^7*e^4*x^4 + (4*(b*d - a*e)^7)/(d + e*x)^3 - (42*b*(b*d - a*e)^6)/(d + e*x)^2 + (252*b^2*(b*d - a*e)^5)/(d + e*x) + 420*b^3*(b*d - a*e)^4*Log[d + e*x])/(12*e^8)","A",1
1927,1,114,97,0.0445569,"\int \frac{(a+b x) (d+e x)^4}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{b e x \left(-12 a^3 e^3+6 a^2 b e^2 (8 d+e x)-4 a b^2 e \left(18 d^2+6 d e x+e^2 x^2\right)+b^3 \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)\right)+12 (b d-a e)^4 \log (a+b x)}{12 b^5}","\frac{(b d-a e)^4 \log (a+b x)}{b^5}+\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{(d+e x)^4}{4 b}",1,"(b*e*x*(-12*a^3*e^3 + 6*a^2*b*e^2*(8*d + e*x) - 4*a*b^2*e*(18*d^2 + 6*d*e*x + e^2*x^2) + b^3*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3)) + 12*(b*d - a*e)^4*Log[a + b*x])/(12*b^5)","A",1
1928,1,74,73,0.0300434,"\int \frac{(a+b x) (d+e x)^3}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{b e x \left(6 a^2 e^2-3 a b e (6 d+e x)+b^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+6 (b d-a e)^3 \log (a+b x)}{6 b^4}","\frac{(b d-a e)^3 \log (a+b x)}{b^4}+\frac{e x (b d-a e)^2}{b^3}+\frac{(d+e x)^2 (b d-a e)}{2 b^2}+\frac{(d+e x)^3}{3 b}",1,"(b*e*x*(6*a^2*e^2 - 3*a*b*e*(6*d + e*x) + b^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2)) + 6*(b*d - a*e)^3*Log[a + b*x])/(6*b^4)","A",1
1929,1,43,49,0.0161651,"\int \frac{(a+b x) (d+e x)^2}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{b e x (-2 a e+4 b d+b e x)+2 (b d-a e)^2 \log (a+b x)}{2 b^3}","\frac{(b d-a e)^2 \log (a+b x)}{b^3}+\frac{e x (b d-a e)}{b^2}+\frac{(d+e x)^2}{2 b}",1,"(b*e*x*(4*b*d - 2*a*e + b*e*x) + 2*(b*d - a*e)^2*Log[a + b*x])/(2*b^3)","A",1
1930,1,25,25,0.0078326,"\int \frac{(a+b x) (d+e x)}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((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",1
1931,1,10,10,0.0012407,"\int \frac{a+b x}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(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",1
1932,1,26,36,0.0115432,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(a + b*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{\log (a+b x)-\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] - Log[d + e*x])/(b*d - a*e)","A",1
1933,1,53,56,0.0285072,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(a + b*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{b (d+e x) \log (a+b x)-a e-b (d+e x) \log (d+e x)+b d}{(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,"(b*d - a*e + b*(d + e*x)*Log[a + b*x] - b*(d + e*x)*Log[d + e*x])/((b*d - a*e)^2*(d + e*x))","A",1
1934,1,67,82,0.0492774,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{2 b^2 \log (a+b x)+\frac{(b d-a e) (-a e+3 b d+2 b e x)}{(d+e x)^2}-2 b^2 \log (d+e x)}{2 (b d-a e)^3}","\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,"(((b*d - a*e)*(3*b*d - a*e + 2*b*e*x))/(d + e*x)^2 + 2*b^2*Log[a + b*x] - 2*b^2*Log[d + e*x])/(2*(b*d - a*e)^3)","A",1
1935,1,106,106,0.0392378,"\int \frac{a+b x}{(d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(a + b*x)/((d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)),x]","\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) (b d-a e)^3}+\frac{b}{2 (d+e x)^2 (b d-a e)^2}-\frac{1}{3 (d+e x)^3 (a e-b d)}","\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) (b d-a e)^3}+\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*1/((-(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",1
1936,1,163,102,0.0552382,"\int \frac{(a+b x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{7 a^4 e^4+2 a^3 b e^3 (e x-10 d)+a^2 b^2 e^2 \left(18 d^2-16 d e x-11 e^2 x^2\right)-4 a b^3 e \left(d^3-6 d^2 e x-4 d e^2 x^2+e^3 x^3\right)+12 e^2 (a+b x)^2 (b d-a e)^2 \log (a+b x)+b^4 \left(-d^4-8 d^3 e x+8 d e^3 x^3+e^4 x^4\right)}{2 b^5 (a+b x)^2}","\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^3 x (4 b d-3 a e)}{b^4}+\frac{e^4 x^2}{2 b^3}",1,"(7*a^4*e^4 + 2*a^3*b*e^3*(-10*d + e*x) + a^2*b^2*e^2*(18*d^2 - 16*d*e*x - 11*e^2*x^2) - 4*a*b^3*e*(d^3 - 6*d^2*e*x - 4*d*e^2*x^2 + e^3*x^3) + b^4*(-d^4 - 8*d^3*e*x + 8*d*e^3*x^3 + e^4*x^4) + 12*e^2*(b*d - a*e)^2*(a + b*x)^2*Log[a + b*x])/(2*b^5*(a + b*x)^2)","A",1
1937,1,114,78,0.0416672,"\int \frac{(a+b x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{-5 a^3 e^3+a^2 b e^2 (9 d-4 e x)+a b^2 e \left(-3 d^2+12 d e x+4 e^2 x^2\right)-6 e^2 (a+b x)^2 (a e-b d) \log (a+b x)-\left(b^3 \left(d^3+6 d^2 e x-2 e^3 x^3\right)\right)}{2 b^4 (a+b x)^2}","\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,"(-5*a^3*e^3 + a^2*b*e^2*(9*d - 4*e*x) + a*b^2*e*(-3*d^2 + 12*d*e*x + 4*e^2*x^2) - b^3*(d^3 + 6*d^2*e*x - 2*e^3*x^3) - 6*e^2*(-(b*d) + a*e)*(a + b*x)^2*Log[a + b*x])/(2*b^4*(a + b*x)^2)","A",1
1938,1,49,59,0.0237822,"\int \frac{(a+b x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 e^2 \log (a+b x)-\frac{(b d-a e) (3 a e+b (d+4 e x))}{(a+b x)^2}}{2 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)*(3*a*e + b*(d + 4*e*x)))/(a + b*x)^2) + 2*e^2*Log[a + b*x])/(2*b^3)","A",1
1939,1,26,28,0.0089054,"\int \frac{(a+b x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((a + b*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{a e+b (d+2 e x)}{2 b^2 (a+b x)^2}","-\frac{(d+e x)^2}{2 (a+b x)^2 (b d-a e)}",1,"-1/2*(a*e + b*(d + 2*e*x))/(b^2*(a + b*x)^2)","A",1
1940,1,14,14,0.0026669,"\int \frac{a+b x}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(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*1/(b*(a + b*x)^2)","A",1
1941,1,67,82,0.0535173,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(a + b*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{(b d-a e) (3 a e-b d+2 b e x)}{(a+b x)^2}+2 e^2 \log (a+b x)-2 e^2 \log (d+e x)}{2 (b d-a e)^3}","\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,"(((b*d - a*e)*(-(b*d) + 3*a*e + 2*b*e*x))/(a + b*x)^2 + 2*e^2*Log[a + b*x] - 2*e^2*Log[d + e*x])/(2*(b*d - a*e)^3)","A",1
1942,1,98,109,0.0698014,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(a + b*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{2 e^2 (b d-a e)}{d+e x}+\frac{4 b e (b d-a e)}{a+b x}-\frac{b (b d-a e)^2}{(a+b x)^2}+6 b e^2 \log (a+b x)-6 b e^2 \log (d+e x)}{2 (b d-a e)^4}","\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*(b*d - a*e)^2)/(a + b*x)^2) + (4*b*e*(b*d - a*e))/(a + b*x) + (2*e^2*(b*d - a*e))/(d + e*x) + 6*b*e^2*Log[a + b*x] - 6*b*e^2*Log[d + e*x])/(2*(b*d - a*e)^4)","A",1
1943,1,128,143,0.1043875,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{6 b^2 e (b d-a e)}{a+b x}-\frac{b^2 (b d-a e)^2}{(a+b x)^2}+12 b^2 e^2 \log (a+b x)+\frac{6 b e^2 (b d-a e)}{d+e x}+\frac{e^2 (b d-a e)^2}{(d+e x)^2}-12 b^2 e^2 \log (d+e x)}{2 (b d-a e)^5}","\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*(b*d - a*e)^2)/(a + b*x)^2) + (6*b^2*e*(b*d - a*e))/(a + b*x) + (e^2*(b*d - a*e)^2)/(d + e*x)^2 + (6*b*e^2*(b*d - a*e))/(d + e*x) + 12*b^2*e^2*Log[a + b*x] - 12*b^2*e^2*Log[d + e*x])/(2*(b*d - a*e)^5)","A",1
1944,1,154,170,0.1506438,"\int \frac{a+b x}{(d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(a + b*x)/((d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{\frac{24 b^3 e (b d-a e)}{a+b x}-\frac{3 b^3 (b d-a e)^2}{(a+b x)^2}+60 b^3 e^2 \log (a+b x)+\frac{36 b^2 e^2 (b d-a e)}{d+e x}+\frac{9 b e^2 (b d-a e)^2}{(d+e x)^2}+\frac{2 e^2 (b d-a e)^3}{(d+e x)^3}-60 b^3 e^2 \log (d+e x)}{6 (b d-a e)^6}","\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{6 b^2 e^2}{(d+e x) (b d-a e)^5}+\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,"((-3*b^3*(b*d - a*e)^2)/(a + b*x)^2 + (24*b^3*e*(b*d - a*e))/(a + b*x) + (2*e^2*(b*d - a*e)^3)/(d + e*x)^3 + (9*b*e^2*(b*d - a*e)^2)/(d + e*x)^2 + (36*b^2*e^2*(b*d - a*e))/(d + e*x) + 60*b^3*e^2*Log[a + b*x] - 60*b^3*e^2*Log[d + e*x])/(6*(b*d - a*e)^6)","A",1
1945,1,120,111,0.0587235,"\int \frac{(a+b x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{e^4 \log (a+b x)}{b^5}-\frac{(b d-a e) \left(25 a^3 e^3+a^2 b e^2 (13 d+88 e x)+a b^2 e \left(7 d^2+40 d e x+108 e^2 x^2\right)+b^3 \left(3 d^3+16 d^2 e x+36 d e^2 x^2+48 e^3 x^3\right)\right)}{12 b^5 (a+b x)^4}","-\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,"-1/12*((b*d - a*e)*(25*a^3*e^3 + a^2*b*e^2*(13*d + 88*e*x) + a*b^2*e*(7*d^2 + 40*d*e*x + 108*e^2*x^2) + b^3*(3*d^3 + 16*d^2*e*x + 36*d*e^2*x^2 + 48*e^3*x^3)))/(b^5*(a + b*x)^4) + (e^4*Log[a + b*x])/b^5","A",1
1946,1,91,28,0.0279152,"\int \frac{(a+b x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{a^3 e^3+a^2 b e^2 (d+4 e x)+a b^2 e \left(d^2+4 d e x+6 e^2 x^2\right)+b^3 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)}{4 b^4 (a+b x)^4}","-\frac{(d+e x)^4}{4 (a+b x)^4 (b d-a e)}",1,"-1/4*(a^3*e^3 + a^2*b*e^2*(d + 4*e*x) + a*b^2*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + b^3*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3))/(b^4*(a + b*x)^4)","B",1
1947,1,56,65,0.019051,"\int \frac{(a+b x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{a^2 e^2+2 a b e (d+2 e x)+b^2 \left(3 d^2+8 d e x+6 e^2 x^2\right)}{12 b^3 (a+b x)^4}","-\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,"-1/12*(a^2*e^2 + 2*a*b*e*(d + 2*e*x) + b^2*(3*d^2 + 8*d*e*x + 6*e^2*x^2))/(b^3*(a + b*x)^4)","A",1
1948,1,27,38,0.0084841,"\int \frac{(a+b x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{a e+3 b d+4 b e x}{12 b^2 (a+b x)^4}","-\frac{b d-a e}{4 b^2 (a+b x)^4}-\frac{e}{3 b^2 (a+b x)^3}",1,"-1/12*(3*b*d + a*e + 4*b*e*x)/(b^2*(a + b*x)^4)","A",1
1949,1,14,14,0.0031285,"\int \frac{a+b x}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(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*1/(b*(a + b*x)^4)","A",1
1950,1,130,130,0.0466967,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(a + b*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\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) (b d-a e)^4}-\frac{e^2}{2 (a+b x)^2 (b d-a e)^3}+\frac{e}{3 (a+b x)^3 (b d-a e)^2}+\frac{1}{4 (a+b x)^4 (a e-b d)}","\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) (b d-a e)^4}-\frac{e^2}{2 (a+b x)^2 (b d-a e)^3}+\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",1
1951,1,144,159,0.0744659,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(a + b*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{12 e^4 (b d-a e)}{d+e x}+\frac{48 b e^3 (b d-a e)}{a+b x}-\frac{18 b e^2 (b d-a e)^2}{(a+b x)^2}+\frac{8 b e (b d-a e)^3}{(a+b x)^3}-\frac{3 b (b d-a e)^4}{(a+b x)^4}+60 b e^4 \log (a+b x)-60 b e^4 \log (d+e x)}{12 (b d-a e)^6}","\frac{e^4}{(d+e x) (b d-a e)^5}+\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{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{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,"((-3*b*(b*d - a*e)^4)/(a + b*x)^4 + (8*b*e*(b*d - a*e)^3)/(a + b*x)^3 - (18*b*e^2*(b*d - a*e)^2)/(a + b*x)^2 + (48*b*e^3*(b*d - a*e))/(a + b*x) + (12*e^4*(b*d - a*e))/(d + e*x) + 60*b*e^4*Log[a + b*x] - 60*b*e^4*Log[d + e*x])/(12*(b*d - a*e)^6)","A",1
1952,1,179,192,0.0978234,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{40 b^2 e^3 (b d-a e)}{a+b x}-\frac{12 b^2 e^2 (b d-a e)^2}{(a+b x)^2}+\frac{4 b^2 e (b d-a e)^3}{(a+b x)^3}-\frac{b^2 (b d-a e)^4}{(a+b x)^4}+60 b^2 e^4 \log (a+b x)+\frac{20 b e^4 (b d-a e)}{d+e x}+\frac{2 e^4 (b d-a e)^2}{(d+e x)^2}-60 b^2 e^4 \log (d+e x)}{4 (b d-a e)^7}","\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{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{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*(b*d - a*e)^4)/(a + b*x)^4) + (4*b^2*e*(b*d - a*e)^3)/(a + b*x)^3 - (12*b^2*e^2*(b*d - a*e)^2)/(a + b*x)^2 + (40*b^2*e^3*(b*d - a*e))/(a + b*x) + (2*e^4*(b*d - a*e)^2)/(d + e*x)^2 + (20*b*e^4*(b*d - a*e))/(d + e*x) + 60*b^2*e^4*Log[a + b*x] - 60*b^2*e^4*Log[d + e*x])/(4*(b*d - a*e)^7)","A",1
1953,1,204,222,0.1288578,"\int \frac{a+b x}{(d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(a + b*x)/((d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{\frac{240 b^3 e^3 (b d-a e)}{a+b x}-\frac{60 b^3 e^2 (b d-a e)^2}{(a+b x)^2}+\frac{16 b^3 e (b d-a e)^3}{(a+b x)^3}-\frac{3 b^3 (b d-a e)^4}{(a+b x)^4}+420 b^3 e^4 \log (a+b x)+\frac{180 b^2 e^4 (b d-a e)}{d+e x}+\frac{30 b e^4 (b d-a e)^2}{(d+e x)^2}+\frac{4 e^4 (b d-a e)^3}{(d+e x)^3}-420 b^3 e^4 \log (d+e x)}{12 (b d-a e)^8}","\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{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{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{15 b^2 e^4}{(d+e x) (b d-a e)^7}+\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,"((-3*b^3*(b*d - a*e)^4)/(a + b*x)^4 + (16*b^3*e*(b*d - a*e)^3)/(a + b*x)^3 - (60*b^3*e^2*(b*d - a*e)^2)/(a + b*x)^2 + (240*b^3*e^3*(b*d - a*e))/(a + b*x) + (4*e^4*(b*d - a*e)^3)/(d + e*x)^3 + (30*b*e^4*(b*d - a*e)^2)/(d + e*x)^2 + (180*b^2*e^4*(b*d - a*e))/(d + e*x) + 420*b^3*e^4*Log[a + b*x] - 420*b^3*e^4*Log[d + e*x])/(12*(b*d - a*e)^8)","A",1
1954,1,196,146,0.0610861,"\int (a+b x) (d+e x)^5 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} \left(28 a^2 \left(6 d^5+15 d^4 e x+20 d^3 e^2 x^2+15 d^2 e^3 x^3+6 d e^4 x^4+e^5 x^5\right)+8 a b x \left(21 d^5+70 d^4 e x+105 d^3 e^2 x^2+84 d^2 e^3 x^3+35 d e^4 x^4+6 e^5 x^5\right)+b^2 x^2 \left(56 d^5+210 d^4 e x+336 d^3 e^2 x^2+280 d^2 e^3 x^3+120 d e^4 x^4+21 e^5 x^5\right)\right)}{168 (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,"(x*Sqrt[(a + b*x)^2]*(28*a^2*(6*d^5 + 15*d^4*e*x + 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 + 6*d*e^4*x^4 + e^5*x^5) + 8*a*b*x*(21*d^5 + 70*d^4*e*x + 105*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 35*d*e^4*x^4 + 6*e^5*x^5) + b^2*x^2*(56*d^5 + 210*d^4*e*x + 336*d^3*e^2*x^2 + 280*d^2*e^3*x^3 + 120*d*e^4*x^4 + 21*e^5*x^5)))/(168*(a + b*x))","A",1
1955,1,163,146,0.0473725,"\int (a+b x) (d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} \left(21 a^2 \left(5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right)+7 a b x \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)+b^2 x^2 \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)\right)}{105 (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,"(x*Sqrt[(a + b*x)^2]*(21*a^2*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4) + 7*a*b*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4) + b^2*x^2*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4)))/(105*(a + b*x))","A",1
1956,1,130,146,0.0402825,"\int (a+b x) (d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} \left(15 a^2 \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+6 a b x \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)+b^2 x^2 \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)\right)}{60 (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,"(x*Sqrt[(a + b*x)^2]*(15*a^2*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) + 6*a*b*x*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3) + b^2*x^2*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3)))/(60*(a + b*x))","A",1
1957,1,97,125,0.0324867,"\int (a+b x) (d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} \left(10 a^2 \left(3 d^2+3 d e x+e^2 x^2\right)+5 a b x \left(6 d^2+8 d e x+3 e^2 x^2\right)+b^2 x^2 \left(10 d^2+15 d e x+6 e^2 x^2\right)\right)}{30 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(10*a^2*(3*d^2 + 3*d*e*x + e^2*x^2) + 5*a*b*x*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + b^2*x^2*(10*d^2 + 15*d*e*x + 6*e^2*x^2)))/(30*(a + b*x))","A",1
1958,1,64,78,0.0216122,"\int (a+b x) (d+e x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x \sqrt{(a+b x)^2} \left(6 a^2 (2 d+e x)+4 a b x (3 d+2 e x)+b^2 x^2 (4 d+3 e x)\right)}{12 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(6*a^2*(2*d + e*x) + 4*a*b*x*(3*d + 2*e*x) + b^2*x^2*(4*d + 3*e*x)))/(12*(a + b*x))","A",1
1959,1,18,27,0.0079692,"\int (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\left((a+b 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 + b*x)^2)^(3/2)/(3*b)","A",1
1960,1,61,122,0.0288588,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{d+e x} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x),x]","\frac{\sqrt{(a+b x)^2} \left(b e x (4 a e-2 b d+b e x)+2 (b d-a e)^2 \log (d+e x)\right)}{2 e^3 (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{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^2 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 e}",1,"(Sqrt[(a + b*x)^2]*(b*e*x*(-2*b*d + 4*a*e + b*e*x) + 2*(b*d - a*e)^2*Log[d + e*x]))/(2*e^3*(a + b*x))","A",1
1961,1,87,132,0.0479737,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^2} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^2,x]","\frac{\sqrt{(a+b x)^2} \left(-a^2 e^2-2 b (d+e x) (b d-a e) \log (d+e x)+2 a b d e+b^2 \left(-d^2+d e x+e^2 x^2\right)\right)}{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}{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,"(Sqrt[(a + b*x)^2]*(2*a*b*d*e - a^2*e^2 + b^2*(-d^2 + d*e*x + e^2*x^2) - 2*b*(b*d - a*e)*(d + e*x)*Log[d + e*x]))/(e^3*(a + b*x)*(d + e*x))","A",1
1962,1,73,140,0.034363,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^3} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^3,x]","\frac{\sqrt{(a+b x)^2} \left((b d-a e) (a e+3 b d+4 b e x)+2 b^2 (d+e x)^2 \log (d+e x)\right)}{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)}{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,"(Sqrt[(a + b*x)^2]*((b*d - a*e)*(3*b*d + a*e + 4*b*e*x) + 2*b^2*(d + e*x)^2*Log[d + e*x]))/(2*e^3*(a + b*x)*(d + e*x)^2)","A",1
1963,1,71,41,0.0306213,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^4} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^4,x]","-\frac{\sqrt{(a+b x)^2} \left(a^2 e^2+a b e (d+3 e x)+b^2 \left(d^2+3 d e x+3 e^2 x^2\right)\right)}{3 e^3 (a+b x) (d+e x)^3}","\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,"-1/3*(Sqrt[(a + b*x)^2]*(a^2*e^2 + a*b*e*(d + 3*e*x) + b^2*(d^2 + 3*d*e*x + 3*e^2*x^2)))/(e^3*(a + b*x)*(d + e*x)^3)","A",1
1964,1,73,146,0.0271753,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^5} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^5,x]","-\frac{\sqrt{(a+b x)^2} \left(3 a^2 e^2+2 a b e (d+4 e x)+b^2 \left(d^2+4 d e x+6 e^2 x^2\right)\right)}{12 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,"-1/12*(Sqrt[(a + b*x)^2]*(3*a^2*e^2 + 2*a*b*e*(d + 4*e*x) + b^2*(d^2 + 4*d*e*x + 6*e^2*x^2)))/(e^3*(a + b*x)*(d + e*x)^4)","A",1
1965,1,73,146,0.0336572,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^6} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^6,x]","-\frac{\sqrt{(a+b x)^2} \left(6 a^2 e^2+3 a b e (d+5 e x)+b^2 \left(d^2+5 d e x+10 e^2 x^2\right)\right)}{30 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,"-1/30*(Sqrt[(a + b*x)^2]*(6*a^2*e^2 + 3*a*b*e*(d + 5*e*x) + b^2*(d^2 + 5*d*e*x + 10*e^2*x^2)))/(e^3*(a + b*x)*(d + e*x)^5)","A",1
1966,1,73,146,0.0282557,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^7} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^7,x]","-\frac{\sqrt{(a+b x)^2} \left(10 a^2 e^2+4 a b e (d+6 e x)+b^2 \left(d^2+6 d e x+15 e^2 x^2\right)\right)}{60 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,"-1/60*(Sqrt[(a + b*x)^2]*(10*a^2*e^2 + 4*a*b*e*(d + 6*e*x) + b^2*(d^2 + 6*d*e*x + 15*e^2*x^2)))/(e^3*(a + b*x)*(d + e*x)^6)","A",1
1967,1,73,146,0.0311186,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^8} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^8,x]","-\frac{\sqrt{(a+b x)^2} \left(15 a^2 e^2+5 a b e (d+7 e x)+b^2 \left(d^2+7 d e x+21 e^2 x^2\right)\right)}{105 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,"-1/105*(Sqrt[(a + b*x)^2]*(15*a^2*e^2 + 5*a*b*e*(d + 7*e*x) + b^2*(d^2 + 7*d*e*x + 21*e^2*x^2)))/(e^3*(a + b*x)*(d + e*x)^7)","A",1
1968,1,432,254,0.1318664,"\int (a+b x) (d+e x)^7 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(495 a^4 \left(8 d^7+28 d^6 e x+56 d^5 e^2 x^2+70 d^4 e^3 x^3+56 d^3 e^4 x^4+28 d^2 e^5 x^5+8 d e^6 x^6+e^7 x^7\right)+220 a^3 b x \left(36 d^7+168 d^6 e x+378 d^5 e^2 x^2+504 d^4 e^3 x^3+420 d^3 e^4 x^4+216 d^2 e^5 x^5+63 d e^6 x^6+8 e^7 x^7\right)+66 a^2 b^2 x^2 \left(120 d^7+630 d^6 e x+1512 d^5 e^2 x^2+2100 d^4 e^3 x^3+1800 d^3 e^4 x^4+945 d^2 e^5 x^5+280 d e^6 x^6+36 e^7 x^7\right)+12 a b^3 x^3 \left(330 d^7+1848 d^6 e x+4620 d^5 e^2 x^2+6600 d^4 e^3 x^3+5775 d^3 e^4 x^4+3080 d^2 e^5 x^5+924 d e^6 x^6+120 e^7 x^7\right)+b^4 x^4 \left(792 d^7+4620 d^6 e x+11880 d^5 e^2 x^2+17325 d^4 e^3 x^3+15400 d^3 e^4 x^4+8316 d^2 e^5 x^5+2520 d e^6 x^6+330 e^7 x^7\right)\right)}{3960 (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)}",1,"(x*Sqrt[(a + b*x)^2]*(495*a^4*(8*d^7 + 28*d^6*e*x + 56*d^5*e^2*x^2 + 70*d^4*e^3*x^3 + 56*d^3*e^4*x^4 + 28*d^2*e^5*x^5 + 8*d*e^6*x^6 + e^7*x^7) + 220*a^3*b*x*(36*d^7 + 168*d^6*e*x + 378*d^5*e^2*x^2 + 504*d^4*e^3*x^3 + 420*d^3*e^4*x^4 + 216*d^2*e^5*x^5 + 63*d*e^6*x^6 + 8*e^7*x^7) + 66*a^2*b^2*x^2*(120*d^7 + 630*d^6*e*x + 1512*d^5*e^2*x^2 + 2100*d^4*e^3*x^3 + 1800*d^3*e^4*x^4 + 945*d^2*e^5*x^5 + 280*d*e^6*x^6 + 36*e^7*x^7) + 12*a*b^3*x^3*(330*d^7 + 1848*d^6*e*x + 4620*d^5*e^2*x^2 + 6600*d^4*e^3*x^3 + 5775*d^3*e^4*x^4 + 3080*d^2*e^5*x^5 + 924*d*e^6*x^6 + 120*e^7*x^7) + b^4*x^4*(792*d^7 + 4620*d^6*e*x + 11880*d^5*e^2*x^2 + 17325*d^4*e^3*x^3 + 15400*d^3*e^4*x^4 + 8316*d^2*e^5*x^5 + 2520*d*e^6*x^6 + 330*e^7*x^7)))/(3960*(a + b*x))","A",1
1969,1,377,254,0.1211166,"\int (a+b x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(330 a^4 \left(7 d^6+21 d^5 e x+35 d^4 e^2 x^2+35 d^3 e^3 x^3+21 d^2 e^4 x^4+7 d e^5 x^5+e^6 x^6\right)+165 a^3 b x \left(28 d^6+112 d^5 e x+210 d^4 e^2 x^2+224 d^3 e^3 x^3+140 d^2 e^4 x^4+48 d e^5 x^5+7 e^6 x^6\right)+55 a^2 b^2 x^2 \left(84 d^6+378 d^5 e x+756 d^4 e^2 x^2+840 d^3 e^3 x^3+540 d^2 e^4 x^4+189 d e^5 x^5+28 e^6 x^6\right)+11 a b^3 x^3 \left(210 d^6+1008 d^5 e x+2100 d^4 e^2 x^2+2400 d^3 e^3 x^3+1575 d^2 e^4 x^4+560 d e^5 x^5+84 e^6 x^6\right)+b^4 x^4 \left(462 d^6+2310 d^5 e x+4950 d^4 e^2 x^2+5775 d^3 e^3 x^3+3850 d^2 e^4 x^4+1386 d e^5 x^5+210 e^6 x^6\right)\right)}{2310 (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)}",1,"(x*Sqrt[(a + b*x)^2]*(330*a^4*(7*d^6 + 21*d^5*e*x + 35*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 21*d^2*e^4*x^4 + 7*d*e^5*x^5 + e^6*x^6) + 165*a^3*b*x*(28*d^6 + 112*d^5*e*x + 210*d^4*e^2*x^2 + 224*d^3*e^3*x^3 + 140*d^2*e^4*x^4 + 48*d*e^5*x^5 + 7*e^6*x^6) + 55*a^2*b^2*x^2*(84*d^6 + 378*d^5*e*x + 756*d^4*e^2*x^2 + 840*d^3*e^3*x^3 + 540*d^2*e^4*x^4 + 189*d*e^5*x^5 + 28*e^6*x^6) + 11*a*b^3*x^3*(210*d^6 + 1008*d^5*e*x + 2100*d^4*e^2*x^2 + 2400*d^3*e^3*x^3 + 1575*d^2*e^4*x^4 + 560*d*e^5*x^5 + 84*e^6*x^6) + b^4*x^4*(462*d^6 + 2310*d^5*e*x + 4950*d^4*e^2*x^2 + 5775*d^3*e^3*x^3 + 3850*d^2*e^4*x^4 + 1386*d*e^5*x^5 + 210*e^6*x^6)))/(2310*(a + b*x))","A",1
1970,1,322,254,0.0995444,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(210 a^4 \left(6 d^5+15 d^4 e x+20 d^3 e^2 x^2+15 d^2 e^3 x^3+6 d e^4 x^4+e^5 x^5\right)+120 a^3 b x \left(21 d^5+70 d^4 e x+105 d^3 e^2 x^2+84 d^2 e^3 x^3+35 d e^4 x^4+6 e^5 x^5\right)+45 a^2 b^2 x^2 \left(56 d^5+210 d^4 e x+336 d^3 e^2 x^2+280 d^2 e^3 x^3+120 d e^4 x^4+21 e^5 x^5\right)+10 a b^3 x^3 \left(126 d^5+504 d^4 e x+840 d^3 e^2 x^2+720 d^2 e^3 x^3+315 d e^4 x^4+56 e^5 x^5\right)+b^4 x^4 \left(252 d^5+1050 d^4 e x+1800 d^3 e^2 x^2+1575 d^2 e^3 x^3+700 d e^4 x^4+126 e^5 x^5\right)\right)}{1260 (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)}",1,"(x*Sqrt[(a + b*x)^2]*(210*a^4*(6*d^5 + 15*d^4*e*x + 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 + 6*d*e^4*x^4 + e^5*x^5) + 120*a^3*b*x*(21*d^5 + 70*d^4*e*x + 105*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 35*d*e^4*x^4 + 6*e^5*x^5) + 45*a^2*b^2*x^2*(56*d^5 + 210*d^4*e*x + 336*d^3*e^2*x^2 + 280*d^2*e^3*x^3 + 120*d*e^4*x^4 + 21*e^5*x^5) + 10*a*b^3*x^3*(126*d^5 + 504*d^4*e*x + 840*d^3*e^2*x^2 + 720*d^2*e^3*x^3 + 315*d*e^4*x^4 + 56*e^5*x^5) + b^4*x^4*(252*d^5 + 1050*d^4*e*x + 1800*d^3*e^2*x^2 + 1575*d^2*e^3*x^3 + 700*d*e^4*x^4 + 126*e^5*x^5)))/(1260*(a + b*x))","A",1
1971,1,267,219,0.0838826,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(126 a^4 \left(5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right)+84 a^3 b x \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)+36 a^2 b^2 x^2 \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)+9 a b^3 x^3 \left(70 d^4+224 d^3 e x+280 d^2 e^2 x^2+160 d e^3 x^3+35 e^4 x^4\right)+b^4 x^4 \left(126 d^4+420 d^3 e x+540 d^2 e^2 x^2+315 d e^3 x^3+70 e^4 x^4\right)\right)}{630 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(126*a^4*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4) + 84*a^3*b*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4) + 36*a^2*b^2*x^2*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4) + 9*a*b^3*x^3*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4) + b^4*x^4*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4)))/(630*(a + b*x))","A",1
1972,1,212,172,0.0688444,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(70 a^4 \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+56 a^3 b x \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)+28 a^2 b^2 x^2 \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)+8 a b^3 x^3 \left(35 d^3+84 d^2 e x+70 d e^2 x^2+20 e^3 x^3\right)+b^4 x^4 \left(56 d^3+140 d^2 e x+120 d e^2 x^2+35 e^3 x^3\right)\right)}{280 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(70*a^4*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) + 56*a^3*b*x*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3) + 28*a^2*b^2*x^2*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3) + 8*a*b^3*x^3*(35*d^3 + 84*d^2*e*x + 70*d*e^2*x^2 + 20*e^3*x^3) + b^4*x^4*(56*d^3 + 140*d^2*e*x + 120*d*e^2*x^2 + 35*e^3*x^3)))/(280*(a + b*x))","A",1
1973,1,157,125,0.0540559,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(35 a^4 \left(3 d^2+3 d e x+e^2 x^2\right)+35 a^3 b x \left(6 d^2+8 d e x+3 e^2 x^2\right)+21 a^2 b^2 x^2 \left(10 d^2+15 d e x+6 e^2 x^2\right)+7 a b^3 x^3 \left(15 d^2+24 d e x+10 e^2 x^2\right)+b^4 x^4 \left(21 d^2+35 d e x+15 e^2 x^2\right)\right)}{105 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(35*a^4*(3*d^2 + 3*d*e*x + e^2*x^2) + 35*a^3*b*x*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + 21*a^2*b^2*x^2*(10*d^2 + 15*d*e*x + 6*e^2*x^2) + 7*a*b^3*x^3*(15*d^2 + 24*d*e*x + 10*e^2*x^2) + b^4*x^4*(21*d^2 + 35*d*e*x + 15*e^2*x^2)))/(105*(a + b*x))","A",1
1974,1,102,78,0.0335923,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x \sqrt{(a+b x)^2} \left(15 a^4 (2 d+e x)+20 a^3 b x (3 d+2 e x)+15 a^2 b^2 x^2 (4 d+3 e x)+6 a b^3 x^3 (5 d+4 e x)+b^4 x^4 (6 d+5 e x)\right)}{30 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(15*a^4*(2*d + e*x) + 20*a^3*b*x*(3*d + 2*e*x) + 15*a^2*b^2*x^2*(4*d + 3*e*x) + 6*a*b^3*x^3*(5*d + 4*e*x) + b^4*x^4*(6*d + 5*e*x)))/(30*(a + b*x))","A",1
1975,1,25,27,0.0071723,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x)^4 \sqrt{(a+b x)^2}}{5 b}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b}",1,"((a + b*x)^4*Sqrt[(a + b*x)^2])/(5*b)","A",1
1976,1,133,210,0.063084,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{d+e x} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x),x]","\frac{\sqrt{(a+b x)^2} \left(b e x \left(48 a^3 e^3+36 a^2 b e^2 (e x-2 d)+8 a b^2 e \left(6 d^2-3 d e x+2 e^2 x^2\right)+b^3 \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)+12 (b d-a e)^4 \log (d+e x)\right)}{12 e^5 (a+b x)}","\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{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{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 e}",1,"(Sqrt[(a + b*x)^2]*(b*e*x*(48*a^3*e^3 + 36*a^2*b*e^2*(-2*d + e*x) + 8*a*b^2*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + b^3*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)) + 12*(b*d - a*e)^4*Log[d + e*x]))/(12*e^5*(a + b*x))","A",1
1977,1,183,239,0.1226448,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^2} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^2,x]","\frac{\sqrt{(a+b x)^2} \left(-3 a^4 e^4+12 a^3 b d e^3+18 a^2 b^2 e^2 \left(-d^2+d e x+e^2 x^2\right)+6 a b^3 e \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)-12 b (d+e x) (b d-a e)^3 \log (d+e x)+b^4 \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)\right)}{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}{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{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{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)}",1,"(Sqrt[(a + b*x)^2]*(12*a^3*b*d*e^3 - 3*a^4*e^4 + 18*a^2*b^2*e^2*(-d^2 + d*e*x + e^2*x^2) + 6*a*b^3*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + b^4*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) - 12*b*(b*d - a*e)^3*(d + e*x)*Log[d + e*x]))/(3*e^5*(a + b*x)*(d + e*x))","A",1
1978,1,185,238,0.1191248,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^3} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^3,x]","\frac{\sqrt{(a+b x)^2} \left(-a^4 e^4-4 a^3 b e^3 (d+2 e x)+6 a^2 b^2 d e^2 (3 d+4 e x)+4 a b^3 e \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)+12 b^2 (d+e x)^2 (b d-a e)^2 \log (d+e x)+b^4 \left(7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right)\right)}{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}{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)}",1,"(Sqrt[(a + b*x)^2]*(-(a^4*e^4) - 4*a^3*b*e^3*(d + 2*e*x) + 6*a^2*b^2*d*e^2*(3*d + 4*e*x) + 4*a*b^3*e*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + b^4*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4) + 12*b^2*(b*d - a*e)^2*(d + e*x)^2*Log[d + e*x]))/(2*e^5*(a + b*x)*(d + e*x)^2)","A",1
1979,1,181,238,0.0863527,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^4} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^4,x]","-\frac{\sqrt{(a+b x)^2} \left(a^4 e^4+2 a^3 b e^3 (d+3 e x)+6 a^2 b^2 e^2 \left(d^2+3 d e x+3 e^2 x^2\right)-2 a b^3 d e \left(11 d^2+27 d e x+18 e^2 x^2\right)+12 b^3 (d+e x)^3 (b d-a e) \log (d+e x)+b^4 \left(13 d^4+27 d^3 e x+9 d^2 e^2 x^2-9 d e^3 x^3-3 e^4 x^4\right)\right)}{3 e^5 (a+b x) (d+e x)^3}","-\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{b^4 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^4 (a+b x)}-\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)}",1,"-1/3*(Sqrt[(a + b*x)^2]*(a^4*e^4 + 2*a^3*b*e^3*(d + 3*e*x) + 6*a^2*b^2*e^2*(d^2 + 3*d*e*x + 3*e^2*x^2) - 2*a*b^3*d*e*(11*d^2 + 27*d*e*x + 18*e^2*x^2) + b^4*(13*d^4 + 27*d^3*e*x + 9*d^2*e^2*x^2 - 9*d*e^3*x^3 - 3*e^4*x^4) + 12*b^3*(b*d - a*e)*(d + e*x)^3*Log[d + e*x]))/(e^5*(a + b*x)*(d + e*x)^3)","A",1
1980,1,144,246,0.0919197,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^5} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^5,x]","\frac{\sqrt{(a+b x)^2} \left((b d-a e) \left(3 a^3 e^3+a^2 b e^2 (7 d+16 e x)+a b^2 e \left(13 d^2+40 d e x+36 e^2 x^2\right)+b^3 \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)\right)+12 b^4 (d+e x)^4 \log (d+e x)\right)}{12 e^5 (a+b x) (d+e x)^4}","-\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)}",1,"(Sqrt[(a + b*x)^2]*((b*d - a*e)*(3*a^3*e^3 + a^2*b*e^2*(7*d + 16*e*x) + a*b^2*e*(13*d^2 + 40*d*e*x + 36*e^2*x^2) + b^3*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) + 12*b^4*(d + e*x)^4*Log[d + e*x]))/(12*e^5*(a + b*x)*(d + e*x)^4)","A",1
1981,1,158,41,0.0597718,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^6} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^6,x]","-\frac{\sqrt{(a+b x)^2} \left(a^4 e^4+a^3 b e^3 (d+5 e x)+a^2 b^2 e^2 \left(d^2+5 d e x+10 e^2 x^2\right)+a b^3 e \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+b^4 \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)}{5 e^5 (a+b x) (d+e x)^5}","\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,"-1/5*(Sqrt[(a + b*x)^2]*(a^4*e^4 + a^3*b*e^3*(d + 5*e*x) + a^2*b^2*e^2*(d^2 + 5*d*e*x + 10*e^2*x^2) + a*b^3*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + b^4*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4)))/(e^5*(a + b*x)*(d + e*x)^5)","B",1
1982,1,162,98,0.0584531,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^7} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^7,x]","-\frac{\sqrt{(a+b x)^2} \left(5 a^4 e^4+4 a^3 b e^3 (d+6 e x)+3 a^2 b^2 e^2 \left(d^2+6 d e x+15 e^2 x^2\right)+2 a b^3 e \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+b^4 \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)}{30 e^5 (a+b x) (d+e x)^6}","\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,"-1/30*(Sqrt[(a + b*x)^2]*(5*a^4*e^4 + 4*a^3*b*e^3*(d + 6*e*x) + 3*a^2*b^2*e^2*(d^2 + 6*d*e*x + 15*e^2*x^2) + 2*a*b^3*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + b^4*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)))/(e^5*(a + b*x)*(d + e*x)^6)","A",1
1983,1,162,149,0.0575552,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^8} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^8,x]","-\frac{\sqrt{(a+b x)^2} \left(15 a^4 e^4+10 a^3 b e^3 (d+7 e x)+6 a^2 b^2 e^2 \left(d^2+7 d e x+21 e^2 x^2\right)+3 a b^3 e \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+b^4 \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)}{105 e^5 (a+b x) (d+e x)^7}","\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,"-1/105*(Sqrt[(a + b*x)^2]*(15*a^4*e^4 + 10*a^3*b*e^3*(d + 7*e*x) + 6*a^2*b^2*e^2*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*a*b^3*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + b^4*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)))/(e^5*(a + b*x)*(d + e*x)^7)","A",1
1984,1,162,252,0.0573286,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^9} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^9,x]","-\frac{\sqrt{(a+b x)^2} \left(35 a^4 e^4+20 a^3 b e^3 (d+8 e x)+10 a^2 b^2 e^2 \left(d^2+8 d e x+28 e^2 x^2\right)+4 a b^3 e \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+b^4 \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)\right)}{280 e^5 (a+b x) (d+e x)^8}","-\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}",1,"-1/280*(Sqrt[(a + b*x)^2]*(35*a^4*e^4 + 20*a^3*b*e^3*(d + 8*e*x) + 10*a^2*b^2*e^2*(d^2 + 8*d*e*x + 28*e^2*x^2) + 4*a*b^3*e*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + b^4*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4)))/(e^5*(a + b*x)*(d + e*x)^8)","A",1
1985,1,162,254,0.0603338,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{10}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^10,x]","-\frac{\sqrt{(a+b x)^2} \left(70 a^4 e^4+35 a^3 b e^3 (d+9 e x)+15 a^2 b^2 e^2 \left(d^2+9 d e x+36 e^2 x^2\right)+5 a b^3 e \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)+b^4 \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)\right)}{630 e^5 (a+b x) (d+e x)^9}","-\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}",1,"-1/630*(Sqrt[(a + b*x)^2]*(70*a^4*e^4 + 35*a^3*b*e^3*(d + 9*e*x) + 15*a^2*b^2*e^2*(d^2 + 9*d*e*x + 36*e^2*x^2) + 5*a*b^3*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + b^4*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4)))/(e^5*(a + b*x)*(d + e*x)^9)","A",1
1986,1,162,254,0.0555521,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{11}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^11,x]","-\frac{\sqrt{(a+b x)^2} \left(126 a^4 e^4+56 a^3 b e^3 (d+10 e x)+21 a^2 b^2 e^2 \left(d^2+10 d e x+45 e^2 x^2\right)+6 a b^3 e \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)+b^4 \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)\right)}{1260 e^5 (a+b x) (d+e x)^{10}}","-\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}",1,"-1/1260*(Sqrt[(a + b*x)^2]*(126*a^4*e^4 + 56*a^3*b*e^3*(d + 10*e*x) + 21*a^2*b^2*e^2*(d^2 + 10*d*e*x + 45*e^2*x^2) + 6*a*b^3*e*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + b^4*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4)))/(e^5*(a + b*x)*(d + e*x)^10)","A",1
1987,1,162,254,0.0698637,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{12}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^12,x]","-\frac{\sqrt{(a+b x)^2} \left(210 a^4 e^4+84 a^3 b e^3 (d+11 e x)+28 a^2 b^2 e^2 \left(d^2+11 d e x+55 e^2 x^2\right)+7 a b^3 e \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)+b^4 \left(d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right)\right)}{2310 e^5 (a+b x) (d+e x)^{11}}","-\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}",1,"-1/2310*(Sqrt[(a + b*x)^2]*(210*a^4*e^4 + 84*a^3*b*e^3*(d + 11*e*x) + 28*a^2*b^2*e^2*(d^2 + 11*d*e*x + 55*e^2*x^2) + 7*a*b^3*e*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3) + b^4*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4)))/(e^5*(a + b*x)*(d + e*x)^11)","A",1
1988,1,756,362,0.2322593,"\int (a+b x) (d+e x)^9 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^9*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(8008 a^6 \left(10 d^9+45 d^8 e x+120 d^7 e^2 x^2+210 d^6 e^3 x^3+252 d^5 e^4 x^4+210 d^4 e^5 x^5+120 d^3 e^6 x^6+45 d^2 e^7 x^7+10 d e^8 x^8+e^9 x^9\right)+4368 a^5 b x \left(55 d^9+330 d^8 e x+990 d^7 e^2 x^2+1848 d^6 e^3 x^3+2310 d^5 e^4 x^4+1980 d^4 e^5 x^5+1155 d^3 e^6 x^6+440 d^2 e^7 x^7+99 d e^8 x^8+10 e^9 x^9\right)+1820 a^4 b^2 x^2 \left(220 d^9+1485 d^8 e x+4752 d^7 e^2 x^2+9240 d^6 e^3 x^3+11880 d^5 e^4 x^4+10395 d^4 e^5 x^5+6160 d^3 e^6 x^6+2376 d^2 e^7 x^7+540 d e^8 x^8+55 e^9 x^9\right)+560 a^3 b^3 x^3 \left(715 d^9+5148 d^8 e x+17160 d^7 e^2 x^2+34320 d^6 e^3 x^3+45045 d^5 e^4 x^4+40040 d^4 e^5 x^5+24024 d^3 e^6 x^6+9360 d^2 e^7 x^7+2145 d e^8 x^8+220 e^9 x^9\right)+120 a^2 b^4 x^4 \left(2002 d^9+15015 d^8 e x+51480 d^7 e^2 x^2+105105 d^6 e^3 x^3+140140 d^5 e^4 x^4+126126 d^4 e^5 x^5+76440 d^3 e^6 x^6+30030 d^2 e^7 x^7+6930 d e^8 x^8+715 e^9 x^9\right)+16 a b^5 x^5 \left(5005 d^9+38610 d^8 e x+135135 d^7 e^2 x^2+280280 d^6 e^3 x^3+378378 d^5 e^4 x^4+343980 d^4 e^5 x^5+210210 d^3 e^6 x^6+83160 d^2 e^7 x^7+19305 d e^8 x^8+2002 e^9 x^9\right)+b^6 x^6 \left(11440 d^9+90090 d^8 e x+320320 d^7 e^2 x^2+672672 d^6 e^3 x^3+917280 d^5 e^4 x^4+840840 d^4 e^5 x^5+517440 d^3 e^6 x^6+205920 d^2 e^7 x^7+48048 d e^8 x^8+5005 e^9 x^9\right)\right)}{80080 (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)}",1,"(x*Sqrt[(a + b*x)^2]*(8008*a^6*(10*d^9 + 45*d^8*e*x + 120*d^7*e^2*x^2 + 210*d^6*e^3*x^3 + 252*d^5*e^4*x^4 + 210*d^4*e^5*x^5 + 120*d^3*e^6*x^6 + 45*d^2*e^7*x^7 + 10*d*e^8*x^8 + e^9*x^9) + 4368*a^5*b*x*(55*d^9 + 330*d^8*e*x + 990*d^7*e^2*x^2 + 1848*d^6*e^3*x^3 + 2310*d^5*e^4*x^4 + 1980*d^4*e^5*x^5 + 1155*d^3*e^6*x^6 + 440*d^2*e^7*x^7 + 99*d*e^8*x^8 + 10*e^9*x^9) + 1820*a^4*b^2*x^2*(220*d^9 + 1485*d^8*e*x + 4752*d^7*e^2*x^2 + 9240*d^6*e^3*x^3 + 11880*d^5*e^4*x^4 + 10395*d^4*e^5*x^5 + 6160*d^3*e^6*x^6 + 2376*d^2*e^7*x^7 + 540*d*e^8*x^8 + 55*e^9*x^9) + 560*a^3*b^3*x^3*(715*d^9 + 5148*d^8*e*x + 17160*d^7*e^2*x^2 + 34320*d^6*e^3*x^3 + 45045*d^5*e^4*x^4 + 40040*d^4*e^5*x^5 + 24024*d^3*e^6*x^6 + 9360*d^2*e^7*x^7 + 2145*d*e^8*x^8 + 220*e^9*x^9) + 120*a^2*b^4*x^4*(2002*d^9 + 15015*d^8*e*x + 51480*d^7*e^2*x^2 + 105105*d^6*e^3*x^3 + 140140*d^5*e^4*x^4 + 126126*d^4*e^5*x^5 + 76440*d^3*e^6*x^6 + 30030*d^2*e^7*x^7 + 6930*d*e^8*x^8 + 715*e^9*x^9) + 16*a*b^5*x^5*(5005*d^9 + 38610*d^8*e*x + 135135*d^7*e^2*x^2 + 280280*d^6*e^3*x^3 + 378378*d^5*e^4*x^4 + 343980*d^4*e^5*x^5 + 210210*d^3*e^6*x^6 + 83160*d^2*e^7*x^7 + 19305*d*e^8*x^8 + 2002*e^9*x^9) + b^6*x^6*(11440*d^9 + 90090*d^8*e*x + 320320*d^7*e^2*x^2 + 672672*d^6*e^3*x^3 + 917280*d^5*e^4*x^4 + 840840*d^4*e^5*x^5 + 517440*d^3*e^6*x^6 + 205920*d^2*e^7*x^7 + 48048*d*e^8*x^8 + 5005*e^9*x^9)))/(80080*(a + b*x))","B",1
1989,1,679,362,0.2189388,"\int (a+b x) (d+e x)^8 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^8*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(5005 a^6 \left(9 d^8+36 d^7 e x+84 d^6 e^2 x^2+126 d^5 e^3 x^3+126 d^4 e^4 x^4+84 d^3 e^5 x^5+36 d^2 e^6 x^6+9 d e^7 x^7+e^8 x^8\right)+3003 a^5 b x \left(45 d^8+240 d^7 e x+630 d^6 e^2 x^2+1008 d^5 e^3 x^3+1050 d^4 e^4 x^4+720 d^3 e^5 x^5+315 d^2 e^6 x^6+80 d e^7 x^7+9 e^8 x^8\right)+1365 a^4 b^2 x^2 \left(165 d^8+990 d^7 e x+2772 d^6 e^2 x^2+4620 d^5 e^3 x^3+4950 d^4 e^4 x^4+3465 d^3 e^5 x^5+1540 d^2 e^6 x^6+396 d e^7 x^7+45 e^8 x^8\right)+455 a^3 b^3 x^3 \left(495 d^8+3168 d^7 e x+9240 d^6 e^2 x^2+15840 d^5 e^3 x^3+17325 d^4 e^4 x^4+12320 d^3 e^5 x^5+5544 d^2 e^6 x^6+1440 d e^7 x^7+165 e^8 x^8\right)+105 a^2 b^4 x^4 \left(1287 d^8+8580 d^7 e x+25740 d^6 e^2 x^2+45045 d^5 e^3 x^3+50050 d^4 e^4 x^4+36036 d^3 e^5 x^5+16380 d^2 e^6 x^6+4290 d e^7 x^7+495 e^8 x^8\right)+15 a b^5 x^5 \left(3003 d^8+20592 d^7 e x+63063 d^6 e^2 x^2+112112 d^5 e^3 x^3+126126 d^4 e^4 x^4+91728 d^3 e^5 x^5+42042 d^2 e^6 x^6+11088 d e^7 x^7+1287 e^8 x^8\right)+b^6 x^6 \left(6435 d^8+45045 d^7 e x+140140 d^6 e^2 x^2+252252 d^5 e^3 x^3+286650 d^4 e^4 x^4+210210 d^3 e^5 x^5+97020 d^2 e^6 x^6+25740 d e^7 x^7+3003 e^8 x^8\right)\right)}{45045 (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)}",1,"(x*Sqrt[(a + b*x)^2]*(5005*a^6*(9*d^8 + 36*d^7*e*x + 84*d^6*e^2*x^2 + 126*d^5*e^3*x^3 + 126*d^4*e^4*x^4 + 84*d^3*e^5*x^5 + 36*d^2*e^6*x^6 + 9*d*e^7*x^7 + e^8*x^8) + 3003*a^5*b*x*(45*d^8 + 240*d^7*e*x + 630*d^6*e^2*x^2 + 1008*d^5*e^3*x^3 + 1050*d^4*e^4*x^4 + 720*d^3*e^5*x^5 + 315*d^2*e^6*x^6 + 80*d*e^7*x^7 + 9*e^8*x^8) + 1365*a^4*b^2*x^2*(165*d^8 + 990*d^7*e*x + 2772*d^6*e^2*x^2 + 4620*d^5*e^3*x^3 + 4950*d^4*e^4*x^4 + 3465*d^3*e^5*x^5 + 1540*d^2*e^6*x^6 + 396*d*e^7*x^7 + 45*e^8*x^8) + 455*a^3*b^3*x^3*(495*d^8 + 3168*d^7*e*x + 9240*d^6*e^2*x^2 + 15840*d^5*e^3*x^3 + 17325*d^4*e^4*x^4 + 12320*d^3*e^5*x^5 + 5544*d^2*e^6*x^6 + 1440*d*e^7*x^7 + 165*e^8*x^8) + 105*a^2*b^4*x^4*(1287*d^8 + 8580*d^7*e*x + 25740*d^6*e^2*x^2 + 45045*d^5*e^3*x^3 + 50050*d^4*e^4*x^4 + 36036*d^3*e^5*x^5 + 16380*d^2*e^6*x^6 + 4290*d*e^7*x^7 + 495*e^8*x^8) + 15*a*b^5*x^5*(3003*d^8 + 20592*d^7*e*x + 63063*d^6*e^2*x^2 + 112112*d^5*e^3*x^3 + 126126*d^4*e^4*x^4 + 91728*d^3*e^5*x^5 + 42042*d^2*e^6*x^6 + 11088*d*e^7*x^7 + 1287*e^8*x^8) + b^6*x^6*(6435*d^8 + 45045*d^7*e*x + 140140*d^6*e^2*x^2 + 252252*d^5*e^3*x^3 + 286650*d^4*e^4*x^4 + 210210*d^3*e^5*x^5 + 97020*d^2*e^6*x^6 + 25740*d*e^7*x^7 + 3003*e^8*x^8)))/(45045*(a + b*x))","A",1
1990,1,602,362,0.1881393,"\int (a+b x) (d+e x)^7 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(3003 a^6 \left(8 d^7+28 d^6 e x+56 d^5 e^2 x^2+70 d^4 e^3 x^3+56 d^3 e^4 x^4+28 d^2 e^5 x^5+8 d e^6 x^6+e^7 x^7\right)+2002 a^5 b x \left(36 d^7+168 d^6 e x+378 d^5 e^2 x^2+504 d^4 e^3 x^3+420 d^3 e^4 x^4+216 d^2 e^5 x^5+63 d e^6 x^6+8 e^7 x^7\right)+1001 a^4 b^2 x^2 \left(120 d^7+630 d^6 e x+1512 d^5 e^2 x^2+2100 d^4 e^3 x^3+1800 d^3 e^4 x^4+945 d^2 e^5 x^5+280 d e^6 x^6+36 e^7 x^7\right)+364 a^3 b^3 x^3 \left(330 d^7+1848 d^6 e x+4620 d^5 e^2 x^2+6600 d^4 e^3 x^3+5775 d^3 e^4 x^4+3080 d^2 e^5 x^5+924 d e^6 x^6+120 e^7 x^7\right)+91 a^2 b^4 x^4 \left(792 d^7+4620 d^6 e x+11880 d^5 e^2 x^2+17325 d^4 e^3 x^3+15400 d^3 e^4 x^4+8316 d^2 e^5 x^5+2520 d e^6 x^6+330 e^7 x^7\right)+14 a b^5 x^5 \left(1716 d^7+10296 d^6 e x+27027 d^5 e^2 x^2+40040 d^4 e^3 x^3+36036 d^3 e^4 x^4+19656 d^2 e^5 x^5+6006 d e^6 x^6+792 e^7 x^7\right)+b^6 x^6 \left(3432 d^7+21021 d^6 e x+56056 d^5 e^2 x^2+84084 d^4 e^3 x^3+76440 d^3 e^4 x^4+42042 d^2 e^5 x^5+12936 d e^6 x^6+1716 e^7 x^7\right)\right)}{24024 (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)}",1,"(x*Sqrt[(a + b*x)^2]*(3003*a^6*(8*d^7 + 28*d^6*e*x + 56*d^5*e^2*x^2 + 70*d^4*e^3*x^3 + 56*d^3*e^4*x^4 + 28*d^2*e^5*x^5 + 8*d*e^6*x^6 + e^7*x^7) + 2002*a^5*b*x*(36*d^7 + 168*d^6*e*x + 378*d^5*e^2*x^2 + 504*d^4*e^3*x^3 + 420*d^3*e^4*x^4 + 216*d^2*e^5*x^5 + 63*d*e^6*x^6 + 8*e^7*x^7) + 1001*a^4*b^2*x^2*(120*d^7 + 630*d^6*e*x + 1512*d^5*e^2*x^2 + 2100*d^4*e^3*x^3 + 1800*d^3*e^4*x^4 + 945*d^2*e^5*x^5 + 280*d*e^6*x^6 + 36*e^7*x^7) + 364*a^3*b^3*x^3*(330*d^7 + 1848*d^6*e*x + 4620*d^5*e^2*x^2 + 6600*d^4*e^3*x^3 + 5775*d^3*e^4*x^4 + 3080*d^2*e^5*x^5 + 924*d*e^6*x^6 + 120*e^7*x^7) + 91*a^2*b^4*x^4*(792*d^7 + 4620*d^6*e*x + 11880*d^5*e^2*x^2 + 17325*d^4*e^3*x^3 + 15400*d^3*e^4*x^4 + 8316*d^2*e^5*x^5 + 2520*d*e^6*x^6 + 330*e^7*x^7) + 14*a*b^5*x^5*(1716*d^7 + 10296*d^6*e*x + 27027*d^5*e^2*x^2 + 40040*d^4*e^3*x^3 + 36036*d^3*e^4*x^4 + 19656*d^2*e^5*x^5 + 6006*d*e^6*x^6 + 792*e^7*x^7) + b^6*x^6*(3432*d^7 + 21021*d^6*e*x + 56056*d^5*e^2*x^2 + 84084*d^4*e^3*x^3 + 76440*d^3*e^4*x^4 + 42042*d^2*e^5*x^5 + 12936*d*e^6*x^6 + 1716*e^7*x^7)))/(24024*(a + b*x))","A",1
1991,1,525,311,0.1599879,"\int (a+b x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(1716 a^6 \left(7 d^6+21 d^5 e x+35 d^4 e^2 x^2+35 d^3 e^3 x^3+21 d^2 e^4 x^4+7 d e^5 x^5+e^6 x^6\right)+1287 a^5 b x \left(28 d^6+112 d^5 e x+210 d^4 e^2 x^2+224 d^3 e^3 x^3+140 d^2 e^4 x^4+48 d e^5 x^5+7 e^6 x^6\right)+715 a^4 b^2 x^2 \left(84 d^6+378 d^5 e x+756 d^4 e^2 x^2+840 d^3 e^3 x^3+540 d^2 e^4 x^4+189 d e^5 x^5+28 e^6 x^6\right)+286 a^3 b^3 x^3 \left(210 d^6+1008 d^5 e x+2100 d^4 e^2 x^2+2400 d^3 e^3 x^3+1575 d^2 e^4 x^4+560 d e^5 x^5+84 e^6 x^6\right)+78 a^2 b^4 x^4 \left(462 d^6+2310 d^5 e x+4950 d^4 e^2 x^2+5775 d^3 e^3 x^3+3850 d^2 e^4 x^4+1386 d e^5 x^5+210 e^6 x^6\right)+13 a b^5 x^5 \left(924 d^6+4752 d^5 e x+10395 d^4 e^2 x^2+12320 d^3 e^3 x^3+8316 d^2 e^4 x^4+3024 d e^5 x^5+462 e^6 x^6\right)+b^6 x^6 \left(1716 d^6+9009 d^5 e x+20020 d^4 e^2 x^2+24024 d^3 e^3 x^3+16380 d^2 e^4 x^4+6006 d e^5 x^5+924 e^6 x^6\right)\right)}{12012 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(1716*a^6*(7*d^6 + 21*d^5*e*x + 35*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 21*d^2*e^4*x^4 + 7*d*e^5*x^5 + e^6*x^6) + 1287*a^5*b*x*(28*d^6 + 112*d^5*e*x + 210*d^4*e^2*x^2 + 224*d^3*e^3*x^3 + 140*d^2*e^4*x^4 + 48*d*e^5*x^5 + 7*e^6*x^6) + 715*a^4*b^2*x^2*(84*d^6 + 378*d^5*e*x + 756*d^4*e^2*x^2 + 840*d^3*e^3*x^3 + 540*d^2*e^4*x^4 + 189*d*e^5*x^5 + 28*e^6*x^6) + 286*a^3*b^3*x^3*(210*d^6 + 1008*d^5*e*x + 2100*d^4*e^2*x^2 + 2400*d^3*e^3*x^3 + 1575*d^2*e^4*x^4 + 560*d*e^5*x^5 + 84*e^6*x^6) + 78*a^2*b^4*x^4*(462*d^6 + 2310*d^5*e*x + 4950*d^4*e^2*x^2 + 5775*d^3*e^3*x^3 + 3850*d^2*e^4*x^4 + 1386*d*e^5*x^5 + 210*e^6*x^6) + 13*a*b^5*x^5*(924*d^6 + 4752*d^5*e*x + 10395*d^4*e^2*x^2 + 12320*d^3*e^3*x^3 + 8316*d^2*e^4*x^4 + 3024*d*e^5*x^5 + 462*e^6*x^6) + b^6*x^6*(1716*d^6 + 9009*d^5*e*x + 20020*d^4*e^2*x^2 + 24024*d^3*e^3*x^3 + 16380*d^2*e^4*x^4 + 6006*d*e^5*x^5 + 924*e^6*x^6)))/(12012*(a + b*x))","A",1
1992,1,448,263,0.1379383,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(924 a^6 \left(6 d^5+15 d^4 e x+20 d^3 e^2 x^2+15 d^2 e^3 x^3+6 d e^4 x^4+e^5 x^5\right)+792 a^5 b x \left(21 d^5+70 d^4 e x+105 d^3 e^2 x^2+84 d^2 e^3 x^3+35 d e^4 x^4+6 e^5 x^5\right)+495 a^4 b^2 x^2 \left(56 d^5+210 d^4 e x+336 d^3 e^2 x^2+280 d^2 e^3 x^3+120 d e^4 x^4+21 e^5 x^5\right)+220 a^3 b^3 x^3 \left(126 d^5+504 d^4 e x+840 d^3 e^2 x^2+720 d^2 e^3 x^3+315 d e^4 x^4+56 e^5 x^5\right)+66 a^2 b^4 x^4 \left(252 d^5+1050 d^4 e x+1800 d^3 e^2 x^2+1575 d^2 e^3 x^3+700 d e^4 x^4+126 e^5 x^5\right)+12 a b^5 x^5 \left(462 d^5+1980 d^4 e x+3465 d^3 e^2 x^2+3080 d^2 e^3 x^3+1386 d e^4 x^4+252 e^5 x^5\right)+b^6 x^6 \left(792 d^5+3465 d^4 e x+6160 d^3 e^2 x^2+5544 d^2 e^3 x^3+2520 d e^4 x^4+462 e^5 x^5\right)\right)}{5544 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(924*a^6*(6*d^5 + 15*d^4*e*x + 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 + 6*d*e^4*x^4 + e^5*x^5) + 792*a^5*b*x*(21*d^5 + 70*d^4*e*x + 105*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 35*d*e^4*x^4 + 6*e^5*x^5) + 495*a^4*b^2*x^2*(56*d^5 + 210*d^4*e*x + 336*d^3*e^2*x^2 + 280*d^2*e^3*x^3 + 120*d*e^4*x^4 + 21*e^5*x^5) + 220*a^3*b^3*x^3*(126*d^5 + 504*d^4*e*x + 840*d^3*e^2*x^2 + 720*d^2*e^3*x^3 + 315*d*e^4*x^4 + 56*e^5*x^5) + 66*a^2*b^4*x^4*(252*d^5 + 1050*d^4*e*x + 1800*d^3*e^2*x^2 + 1575*d^2*e^3*x^3 + 700*d*e^4*x^4 + 126*e^5*x^5) + 12*a*b^5*x^5*(462*d^5 + 1980*d^4*e*x + 3465*d^3*e^2*x^2 + 3080*d^2*e^3*x^3 + 1386*d*e^4*x^4 + 252*e^5*x^5) + b^6*x^6*(792*d^5 + 3465*d^4*e*x + 6160*d^3*e^2*x^2 + 5544*d^2*e^3*x^3 + 2520*d*e^4*x^4 + 462*e^5*x^5)))/(5544*(a + b*x))","A",1
1993,1,371,219,0.1179211,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(462 a^6 \left(5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right)+462 a^5 b x \left(15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right)+330 a^4 b^2 x^2 \left(35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right)+165 a^3 b^3 x^3 \left(70 d^4+224 d^3 e x+280 d^2 e^2 x^2+160 d e^3 x^3+35 e^4 x^4\right)+55 a^2 b^4 x^4 \left(126 d^4+420 d^3 e x+540 d^2 e^2 x^2+315 d e^3 x^3+70 e^4 x^4\right)+11 a b^5 x^5 \left(210 d^4+720 d^3 e x+945 d^2 e^2 x^2+560 d e^3 x^3+126 e^4 x^4\right)+b^6 x^6 \left(330 d^4+1155 d^3 e x+1540 d^2 e^2 x^2+924 d e^3 x^3+210 e^4 x^4\right)\right)}{2310 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(462*a^6*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4) + 462*a^5*b*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4) + 330*a^4*b^2*x^2*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4) + 165*a^3*b^3*x^3*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4) + 55*a^2*b^4*x^4*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4) + 11*a*b^5*x^5*(210*d^4 + 720*d^3*e*x + 945*d^2*e^2*x^2 + 560*d*e^3*x^3 + 126*e^4*x^4) + b^6*x^6*(330*d^4 + 1155*d^3*e*x + 1540*d^2*e^2*x^2 + 924*d*e^3*x^3 + 210*e^4*x^4)))/(2310*(a + b*x))","A",1
1994,1,294,172,0.0965296,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(210 a^6 \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+252 a^5 b x \left(10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right)+210 a^4 b^2 x^2 \left(20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right)+120 a^3 b^3 x^3 \left(35 d^3+84 d^2 e x+70 d e^2 x^2+20 e^3 x^3\right)+45 a^2 b^4 x^4 \left(56 d^3+140 d^2 e x+120 d e^2 x^2+35 e^3 x^3\right)+10 a b^5 x^5 \left(84 d^3+216 d^2 e x+189 d e^2 x^2+56 e^3 x^3\right)+b^6 x^6 \left(120 d^3+315 d^2 e x+280 d e^2 x^2+84 e^3 x^3\right)\right)}{840 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(210*a^6*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) + 252*a^5*b*x*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3) + 210*a^4*b^2*x^2*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3) + 120*a^3*b^3*x^3*(35*d^3 + 84*d^2*e*x + 70*d*e^2*x^2 + 20*e^3*x^3) + 45*a^2*b^4*x^4*(56*d^3 + 140*d^2*e*x + 120*d*e^2*x^2 + 35*e^3*x^3) + 10*a*b^5*x^5*(84*d^3 + 216*d^2*e*x + 189*d*e^2*x^2 + 56*e^3*x^3) + b^6*x^6*(120*d^3 + 315*d^2*e*x + 280*d*e^2*x^2 + 84*e^3*x^3)))/(840*(a + b*x))","A",1
1995,1,217,125,0.0755285,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(84 a^6 \left(3 d^2+3 d e x+e^2 x^2\right)+126 a^5 b x \left(6 d^2+8 d e x+3 e^2 x^2\right)+126 a^4 b^2 x^2 \left(10 d^2+15 d e x+6 e^2 x^2\right)+84 a^3 b^3 x^3 \left(15 d^2+24 d e x+10 e^2 x^2\right)+36 a^2 b^4 x^4 \left(21 d^2+35 d e x+15 e^2 x^2\right)+9 a b^5 x^5 \left(28 d^2+48 d e x+21 e^2 x^2\right)+b^6 x^6 \left(36 d^2+63 d e x+28 e^2 x^2\right)\right)}{252 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(84*a^6*(3*d^2 + 3*d*e*x + e^2*x^2) + 126*a^5*b*x*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + 126*a^4*b^2*x^2*(10*d^2 + 15*d*e*x + 6*e^2*x^2) + 84*a^3*b^3*x^3*(15*d^2 + 24*d*e*x + 10*e^2*x^2) + 36*a^2*b^4*x^4*(21*d^2 + 35*d*e*x + 15*e^2*x^2) + 9*a*b^5*x^5*(28*d^2 + 48*d*e*x + 21*e^2*x^2) + b^6*x^6*(36*d^2 + 63*d*e*x + 28*e^2*x^2)))/(252*(a + b*x))","A",1
1996,1,140,78,0.049127,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x \sqrt{(a+b x)^2} \left(28 a^6 (2 d+e x)+56 a^5 b x (3 d+2 e x)+70 a^4 b^2 x^2 (4 d+3 e x)+56 a^3 b^3 x^3 (5 d+4 e x)+28 a^2 b^4 x^4 (6 d+5 e x)+8 a b^5 x^5 (7 d+6 e x)+b^6 x^6 (8 d+7 e x)\right)}{56 (a+b 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}",1,"(x*Sqrt[(a + b*x)^2]*(28*a^6*(2*d + e*x) + 56*a^5*b*x*(3*d + 2*e*x) + 70*a^4*b^2*x^2*(4*d + 3*e*x) + 56*a^3*b^3*x^3*(5*d + 4*e*x) + 28*a^2*b^4*x^4*(6*d + 5*e*x) + 8*a*b^5*x^5*(7*d + 6*e*x) + b^6*x^6*(8*d + 7*e*x)))/(56*(a + b*x))","A",1
1997,1,25,27,0.0092641,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(a+b x)^6 \sqrt{(a+b x)^2}}{7 b}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b}",1,"((a + b*x)^6*Sqrt[(a + b*x)^2])/(7*b)","A",1
1998,1,248,298,0.1131542,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{d+e x} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x),x]","\frac{\sqrt{(a+b x)^2} \left(b e x \left(360 a^5 e^5+450 a^4 b e^4 (e x-2 d)+200 a^3 b^2 e^3 \left(6 d^2-3 d e x+2 e^2 x^2\right)+75 a^2 b^3 e^2 \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+6 a b^4 e \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)+b^5 \left(-60 d^5+30 d^4 e x-20 d^3 e^2 x^2+15 d^2 e^3 x^3-12 d e^4 x^4+10 e^5 x^5\right)\right)+60 (b d-a e)^6 \log (d+e x)\right)}{60 e^7 (a+b x)}","\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{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{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 e}",1,"(Sqrt[(a + b*x)^2]*(b*e*x*(360*a^5*e^5 + 450*a^4*b*e^4*(-2*d + e*x) + 200*a^3*b^2*e^3*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + 75*a^2*b^3*e^2*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + 6*a*b^4*e*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + b^5*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5)) + 60*(b*d - a*e)^6*Log[d + e*x]))/(60*e^7*(a + b*x))","A",1
1999,1,320,345,0.200881,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^2,x]","\frac{\sqrt{(a+b x)^2} \left(-10 a^6 e^6+60 a^5 b d e^5+150 a^4 b^2 e^4 \left(-d^2+d e x+e^2 x^2\right)+100 a^3 b^3 e^3 \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+50 a^2 b^4 e^2 \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)+5 a b^5 e \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)-60 b (d+e x) (b d-a e)^5 \log (d+e x)+b^6 \left(-10 d^6+50 d^5 e x+30 d^4 e^2 x^2-10 d^3 e^3 x^3+5 d^2 e^4 x^4-3 d e^5 x^5+2 e^6 x^6\right)\right)}{10 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}{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{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{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)}",1,"(Sqrt[(a + b*x)^2]*(60*a^5*b*d*e^5 - 10*a^6*e^6 + 150*a^4*b^2*e^4*(-d^2 + d*e*x + e^2*x^2) + 100*a^3*b^3*e^3*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 50*a^2*b^4*e^2*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + 5*a*b^5*e*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5) + b^6*(-10*d^6 + 50*d^5*e*x + 30*d^4*e^2*x^2 - 10*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 3*d*e^5*x^5 + 2*e^6*x^6) - 60*b*(b*d - a*e)^5*(d + e*x)*Log[d + e*x]))/(10*e^7*(a + b*x)*(d + e*x))","A",1
2000,1,321,347,0.1426845,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^3} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^3,x]","\frac{\sqrt{(a+b x)^2} \left(-2 a^6 e^6-12 a^5 b e^5 (d+2 e x)+30 a^4 b^2 d e^4 (3 d+4 e x)+40 a^3 b^3 e^3 \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)+30 a^2 b^4 e^2 \left(7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right)+4 a b^5 e \left(-27 d^5+6 d^4 e x+63 d^3 e^2 x^2+20 d^2 e^3 x^3-5 d e^4 x^4+2 e^5 x^5\right)+60 b^2 (d+e x)^2 (b d-a e)^4 \log (d+e x)+b^6 \left(22 d^6-16 d^5 e x-68 d^4 e^2 x^2-20 d^3 e^3 x^3+5 d^2 e^4 x^4-2 d e^5 x^5+e^6 x^6\right)\right)}{4 e^7 (a+b x) (d+e x)^2}","\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)}",1,"(Sqrt[(a + b*x)^2]*(-2*a^6*e^6 - 12*a^5*b*e^5*(d + 2*e*x) + 30*a^4*b^2*d*e^4*(3*d + 4*e*x) + 40*a^3*b^3*e^3*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + 30*a^2*b^4*e^2*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4) + 4*a*b^5*e*(-27*d^5 + 6*d^4*e*x + 63*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5) + b^6*(22*d^6 - 16*d^5*e*x - 68*d^4*e^2*x^2 - 20*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 2*d*e^5*x^5 + e^6*x^6) + 60*b^2*(b*d - a*e)^4*(d + e*x)^2*Log[d + e*x]))/(4*e^7*(a + b*x)*(d + e*x)^2)","A",1
2001,1,320,345,0.1478048,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^4,x]","-\frac{\sqrt{(a+b x)^2} \left(a^6 e^6+3 a^5 b e^5 (d+3 e x)+15 a^4 b^2 e^4 \left(d^2+3 d e x+3 e^2 x^2\right)-10 a^3 b^3 d e^3 \left(11 d^2+27 d e x+18 e^2 x^2\right)+15 a^2 b^4 e^2 \left(13 d^4+27 d^3 e x+9 d^2 e^2 x^2-9 d e^3 x^3-3 e^4 x^4\right)-3 a b^5 e \left(47 d^5+81 d^4 e x-9 d^3 e^2 x^2-63 d^2 e^3 x^3-15 d e^4 x^4+3 e^5 x^5\right)+60 b^3 (d+e x)^3 (b d-a e)^3 \log (d+e x)+b^6 \left(37 d^6+51 d^5 e x-39 d^4 e^2 x^2-73 d^3 e^3 x^3-15 d^2 e^4 x^4+3 d e^5 x^5-e^6 x^6\right)\right)}{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}{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{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{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,"-1/3*(Sqrt[(a + b*x)^2]*(a^6*e^6 + 3*a^5*b*e^5*(d + 3*e*x) + 15*a^4*b^2*e^4*(d^2 + 3*d*e*x + 3*e^2*x^2) - 10*a^3*b^3*d*e^3*(11*d^2 + 27*d*e*x + 18*e^2*x^2) + 15*a^2*b^4*e^2*(13*d^4 + 27*d^3*e*x + 9*d^2*e^2*x^2 - 9*d*e^3*x^3 - 3*e^4*x^4) - 3*a*b^5*e*(47*d^5 + 81*d^4*e*x - 9*d^3*e^2*x^2 - 63*d^2*e^3*x^3 - 15*d*e^4*x^4 + 3*e^5*x^5) + b^6*(37*d^6 + 51*d^5*e*x - 39*d^4*e^2*x^2 - 73*d^3*e^3*x^3 - 15*d^2*e^4*x^4 + 3*d*e^5*x^5 - e^6*x^6) + 60*b^3*(b*d - a*e)^3*(d + e*x)^3*Log[d + e*x]))/(e^7*(a + b*x)*(d + e*x)^3)","A",1
2002,1,318,344,0.1465565,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^5} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^5,x]","-\frac{\sqrt{(a+b x)^2} \left(a^6 e^6+2 a^5 b e^5 (d+4 e x)+5 a^4 b^2 e^4 \left(d^2+4 d e x+6 e^2 x^2\right)+20 a^3 b^3 e^3 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)-5 a^2 b^4 d e^2 \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)+2 a b^5 e \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)-60 b^4 (d+e x)^4 (b d-a e)^2 \log (d+e x)+b^6 \left(-57 d^6-168 d^5 e x-132 d^4 e^2 x^2+32 d^3 e^3 x^3+68 d^2 e^4 x^4+12 d e^5 x^5-2 e^6 x^6\right)\right)}{4 e^7 (a+b x) (d+e x)^4}","-\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{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{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{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)}",1,"-1/4*(Sqrt[(a + b*x)^2]*(a^6*e^6 + 2*a^5*b*e^5*(d + 4*e*x) + 5*a^4*b^2*e^4*(d^2 + 4*d*e*x + 6*e^2*x^2) + 20*a^3*b^3*e^3*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) - 5*a^2*b^4*d*e^2*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3) + 2*a*b^5*e*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5) + b^6*(-57*d^6 - 168*d^5*e*x - 132*d^4*e^2*x^2 + 32*d^3*e^3*x^3 + 68*d^2*e^4*x^4 + 12*d*e^5*x^5 - 2*e^6*x^6) - 60*b^4*(b*d - a*e)^2*(d + e*x)^4*Log[d + e*x]))/(e^7*(a + b*x)*(d + e*x)^4)","A",1
2003,1,315,344,0.1573146,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^6} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^6,x]","-\frac{\sqrt{(a+b x)^2} \left(2 a^6 e^6+3 a^5 b e^5 (d+5 e x)+5 a^4 b^2 e^4 \left(d^2+5 d e x+10 e^2 x^2\right)+10 a^3 b^3 e^3 \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+30 a^2 b^4 e^2 \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)-a b^5 d e \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)+60 b^5 (d+e x)^5 (b d-a e) \log (d+e x)+b^6 \left(87 d^6+375 d^5 e x+600 d^4 e^2 x^2+400 d^3 e^3 x^3+50 d^2 e^4 x^4-50 d e^5 x^5-10 e^6 x^6\right)\right)}{10 e^7 (a+b x) (d+e x)^5}","-\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{b^6 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^6 (a+b x)}-\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{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}",1,"-1/10*(Sqrt[(a + b*x)^2]*(2*a^6*e^6 + 3*a^5*b*e^5*(d + 5*e*x) + 5*a^4*b^2*e^4*(d^2 + 5*d*e*x + 10*e^2*x^2) + 10*a^3*b^3*e^3*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 30*a^2*b^4*e^2*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4) - a*b^5*d*e*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4) + b^6*(87*d^6 + 375*d^5*e*x + 600*d^4*e^2*x^2 + 400*d^3*e^3*x^3 + 50*d^2*e^4*x^4 - 50*d*e^5*x^5 - 10*e^6*x^6) + 60*b^5*(b*d - a*e)*(d + e*x)^5*Log[d + e*x]))/(e^7*(a + b*x)*(d + e*x)^5)","A",1
2004,1,258,356,0.1712276,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^7} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^7,x]","\frac{\sqrt{(a+b x)^2} \left((b d-a e) \left(10 a^5 e^5+2 a^4 b e^4 (11 d+36 e x)+a^3 b^2 e^3 \left(37 d^2+162 d e x+225 e^2 x^2\right)+a^2 b^3 e^2 \left(57 d^3+282 d^2 e x+525 d e^2 x^2+400 e^3 x^3\right)+a b^4 e \left(87 d^4+462 d^3 e x+975 d^2 e^2 x^2+1000 d e^3 x^3+450 e^4 x^4\right)+b^5 \left(147 d^5+822 d^4 e x+1875 d^3 e^2 x^2+2200 d^2 e^3 x^3+1350 d e^4 x^4+360 e^5 x^5\right)\right)+60 b^6 (d+e x)^6 \log (d+e x)\right)}{60 e^7 (a+b x) (d+e x)^6}","-\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}",1,"(Sqrt[(a + b*x)^2]*((b*d - a*e)*(10*a^5*e^5 + 2*a^4*b*e^4*(11*d + 36*e*x) + a^3*b^2*e^3*(37*d^2 + 162*d*e*x + 225*e^2*x^2) + a^2*b^3*e^2*(57*d^3 + 282*d^2*e*x + 525*d*e^2*x^2 + 400*e^3*x^3) + a*b^4*e*(87*d^4 + 462*d^3*e*x + 975*d^2*e^2*x^2 + 1000*d*e^3*x^3 + 450*e^4*x^4) + b^5*(147*d^5 + 822*d^4*e*x + 1875*d^3*e^2*x^2 + 2200*d^2*e^3*x^3 + 1350*d*e^4*x^4 + 360*e^5*x^5)) + 60*b^6*(d + e*x)^6*Log[d + e*x]))/(60*e^7*(a + b*x)*(d + e*x)^6)","A",1
2005,1,289,41,0.1087558,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^8} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^8,x]","-\frac{\sqrt{(a+b x)^2} \left(a^6 e^6+a^5 b e^5 (d+7 e x)+a^4 b^2 e^4 \left(d^2+7 d e x+21 e^2 x^2\right)+a^3 b^3 e^3 \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+a^2 b^4 e^2 \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)+a b^5 e \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)+b^6 \left(d^6+7 d^5 e x+21 d^4 e^2 x^2+35 d^3 e^3 x^3+35 d^2 e^4 x^4+21 d e^5 x^5+7 e^6 x^6\right)\right)}{7 e^7 (a+b x) (d+e x)^7}","\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,"-1/7*(Sqrt[(a + b*x)^2]*(a^6*e^6 + a^5*b*e^5*(d + 7*e*x) + a^4*b^2*e^4*(d^2 + 7*d*e*x + 21*e^2*x^2) + a^3*b^3*e^3*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + a^2*b^4*e^2*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4) + a*b^5*e*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5) + b^6*(d^6 + 7*d^5*e*x + 21*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 35*d^2*e^4*x^4 + 21*d*e^5*x^5 + 7*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^7)","B",1
2006,1,295,98,0.1091715,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^9} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^9,x]","-\frac{\sqrt{(a+b x)^2} \left(7 a^6 e^6+6 a^5 b e^5 (d+8 e x)+5 a^4 b^2 e^4 \left(d^2+8 d e x+28 e^2 x^2\right)+4 a^3 b^3 e^3 \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+3 a^2 b^4 e^2 \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)+2 a b^5 e \left(d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right)+b^6 \left(d^6+8 d^5 e x+28 d^4 e^2 x^2+56 d^3 e^3 x^3+70 d^2 e^4 x^4+56 d e^5 x^5+28 e^6 x^6\right)\right)}{56 e^7 (a+b x) (d+e x)^8}","\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,"-1/56*(Sqrt[(a + b*x)^2]*(7*a^6*e^6 + 6*a^5*b*e^5*(d + 8*e*x) + 5*a^4*b^2*e^4*(d^2 + 8*d*e*x + 28*e^2*x^2) + 4*a^3*b^3*e^3*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + 3*a^2*b^4*e^2*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4) + 2*a*b^5*e*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5) + b^6*(d^6 + 8*d^5*e*x + 28*d^4*e^2*x^2 + 56*d^3*e^3*x^3 + 70*d^2*e^4*x^4 + 56*d*e^5*x^5 + 28*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^8)","B",1
2007,1,295,149,0.1090895,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{10}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^10,x]","-\frac{\sqrt{(a+b x)^2} \left(28 a^6 e^6+21 a^5 b e^5 (d+9 e x)+15 a^4 b^2 e^4 \left(d^2+9 d e x+36 e^2 x^2\right)+10 a^3 b^3 e^3 \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)+6 a^2 b^4 e^2 \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)+3 a b^5 e \left(d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right)+b^6 \left(d^6+9 d^5 e x+36 d^4 e^2 x^2+84 d^3 e^3 x^3+126 d^2 e^4 x^4+126 d e^5 x^5+84 e^6 x^6\right)\right)}{252 e^7 (a+b x) (d+e x)^9}","\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,"-1/252*(Sqrt[(a + b*x)^2]*(28*a^6*e^6 + 21*a^5*b*e^5*(d + 9*e*x) + 15*a^4*b^2*e^4*(d^2 + 9*d*e*x + 36*e^2*x^2) + 10*a^3*b^3*e^3*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 6*a^2*b^4*e^2*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4) + 3*a*b^5*e*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5) + b^6*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^9)","A",1
2008,1,295,200,0.105947,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{11}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^11,x]","-\frac{\sqrt{(a+b x)^2} \left(84 a^6 e^6+56 a^5 b e^5 (d+10 e x)+35 a^4 b^2 e^4 \left(d^2+10 d e x+45 e^2 x^2\right)+20 a^3 b^3 e^3 \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)+10 a^2 b^4 e^2 \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)+4 a b^5 e \left(d^5+10 d^4 e x+45 d^3 e^2 x^2+120 d^2 e^3 x^3+210 d e^4 x^4+252 e^5 x^5\right)+b^6 \left(d^6+10 d^5 e x+45 d^4 e^2 x^2+120 d^3 e^3 x^3+210 d^2 e^4 x^4+252 d e^5 x^5+210 e^6 x^6\right)\right)}{840 e^7 (a+b x) (d+e x)^{10}}","\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}",1,"-1/840*(Sqrt[(a + b*x)^2]*(84*a^6*e^6 + 56*a^5*b*e^5*(d + 10*e*x) + 35*a^4*b^2*e^4*(d^2 + 10*d*e*x + 45*e^2*x^2) + 20*a^3*b^3*e^3*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 10*a^2*b^4*e^2*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4) + 4*a*b^5*e*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5) + b^6*(d^6 + 10*d^5*e*x + 45*d^4*e^2*x^2 + 120*d^3*e^3*x^3 + 210*d^2*e^4*x^4 + 252*d*e^5*x^5 + 210*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^10)","A",1
2009,1,295,359,0.1055689,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{12}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^12,x]","-\frac{\sqrt{(a+b x)^2} \left(210 a^6 e^6+126 a^5 b e^5 (d+11 e x)+70 a^4 b^2 e^4 \left(d^2+11 d e x+55 e^2 x^2\right)+35 a^3 b^3 e^3 \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)+15 a^2 b^4 e^2 \left(d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right)+5 a b^5 e \left(d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right)+b^6 \left(d^6+11 d^5 e x+55 d^4 e^2 x^2+165 d^3 e^3 x^3+330 d^2 e^4 x^4+462 d e^5 x^5+462 e^6 x^6\right)\right)}{2310 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}{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}",1,"-1/2310*(Sqrt[(a + b*x)^2]*(210*a^6*e^6 + 126*a^5*b*e^5*(d + 11*e*x) + 70*a^4*b^2*e^4*(d^2 + 11*d*e*x + 55*e^2*x^2) + 35*a^3*b^3*e^3*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3) + 15*a^2*b^4*e^2*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4) + 5*a*b^5*e*(d^5 + 11*d^4*e*x + 55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*e^5*x^5) + b^6*(d^6 + 11*d^5*e*x + 55*d^4*e^2*x^2 + 165*d^3*e^3*x^3 + 330*d^2*e^4*x^4 + 462*d*e^5*x^5 + 462*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^11)","A",1
2010,1,295,362,0.100958,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{13}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^13,x]","-\frac{\sqrt{(a+b x)^2} \left(462 a^6 e^6+252 a^5 b e^5 (d+12 e x)+126 a^4 b^2 e^4 \left(d^2+12 d e x+66 e^2 x^2\right)+56 a^3 b^3 e^3 \left(d^3+12 d^2 e x+66 d e^2 x^2+220 e^3 x^3\right)+21 a^2 b^4 e^2 \left(d^4+12 d^3 e x+66 d^2 e^2 x^2+220 d e^3 x^3+495 e^4 x^4\right)+6 a b^5 e \left(d^5+12 d^4 e x+66 d^3 e^2 x^2+220 d^2 e^3 x^3+495 d e^4 x^4+792 e^5 x^5\right)+b^6 \left(d^6+12 d^5 e x+66 d^4 e^2 x^2+220 d^3 e^3 x^3+495 d^2 e^4 x^4+792 d e^5 x^5+924 e^6 x^6\right)\right)}{5544 e^7 (a+b x) (d+e x)^{12}}","-\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}",1,"-1/5544*(Sqrt[(a + b*x)^2]*(462*a^6*e^6 + 252*a^5*b*e^5*(d + 12*e*x) + 126*a^4*b^2*e^4*(d^2 + 12*d*e*x + 66*e^2*x^2) + 56*a^3*b^3*e^3*(d^3 + 12*d^2*e*x + 66*d*e^2*x^2 + 220*e^3*x^3) + 21*a^2*b^4*e^2*(d^4 + 12*d^3*e*x + 66*d^2*e^2*x^2 + 220*d*e^3*x^3 + 495*e^4*x^4) + 6*a*b^5*e*(d^5 + 12*d^4*e*x + 66*d^3*e^2*x^2 + 220*d^2*e^3*x^3 + 495*d*e^4*x^4 + 792*e^5*x^5) + b^6*(d^6 + 12*d^5*e*x + 66*d^4*e^2*x^2 + 220*d^3*e^3*x^3 + 495*d^2*e^4*x^4 + 792*d*e^5*x^5 + 924*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^12)","A",1
2011,1,295,360,0.1154243,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{14}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^14,x]","-\frac{\sqrt{(a+b x)^2} \left(924 a^6 e^6+462 a^5 b e^5 (d+13 e x)+210 a^4 b^2 e^4 \left(d^2+13 d e x+78 e^2 x^2\right)+84 a^3 b^3 e^3 \left(d^3+13 d^2 e x+78 d e^2 x^2+286 e^3 x^3\right)+28 a^2 b^4 e^2 \left(d^4+13 d^3 e x+78 d^2 e^2 x^2+286 d e^3 x^3+715 e^4 x^4\right)+7 a b^5 e \left(d^5+13 d^4 e x+78 d^3 e^2 x^2+286 d^2 e^3 x^3+715 d e^4 x^4+1287 e^5 x^5\right)+b^6 \left(d^6+13 d^5 e x+78 d^4 e^2 x^2+286 d^3 e^3 x^3+715 d^2 e^4 x^4+1287 d e^5 x^5+1716 e^6 x^6\right)\right)}{12012 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}{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}}",1,"-1/12012*(Sqrt[(a + b*x)^2]*(924*a^6*e^6 + 462*a^5*b*e^5*(d + 13*e*x) + 210*a^4*b^2*e^4*(d^2 + 13*d*e*x + 78*e^2*x^2) + 84*a^3*b^3*e^3*(d^3 + 13*d^2*e*x + 78*d*e^2*x^2 + 286*e^3*x^3) + 28*a^2*b^4*e^2*(d^4 + 13*d^3*e*x + 78*d^2*e^2*x^2 + 286*d*e^3*x^3 + 715*e^4*x^4) + 7*a*b^5*e*(d^5 + 13*d^4*e*x + 78*d^3*e^2*x^2 + 286*d^2*e^3*x^3 + 715*d*e^4*x^4 + 1287*e^5*x^5) + b^6*(d^6 + 13*d^5*e*x + 78*d^4*e^2*x^2 + 286*d^3*e^3*x^3 + 715*d^2*e^4*x^4 + 1287*d*e^5*x^5 + 1716*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^13)","A",1
2012,1,295,362,0.1091756,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{15}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^15,x]","-\frac{\sqrt{(a+b x)^2} \left(1716 a^6 e^6+792 a^5 b e^5 (d+14 e x)+330 a^4 b^2 e^4 \left(d^2+14 d e x+91 e^2 x^2\right)+120 a^3 b^3 e^3 \left(d^3+14 d^2 e x+91 d e^2 x^2+364 e^3 x^3\right)+36 a^2 b^4 e^2 \left(d^4+14 d^3 e x+91 d^2 e^2 x^2+364 d e^3 x^3+1001 e^4 x^4\right)+8 a b^5 e \left(d^5+14 d^4 e x+91 d^3 e^2 x^2+364 d^2 e^3 x^3+1001 d e^4 x^4+2002 e^5 x^5\right)+b^6 \left(d^6+14 d^5 e x+91 d^4 e^2 x^2+364 d^3 e^3 x^3+1001 d^2 e^4 x^4+2002 d e^5 x^5+3003 e^6 x^6\right)\right)}{24024 e^7 (a+b x) (d+e x)^{14}}","-\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}}",1,"-1/24024*(Sqrt[(a + b*x)^2]*(1716*a^6*e^6 + 792*a^5*b*e^5*(d + 14*e*x) + 330*a^4*b^2*e^4*(d^2 + 14*d*e*x + 91*e^2*x^2) + 120*a^3*b^3*e^3*(d^3 + 14*d^2*e*x + 91*d*e^2*x^2 + 364*e^3*x^3) + 36*a^2*b^4*e^2*(d^4 + 14*d^3*e*x + 91*d^2*e^2*x^2 + 364*d*e^3*x^3 + 1001*e^4*x^4) + 8*a*b^5*e*(d^5 + 14*d^4*e*x + 91*d^3*e^2*x^2 + 364*d^2*e^3*x^3 + 1001*d*e^4*x^4 + 2002*e^5*x^5) + b^6*(d^6 + 14*d^5*e*x + 91*d^4*e^2*x^2 + 364*d^3*e^3*x^3 + 1001*d^2*e^4*x^4 + 2002*d*e^5*x^5 + 3003*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^14)","A",1
2013,1,295,362,0.1154104,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{16}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^16,x]","-\frac{\sqrt{(a+b x)^2} \left(3003 a^6 e^6+1287 a^5 b e^5 (d+15 e x)+495 a^4 b^2 e^4 \left(d^2+15 d e x+105 e^2 x^2\right)+165 a^3 b^3 e^3 \left(d^3+15 d^2 e x+105 d e^2 x^2+455 e^3 x^3\right)+45 a^2 b^4 e^2 \left(d^4+15 d^3 e x+105 d^2 e^2 x^2+455 d e^3 x^3+1365 e^4 x^4\right)+9 a b^5 e \left(d^5+15 d^4 e x+105 d^3 e^2 x^2+455 d^2 e^3 x^3+1365 d e^4 x^4+3003 e^5 x^5\right)+b^6 \left(d^6+15 d^5 e x+105 d^4 e^2 x^2+455 d^3 e^3 x^3+1365 d^2 e^4 x^4+3003 d e^5 x^5+5005 e^6 x^6\right)\right)}{45045 e^7 (a+b x) (d+e x)^{15}}","-\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}}",1,"-1/45045*(Sqrt[(a + b*x)^2]*(3003*a^6*e^6 + 1287*a^5*b*e^5*(d + 15*e*x) + 495*a^4*b^2*e^4*(d^2 + 15*d*e*x + 105*e^2*x^2) + 165*a^3*b^3*e^3*(d^3 + 15*d^2*e*x + 105*d*e^2*x^2 + 455*e^3*x^3) + 45*a^2*b^4*e^2*(d^4 + 15*d^3*e*x + 105*d^2*e^2*x^2 + 455*d*e^3*x^3 + 1365*e^4*x^4) + 9*a*b^5*e*(d^5 + 15*d^4*e*x + 105*d^3*e^2*x^2 + 455*d^2*e^3*x^3 + 1365*d*e^4*x^4 + 3003*e^5*x^5) + b^6*(d^6 + 15*d^5*e*x + 105*d^4*e^2*x^2 + 455*d^3*e^3*x^3 + 1365*d^2*e^4*x^4 + 3003*d*e^5*x^5 + 5005*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^15)","A",1
2014,1,295,362,0.1028328,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{17}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^17,x]","-\frac{\sqrt{(a+b x)^2} \left(5005 a^6 e^6+2002 a^5 b e^5 (d+16 e x)+715 a^4 b^2 e^4 \left(d^2+16 d e x+120 e^2 x^2\right)+220 a^3 b^3 e^3 \left(d^3+16 d^2 e x+120 d e^2 x^2+560 e^3 x^3\right)+55 a^2 b^4 e^2 \left(d^4+16 d^3 e x+120 d^2 e^2 x^2+560 d e^3 x^3+1820 e^4 x^4\right)+10 a b^5 e \left(d^5+16 d^4 e x+120 d^3 e^2 x^2+560 d^2 e^3 x^3+1820 d e^4 x^4+4368 e^5 x^5\right)+b^6 \left(d^6+16 d^5 e x+120 d^4 e^2 x^2+560 d^3 e^3 x^3+1820 d^2 e^4 x^4+4368 d e^5 x^5+8008 e^6 x^6\right)\right)}{80080 e^7 (a+b x) (d+e x)^{16}}","-\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}}",1,"-1/80080*(Sqrt[(a + b*x)^2]*(5005*a^6*e^6 + 2002*a^5*b*e^5*(d + 16*e*x) + 715*a^4*b^2*e^4*(d^2 + 16*d*e*x + 120*e^2*x^2) + 220*a^3*b^3*e^3*(d^3 + 16*d^2*e*x + 120*d*e^2*x^2 + 560*e^3*x^3) + 55*a^2*b^4*e^2*(d^4 + 16*d^3*e*x + 120*d^2*e^2*x^2 + 560*d*e^3*x^3 + 1820*e^4*x^4) + 10*a*b^5*e*(d^5 + 16*d^4*e*x + 120*d^3*e^2*x^2 + 560*d^2*e^3*x^3 + 1820*d*e^4*x^4 + 4368*e^5*x^5) + b^6*(d^6 + 16*d^5*e*x + 120*d^4*e^2*x^2 + 560*d^3*e^3*x^3 + 1820*d^2*e^4*x^4 + 4368*d*e^5*x^5 + 8008*e^6*x^6)))/(e^7*(a + b*x)*(d + e*x)^16)","A",1
2015,1,30,39,0.0156036,"\int \frac{(a+b x) (d+e x)^4}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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+b 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 + b*x)^2])","A",1
2016,1,30,39,0.0098874,"\int \frac{(a+b x) (d+e x)^3}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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+b 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 + b*x)^2])","A",1
2017,1,30,39,0.0098102,"\int \frac{(a+b x) (d+e x)^2}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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+b 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 + b*x)^2])","A",1
2018,1,28,62,0.011474,"\int \frac{(a+b x) (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((a + b*x)*(d + e*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x (a+b x) (2 d+e x)}{2 \sqrt{(a+b 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,"(x*(a + b*x)*(2*d + e*x))/(2*Sqrt[(a + b*x)^2])","A",1
2019,1,18,24,0.004056,"\int \frac{a+b x}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(a + b*x)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x (a+b x)}{\sqrt{(a+b x)^2}}","\frac{\sqrt{a^2+2 a b x+b^2 x^2}}{b}",1,"(x*(a + b*x))/Sqrt[(a + b*x)^2]","A",1
2020,1,26,35,0.0081072,"\int \frac{a+b x}{(d+e x) \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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+b 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 + b*x)^2])","A",1
2021,1,28,38,0.0099384,"\int \frac{a+b x}{(d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(a + b*x)/((d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{a+b x}{e \sqrt{(a+b x)^2} (d+e x)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x) (b d-a e)}",1,"-((a + b*x)/(e*Sqrt[(a + b*x)^2]*(d + e*x)))","A",1
2022,1,30,42,0.0106332,"\int \frac{a+b x}{(d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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+b 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,"-1/2*(a + b*x)/(e*Sqrt[(a + b*x)^2]*(d + e*x)^2)","A",1
2023,1,30,42,0.0112103,"\int \frac{a+b x}{(d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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+b 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,"-1/3*(a + b*x)/(e*Sqrt[(a + b*x)^2]*(d + e*x)^3)","A",1
2024,1,30,42,0.0122644,"\int \frac{a+b x}{(d+e x)^5 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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+b 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,"-1/4*(a + b*x)/(e*Sqrt[(a + b*x)^2]*(d + e*x)^4)","A",1
2025,1,170,210,0.0816838,"\int \frac{(a+b x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{-3 a^4 e^4+3 a^3 b e^3 (4 d+3 e x)+6 a^2 b^2 e^2 \left(-3 d^2-4 d e x+e^2 x^2\right)-2 a b^3 e \left(-6 d^3-9 d^2 e x+9 d e^2 x^2+e^3 x^3\right)-12 e (a+b x) (a e-b d)^3 \log (a+b x)+b^4 \left(-3 d^4+18 d^2 e^2 x^2+6 d e^3 x^3+e^4 x^4\right)}{3 b^5 \sqrt{(a+b 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{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{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}}",1,"(-3*a^4*e^4 + 3*a^3*b*e^3*(4*d + 3*e*x) + 6*a^2*b^2*e^2*(-3*d^2 - 4*d*e*x + e^2*x^2) - 2*a*b^3*e*(-6*d^3 - 9*d^2*e*x + 9*d*e^2*x^2 + e^3*x^3) + b^4*(-3*d^4 + 18*d^2*e^2*x^2 + 6*d*e^3*x^3 + e^4*x^4) - 12*e*(-(b*d) + a*e)^3*(a + b*x)*Log[a + b*x])/(3*b^5*Sqrt[(a + b*x)^2])","A",1
2026,1,120,162,0.0510901,"\int \frac{(a+b x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 a^3 e^3-2 a^2 b e^2 (3 d+2 e x)+3 a b^2 e \left(2 d^2+2 d e x-e^2 x^2\right)+6 e (a+b x) (b d-a e)^2 \log (a+b x)+b^3 \left(-2 d^3+6 d e^2 x^2+e^3 x^3\right)}{2 b^4 \sqrt{(a+b 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}}",1,"(2*a^3*e^3 - 2*a^2*b*e^2*(3*d + 2*e*x) + 3*a*b^2*e*(2*d^2 + 2*d*e*x - e^2*x^2) + b^3*(-2*d^3 + 6*d*e^2*x^2 + e^3*x^3) + 6*e*(b*d - a*e)^2*(a + b*x)*Log[a + b*x])/(2*b^4*Sqrt[(a + b*x)^2])","A",1
2027,1,74,106,0.0338968,"\int \frac{(a+b x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{-a^2 e^2+a b e (2 d+e x)-2 e (a+b x) (a e-b d) \log (a+b x)+b^2 \left(e^2 x^2-d^2\right)}{b^3 \sqrt{(a+b x)^2}}","-\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,"(-(a^2*e^2) + a*b*e*(2*d + e*x) + b^2*(-d^2 + e^2*x^2) - 2*e*(-(b*d) + a*e)*(a + b*x)*Log[a + b*x])/(b^3*Sqrt[(a + b*x)^2])","A",1
2028,1,36,67,0.0145356,"\int \frac{(a+b x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((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)+a e-b d}{b^2 \sqrt{(a+b 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,"(-(b*d) + a*e + e*(a + b*x)*Log[a + b*x])/(b^2*Sqrt[(a + b*x)^2])","A",1
2029,1,16,25,0.0066582,"\int \frac{a+b x}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{1}{b \sqrt{(a+b x)^2}}","-\frac{1}{b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(1/(b*Sqrt[(a + b*x)^2]))","A",1
2030,1,57,120,0.0361919,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(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 (d+e x)-e (a+b x) \log (a+b x)+a e-b d}{\sqrt{(a+b 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,"(-(b*d) + a*e - e*(a + b*x)*Log[a + b*x] + e*(a + b*x)*Log[d + e*x])/((b*d - a*e)^2*Sqrt[(a + b*x)^2])","A",1
2031,1,92,169,0.0650208,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(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) (a e+b (d+2 e x)))-2 b e (a+b x) (d+e x) \log (a+b x)+2 b e (a+b x) (d+e x) \log (d+e x)}{\sqrt{(a+b x)^2} (d+e x) (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*d - a*e)*(a*e + b*(d + 2*e*x))) - 2*b*e*(a + b*x)*(d + e*x)*Log[a + b*x] + 2*b*e*(a + b*x)*(d + e*x)*Log[d + e*x])/((b*d - a*e)^3*Sqrt[(a + b*x)^2]*(d + e*x))","A",1
2032,1,135,223,0.0950988,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{-(b d-a e) \left(-a^2 e^2+a b e (5 d+3 e x)+b^2 \left(2 d^2+9 d e x+6 e^2 x^2\right)\right)-6 b^2 e (a+b x) (d+e x)^2 \log (a+b x)+6 b^2 e (a+b x) (d+e x)^2 \log (d+e x)}{2 \sqrt{(a+b x)^2} (d+e 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*d - a*e)*(-(a^2*e^2) + a*b*e*(5*d + 3*e*x) + b^2*(2*d^2 + 9*d*e*x + 6*e^2*x^2))) - 6*b^2*e*(a + b*x)*(d + e*x)^2*Log[a + b*x] + 6*b^2*e*(a + b*x)*(d + e*x)^2*Log[d + e*x])/(2*(b*d - a*e)^4*Sqrt[(a + b*x)^2]*(d + e*x)^2)","A",1
2033,1,232,252,0.113895,"\int \frac{(a+b x) (d+e x)^5}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((a + b*x)*(d + e*x)^5)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{47 a^5 e^5+a^4 b e^4 (81 e x-130 d)+a^3 b^2 e^3 \left(110 d^2-270 d e x-9 e^2 x^2\right)-a^2 b^3 e^2 \left(20 d^3-270 d^2 e x+90 d e^2 x^2+63 e^3 x^3\right)-5 a b^4 e \left(d^4+12 d^3 e x-36 d^2 e^2 x^2-18 d e^3 x^3+3 e^4 x^4\right)+60 e^3 (a+b x)^3 (b d-a e)^2 \log (a+b x)+b^5 \left(-2 d^5-15 d^4 e x-60 d^3 e^2 x^2+30 d e^4 x^4+3 e^5 x^5\right)}{6 b^6 \left((a+b x)^2\right)^{3/2}}","-\frac{(d+e x)^5}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}+\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{20 e^2 (b d-a e)^3}{3 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{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{5 e^5 x^2 (a+b x)}{6 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(47*a^5*e^5 + a^4*b*e^4*(-130*d + 81*e*x) + a^3*b^2*e^3*(110*d^2 - 270*d*e*x - 9*e^2*x^2) - a^2*b^3*e^2*(20*d^3 - 270*d^2*e*x + 90*d*e^2*x^2 + 63*e^3*x^3) - 5*a*b^4*e*(d^4 + 12*d^3*e*x - 36*d^2*e^2*x^2 - 18*d*e^3*x^3 + 3*e^4*x^4) + b^5*(-2*d^5 - 15*d^4*e*x - 60*d^3*e^2*x^2 + 30*d*e^4*x^4 + 3*e^5*x^5) + 60*e^3*(b*d - a*e)^2*(a + b*x)^3*Log[a + b*x])/(6*b^6*((a + b*x)^2)^(3/2))","A",1
2034,1,170,201,0.0789651,"\int \frac{(a+b x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-13 a^4 e^4+a^3 b e^3 (22 d-27 e x)-3 a^2 b^2 e^2 \left(2 d^2-18 d e x+3 e^2 x^2\right)+a b^3 e \left(-2 d^3-18 d^2 e x+36 d e^2 x^2+9 e^3 x^3\right)-12 e^3 (a+b x)^3 (a e-b d) \log (a+b x)-\left(b^4 \left(d^4+6 d^3 e x+18 d^2 e^2 x^2-3 e^4 x^4\right)\right)}{3 b^5 \left((a+b x)^2\right)^{3/2}}","-\frac{(d+e x)^4}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}+\frac{4 e^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{4 e^2 (b d-a e)^2}{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{4 e^4 x (a+b x)}{3 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-13*a^4*e^4 + a^3*b*e^3*(22*d - 27*e*x) - 3*a^2*b^2*e^2*(2*d^2 - 18*d*e*x + 3*e^2*x^2) + a*b^3*e*(-2*d^3 - 18*d^2*e*x + 36*d*e^2*x^2 + 9*e^3*x^3) - b^4*(d^4 + 6*d^3*e*x + 18*d^2*e^2*x^2 - 3*e^4*x^4) - 12*e^3*(-(b*d) + a*e)*(a + b*x)^3*Log[a + b*x])/(3*b^5*((a + b*x)^2)^(3/2))","A",1
2035,1,91,154,0.0471683,"\int \frac{(a+b x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{6 e^3 (a+b x)^3 \log (a+b x)-(b d-a e) \left(11 a^2 e^2+a b e (5 d+27 e x)+b^2 \left(2 d^2+9 d e x+18 e^2 x^2\right)\right)}{6 b^4 \left((a+b x)^2\right)^{3/2}}","-\frac{(d+e x)^3}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\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{e^3 (a+b x) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-((b*d - a*e)*(11*a^2*e^2 + a*b*e*(5*d + 27*e*x) + b^2*(2*d^2 + 9*d*e*x + 18*e^2*x^2))) + 6*e^3*(a + b*x)^3*Log[a + b*x])/(6*b^4*((a + b*x)^2)^(3/2))","A",1
2036,1,60,41,0.0293973,"\int \frac{(a+b x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-a^2 e^2-a b e (d+3 e x)-\left(b^2 \left(d^2+3 d e x+3 e^2 x^2\right)\right)}{3 b^3 \left((a+b x)^2\right)^{3/2}}","-\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,"(-(a^2*e^2) - a*b*e*(d + 3*e*x) - b^2*(d^2 + 3*d*e*x + 3*e^2*x^2))/(3*b^3*((a + b*x)^2)^(3/2))","A",1
2037,1,32,68,0.0187706,"\int \frac{(a+b x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((a + b*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{-a e-2 b d-3 b e x}{6 b^2 \left((a+b x)^2\right)^{3/2}}","-\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,"(-2*b*d - a*e - 3*b*e*x)/(6*b^2*((a + b*x)^2)^(3/2))","A",1
2038,1,18,27,0.0081593,"\int \frac{a+b x}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{1}{3 b \left((a+b 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*1/(b*((a + b*x)^2)^(3/2))","A",1
2039,1,116,210,0.08462,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{-(b d-a e) \left(11 a^2 e^2+a b e (15 e x-7 d)+b^2 \left(2 d^2-3 d e x+6 e^2 x^2\right)\right)+6 e^3 (a+b x)^3 \log (d+e x)-6 e^3 (a+b x)^3 \log (a+b x)}{6 \left((a+b x)^2\right)^{3/2} (b d-a e)^4}","-\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}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\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,"(-((b*d - a*e)*(11*a^2*e^2 + a*b*e*(-7*d + 15*e*x) + b^2*(2*d^2 - 3*d*e*x + 6*e^2*x^2))) - 6*e^3*(a + b*x)^3*Log[a + b*x] + 6*e^3*(a + b*x)^3*Log[d + e*x])/(6*(b*d - a*e)^4*((a + b*x)^2)^(3/2))","A",1
2040,1,144,260,0.10469,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{\frac{3 e^3 (a+b x)^3 (a e-b d)}{d+e x}+12 b e^3 (a+b x)^3 \log (d+e x)-9 b e^2 (a+b x)^2 (b d-a e)+3 b e (a+b x) (b d-a e)^2-b (b d-a e)^3-12 b e^3 (a+b x)^3 \log (a+b x)}{3 \left((a+b x)^2\right)^{3/2} (b d-a e)^5}","-\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{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{3 b e^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\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,"(-(b*(b*d - a*e)^3) + 3*b*e*(b*d - a*e)^2*(a + b*x) - 9*b*e^2*(b*d - a*e)*(a + b*x)^2 + (3*e^3*(-(b*d) + a*e)*(a + b*x)^3)/(d + e*x) - 12*b*e^3*(a + b*x)^3*Log[a + b*x] + 12*b*e^3*(a + b*x)^3*Log[d + e*x])/(3*(b*d - a*e)^5*((a + b*x)^2)^(3/2))","A",1
2041,1,184,323,0.1199708,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{60 b^2 e^3 (a+b x)^3 \log (d+e x)-36 b^2 e^2 (a+b x)^2 (b d-a e)+9 b^2 e (a+b x) (b d-a e)^2-2 b^2 (b d-a e)^3-60 b^2 e^3 (a+b x)^3 \log (a+b x)-\frac{3 e^3 (a+b x)^3 (b d-a e)^2}{(d+e x)^2}-\frac{24 b e^3 (a+b x)^3 (b d-a e)}{d+e x}}{6 \left((a+b x)^2\right)^{3/2} (b d-a e)^6}","-\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{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{6 b^2 e^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\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,"(-2*b^2*(b*d - a*e)^3 + 9*b^2*e*(b*d - a*e)^2*(a + b*x) - 36*b^2*e^2*(b*d - a*e)*(a + b*x)^2 - (3*e^3*(b*d - a*e)^2*(a + b*x)^3)/(d + e*x)^2 - (24*b*e^3*(b*d - a*e)*(a + b*x)^3)/(d + e*x) - 60*b^2*e^3*(a + b*x)^3*Log[a + b*x] + 60*b^2*e^3*(a + b*x)^3*Log[d + e*x])/(6*(b*d - a*e)^6*((a + b*x)^2)^(3/2))","A",1
2042,1,79,100,0.0771765,"\int (a+b x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (d+e x)^{9/2} \left(-1485 b^2 (d+e x)^2 (b d-a e)+1755 b (d+e x) (b d-a e)^2-715 (b d-a e)^3+429 b^3 (d+e x)^3\right)}{6435 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*(d + e*x)^(9/2)*(-715*(b*d - a*e)^3 + 1755*b*(b*d - a*e)^2*(d + e*x) - 1485*b^2*(b*d - a*e)*(d + e*x)^2 + 429*b^3*(d + e*x)^3))/(6435*e^4)","A",1
2043,1,79,100,0.0622558,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (d+e x)^{7/2} \left(-819 b^2 (d+e x)^2 (b d-a e)+1001 b (d+e x) (b d-a e)^2-429 (b d-a e)^3+231 b^3 (d+e x)^3\right)}{3003 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*(d + e*x)^(7/2)*(-429*(b*d - a*e)^3 + 1001*b*(b*d - a*e)^2*(d + e*x) - 819*b^2*(b*d - a*e)*(d + e*x)^2 + 231*b^3*(d + e*x)^3))/(3003*e^4)","A",1
2044,1,79,100,0.057093,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (d+e x)^{5/2} \left(-385 b^2 (d+e x)^2 (b d-a e)+495 b (d+e x) (b d-a e)^2-231 (b d-a e)^3+105 b^3 (d+e x)^3\right)}{1155 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*(d + e*x)^(5/2)*(-231*(b*d - a*e)^3 + 495*b*(b*d - a*e)^2*(d + e*x) - 385*b^2*(b*d - a*e)*(d + e*x)^2 + 105*b^3*(d + e*x)^3))/(1155*e^4)","A",1
2045,1,79,100,0.0542939,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (d+e x)^{3/2} \left(-135 b^2 (d+e x)^2 (b d-a e)+189 b (d+e x) (b d-a e)^2-105 (b d-a e)^3+35 b^3 (d+e x)^3\right)}{315 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*(d + e*x)^(3/2)*(-105*(b*d - a*e)^3 + 189*b*(b*d - a*e)^2*(d + e*x) - 135*b^2*(b*d - a*e)*(d + e*x)^2 + 35*b^3*(d + e*x)^3))/(315*e^4)","A",1
2046,1,79,96,0.0476298,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-21 b^2 (d+e x)^2 (b d-a e)+35 b (d+e x) (b d-a e)^2-35 (b d-a e)^3+5 b^3 (d+e x)^3\right)}{35 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*Sqrt[d + e*x]*(-35*(b*d - a*e)^3 + 35*b*(b*d - a*e)^2*(d + e*x) - 21*b^2*(b*d - a*e)*(d + e*x)^2 + 5*b^3*(d + e*x)^3))/(35*e^4)","A",1
2047,1,78,94,0.0492618,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{3/2}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(3/2),x]","\frac{2 \left(-5 b^2 (d+e x)^2 (b d-a e)+15 b (d+e x) (b d-a e)^2+5 (b d-a e)^3+b^3 (d+e x)^3\right)}{5 e^4 \sqrt{d+e 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}",1,"(2*(5*(b*d - a*e)^3 + 15*b*(b*d - a*e)^2*(d + e*x) - 5*b^2*(b*d - a*e)*(d + e*x)^2 + b^3*(d + e*x)^3))/(5*e^4*Sqrt[d + e*x])","A",1
2048,1,76,96,0.0508932,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{5/2}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(5/2),x]","\frac{2 \left(-9 b^2 (d+e x)^2 (b d-a e)-9 b (d+e x) (b d-a e)^2+(b d-a e)^3+b^3 (d+e x)^3\right)}{3 e^4 (d+e x)^{3/2}}","-\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 - 9*b*(b*d - a*e)^2*(d + e*x) - 9*b^2*(b*d - a*e)*(d + e*x)^2 + b^3*(d + e*x)^3))/(3*e^4*(d + e*x)^(3/2))","A",1
2049,1,77,94,0.0500875,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{7/2}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(7/2),x]","\frac{2 \left(15 b^2 (d+e x)^2 (b d-a e)-5 b (d+e x) (b d-a e)^2+(b d-a e)^3+5 b^3 (d+e x)^3\right)}{5 e^4 (d+e x)^{5/2}}","\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*b*(b*d - a*e)^2*(d + e*x) + 15*b^2*(b*d - a*e)*(d + e*x)^2 + 5*b^3*(d + e*x)^3))/(5*e^4*(d + e*x)^(5/2))","A",1
2050,1,123,158,0.1073097,"\int (a+b x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 (d+e x)^{9/2} \left(-122265 b^4 (d+e x)^4 (b d-a e)+277134 b^3 (d+e x)^3 (b d-a e)^2-319770 b^2 (d+e x)^2 (b d-a e)^3+188955 b (d+e x) (b d-a e)^4-46189 (b d-a e)^5+21879 b^5 (d+e x)^5\right)}{415701 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*(d + e*x)^(9/2)*(-46189*(b*d - a*e)^5 + 188955*b*(b*d - a*e)^4*(d + e*x) - 319770*b^2*(b*d - a*e)^3*(d + e*x)^2 + 277134*b^3*(b*d - a*e)^2*(d + e*x)^3 - 122265*b^4*(b*d - a*e)*(d + e*x)^4 + 21879*b^5*(d + e*x)^5))/(415701*e^6)","A",1
2051,1,123,158,0.0801434,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 (d+e x)^{7/2} \left(-51051 b^4 (d+e x)^4 (b d-a e)+117810 b^3 (d+e x)^3 (b d-a e)^2-139230 b^2 (d+e x)^2 (b d-a e)^3+85085 b (d+e x) (b d-a e)^4-21879 (b d-a e)^5+9009 b^5 (d+e x)^5\right)}{153153 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*(d + e*x)^(7/2)*(-21879*(b*d - a*e)^5 + 85085*b*(b*d - a*e)^4*(d + e*x) - 139230*b^2*(b*d - a*e)^3*(d + e*x)^2 + 117810*b^3*(b*d - a*e)^2*(d + e*x)^3 - 51051*b^4*(b*d - a*e)*(d + e*x)^4 + 9009*b^5*(d + e*x)^5))/(153153*e^6)","A",1
2052,1,123,158,0.1111255,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 (d+e x)^{5/2} \left(-17325 b^4 (d+e x)^4 (b d-a e)+40950 b^3 (d+e x)^3 (b d-a e)^2-50050 b^2 (d+e x)^2 (b d-a e)^3+32175 b (d+e x) (b d-a e)^4-9009 (b d-a e)^5+3003 b^5 (d+e x)^5\right)}{45045 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*(d + e*x)^(5/2)*(-9009*(b*d - a*e)^5 + 32175*b*(b*d - a*e)^4*(d + e*x) - 50050*b^2*(b*d - a*e)^3*(d + e*x)^2 + 40950*b^3*(b*d - a*e)^2*(d + e*x)^3 - 17325*b^4*(b*d - a*e)*(d + e*x)^4 + 3003*b^5*(d + e*x)^5))/(45045*e^6)","A",1
2053,1,123,156,0.1053198,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 (d+e x)^{3/2} \left(-4095 b^4 (d+e x)^4 (b d-a e)+10010 b^3 (d+e x)^3 (b d-a e)^2-12870 b^2 (d+e x)^2 (b d-a e)^3+9009 b (d+e x) (b d-a e)^4-3003 (b d-a e)^5+693 b^5 (d+e x)^5\right)}{9009 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*(d + e*x)^(3/2)*(-3003*(b*d - a*e)^5 + 9009*b*(b*d - a*e)^4*(d + e*x) - 12870*b^2*(b*d - a*e)^3*(d + e*x)^2 + 10010*b^3*(b*d - a*e)^2*(d + e*x)^3 - 4095*b^4*(b*d - a*e)*(d + e*x)^4 + 693*b^5*(d + e*x)^5))/(9009*e^6)","A",1
2054,1,123,154,0.0655224,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-385 b^4 (d+e x)^4 (b d-a e)+990 b^3 (d+e x)^3 (b d-a e)^2-1386 b^2 (d+e x)^2 (b d-a e)^3+1155 b (d+e x) (b d-a e)^4-693 (b d-a e)^5+63 b^5 (d+e x)^5\right)}{693 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*Sqrt[d + e*x]*(-693*(b*d - a*e)^5 + 1155*b*(b*d - a*e)^4*(d + e*x) - 1386*b^2*(b*d - a*e)^3*(d + e*x)^2 + 990*b^3*(b*d - a*e)^2*(d + e*x)^3 - 385*b^4*(b*d - a*e)*(d + e*x)^4 + 63*b^5*(d + e*x)^5))/(693*e^6)","A",1
2055,1,123,152,0.0904064,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{3/2}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(3/2),x]","\frac{2 \left(-45 b^4 (d+e x)^4 (b d-a e)+126 b^3 (d+e x)^3 (b d-a e)^2-210 b^2 (d+e x)^2 (b d-a e)^3+315 b (d+e x) (b d-a e)^4+63 (b d-a e)^5+7 b^5 (d+e x)^5\right)}{63 e^6 \sqrt{d+e 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}",1,"(2*(63*(b*d - a*e)^5 + 315*b*(b*d - a*e)^4*(d + e*x) - 210*b^2*(b*d - a*e)^3*(d + e*x)^2 + 126*b^3*(b*d - a*e)^2*(d + e*x)^3 - 45*b^4*(b*d - a*e)*(d + e*x)^4 + 7*b^5*(d + e*x)^5))/(63*e^6*Sqrt[d + e*x])","A",1
2056,1,123,152,0.0901022,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{5/2}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(5/2),x]","\frac{2 \left(-21 b^4 (d+e x)^4 (b d-a e)+70 b^3 (d+e x)^3 (b d-a e)^2-210 b^2 (d+e x)^2 (b d-a e)^3-105 b (d+e x) (b d-a e)^4+7 (b d-a e)^5+3 b^5 (d+e x)^5\right)}{21 e^6 (d+e x)^{3/2}}","-\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*(7*(b*d - a*e)^5 - 105*b*(b*d - a*e)^4*(d + e*x) - 210*b^2*(b*d - a*e)^3*(d + e*x)^2 + 70*b^3*(b*d - a*e)^2*(d + e*x)^3 - 21*b^4*(b*d - a*e)*(d + e*x)^4 + 3*b^5*(d + e*x)^5))/(21*e^6*(d + e*x)^(3/2))","A",1
2057,1,123,154,0.0936125,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{7/2}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(7/2),x]","\frac{2 \left(-25 b^4 (d+e x)^4 (b d-a e)+150 b^3 (d+e x)^3 (b d-a e)^2+150 b^2 (d+e x)^2 (b d-a e)^3-25 b (d+e x) (b d-a e)^4+3 (b d-a e)^5+3 b^5 (d+e x)^5\right)}{15 e^6 (d+e x)^{5/2}}","-\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*(3*(b*d - a*e)^5 - 25*b*(b*d - a*e)^4*(d + e*x) + 150*b^2*(b*d - a*e)^3*(d + e*x)^2 + 150*b^3*(b*d - a*e)^2*(d + e*x)^3 - 25*b^4*(b*d - a*e)*(d + e*x)^4 + 3*b^5*(d + e*x)^5))/(15*e^6*(d + e*x)^(5/2))","A",1
2058,1,167,216,0.1753561,"\int (a+b x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 (d+e x)^{9/2} \left(-3187041 b^6 (d+e x)^6 (b d-a e)+10567557 b^5 (d+e x)^5 (b d-a e)^2-19684665 b^4 (d+e x)^4 (b d-a e)^3+22309287 b^3 (d+e x)^3 (b d-a e)^4-15444891 b^2 (d+e x)^2 (b d-a e)^5+6084351 b (d+e x) (b d-a e)^6-1062347 (b d-a e)^7+415701 b^7 (d+e x)^7\right)}{9561123 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*(d + e*x)^(9/2)*(-1062347*(b*d - a*e)^7 + 6084351*b*(b*d - a*e)^6*(d + e*x) - 15444891*b^2*(b*d - a*e)^5*(d + e*x)^2 + 22309287*b^3*(b*d - a*e)^4*(d + e*x)^3 - 19684665*b^4*(b*d - a*e)^3*(d + e*x)^4 + 10567557*b^5*(b*d - a*e)^2*(d + e*x)^5 - 3187041*b^6*(b*d - a*e)*(d + e*x)^6 + 415701*b^7*(d + e*x)^7))/(9561123*e^8)","A",1
2059,1,167,216,0.1304732,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 (d+e x)^{7/2} \left(-1072071 b^6 (d+e x)^6 (b d-a e)+3594591 b^5 (d+e x)^5 (b d-a e)^2-6789783 b^4 (d+e x)^4 (b d-a e)^3+7834365 b^3 (d+e x)^3 (b d-a e)^4-5555277 b^2 (d+e x)^2 (b d-a e)^5+2263261 b (d+e x) (b d-a e)^6-415701 (b d-a e)^7+138567 b^7 (d+e x)^7\right)}{2909907 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*(d + e*x)^(7/2)*(-415701*(b*d - a*e)^7 + 2263261*b*(b*d - a*e)^6*(d + e*x) - 5555277*b^2*(b*d - a*e)^5*(d + e*x)^2 + 7834365*b^3*(b*d - a*e)^4*(d + e*x)^3 - 6789783*b^4*(b*d - a*e)^3*(d + e*x)^4 + 3594591*b^5*(b*d - a*e)^2*(d + e*x)^5 - 1072071*b^6*(b*d - a*e)*(d + e*x)^6 + 138567*b^7*(d + e*x)^7))/(2909907*e^8)","A",1
2060,1,167,214,0.1226832,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 (d+e x)^{5/2} \left(-285285 b^6 (d+e x)^6 (b d-a e)+969969 b^5 (d+e x)^5 (b d-a e)^2-1865325 b^4 (d+e x)^4 (b d-a e)^3+2204475 b^3 (d+e x)^3 (b d-a e)^4-1616615 b^2 (d+e x)^2 (b d-a e)^5+692835 b (d+e x) (b d-a e)^6-138567 (b d-a e)^7+36465 b^7 (d+e x)^7\right)}{692835 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*(d + e*x)^(5/2)*(-138567*(b*d - a*e)^7 + 692835*b*(b*d - a*e)^6*(d + e*x) - 1616615*b^2*(b*d - a*e)^5*(d + e*x)^2 + 2204475*b^3*(b*d - a*e)^4*(d + e*x)^3 - 1865325*b^4*(b*d - a*e)^3*(d + e*x)^4 + 969969*b^5*(b*d - a*e)^2*(d + e*x)^5 - 285285*b^6*(b*d - a*e)*(d + e*x)^6 + 36465*b^7*(d + e*x)^7))/(692835*e^8)","A",1
2061,1,167,214,0.1142617,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 (d+e x)^{3/2} \left(-51051 b^6 (d+e x)^6 (b d-a e)+176715 b^5 (d+e x)^5 (b d-a e)^2-348075 b^4 (d+e x)^4 (b d-a e)^3+425425 b^3 (d+e x)^3 (b d-a e)^4-328185 b^2 (d+e x)^2 (b d-a e)^5+153153 b (d+e x) (b d-a e)^6-36465 (b d-a e)^7+6435 b^7 (d+e x)^7\right)}{109395 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*(d + e*x)^(3/2)*(-36465*(b*d - a*e)^7 + 153153*b*(b*d - a*e)^6*(d + e*x) - 328185*b^2*(b*d - a*e)^5*(d + e*x)^2 + 425425*b^3*(b*d - a*e)^4*(d + e*x)^3 - 348075*b^4*(b*d - a*e)^3*(d + e*x)^4 + 176715*b^5*(b*d - a*e)^2*(d + e*x)^5 - 51051*b^6*(b*d - a*e)*(d + e*x)^6 + 6435*b^7*(d + e*x)^7))/(109395*e^8)","A",1
2062,1,167,212,0.0979332,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-3465 b^6 (d+e x)^6 (b d-a e)+12285 b^5 (d+e x)^5 (b d-a e)^2-25025 b^4 (d+e x)^4 (b d-a e)^3+32175 b^3 (d+e x)^3 (b d-a e)^4-27027 b^2 (d+e x)^2 (b d-a e)^5+15015 b (d+e x) (b d-a e)^6-6435 (b d-a e)^7+429 b^7 (d+e x)^7\right)}{6435 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*Sqrt[d + e*x]*(-6435*(b*d - a*e)^7 + 15015*b*(b*d - a*e)^6*(d + e*x) - 27027*b^2*(b*d - a*e)^5*(d + e*x)^2 + 32175*b^3*(b*d - a*e)^4*(d + e*x)^3 - 25025*b^4*(b*d - a*e)^3*(d + e*x)^4 + 12285*b^5*(b*d - a*e)^2*(d + e*x)^5 - 3465*b^6*(b*d - a*e)*(d + e*x)^6 + 429*b^7*(d + e*x)^7))/(6435*e^8)","A",1
2063,1,167,206,0.0960798,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{3/2}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(3/2),x]","\frac{2 \left(-273 b^6 (d+e x)^6 (b d-a e)+1001 b^5 (d+e x)^5 (b d-a e)^2-2145 b^4 (d+e x)^4 (b d-a e)^3+3003 b^3 (d+e x)^3 (b d-a e)^4-3003 b^2 (d+e x)^2 (b d-a e)^5+3003 b (d+e x) (b d-a e)^6+429 (b d-a e)^7+33 b^7 (d+e x)^7\right)}{429 e^8 \sqrt{d+e 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}",1,"(2*(429*(b*d - a*e)^7 + 3003*b*(b*d - a*e)^6*(d + e*x) - 3003*b^2*(b*d - a*e)^5*(d + e*x)^2 + 3003*b^3*(b*d - a*e)^4*(d + e*x)^3 - 2145*b^4*(b*d - a*e)^3*(d + e*x)^4 + 1001*b^5*(b*d - a*e)^2*(d + e*x)^5 - 273*b^6*(b*d - a*e)*(d + e*x)^6 + 33*b^7*(d + e*x)^7))/(429*e^8*Sqrt[d + e*x])","A",1
2064,1,167,208,0.0984243,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{5/2}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(5/2),x]","\frac{2 \left(-77 b^6 (d+e x)^6 (b d-a e)+297 b^5 (d+e x)^5 (b d-a e)^2-693 b^4 (d+e x)^4 (b d-a e)^3+1155 b^3 (d+e x)^3 (b d-a e)^4-2079 b^2 (d+e x)^2 (b d-a e)^5-693 b (d+e x) (b d-a e)^6+33 (b d-a e)^7+9 b^7 (d+e x)^7\right)}{99 e^8 (d+e x)^{3/2}}","-\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*(33*(b*d - a*e)^7 - 693*b*(b*d - a*e)^6*(d + e*x) - 2079*b^2*(b*d - a*e)^5*(d + e*x)^2 + 1155*b^3*(b*d - a*e)^4*(d + e*x)^3 - 693*b^4*(b*d - a*e)^3*(d + e*x)^4 + 297*b^5*(b*d - a*e)^2*(d + e*x)^5 - 77*b^6*(b*d - a*e)*(d + e*x)^6 + 9*b^7*(d + e*x)^7))/(99*e^8*(d + e*x)^(3/2))","A",1
2065,1,167,210,0.1038711,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{7/2}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(7/2),x]","\frac{2 \left(-45 b^6 (d+e x)^6 (b d-a e)+189 b^5 (d+e x)^5 (b d-a e)^2-525 b^4 (d+e x)^4 (b d-a e)^3+1575 b^3 (d+e x)^3 (b d-a e)^4+945 b^2 (d+e x)^2 (b d-a e)^5-105 b (d+e x) (b d-a e)^6+9 (b d-a e)^7+5 b^7 (d+e x)^7\right)}{45 e^8 (d+e x)^{5/2}}","-\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*(9*(b*d - a*e)^7 - 105*b*(b*d - a*e)^6*(d + e*x) + 945*b^2*(b*d - a*e)^5*(d + e*x)^2 + 1575*b^3*(b*d - a*e)^4*(d + e*x)^3 - 525*b^4*(b*d - a*e)^3*(d + e*x)^4 + 189*b^5*(b*d - a*e)^2*(d + e*x)^5 - 45*b^6*(b*d - a*e)*(d + e*x)^6 + 5*b^7*(d + e*x)^7))/(45*e^8*(d + e*x)^(5/2))","A",1
2066,1,132,138,0.2159081,"\int \frac{(a+b x) (d+e x)^{7/2}}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (b d-a e) \left(5 (b d-a e) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)+3 b^{5/2} (d+e x)^{5/2}\right)}{15 b^{9/2}}+\frac{2 (d+e x)^{7/2}}{7 b}","-\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 \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 (d+e x)^{7/2}}{7 b}",1,"(2*(d + e*x)^(7/2))/(7*b) + (2*(b*d - a*e)*(3*b^(5/2)*(d + e*x)^(5/2) + 5*(b*d - a*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])))/(15*b^(9/2))","A",1
2067,1,105,112,0.1150356,"\int \frac{(a+b x) (d+e x)^{5/2}}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 (b d-a e) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)}{3 b^{7/2}}+\frac{2 (d+e x)^{5/2}}{5 b}","-\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 \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 (d+e x)^{5/2}}{5 b}",1,"(2*(d + e*x)^(5/2))/(5*b) + (2*(b*d - a*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/(3*b^(7/2))","A",1
2068,1,77,86,0.0556743,"\int \frac{(a+b x) (d+e x)^{3/2}}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((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} (-3 a e+4 b d+b e x)}{3 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 (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 \sqrt{d+e x} (b d-a e)}{b^2}+\frac{2 (d+e x)^{3/2}}{3 b}",1,"(2*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x))/(3*b^2) - (2*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(5/2)","A",1
2069,1,62,62,0.0244779,"\int \frac{(a+b x) \sqrt{d+e x}}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((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",1
2070,1,47,47,0.0116215,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(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",1
2071,1,46,69,0.0104584,"\int \frac{a+b x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{\sqrt{d+e x} (a e-b d)}","\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*Hypergeometric2F1[-1/2, 1, 1/2, (b*(d + e*x))/(b*d - a*e)])/((-(b*d) + a*e)*Sqrt[d + e*x])","C",1
2072,1,48,93,0.0097127,"\int \frac{a+b x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{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*Hypergeometric2F1[-3/2, 1, -1/2, (b*(d + e*x))/(b*d - a*e)])/(3*(b*d - a*e)*(d + e*x)^(3/2))","C",1
2073,1,48,119,0.0106373,"\int \frac{a+b x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Integrate[(a + b*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{2 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{5 (d+e x)^{5/2} (b d-a e)}","-\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^2}{\sqrt{d+e x} (b d-a e)^3}+\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*Hypergeometric2F1[-5/2, 1, -3/2, (b*(d + e*x))/(b*d - a*e)])/(5*(b*d - a*e)*(d + e*x)^(5/2))","C",1
2074,1,52,175,0.0213808,"\int \frac{(a+b x) (d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((a + b*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 e^2 (d+e x)^{11/2} \, _2F_1\left(3,\frac{11}{2};\frac{13}{2};-\frac{b (d+e x)}{a e-b d}\right)}{11 (a e-b d)^3}","-\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{63 e^2 \sqrt{d+e x} (b d-a e)^2}{4 b^5}+\frac{21 e^2 (d+e x)^{3/2} (b d-a e)}{4 b^4}-\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,"(2*e^2*(d + e*x)^(11/2)*Hypergeometric2F1[3, 11/2, 13/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(11*(-(b*d) + a*e)^3)","C",1
2075,1,52,146,0.0175165,"\int \frac{(a+b x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 e^2 (d+e x)^{9/2} \, _2F_1\left(3,\frac{9}{2};\frac{11}{2};-\frac{b (d+e x)}{a e-b d}\right)}{9 (a e-b d)^3}","-\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{35 e^2 \sqrt{d+e x} (b d-a e)}{4 b^4}-\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,"(2*e^2*(d + e*x)^(9/2)*Hypergeometric2F1[3, 9/2, 11/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(9*(-(b*d) + a*e)^3)","C",1
2076,1,52,119,0.0160897,"\int \frac{(a+b x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 e^2 (d+e x)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};-\frac{b (d+e x)}{a e-b d}\right)}{7 (a e-b d)^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,"(2*e^2*(d + e*x)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(7*(-(b*d) + a*e)^3)","C",1
2077,1,90,100,0.0917321,"\int \frac{(a+b x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((a + b*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{3 e^2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)}{4 b^{5/2} \sqrt{a e-b d}}-\frac{\sqrt{d+e x} (3 a e+2 b d+5 b e x)}{4 b^2 (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,"-1/4*(Sqrt[d + e*x]*(2*b*d + 3*a*e + 5*b*e*x))/(b^2*(a + b*x)^2) + (3*e^2*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]])/(4*b^(5/2)*Sqrt[-(b*d) + a*e])","A",1
2078,1,52,110,0.0131524,"\int \frac{(a+b x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((a + b*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 e^2 (d+e x)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};-\frac{b (d+e x)}{a e-b d}\right)}{3 (a e-b d)^3}","\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,"(2*e^2*(d + e*x)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(3*(-(b*d) + a*e)^3)","C",1
2079,1,50,114,0.0111816,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(a + b*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{2 e^2 \sqrt{d+e x} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};-\frac{b (d+e x)}{a e-b d}\right)}{(a e-b d)^3}","-\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,"(2*e^2*Sqrt[d + e*x]*Hypergeometric2F1[1/2, 3, 3/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(-(b*d) + a*e)^3","C",1
2080,1,50,140,0.0142859,"\int \frac{a+b x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{2 e^2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};-\frac{b (d+e x)}{a e-b d}\right)}{\sqrt{d+e x} (a e-b d)^3}","\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,"(-2*e^2*Hypergeometric2F1[-1/2, 3, 1/2, -((b*(d + e*x))/(-(b*d) + a*e))])/((-(b*d) + a*e)^3*Sqrt[d + e*x])","C",1
2081,1,52,167,0.0156639,"\int \frac{a+b x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{2 e^2 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};-\frac{b (d+e x)}{a e-b d}\right)}{3 (d+e x)^{3/2} (a e-b d)^3}","-\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,"(-2*e^2*Hypergeometric2F1[-3/2, 3, -1/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(3*(-(b*d) + a*e)^3*(d + e*x)^(3/2))","C",1
2082,1,52,196,0.0214247,"\int \frac{a+b x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[(a + b*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{2 e^2 \, _2F_1\left(-\frac{5}{2},3;-\frac{3}{2};-\frac{b (d+e x)}{a e-b d}\right)}{5 (d+e x)^{5/2} (a e-b d)^3}","-\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{63 b^2 e^2}{4 \sqrt{d+e x} (b d-a e)^5}+\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,"(-2*e^2*Hypergeometric2F1[-5/2, 3, -3/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(5*(-(b*d) + a*e)^3*(d + e*x)^(5/2))","C",1
2083,1,52,198,0.0257244,"\int \frac{(a+b x) (d+e x)^{11/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*(d + e*x)^(11/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 e^4 (d+e x)^{13/2} \, _2F_1\left(5,\frac{13}{2};\frac{15}{2};-\frac{b (d+e x)}{a e-b d}\right)}{13 (a e-b d)^5}","-\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{1155 e^4 \sqrt{d+e x} (b d-a e)}{64 b^6}-\frac{231 e^3 (d+e x)^{5/2}}{64 b^4 (a+b x)}-\frac{33 e^2 (d+e x)^{7/2}}{32 b^3 (a+b x)^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,"(2*e^4*(d + e*x)^(13/2)*Hypergeometric2F1[5, 13/2, 15/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(13*(-(b*d) + a*e)^5)","C",1
2084,1,52,171,0.0199759,"\int \frac{(a+b x) (d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 e^4 (d+e x)^{11/2} \, _2F_1\left(5,\frac{11}{2};\frac{13}{2};-\frac{b (d+e x)}{a e-b d}\right)}{11 (a e-b d)^5}","-\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{105 e^3 (d+e x)^{3/2}}{64 b^4 (a+b x)}-\frac{21 e^2 (d+e x)^{5/2}}{32 b^3 (a+b x)^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,"(2*e^4*(d + e*x)^(11/2)*Hypergeometric2F1[5, 11/2, 13/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(11*(-(b*d) + a*e)^5)","C",1
2085,1,152,152,0.2062335,"\int \frac{(a+b x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{35 e^4 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)}{64 b^{9/2} \sqrt{a e-b d}}-\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{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^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{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{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*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]])/(64*b^(9/2)*Sqrt[-(b*d) + a*e])","A",1
2086,1,52,162,0.0167378,"\int \frac{(a+b x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 e^4 (d+e x)^{7/2} \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};-\frac{b (d+e x)}{a e-b d}\right)}{7 (a e-b d)^5}","\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^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 (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,"(2*e^4*(d + e*x)^(7/2)*Hypergeometric2F1[7/2, 5, 9/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(7*(-(b*d) + a*e)^5)","C",1
2087,1,52,172,0.0155304,"\int \frac{(a+b x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 e^4 (d+e x)^{5/2} \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};-\frac{b (d+e x)}{a e-b d}\right)}{5 (a e-b d)^5}","-\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{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{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,"(2*e^4*(d + e*x)^(5/2)*Hypergeometric2F1[5/2, 5, 7/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(5*(-(b*d) + a*e)^5)","C",1
2088,1,52,182,0.0142486,"\int \frac{(a+b x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[((a + b*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 e^4 (d+e x)^{3/2} \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};-\frac{b (d+e x)}{a e-b d}\right)}{3 (a e-b d)^5}","\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,"(2*e^4*(d + e*x)^(3/2)*Hypergeometric2F1[3/2, 5, 5/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(3*(-(b*d) + a*e)^5)","C",1
2089,1,50,180,0.0114576,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(a + b*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{2 e^4 \sqrt{d+e x} \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};-\frac{b (d+e x)}{a e-b d}\right)}{(a e-b d)^5}","-\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{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{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,"(2*e^4*Sqrt[d + e*x]*Hypergeometric2F1[1/2, 5, 3/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(-(b*d) + a*e)^5","C",1
2090,1,50,206,0.0148754,"\int \frac{a+b x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{2 e^4 \, _2F_1\left(-\frac{1}{2},5;\frac{1}{2};-\frac{b (d+e x)}{a e-b d}\right)}{\sqrt{d+e x} (a e-b d)^5}","\frac{315 e^4}{64 \sqrt{d+e x} (b d-a e)^5}-\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{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{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,"(-2*e^4*Hypergeometric2F1[-1/2, 5, 1/2, -((b*(d + e*x))/(-(b*d) + a*e))])/((-(b*d) + a*e)^5*Sqrt[d + e*x])","C",1
2091,1,52,233,0.0168179,"\int \frac{a+b x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Integrate[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{2 e^4 \, _2F_1\left(-\frac{3}{2},5;-\frac{1}{2};-\frac{b (d+e x)}{a e-b d}\right)}{3 (d+e x)^{3/2} (a e-b d)^5}","-\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,"(-2*e^4*Hypergeometric2F1[-3/2, 5, -1/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(3*(-(b*d) + a*e)^5*(d + e*x)^(3/2))","C",1
2092,1,79,152,0.0624225,"\int (a+b x) (d+e x)^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{9/2} \left(143 a^2 e^2+26 a b e (9 e x-2 d)+b^2 \left(8 d^2-36 d e x+99 e^2 x^2\right)\right)}{1287 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*Sqrt[(a + b*x)^2]*(d + e*x)^(9/2)*(143*a^2*e^2 + 26*a*b*e*(-2*d + 9*e*x) + b^2*(8*d^2 - 36*d*e*x + 99*e^2*x^2)))/(1287*e^3*(a + b*x))","A",1
2093,1,79,152,0.0538168,"\int (a+b x) (d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{7/2} \left(99 a^2 e^2+22 a b e (7 e x-2 d)+b^2 \left(8 d^2-28 d e x+63 e^2 x^2\right)\right)}{693 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*Sqrt[(a + b*x)^2]*(d + e*x)^(7/2)*(99*a^2*e^2 + 22*a*b*e*(-2*d + 7*e*x) + b^2*(8*d^2 - 28*d*e*x + 63*e^2*x^2)))/(693*e^3*(a + b*x))","A",1
2094,1,79,152,0.04517,"\int (a+b x) (d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{5/2} \left(63 a^2 e^2+18 a b e (5 e x-2 d)+b^2 \left(8 d^2-20 d e x+35 e^2 x^2\right)\right)}{315 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*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2)*(63*a^2*e^2 + 18*a*b*e*(-2*d + 5*e*x) + b^2*(8*d^2 - 20*d*e*x + 35*e^2*x^2)))/(315*e^3*(a + b*x))","A",1
2095,1,79,152,0.0414415,"\int (a+b x) \sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{3/2} \left(35 a^2 e^2+14 a b e (3 e x-2 d)+b^2 \left(8 d^2-12 d e x+15 e^2 x^2\right)\right)}{105 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*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2)*(35*a^2*e^2 + 14*a*b*e*(-2*d + 3*e*x) + b^2*(8*d^2 - 12*d*e*x + 15*e^2*x^2)))/(105*e^3*(a + b*x))","A",1
2096,1,78,150,0.0454821,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/Sqrt[d + e*x],x]","\frac{2 \sqrt{(a+b x)^2} \sqrt{d+e x} \left(15 a^2 e^2+10 a b e (e x-2 d)+b^2 \left(8 d^2-4 d e x+3 e^2 x^2\right)\right)}{15 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*Sqrt[(a + b*x)^2]*Sqrt[d + e*x]*(15*a^2*e^2 + 10*a*b*e*(-2*d + e*x) + b^2*(8*d^2 - 4*d*e*x + 3*e^2*x^2)))/(15*e^3*(a + b*x))","A",1
2097,1,78,148,0.0409723,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{3/2}} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(3/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(3 a^2 e^2-6 a b e (2 d+e x)+b^2 \left(8 d^2+4 d e x-e^2 x^2\right)\right)}{3 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*Sqrt[(a + b*x)^2]*(3*a^2*e^2 - 6*a*b*e*(2*d + e*x) + b^2*(8*d^2 + 4*d*e*x - e^2*x^2)))/(3*e^3*(a + b*x)*Sqrt[d + e*x])","A",1
2098,1,79,148,0.0425286,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{5/2}} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(5/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(a^2 e^2+2 a b e (2 d+3 e x)-\left(b^2 \left(8 d^2+12 d e x+3 e^2 x^2\right)\right)\right)}{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*Sqrt[(a + b*x)^2]*(a^2*e^2 + 2*a*b*e*(2*d + 3*e*x) - b^2*(8*d^2 + 12*d*e*x + 3*e^2*x^2)))/(3*e^3*(a + b*x)*(d + e*x)^(3/2))","A",1
2099,1,79,150,0.0419637,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{7/2}} \, dx","Integrate[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(3 a^2 e^2+2 a b e (2 d+5 e x)+b^2 \left(8 d^2+20 d e x+15 e^2 x^2\right)\right)}{15 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*Sqrt[(a + b*x)^2]*(3*a^2*e^2 + 2*a*b*e*(2*d + 5*e*x) + b^2*(8*d^2 + 20*d*e*x + 15*e^2*x^2)))/(15*e^3*(a + b*x)*(d + e*x)^(5/2))","A",1
2100,1,172,264,0.1160305,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{7/2} \left(6435 a^4 e^4+2860 a^3 b e^3 (7 e x-2 d)+390 a^2 b^2 e^2 \left(8 d^2-28 d e x+63 e^2 x^2\right)+60 a b^3 e \left(-16 d^3+56 d^2 e x-126 d e^2 x^2+231 e^3 x^3\right)+b^4 \left(128 d^4-448 d^3 e x+1008 d^2 e^2 x^2-1848 d e^3 x^3+3003 e^4 x^4\right)\right)}{45045 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)}",1,"(2*Sqrt[(a + b*x)^2]*(d + e*x)^(7/2)*(6435*a^4*e^4 + 2860*a^3*b*e^3*(-2*d + 7*e*x) + 390*a^2*b^2*e^2*(8*d^2 - 28*d*e*x + 63*e^2*x^2) + 60*a*b^3*e*(-16*d^3 + 56*d^2*e*x - 126*d*e^2*x^2 + 231*e^3*x^3) + b^4*(128*d^4 - 448*d^3*e*x + 1008*d^2*e^2*x^2 - 1848*d*e^3*x^3 + 3003*e^4*x^4)))/(45045*e^5*(a + b*x))","A",1
2101,1,172,264,0.0848886,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{5/2} \left(3003 a^4 e^4+1716 a^3 b e^3 (5 e x-2 d)+286 a^2 b^2 e^2 \left(8 d^2-20 d e x+35 e^2 x^2\right)+52 a b^3 e \left(-16 d^3+40 d^2 e x-70 d e^2 x^2+105 e^3 x^3\right)+b^4 \left(128 d^4-320 d^3 e x+560 d^2 e^2 x^2-840 d e^3 x^3+1155 e^4 x^4\right)\right)}{15015 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)}",1,"(2*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2)*(3003*a^4*e^4 + 1716*a^3*b*e^3*(-2*d + 5*e*x) + 286*a^2*b^2*e^2*(8*d^2 - 20*d*e*x + 35*e^2*x^2) + 52*a*b^3*e*(-16*d^3 + 40*d^2*e*x - 70*d*e^2*x^2 + 105*e^3*x^3) + b^4*(128*d^4 - 320*d^3*e*x + 560*d^2*e^2*x^2 - 840*d*e^3*x^3 + 1155*e^4*x^4)))/(15015*e^5*(a + b*x))","A",1
2102,1,172,264,0.0807897,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{3/2} \left(1155 a^4 e^4+924 a^3 b e^3 (3 e x-2 d)+198 a^2 b^2 e^2 \left(8 d^2-12 d e x+15 e^2 x^2\right)+44 a b^3 e \left(-16 d^3+24 d^2 e x-30 d e^2 x^2+35 e^3 x^3\right)+b^4 \left(128 d^4-192 d^3 e x+240 d^2 e^2 x^2-280 d e^3 x^3+315 e^4 x^4\right)\right)}{3465 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)}",1,"(2*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2)*(1155*a^4*e^4 + 924*a^3*b*e^3*(-2*d + 3*e*x) + 198*a^2*b^2*e^2*(8*d^2 - 12*d*e*x + 15*e^2*x^2) + 44*a*b^3*e*(-16*d^3 + 24*d^2*e*x - 30*d*e^2*x^2 + 35*e^3*x^3) + b^4*(128*d^4 - 192*d^3*e*x + 240*d^2*e^2*x^2 - 280*d*e^3*x^3 + 315*e^4*x^4)))/(3465*e^5*(a + b*x))","A",1
2103,1,171,262,0.0927581,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{(a+b x)^2} \sqrt{d+e x} \left(315 a^4 e^4+420 a^3 b e^3 (e x-2 d)+126 a^2 b^2 e^2 \left(8 d^2-4 d e x+3 e^2 x^2\right)+36 a b^3 e \left(-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right)+b^4 \left(128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right)\right)}{315 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)}",1,"(2*Sqrt[(a + b*x)^2]*Sqrt[d + e*x]*(315*a^4*e^4 + 420*a^3*b*e^3*(-2*d + e*x) + 126*a^2*b^2*e^2*(8*d^2 - 4*d*e*x + 3*e^2*x^2) + 36*a*b^3*e*(-16*d^3 + 8*d^2*e*x - 6*d*e^2*x^2 + 5*e^3*x^3) + b^4*(128*d^4 - 64*d^3*e*x + 48*d^2*e^2*x^2 - 40*d*e^3*x^3 + 35*e^4*x^4)))/(315*e^5*(a + b*x))","A",1
2104,1,169,258,0.0962202,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-35 a^4 e^4+140 a^3 b e^3 (2 d+e x)+70 a^2 b^2 e^2 \left(-8 d^2-4 d e x+e^2 x^2\right)+28 a b^3 e \left(16 d^3+8 d^2 e x-2 d e^2 x^2+e^3 x^3\right)+b^4 \left(-128 d^4-64 d^3 e x+16 d^2 e^2 x^2-8 d e^3 x^3+5 e^4 x^4\right)\right)}{35 e^5 (a+b x) \sqrt{d+e 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)}",1,"(2*Sqrt[(a + b*x)^2]*(-35*a^4*e^4 + 140*a^3*b*e^3*(2*d + e*x) + 70*a^2*b^2*e^2*(-8*d^2 - 4*d*e*x + e^2*x^2) + 28*a*b^3*e*(16*d^3 + 8*d^2*e*x - 2*d*e^2*x^2 + e^3*x^3) + b^4*(-128*d^4 - 64*d^3*e*x + 16*d^2*e^2*x^2 - 8*d*e^3*x^3 + 5*e^4*x^4)))/(35*e^5*(a + b*x)*Sqrt[d + e*x])","A",1
2105,1,171,260,0.0927628,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-5 a^4 e^4-20 a^3 b e^3 (2 d+3 e x)+30 a^2 b^2 e^2 \left(8 d^2+12 d e x+3 e^2 x^2\right)+20 a b^3 e \left(-16 d^3-24 d^2 e x-6 d e^2 x^2+e^3 x^3\right)+b^4 \left(128 d^4+192 d^3 e x+48 d^2 e^2 x^2-8 d e^3 x^3+3 e^4 x^4\right)\right)}{15 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} \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)}",1,"(2*Sqrt[(a + b*x)^2]*(-5*a^4*e^4 - 20*a^3*b*e^3*(2*d + 3*e*x) + 30*a^2*b^2*e^2*(8*d^2 + 12*d*e*x + 3*e^2*x^2) + 20*a*b^3*e*(-16*d^3 - 24*d^2*e*x - 6*d*e^2*x^2 + e^3*x^3) + b^4*(128*d^4 + 192*d^3*e*x + 48*d^2*e^2*x^2 - 8*d*e^3*x^3 + 3*e^4*x^4)))/(15*e^5*(a + b*x)*(d + e*x)^(3/2))","A",1
2106,1,172,260,0.0848852,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(3 a^4 e^4+4 a^3 b e^3 (2 d+5 e x)+6 a^2 b^2 e^2 \left(8 d^2+20 d e x+15 e^2 x^2\right)-12 a b^3 e \left(16 d^3+40 d^2 e x+30 d e^2 x^2+5 e^3 x^3\right)+b^4 \left(128 d^4+320 d^3 e x+240 d^2 e^2 x^2+40 d e^3 x^3-5 e^4 x^4\right)\right)}{15 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}{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)}",1,"(-2*Sqrt[(a + b*x)^2]*(3*a^4*e^4 + 4*a^3*b*e^3*(2*d + 5*e*x) + 6*a^2*b^2*e^2*(8*d^2 + 20*d*e*x + 15*e^2*x^2) - 12*a*b^3*e*(16*d^3 + 40*d^2*e*x + 30*d*e^2*x^2 + 5*e^3*x^3) + b^4*(128*d^4 + 320*d^3*e*x + 240*d^2*e^2*x^2 + 40*d*e^3*x^3 - 5*e^4*x^4)))/(15*e^5*(a + b*x)*(d + e*x)^(5/2))","A",1
2107,1,173,258,0.0853686,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(9/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(5 a^4 e^4+4 a^3 b e^3 (2 d+7 e x)+2 a^2 b^2 e^2 \left(8 d^2+28 d e x+35 e^2 x^2\right)+4 a b^3 e \left(16 d^3+56 d^2 e x+70 d e^2 x^2+35 e^3 x^3\right)-\left(b^4 \left(128 d^4+448 d^3 e x+560 d^2 e^2 x^2+280 d e^3 x^3+35 e^4 x^4\right)\right)\right)}{35 e^5 (a+b x) (d+e x)^{7/2}}","-\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}}",1,"(-2*Sqrt[(a + b*x)^2]*(5*a^4*e^4 + 4*a^3*b*e^3*(2*d + 7*e*x) + 2*a^2*b^2*e^2*(8*d^2 + 28*d*e*x + 35*e^2*x^2) + 4*a*b^3*e*(16*d^3 + 56*d^2*e*x + 70*d*e^2*x^2 + 35*e^3*x^3) - b^4*(128*d^4 + 448*d^3*e*x + 560*d^2*e^2*x^2 + 280*d*e^3*x^3 + 35*e^4*x^4)))/(35*e^5*(a + b*x)*(d + e*x)^(7/2))","A",1
2108,1,172,262,0.0792493,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(11/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(35 a^4 e^4+20 a^3 b e^3 (2 d+9 e x)+6 a^2 b^2 e^2 \left(8 d^2+36 d e x+63 e^2 x^2\right)+4 a b^3 e \left(16 d^3+72 d^2 e x+126 d e^2 x^2+105 e^3 x^3\right)+b^4 \left(128 d^4+576 d^3 e x+1008 d^2 e^2 x^2+840 d e^3 x^3+315 e^4 x^4\right)\right)}{315 e^5 (a+b x) (d+e x)^{9/2}}","-\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}}",1,"(-2*Sqrt[(a + b*x)^2]*(35*a^4*e^4 + 20*a^3*b*e^3*(2*d + 9*e*x) + 6*a^2*b^2*e^2*(8*d^2 + 36*d*e*x + 63*e^2*x^2) + 4*a*b^3*e*(16*d^3 + 72*d^2*e*x + 126*d*e^2*x^2 + 105*e^3*x^3) + b^4*(128*d^4 + 576*d^3*e*x + 1008*d^2*e^2*x^2 + 840*d*e^3*x^3 + 315*e^4*x^4)))/(315*e^5*(a + b*x)*(d + e*x)^(9/2))","A",1
2109,1,172,264,0.0861552,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(13/2),x]","-\frac{2 \sqrt{(a+b x)^2} \left(315 a^4 e^4+140 a^3 b e^3 (2 d+11 e x)+30 a^2 b^2 e^2 \left(8 d^2+44 d e x+99 e^2 x^2\right)+12 a b^3 e \left(16 d^3+88 d^2 e x+198 d e^2 x^2+231 e^3 x^3\right)+b^4 \left(128 d^4+704 d^3 e x+1584 d^2 e^2 x^2+1848 d e^3 x^3+1155 e^4 x^4\right)\right)}{3465 e^5 (a+b x) (d+e x)^{11/2}}","-\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}}",1,"(-2*Sqrt[(a + b*x)^2]*(315*a^4*e^4 + 140*a^3*b*e^3*(2*d + 11*e*x) + 30*a^2*b^2*e^2*(8*d^2 + 44*d*e*x + 99*e^2*x^2) + 12*a*b^3*e*(16*d^3 + 88*d^2*e*x + 198*d*e^2*x^2 + 231*e^3*x^3) + b^4*(128*d^4 + 704*d^3*e*x + 1584*d^2*e^2*x^2 + 1848*d*e^3*x^3 + 1155*e^4*x^4)))/(3465*e^5*(a + b*x)*(d + e*x)^(11/2))","A",1
2110,1,163,374,0.2025294,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{7/2} \left(-342342 b^5 (d+e x)^5 (b d-a e)+969969 b^4 (d+e x)^4 (b d-a e)^2-1492260 b^3 (d+e x)^3 (b d-a e)^3+1322685 b^2 (d+e x)^2 (b d-a e)^4-646646 b (d+e x) (b d-a e)^5+138567 (b d-a e)^6+51051 b^6 (d+e x)^6\right)}{969969 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)}",1,"(2*Sqrt[(a + b*x)^2]*(d + e*x)^(7/2)*(138567*(b*d - a*e)^6 - 646646*b*(b*d - a*e)^5*(d + e*x) + 1322685*b^2*(b*d - a*e)^4*(d + e*x)^2 - 1492260*b^3*(b*d - a*e)^3*(d + e*x)^3 + 969969*b^4*(b*d - a*e)^2*(d + e*x)^4 - 342342*b^5*(b*d - a*e)*(d + e*x)^5 + 51051*b^6*(d + e*x)^6))/(969969*e^7*(a + b*x))","A",1
2111,1,163,376,0.1649996,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{5/2} \left(-102102 b^5 (d+e x)^5 (b d-a e)+294525 b^4 (d+e x)^4 (b d-a e)^2-464100 b^3 (d+e x)^3 (b d-a e)^3+425425 b^2 (d+e x)^2 (b d-a e)^4-218790 b (d+e x) (b d-a e)^5+51051 (b d-a e)^6+15015 b^6 (d+e x)^6\right)}{255255 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)}",1,"(2*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2)*(51051*(b*d - a*e)^6 - 218790*b*(b*d - a*e)^5*(d + e*x) + 425425*b^2*(b*d - a*e)^4*(d + e*x)^2 - 464100*b^3*(b*d - a*e)^3*(d + e*x)^3 + 294525*b^4*(b*d - a*e)^2*(d + e*x)^4 - 102102*b^5*(b*d - a*e)*(d + e*x)^5 + 15015*b^6*(d + e*x)^6))/(255255*e^7*(a + b*x))","A",1
2112,1,163,376,0.1514442,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} (d+e x)^{3/2} \left(-20790 b^5 (d+e x)^5 (b d-a e)+61425 b^4 (d+e x)^4 (b d-a e)^2-100100 b^3 (d+e x)^3 (b d-a e)^3+96525 b^2 (d+e x)^2 (b d-a e)^4-54054 b (d+e x) (b d-a e)^5+15015 (b d-a e)^6+3003 b^6 (d+e x)^6\right)}{45045 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)}",1,"(2*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2)*(15015*(b*d - a*e)^6 - 54054*b*(b*d - a*e)^5*(d + e*x) + 96525*b^2*(b*d - a*e)^4*(d + e*x)^2 - 100100*b^3*(b*d - a*e)^3*(d + e*x)^3 + 61425*b^4*(b*d - a*e)^2*(d + e*x)^4 - 20790*b^5*(b*d - a*e)*(d + e*x)^5 + 3003*b^6*(d + e*x)^6))/(45045*e^7*(a + b*x))","A",1
2113,1,163,370,0.0967472,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{(a+b x)^2} \sqrt{d+e x} \left(-1638 b^5 (d+e x)^5 (b d-a e)+5005 b^4 (d+e x)^4 (b d-a e)^2-8580 b^3 (d+e x)^3 (b d-a e)^3+9009 b^2 (d+e x)^2 (b d-a e)^4-6006 b (d+e x) (b d-a e)^5+3003 (b d-a e)^6+231 b^6 (d+e x)^6\right)}{3003 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)}",1,"(2*Sqrt[(a + b*x)^2]*Sqrt[d + e*x]*(3003*(b*d - a*e)^6 - 6006*b*(b*d - a*e)^5*(d + e*x) + 9009*b^2*(b*d - a*e)^4*(d + e*x)^2 - 8580*b^3*(b*d - a*e)^3*(d + e*x)^3 + 5005*b^4*(b*d - a*e)^2*(d + e*x)^4 - 1638*b^5*(b*d - a*e)*(d + e*x)^5 + 231*b^6*(d + e*x)^6))/(3003*e^7*(a + b*x))","A",1
2114,1,163,368,0.143177,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-154 b^5 (d+e x)^5 (b d-a e)+495 b^4 (d+e x)^4 (b d-a e)^2-924 b^3 (d+e x)^3 (b d-a e)^3+1155 b^2 (d+e x)^2 (b d-a e)^4-1386 b (d+e x) (b d-a e)^5-231 (b d-a e)^6+21 b^6 (d+e x)^6\right)}{231 e^7 (a+b x) \sqrt{d+e 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)}",1,"(2*Sqrt[(a + b*x)^2]*(-231*(b*d - a*e)^6 - 1386*b*(b*d - a*e)^5*(d + e*x) + 1155*b^2*(b*d - a*e)^4*(d + e*x)^2 - 924*b^3*(b*d - a*e)^3*(d + e*x)^3 + 495*b^4*(b*d - a*e)^2*(d + e*x)^4 - 154*b^5*(b*d - a*e)*(d + e*x)^5 + 21*b^6*(d + e*x)^6))/(231*e^7*(a + b*x)*Sqrt[d + e*x])","A",1
2115,1,163,370,0.1474785,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(5/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-54 b^5 (d+e x)^5 (b d-a e)+189 b^4 (d+e x)^4 (b d-a e)^2-420 b^3 (d+e x)^3 (b d-a e)^3+945 b^2 (d+e x)^2 (b d-a e)^4+378 b (d+e x) (b d-a e)^5-21 (b d-a e)^6+7 b^6 (d+e x)^6\right)}{63 e^7 (a+b x) (d+e x)^{3/2}}","\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)}",1,"(2*Sqrt[(a + b*x)^2]*(-21*(b*d - a*e)^6 + 378*b*(b*d - a*e)^5*(d + e*x) + 945*b^2*(b*d - a*e)^4*(d + e*x)^2 - 420*b^3*(b*d - a*e)^3*(d + e*x)^3 + 189*b^4*(b*d - a*e)^2*(d + e*x)^4 - 54*b^5*(b*d - a*e)*(d + e*x)^5 + 7*b^6*(d + e*x)^6))/(63*e^7*(a + b*x)*(d + e*x)^(3/2))","A",1
2116,1,163,368,0.1523504,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(7/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-42 b^5 (d+e x)^5 (b d-a e)+175 b^4 (d+e x)^4 (b d-a e)^2-700 b^3 (d+e x)^3 (b d-a e)^3-525 b^2 (d+e x)^2 (b d-a e)^4+70 b (d+e x) (b d-a e)^5-7 (b d-a e)^6+5 b^6 (d+e x)^6\right)}{35 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}{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)}",1,"(2*Sqrt[(a + b*x)^2]*(-7*(b*d - a*e)^6 + 70*b*(b*d - a*e)^5*(d + e*x) - 525*b^2*(b*d - a*e)^4*(d + e*x)^2 - 700*b^3*(b*d - a*e)^3*(d + e*x)^3 + 175*b^4*(b*d - a*e)^2*(d + e*x)^4 - 42*b^5*(b*d - a*e)*(d + e*x)^5 + 5*b^6*(d + e*x)^6))/(35*e^7*(a + b*x)*(d + e*x)^(5/2))","A",1
2117,1,163,368,0.1565507,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(9/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-70 b^5 (d+e x)^5 (b d-a e)+525 b^4 (d+e x)^4 (b d-a e)^2+700 b^3 (d+e x)^3 (b d-a e)^3-175 b^2 (d+e x)^2 (b d-a e)^4+42 b (d+e x) (b d-a e)^5-5 (b d-a e)^6+7 b^6 (d+e x)^6\right)}{35 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}{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}}",1,"(2*Sqrt[(a + b*x)^2]*(-5*(b*d - a*e)^6 + 42*b*(b*d - a*e)^5*(d + e*x) - 175*b^2*(b*d - a*e)^4*(d + e*x)^2 + 700*b^3*(b*d - a*e)^3*(d + e*x)^3 + 525*b^4*(b*d - a*e)^2*(d + e*x)^4 - 70*b^5*(b*d - a*e)*(d + e*x)^5 + 7*b^6*(d + e*x)^6))/(35*e^7*(a + b*x)*(d + e*x)^(7/2))","A",1
2118,1,163,370,0.1470171,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(11/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(-378 b^5 (d+e x)^5 (b d-a e)-945 b^4 (d+e x)^4 (b d-a e)^2+420 b^3 (d+e x)^3 (b d-a e)^3-189 b^2 (d+e x)^2 (b d-a e)^4+54 b (d+e x) (b d-a e)^5-7 (b d-a e)^6+21 b^6 (d+e x)^6\right)}{63 e^7 (a+b x) (d+e x)^{9/2}}","-\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}}",1,"(2*Sqrt[(a + b*x)^2]*(-7*(b*d - a*e)^6 + 54*b*(b*d - a*e)^5*(d + e*x) - 189*b^2*(b*d - a*e)^4*(d + e*x)^2 + 420*b^3*(b*d - a*e)^3*(d + e*x)^3 - 945*b^4*(b*d - a*e)^2*(d + e*x)^4 - 378*b^5*(b*d - a*e)*(d + e*x)^5 + 21*b^6*(d + e*x)^6))/(63*e^7*(a + b*x)*(d + e*x)^(9/2))","A",1
2119,1,163,368,0.1518213,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(13/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(1386 b^5 (d+e x)^5 (b d-a e)-1155 b^4 (d+e x)^4 (b d-a e)^2+924 b^3 (d+e x)^3 (b d-a e)^3-495 b^2 (d+e x)^2 (b d-a e)^4+154 b (d+e x) (b d-a e)^5-21 (b d-a e)^6+231 b^6 (d+e x)^6\right)}{231 e^7 (a+b x) (d+e x)^{11/2}}","-\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}}",1,"(2*Sqrt[(a + b*x)^2]*(-21*(b*d - a*e)^6 + 154*b*(b*d - a*e)^5*(d + e*x) - 495*b^2*(b*d - a*e)^4*(d + e*x)^2 + 924*b^3*(b*d - a*e)^3*(d + e*x)^3 - 1155*b^4*(b*d - a*e)^2*(d + e*x)^4 + 1386*b^5*(b*d - a*e)*(d + e*x)^5 + 231*b^6*(d + e*x)^6))/(231*e^7*(a + b*x)*(d + e*x)^(11/2))","A",1
2120,1,163,370,0.1614107,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(15/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(6006 b^5 (d+e x)^5 (b d-a e)-9009 b^4 (d+e x)^4 (b d-a e)^2+8580 b^3 (d+e x)^3 (b d-a e)^3-5005 b^2 (d+e x)^2 (b d-a e)^4+1638 b (d+e x) (b d-a e)^5-231 (b d-a e)^6-3003 b^6 (d+e x)^6\right)}{3003 e^7 (a+b x) (d+e x)^{13/2}}","-\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}}",1,"(2*Sqrt[(a + b*x)^2]*(-231*(b*d - a*e)^6 + 1638*b*(b*d - a*e)^5*(d + e*x) - 5005*b^2*(b*d - a*e)^4*(d + e*x)^2 + 8580*b^3*(b*d - a*e)^3*(d + e*x)^3 - 9009*b^4*(b*d - a*e)^2*(d + e*x)^4 + 6006*b^5*(b*d - a*e)*(d + e*x)^5 - 3003*b^6*(d + e*x)^6))/(3003*e^7*(a + b*x)*(d + e*x)^(13/2))","A",1
2121,1,163,376,0.1570368,"\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","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(17/2),x]","\frac{2 \sqrt{(a+b x)^2} \left(54054 b^5 (d+e x)^5 (b d-a e)-96525 b^4 (d+e x)^4 (b d-a e)^2+100100 b^3 (d+e x)^3 (b d-a e)^3-61425 b^2 (d+e x)^2 (b d-a e)^4+20790 b (d+e x) (b d-a e)^5-3003 (b d-a e)^6-15015 b^6 (d+e x)^6\right)}{45045 e^7 (a+b x) (d+e x)^{15/2}}","-\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}}",1,"(2*Sqrt[(a + b*x)^2]*(-3003*(b*d - a*e)^6 + 20790*b*(b*d - a*e)^5*(d + e*x) - 61425*b^2*(b*d - a*e)^4*(d + e*x)^2 + 100100*b^3*(b*d - a*e)^3*(d + e*x)^3 - 96525*b^4*(b*d - a*e)^2*(d + e*x)^4 + 54054*b^5*(b*d - a*e)*(d + e*x)^5 - 15015*b^6*(d + e*x)^6))/(45045*e^7*(a + b*x)*(d + e*x)^(15/2))","A",1
2122,1,32,41,0.0272879,"\int \frac{(a+b x) (d+e x)^{7/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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+b 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 + b*x)^2])","A",1
2123,1,32,41,0.0216876,"\int \frac{(a+b x) (d+e x)^{5/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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+b 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 + b*x)^2])","A",1
2124,1,32,41,0.0173761,"\int \frac{(a+b x) (d+e x)^{3/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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+b 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 + b*x)^2])","A",1
2125,1,32,41,0.0127197,"\int \frac{(a+b x) \sqrt{d+e x}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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+b 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 + b*x)^2])","A",1
2126,1,30,39,0.0123561,"\int \frac{a+b x}{\sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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+b 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 + b*x)^2])","A",1
2127,1,30,39,0.0141507,"\int \frac{a+b x}{(d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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+b 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[(a + b*x)^2]*Sqrt[d + e*x])","A",1
2128,1,32,41,0.0149542,"\int \frac{a+b x}{(d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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+b 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*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2))","A",1
2129,1,32,41,0.0169724,"\int \frac{a+b x}{(d+e x)^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[(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+b 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*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2))","A",1
2130,1,66,250,0.0348792,"\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","Integrate[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 e (a+b x) (d+e x)^{9/2} \, _2F_1\left(2,\frac{9}{2};\frac{11}{2};-\frac{b (d+e x)}{a e-b d}\right)}{9 \sqrt{(a+b x)^2} (a e-b d)^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) (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{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) (d+e x)^{3/2} (b d-a e)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*e*(a + b*x)*(d + e*x)^(9/2)*Hypergeometric2F1[2, 9/2, 11/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(9*(-(b*d) + a*e)^2*Sqrt[(a + b*x)^2])","C",1
2131,1,66,198,0.0301853,"\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","Integrate[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 e (a+b x) (d+e x)^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{b (d+e x)}{a e-b d}\right)}{7 \sqrt{(a+b x)^2} (a e-b d)^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) (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{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}}",1,"(2*e*(a + b*x)*(d + e*x)^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(7*(-(b*d) + a*e)^2*Sqrt[(a + b*x)^2])","C",1
2132,1,66,148,0.0278668,"\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","Integrate[((a + b*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 e (a+b x) (d+e x)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};-\frac{b (d+e x)}{a e-b d}\right)}{5 \sqrt{(a+b x)^2} (a e-b d)^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,"(2*e*(a + b*x)*(d + e*x)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(5*(-(b*d) + a*e)^2*Sqrt[(a + b*x)^2])","C",1
2133,1,81,108,0.0820924,"\int \frac{(a+b x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((a + b*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\frac{e (a+b x) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)}{\sqrt{a e-b d}}-\sqrt{b} \sqrt{d+e x}}{b^{3/2} \sqrt{(a+b x)^2}}","-\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[b]*Sqrt[d + e*x]) + (e*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]])/Sqrt[-(b*d) + a*e])/(b^(3/2)*Sqrt[(a + b*x)^2])","A",1
2134,1,85,114,0.0837563,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{\frac{\sqrt{d+e x}}{a e-b d}+\frac{e (a+b x) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)}{\sqrt{b} (a e-b d)^{3/2}}}{\sqrt{(a+b x)^2}}","\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) + (e*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]])/(Sqrt[b]*(-(b*d) + a*e)^(3/2)))/Sqrt[(a + b*x)^2]","A",1
2135,1,64,162,0.0221378,"\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","Integrate[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{2 e (a+b x) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{b (d+e x)}{a e-b d}\right)}{\sqrt{(a+b x)^2} \sqrt{d+e x} (a e-b d)^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,"(-2*e*(a + b*x)*Hypergeometric2F1[-1/2, 2, 1/2, -((b*(d + e*x))/(-(b*d) + a*e))])/((-(b*d) + a*e)^2*Sqrt[(a + b*x)^2]*Sqrt[d + e*x])","C",1
2136,1,66,212,0.0245415,"\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","Integrate[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{2 e (a+b x) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\frac{b (d+e x)}{a e-b d}\right)}{3 \sqrt{(a+b x)^2} (d+e x)^{3/2} (a e-b d)^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,"(-2*e*(a + b*x)*Hypergeometric2F1[-3/2, 2, -1/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(3*(-(b*d) + a*e)^2*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2))","C",1
2137,1,66,264,0.027572,"\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","Integrate[(a + b*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{2 e (a+b x) \, _2F_1\left(-\frac{5}{2},2;-\frac{3}{2};-\frac{b (d+e x)}{a e-b d}\right)}{5 \sqrt{(a+b x)^2} (d+e x)^{5/2} (a e-b d)^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,"(-2*e*(a + b*x)*Hypergeometric2F1[-5/2, 2, -3/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(5*(-(b*d) + a*e)^2*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2))","C",1
2138,1,68,241,0.037031,"\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","Integrate[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 e^3 (a+b x) (d+e x)^{9/2} \, _2F_1\left(4,\frac{9}{2};\frac{11}{2};-\frac{b (d+e x)}{a e-b d}\right)}{9 \sqrt{(a+b x)^2} (a e-b d)^4}","-\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^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{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^2 (d+e x)^{3/2}}{24 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*e^3*(a + b*x)*(d + e*x)^(9/2)*Hypergeometric2F1[4, 9/2, 11/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(9*(-(b*d) + a*e)^4*Sqrt[(a + b*x)^2])","C",1
2139,1,132,197,0.156666,"\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","Integrate[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\frac{15 e^3 (a+b x)^3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)}{\sqrt{a e-b d}}-\sqrt{b} \sqrt{d+e x} \left(15 a^2 e^2+10 a b e (d+4 e x)+b^2 \left(8 d^2+26 d e x+33 e^2 x^2\right)\right)}{24 b^{7/2} \left((a+b x)^2\right)^{3/2}}","-\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^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^2 \sqrt{d+e x}}{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-(Sqrt[b]*Sqrt[d + e*x]*(15*a^2*e^2 + 10*a*b*e*(d + 4*e*x) + b^2*(8*d^2 + 26*d*e*x + 33*e^2*x^2))) + (15*e^3*(a + b*x)^3*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]])/Sqrt[-(b*d) + a*e])/(24*b^(7/2)*((a + b*x)^2)^(3/2))","A",1
2140,1,68,207,0.0272204,"\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","Integrate[((a + b*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 e^3 (a+b x) (d+e x)^{5/2} \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};-\frac{b (d+e x)}{a e-b d}\right)}{5 \sqrt{(a+b x)^2} (a e-b d)^4}","-\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 \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^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}}",1,"(2*e^3*(a + b*x)*(d + e*x)^(5/2)*Hypergeometric2F1[5/2, 4, 7/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(5*(-(b*d) + a*e)^4*Sqrt[(a + b*x)^2])","C",1
2141,1,68,217,0.0251298,"\int \frac{(a+b x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((a + b*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 e^3 (a+b x) (d+e x)^{3/2} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};-\frac{b (d+e x)}{a e-b d}\right)}{3 \sqrt{(a+b x)^2} (a e-b d)^4}","\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 \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^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}}",1,"(2*e^3*(a + b*x)*(d + e*x)^(3/2)*Hypergeometric2F1[3/2, 4, 5/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(3*(-(b*d) + a*e)^4*Sqrt[(a + b*x)^2])","C",1
2142,1,66,225,0.0248798,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{2 e^3 (a+b x) \sqrt{d+e x} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};-\frac{b (d+e x)}{a e-b d}\right)}{\sqrt{(a+b x)^2} (a e-b d)^4}","\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^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 \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,"(2*e^3*(a + b*x)*Sqrt[d + e*x]*Hypergeometric2F1[1/2, 4, 3/2, -((b*(d + e*x))/(-(b*d) + a*e))])/((-(b*d) + a*e)^4*Sqrt[(a + b*x)^2])","C",1
2143,1,66,276,0.0260104,"\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","Integrate[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{2 e^3 (a+b x) \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};-\frac{b (d+e x)}{a e-b d}\right)}{\sqrt{(a+b x)^2} \sqrt{d+e x} (a e-b d)^4}","-\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 \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{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{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,"(-2*e^3*(a + b*x)*Hypergeometric2F1[-1/2, 4, 1/2, -((b*(d + e*x))/(-(b*d) + a*e))])/((-(b*d) + a*e)^4*Sqrt[(a + b*x)^2]*Sqrt[d + e*x])","C",1
2144,1,68,328,0.0329989,"\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","Integrate[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{2 e^3 (a+b x) \, _2F_1\left(-\frac{3}{2},4;-\frac{1}{2};-\frac{b (d+e x)}{a e-b d}\right)}{3 \sqrt{(a+b x)^2} (d+e x)^{3/2} (a e-b d)^4}","-\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{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^{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}}",1,"(-2*e^3*(a + b*x)*Hypergeometric2F1[-3/2, 4, -1/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(3*(-(b*d) + a*e)^4*Sqrt[(a + b*x)^2]*(d + e*x)^(3/2))","C",1
2145,1,68,382,0.038265,"\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","Integrate[(a + b*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{2 e^3 (a+b x) \, _2F_1\left(-\frac{5}{2},4;-\frac{3}{2};-\frac{b (d+e x)}{a e-b d}\right)}{5 \sqrt{(a+b x)^2} (d+e x)^{5/2} (a e-b d)^4}","-\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{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^{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}}",1,"(-2*e^3*(a + b*x)*Hypergeometric2F1[-5/2, 4, -3/2, -((b*(d + e*x))/(-(b*d) + a*e))])/(5*(-(b*d) + a*e)^4*Sqrt[(a + b*x)^2]*(d + e*x)^(5/2))","C",1
2146,1,203,239,0.2091089,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(d+e x)^{m+1} \left(-\frac{7 b^6 (d+e x)^6 (b d-a e)}{m+7}+\frac{21 b^5 (d+e x)^5 (b d-a e)^2}{m+6}-\frac{35 b^4 (d+e x)^4 (b d-a e)^3}{m+5}+\frac{35 b^3 (d+e x)^3 (b d-a e)^4}{m+4}-\frac{21 b^2 (d+e x)^2 (b d-a e)^5}{m+3}+\frac{7 b (d+e x) (b d-a e)^6}{m+2}-\frac{(b d-a e)^7}{m+1}+\frac{b^7 (d+e x)^7}{m+8}\right)}{e^8}","-\frac{7 b^6 (b d-a e) (d+e x)^{m+7}}{e^8 (m+7)}+\frac{21 b^5 (b d-a e)^2 (d+e x)^{m+6}}{e^8 (m+6)}-\frac{35 b^4 (b d-a e)^3 (d+e x)^{m+5}}{e^8 (m+5)}+\frac{35 b^3 (b d-a e)^4 (d+e x)^{m+4}}{e^8 (m+4)}-\frac{21 b^2 (b d-a e)^5 (d+e x)^{m+3}}{e^8 (m+3)}-\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,"((d + e*x)^(1 + m)*(-((b*d - a*e)^7/(1 + m)) + (7*b*(b*d - a*e)^6*(d + e*x))/(2 + m) - (21*b^2*(b*d - a*e)^5*(d + e*x)^2)/(3 + m) + (35*b^3*(b*d - a*e)^4*(d + e*x)^3)/(4 + m) - (35*b^4*(b*d - a*e)^3*(d + e*x)^4)/(5 + m) + (21*b^5*(b*d - a*e)^2*(d + e*x)^5)/(6 + m) - (7*b^6*(b*d - a*e)*(d + e*x)^6)/(7 + m) + (b^7*(d + e*x)^7)/(8 + m)))/e^8","A",1
2147,1,149,175,0.133065,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Integrate[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(-\frac{5 b^4 (d+e x)^4 (b d-a e)}{m+5}+\frac{10 b^3 (d+e x)^3 (b d-a e)^2}{m+4}-\frac{10 b^2 (d+e x)^2 (b d-a e)^3}{m+3}+\frac{5 b (d+e x) (b d-a e)^4}{m+2}-\frac{(b d-a e)^5}{m+1}+\frac{b^5 (d+e x)^5}{m+6}\right)}{e^6}","-\frac{5 b^4 (b d-a e) (d+e x)^{m+5}}{e^6 (m+5)}+\frac{10 b^3 (b d-a e)^2 (d+e x)^{m+4}}{e^6 (m+4)}-\frac{10 b^2 (b d-a e)^3 (d+e x)^{m+3}}{e^6 (m+3)}-\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,"((d + e*x)^(1 + m)*(-((b*d - a*e)^5/(1 + m)) + (5*b*(b*d - a*e)^4*(d + e*x))/(2 + m) - (10*b^2*(b*d - a*e)^3*(d + e*x)^2)/(3 + m) + (10*b^3*(b*d - a*e)^2*(d + e*x)^3)/(4 + m) - (5*b^4*(b*d - a*e)*(d + e*x)^4)/(5 + m) + (b^5*(d + e*x)^5)/(6 + m)))/e^6","A",1
2148,1,95,111,0.0694593,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right) \, dx","Integrate[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(d+e x)^{m+1} \left(-\frac{3 b^2 (d+e x)^2 (b d-a e)}{m+3}+\frac{3 b (d+e x) (b d-a e)^2}{m+2}-\frac{(b d-a e)^3}{m+1}+\frac{b^3 (d+e x)^3}{m+4}\right)}{e^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,"((d + e*x)^(1 + m)*(-((b*d - a*e)^3/(1 + m)) + (3*b*(b*d - a*e)^2*(d + e*x))/(2 + m) - (3*b^2*(b*d - a*e)*(d + e*x)^2)/(3 + m) + (b^3*(d + e*x)^3)/(4 + m)))/e^4","A",1
2149,1,51,51,0.0091834,"\int \frac{(a+b x) (d+e x)^m}{a^2+2 a b x+b^2 x^2} \, dx","Integrate[((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",1
2150,1,54,54,0.0141958,"\int \frac{(a+b x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Integrate[((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)}{a e-b d}\right)}{(m+1) (a e-b d)^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",1
2151,1,193,395,0.1790044,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Integrate[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{(a+b x)^2} (d+e x)^{m+1} \left(-\frac{6 b^5 (d+e x)^5 (b d-a e)}{m+6}+\frac{15 b^4 (d+e x)^4 (b d-a e)^2}{m+5}-\frac{20 b^3 (d+e x)^3 (b d-a e)^3}{m+4}+\frac{15 b^2 (d+e x)^2 (b d-a e)^4}{m+3}-\frac{6 b (d+e x) (b d-a e)^5}{m+2}+\frac{(b d-a e)^6}{m+1}+\frac{b^6 (d+e x)^6}{m+7}\right)}{e^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{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{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{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{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)}",1,"(Sqrt[(a + b*x)^2]*(d + e*x)^(1 + m)*((b*d - a*e)^6/(1 + m) - (6*b*(b*d - a*e)^5*(d + e*x))/(2 + m) + (15*b^2*(b*d - a*e)^4*(d + e*x)^2)/(3 + m) - (20*b^3*(b*d - a*e)^3*(d + e*x)^3)/(4 + m) + (15*b^4*(b*d - a*e)^2*(d + e*x)^4)/(5 + m) - (6*b^5*(b*d - a*e)*(d + e*x)^5)/(6 + m) + (b^6*(d + e*x)^6)/(7 + m)))/(e^7*(a + b*x))","A",1
2152,1,139,277,0.1621393,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Integrate[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\sqrt{(a+b x)^2} (d+e x)^{m+1} \left(-\frac{4 b^3 (d+e x)^3 (b d-a e)}{m+4}+\frac{6 b^2 (d+e x)^2 (b d-a e)^2}{m+3}-\frac{4 b (d+e x) (b d-a e)^3}{m+2}+\frac{(b d-a e)^4}{m+1}+\frac{b^4 (d+e x)^4}{m+5}\right)}{e^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{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{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)}",1,"(Sqrt[(a + b*x)^2]*(d + e*x)^(1 + m)*((b*d - a*e)^4/(1 + m) - (4*b*(b*d - a*e)^3*(d + e*x))/(2 + m) + (6*b^2*(b*d - a*e)^2*(d + e*x)^2)/(3 + m) - (4*b^3*(b*d - a*e)*(d + e*x)^3)/(4 + m) + (b^4*(d + e*x)^4)/(5 + m)))/(e^5*(a + b*x))","A",1
2153,1,113,159,0.0855785,"\int (a+b x) (d+e x)^m \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Integrate[(a + b*x)*(d + e*x)^m*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sqrt{(a+b x)^2} (d+e x)^{m+1} \left(a^2 e^2 \left(m^2+5 m+6\right)+2 a b e (m+3) (e (m+1) x-d)+b^2 \left(2 d^2-2 d e (m+1) x+e^2 \left(m^2+3 m+2\right) x^2\right)\right)}{e^3 (m+1) (m+2) (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,"(Sqrt[(a + b*x)^2]*(d + e*x)^(1 + m)*(a^2*e^2*(6 + 5*m + m^2) + 2*a*b*e*(3 + m)*(-d + e*(1 + m)*x) + b^2*(2*d^2 - 2*d*e*(1 + m)*x + e^2*(2 + 3*m + m^2)*x^2)))/(e^3*(1 + m)*(2 + m)*(3 + m)*(a + b*x))","A",1
2154,1,34,43,0.0204697,"\int \frac{(a+b x) (d+e x)^m}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Integrate[((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+b 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 + b*x)^2])","A",1
2155,1,68,76,0.02798,"\int \frac{(a+b x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Integrate[((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)}{a e-b d}\right)}{(m+1) \sqrt{(a+b x)^2} (a e-b d)^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 + b*x)^2])","A",1
2156,1,70,78,0.0315772,"\int \frac{(a+b x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Integrate[((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)}{a e-b d}\right)}{(m+1) \sqrt{(a+b x)^2} (a e-b d)^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 + b*x)^2])","A",1
2157,1,42,51,0.0275478,"\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","Integrate[(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+b 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 + b*x)^2)^(1 + p))/(2*(b*d - a*e)*(1 + p)*(d + e*x)^(2*(1 + p)))","A",1
2158,1,104,183,0.0878402,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Integrate[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left((a+b x)^2\right)^{p+1} \left(\frac{3 e^2 (a+b x)^2 (b d-a e)}{p+2}+\frac{6 e (a+b x) (b d-a e)^2}{2 p+3}+\frac{(b d-a e)^3}{p+1}+\frac{2 e^3 (a+b x)^3}{2 p+5}\right)}{2 b^4}","\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,"(((a + b*x)^2)^(1 + p)*((b*d - a*e)^3/(1 + p) + (6*e*(b*d - a*e)^2*(a + b*x))/(3 + 2*p) + (3*e^2*(b*d - a*e)*(a + b*x)^2)/(2 + p) + (2*e^3*(a + b*x)^3)/(5 + 2*p)))/(2*b^4)","A",1
2159,1,109,134,0.0704907,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Integrate[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left((a+b x)^2\right)^{p+1} \left(a^2 e^2-2 a b e (d (p+2)+e (p+1) x)+b^2 \left(d^2 \left(2 p^2+7 p+6\right)+4 d e \left(p^2+3 p+2\right) x+e^2 \left(2 p^2+5 p+3\right) x^2\right)\right)}{2 b^3 (p+1) (p+2) (2 p+3)}","\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,"(((a + b*x)^2)^(1 + p)*(a^2*e^2 - 2*a*b*e*(d*(2 + p) + e*(1 + p)*x) + b^2*(d^2*(6 + 7*p + 2*p^2) + 4*d*e*(2 + 3*p + p^2)*x + e^2*(3 + 5*p + 2*p^2)*x^2)))/(2*b^3*(1 + p)*(2 + p)*(3 + 2*p))","A",1
2160,1,51,83,0.0344718,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Integrate[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left((a+b x)^2\right)^{p+1} (-a e+b d (2 p+3)+2 b e (p+1) x)}{2 b^2 (p+1) (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,"(((a + b*x)^2)^(1 + p)*(-(a*e) + b*d*(3 + 2*p) + 2*b*e*(1 + p)*x))/(2*b^2*(1 + p)*(3 + 2*p))","A",1
2161,1,23,32,0.0110583,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Integrate[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left((a+b 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 + b*x)^2)^(1 + p)/(2*b*(1 + p))","A",1
2162,1,59,74,0.019058,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p}{d+e x} \, dx","Integrate[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(d + e*x),x]","\frac{\left((a+b x)^2\right)^{p+1} \, _2F_1\left(1,2 (p+1);2 p+3;\frac{e (a+b x)}{a e-b d}\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)^(1 + 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",1
2163,1,48,58,0.0449974,"\int (A+B x) (a c+b c x)^m \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(A + B*x)*(a*c + b*c*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(a+b x)^7 (c (a+b x))^m (-a B+A b (m+8)+b B (m+7) x)}{b^2 (m+7) (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*x)^7*(c*(a + b*x))^m*(-(a*B) + A*b*(8 + m) + b*B*(7 + m)*x))/(b^2*(7 + m)*(8 + m))","A",1
2164,1,48,64,0.0381544,"\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","Integrate[((A + B*x)*(a*c + b*c*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(c (a+b x))^m (-a B+A b (m-4)+b B (m-5) x)}{b^2 (m-5) (m-4) (a+b x)^5}","-\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,"((c*(a + b*x))^m*(-(a*B) + A*b*(-4 + m) + b*B*(-5 + m)*x))/(b^2*(-5 + m)*(-4 + m)*(a + b*x)^5)","A",1
2165,1,59,112,0.061265,"\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","Integrate[(A + B*x)*(a*c + b*c*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x)^3 \sqrt{(a+b x)^2} (c (a+b x))^m (-a B+A b (m+5)+b B (m+4) x)}{b^2 (m+4) (m+5)}","\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*x)^3*(c*(a + b*x))^m*Sqrt[(a + b*x)^2]*(-(a*B) + A*b*(5 + m) + b*B*(4 + m)*x))/(b^2*(4 + m)*(5 + m))","A",1
2166,1,55,112,0.0577384,"\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","Integrate[((A + B*x)*(a*c + b*c*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{c (c (a+b x))^{m-1} (-a B+A b (m-1)+b B (m-2) x)}{b^2 (m-2) (m-1) \sqrt{(a+b 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,"(c*(c*(a + b*x))^(-1 + m)*(-(a*B) + A*b*(-1 + m) + b*B*(-2 + m)*x))/(b^2*(-2 + m)*(-1 + m)*Sqrt[(a + b*x)^2])","A",1
2167,1,67,100,0.0534542,"\int (a c+b c x)^m (f+g x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Integrate[(a*c + b*c*x)^m*(f + g*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{(a+b x) \left((a+b x)^2\right)^p (c (a+b x))^m (-a g+b f (m+2 p+2)+b g x (m+2 p+1))}{b^2 (m+2 p+1) (m+2 p+2)}","\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,"((a + b*x)*(c*(a + b*x))^m*((a + b*x)^2)^p*(-(a*g) + b*f*(2 + m + 2*p) + b*g*(1 + m + 2*p)*x))/(b^2*(1 + m + 2*p)*(2 + m + 2*p))","A",1
2168,1,49,61,0.0296468,"\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","Integrate[(a*c + b*c*x)^(-3 - 2*p)*(f + g*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","-\frac{\left((a+b x)^2\right)^p (c (a+b x))^{-2 p} (a g+b (f+2 g x))}{2 b^2 c^3 (a+b x)^2}","-\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,"-1/2*(((a + b*x)^2)^p*(a*g + b*(f + 2*g*x)))/(b^2*c^3*(a + b*x)^2*(c*(a + b*x))^(2*p))","A",1
2169,1,32,45,0.0207625,"\int (a+b x) (a c+b c x)^m \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Integrate[(a + b*x)*(a*c + b*c*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left((a+b x)^2\right)^{p+1} (c (a+b x))^m}{b (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,"((c*(a + b*x))^m*((a + b*x)^2)^(1 + p))/(b*(2 + m + 2*p))","A",1
2170,1,25,24,0.0203563,"\int (a+b x) (a c+b c x)^m \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Integrate[(a + b*x)*(a*c + b*c*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(a+b x)^8 (c (a+b x))^m}{b (m+8)}","\frac{(a c+b c x)^{m+8}}{b c^8 (m+8)}",1,"((a + b*x)^8*(c*(a + b*x))^m)/(b*(8 + m))","A",1
2171,1,25,27,0.0130245,"\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","Integrate[((a + b*x)*(a*c + b*c*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(c (a+b x))^m}{b (m-4) (a+b x)^4}","-\frac{c^4 (a c+b c x)^{m-4}}{b (4-m)}",1,"(c*(a + b*x))^m/(b*(-4 + m)*(a + b*x)^4)","A",1
2172,1,527,414,5.9278304,"\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","Integrate[(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{(d+e x)^3 ((d+e x) (c (d-e x)-b e))^{3/2} \left(\frac{9 (-3 b e g+2 c d g+4 c e f) \left(-384 c^5 e^{12} (d+e x)^5 \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}-48 c^4 e^{12} (d+e x)^4 \sqrt{e (2 c d-b e)} (b e-2 c d)^2 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}+56 c^3 e^{12} (d+e x)^3 \sqrt{e (2 c d-b e)} (b e-2 c d)^3 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}-70 c^2 e^{12} (d+e x)^2 \sqrt{e (2 c d-b e)} (b e-2 c d)^4 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}+105 \sqrt{c} e^{25/2} \sqrt{d+e x} (b e-2 c d)^6 \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)+105 c e^{12} (d+e x) \sqrt{e (2 c d-b e)} (b e-2 c d)^5 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}\right)}{1280 c^5 e^{11} (d+e x)^5 \sqrt{e (2 c d-b e)} (b e-2 c d)^2 \left(\frac{b e-c d+c e x}{b e-2 c d}\right)^{3/2}}-9 e g\right)}{54 c e^3}","\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{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{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,"((d + e*x)^3*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(-9*e*g + (9*(4*c*e*f + 2*c*d*g - 3*b*e*g)*(105*c*e^12*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^5*(d + e*x)*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] - 70*c^2*e^12*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^4*(d + e*x)^2*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + 56*c^3*e^12*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^3*(d + e*x)^3*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] - 48*c^4*e^12*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*(d + e*x)^4*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] - 384*c^5*e^12*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*(d + e*x)^5*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + 105*Sqrt[c]*e^(25/2)*(-2*c*d + b*e)^6*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]]))/(1280*c^5*e^11*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*(d + e*x)^5*((-(c*d) + b*e + c*e*x)/(-2*c*d + b*e))^(3/2))))/(54*c*e^3)","A",1
2173,1,464,339,3.9331426,"\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","Integrate[(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{(d+e x)^2 ((d+e x) (c (d-e x)-b e))^{3/2} \left(\frac{7 (-7 b e g+4 c d g+10 c e f) \left(-48 c^4 e^{10} (d+e x)^4 \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}-e^4 (b e-2 c d)^2 \left(8 c^3 e^6 (d+e x)^3 \sqrt{e (2 c d-b e)} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}-10 c^2 e^6 (d+e x)^2 \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}+15 \sqrt{c} e^{13/2} \sqrt{d+e x} (b e-2 c d)^3 \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)+15 c e^6 (d+e x) \sqrt{e (2 c d-b e)} (b e-2 c d)^2 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}\right)\right)}{384 c^4 e^9 (d+e x)^4 \sqrt{e (2 c d-b e)} (b e-2 c d)^2 \left(\frac{b e-c d+c e x}{b e-2 c d}\right)^{3/2}}-7 e g\right)}{35 c e^3}","\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{(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{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,"((d + e*x)^2*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(-7*e*g + (7*(10*c*e*f + 4*c*d*g - 7*b*e*g)*(-48*c^4*e^10*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*(d + e*x)^4*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] - e^4*(-2*c*d + b*e)^2*(15*c*e^6*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*(d + e*x)*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] - 10*c^2*e^6*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*(d + e*x)^2*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + 8*c^3*e^6*Sqrt[e*(2*c*d - b*e)]*(d + e*x)^3*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + 15*Sqrt[c]*e^(13/2)*(-2*c*d + b*e)^3*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])))/(384*c^4*e^9*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*(d + e*x)^4*((-(c*d) + b*e + c*e*x)/(-2*c*d + b*e))^(3/2))))/(35*c*e^3)","A",1
2174,1,391,223,2.4439071,"\int (d+e x) (f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2} \, dx","Integrate[(d + e*x)*(f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","\frac{(d+e x) ((d+e x) (c (d-e x)-b e))^{3/2} \left(\frac{5 (-5 b e g+2 c d g+8 c e f) \left(-8 c^3 e^8 (d+e x)^3 \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}-2 c^2 e^8 (d+e x)^2 \sqrt{e (2 c d-b e)} (b e-2 c d)^2 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}+3 \sqrt{c} e^{17/2} \sqrt{d+e x} (b e-2 c d)^4 \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)+3 c e^8 (d+e x) \sqrt{e (2 c d-b e)} (b e-2 c d)^3 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}\right)}{48 c^3 e^7 (d+e x)^3 \sqrt{e (2 c d-b e)} (b e-2 c d)^2 \left(\frac{b e-c d+c e x}{b e-2 c d}\right)^{3/2}}-5 e g\right)}{20 c e^3}","\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}",1,"((d + e*x)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(-5*e*g + (5*(8*c*e*f + 2*c*d*g - 5*b*e*g)*(3*c*e^8*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^3*(d + e*x)*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] - 2*c^2*e^8*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*(d + e*x)^2*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] - 8*c^3*e^8*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*(d + e*x)^3*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + 3*Sqrt[c]*e^(17/2)*(-2*c*d + b*e)^4*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]]))/(48*c^3*e^7*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*(d + e*x)^3*((-(c*d) + b*e + c*e*x)/(-2*c*d + b*e))^(3/2))))/(20*c*e^3)","A",1
2175,1,174,192,0.512792,"\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","Integrate[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x),x]","\frac{\sqrt{(d+e x) (c (d-e x)-b e)} \left(\sqrt{c} \sqrt{e} (b e g+2 c (-2 d g+2 e f+e g x))+\frac{\sqrt{e (2 c d-b e)} (-b e g-2 c d g+4 c e f) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)}{\sqrt{d+e x} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}\right)}{4 c^{3/2} e^{5/2}}","\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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(Sqrt[c]*Sqrt[e]*(b*e*g + 2*c*(2*e*f - 2*d*g + e*g*x)) + (Sqrt[e*(2*c*d - b*e)]*(4*c*e*f - 2*c*d*g - b*e*g)*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])/(Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])))/(4*c^(3/2)*e^(5/2))","A",1
2176,1,185,200,0.7056454,"\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","Integrate[((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{\sqrt{(d+e x) (c (d-e x)-b e)} \left(-\frac{\sqrt{e} (b e-2 c d) (3 d g-2 e f+e g x)}{d+e x}-\frac{\sqrt{e (2 c d-b e)} (b e g-4 c d g+2 c e f) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)}{\sqrt{c} \sqrt{d+e x} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}\right)}{e^{5/2} (2 c d-b e)}","-\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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-((Sqrt[e]*(-2*c*d + b*e)*(-2*e*f + 3*d*g + e*g*x))/(d + e*x)) - (Sqrt[e*(2*c*d - b*e)]*(2*c*e*f - 4*c*d*g + b*e*g)*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])/(Sqrt[c]*Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])))/(e^(5/2)*(2*c*d - b*e))","A",1
2177,1,146,168,0.2215372,"\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","Integrate[((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 \sqrt{(d+e x) (c (d-e x)-b e)} \left((b e-c d+c e x) (-b e g+c d g+c e f)+\frac{g (b e-2 c d)^2 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{c (d+e x)}{2 c d-b e}\right)}{\sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}\right)}{3 c e^2 (d+e x)^2 (2 c d-b e)}","-\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*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*((c*e*f + c*d*g - b*e*g)*(-(c*d) + b*e + c*e*x) + ((-2*c*d + b*e)^2*g*Hypergeometric2F1[-3/2, -3/2, -1/2, (c*(d + e*x))/(2*c*d - b*e)])/Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(3*c*e^2*(2*c*d - b*e)*(d + e*x)^2)","C",1
2178,1,102,137,0.0600355,"\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","Integrate[((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 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)} \left(2 c \left(d^2 g+4 d e (f+g x)+e^2 f x\right)-b e (2 d g+3 e f+5 e g x)\right)}{15 e^2 (d+e x)^3 (b e-2 c d)^2}","-\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*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-(b*e*(3*e*f + 2*d*g + 5*e*g*x)) + 2*c*(d^2*g + e^2*f*x + 4*d*e*(f + g*x))))/(15*e^2*(-2*c*d + b*e)^2*(d + e*x)^3)","A",1
2179,1,154,210,0.1183001,"\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","Integrate[((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{2 ((d+e x) (c (d-e x)-b e))^{3/2} \left(3 b^2 e^2 (2 d g+5 e f+7 e g x)-2 b c e \left(13 d^2 g+d e (36 f+50 g x)+e^2 x (6 f+7 g x)\right)+4 c^2 \left(5 d^3 g+d^2 e (23 f+25 g x)+5 d e^2 x (2 f+g x)+2 e^3 f x^2\right)\right)}{105 e^2 (d+e x)^5 (b e-2 c d)^3}","-\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*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(3*b^2*e^2*(5*e*f + 2*d*g + 7*e*g*x) + 4*c^2*(5*d^3*g + 2*e^3*f*x^2 + 5*d*e^2*x*(2*f + g*x) + d^2*e*(23*f + 25*g*x)) - 2*b*c*e*(13*d^2*g + e^2*x*(6*f + 7*g*x) + d*e*(36*f + 50*g*x))))/(105*e^2*(-2*c*d + b*e)^3*(d + e*x)^5)","A",1
2180,1,232,285,0.1728219,"\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","Integrate[((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{2 ((d+e x) (c (d-e x)-b e))^{3/2} \left(-5 b^3 e^3 (2 d g+7 e f+9 e g x)+6 b^2 c e^2 \left(11 d^2 g+d e (40 f+52 g x)+e^2 x (5 f+6 g x)\right)-12 b c^2 e \left(12 d^3 g+d^2 e (47 f+61 g x)+2 d e^2 x (7 f+8 g x)+2 e^3 x^2 (f+g x)\right)+8 c^3 \left(11 d^4 g+d^3 e (58 f+66 g x)+3 d^2 e^2 x (11 f+8 g x)+4 d e^3 x^2 (3 f+g x)+2 e^4 f x^3\right)\right)}{315 e^2 (d+e x)^6 (b e-2 c d)^4}","-\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*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(-5*b^3*e^3*(7*e*f + 2*d*g + 9*e*g*x) + 6*b^2*c*e^2*(11*d^2*g + e^2*x*(5*f + 6*g*x) + d*e*(40*f + 52*g*x)) - 12*b*c^2*e*(12*d^3*g + 2*e^3*x^2*(f + g*x) + 2*d*e^2*x*(7*f + 8*g*x) + d^2*e*(47*f + 61*g*x)) + 8*c^3*(11*d^4*g + 2*e^4*f*x^3 + 4*d*e^3*x^2*(3*f + g*x) + 3*d^2*e^2*x*(11*f + 8*g*x) + d^3*e*(58*f + 66*g*x))))/(315*e^2*(-2*c*d + b*e)^4*(d + e*x)^6)","A",1
2181,1,335,360,0.2558523,"\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","Integrate[((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{2 ((d+e x) (c (d-e x)-b e))^{3/2} \left(35 b^4 e^4 (2 d g+9 e f+11 e g x)-10 b^3 c e^3 \left(61 d^2 g+d e (280 f+346 g x)+e^2 x (28 f+33 g x)\right)+12 b^2 c^2 e^2 \left(167 d^3 g+d^2 e (790 f+986 g x)+d e^2 x (180 f+211 g x)+2 e^3 x^2 (10 f+11 g x)\right)-8 b c^3 e \left(365 d^4 g+2 d^3 e (912 f+1141 g x)+3 d^2 e^2 x (244 f+277 g x)+4 d e^3 x^2 (48 f+49 g x)+2 e^4 x^3 (12 f+11 g x)\right)+16 c^4 \left(91 d^5 g+d^4 e (547 f+637 g x)+7 d^3 e^2 x (52 f+45 g x)+2 d^2 e^3 x^2 (90 f+49 g x)+14 d e^4 x^3 (4 f+g x)+8 e^5 f x^4\right)\right)}{3465 e^2 (d+e x)^7 (b e-2 c d)^5}","-\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*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(35*b^4*e^4*(9*e*f + 2*d*g + 11*e*g*x) - 10*b^3*c*e^3*(61*d^2*g + e^2*x*(28*f + 33*g*x) + d*e*(280*f + 346*g*x)) + 16*c^4*(91*d^5*g + 8*e^5*f*x^4 + 14*d*e^4*x^3*(4*f + g*x) + 7*d^3*e^2*x*(52*f + 45*g*x) + 2*d^2*e^3*x^2*(90*f + 49*g*x) + d^4*e*(547*f + 637*g*x)) + 12*b^2*c^2*e^2*(167*d^3*g + 2*e^3*x^2*(10*f + 11*g*x) + d*e^2*x*(180*f + 211*g*x) + d^2*e*(790*f + 986*g*x)) - 8*b*c^3*e*(365*d^4*g + 2*e^4*x^3*(12*f + 11*g*x) + 4*d*e^3*x^2*(48*f + 49*g*x) + 3*d^2*e^2*x*(244*f + 277*g*x) + 2*d^3*e*(912*f + 1141*g*x))))/(3465*e^2*(-2*c*d + b*e)^5*(d + e*x)^7)","A",1
2182,1,176,439,0.4461905,"\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","Integrate[((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{2 ((d+e x) (c (d-e x)-b e))^{3/2} \left(2 (d+e x) \left(8 c (d+e x) \left(2 c (d+e x) \left(4 c (d+e x) (-3 b e+8 c d+2 c e x)+15 (b e-2 c d)^2\right)+35 (2 c d-b e)^3\right)+315 (b e-2 c d)^4\right) \left(c e (8 d g+5 e f)-\frac{13}{2} b e^2 g\right)-3465 e (b e-2 c d)^5 (e f-d g)\right)}{45045 e^3 (d+e x)^8 (b e-2 c d)^6}","-\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*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(-3465*e*(-2*c*d + b*e)^5*(e*f - d*g) + 2*((-13*b*e^2*g)/2 + c*e*(5*e*f + 8*d*g))*(d + e*x)*(315*(-2*c*d + b*e)^4 + 8*c*(d + e*x)*(35*(2*c*d - b*e)^3 + 2*c*(d + e*x)*(15*(-2*c*d + b*e)^2 + 4*c*(d + e*x)*(8*c*d - 3*b*e + 2*c*e*x))))))/(45045*e^3*(-2*c*d + b*e)^6*(d + e*x)^8)","A",1
2183,1,1418,488,6.4756533,"\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","Integrate[(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{g (c d-b e-c e x) ((d+e x) (c (d-e x)-b e))^{3/2} (d+e x)^4}{8 c e^2}-\frac{(c d e+(c d-b e) e) \left(-8 c f e^2-\left(\frac{11}{2} e (c d-b e)-\frac{5 c d e}{2}\right) g\right) ((d+e x) (c (d-e x)-b e))^{3/2} \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^{5/2} \left(\frac{99 (c d e+(c d-b e) e)^6 \left(-\frac{256 c^5 (d+e x)^5 e^{10}}{315 (c d e+(c d-b e) e)^5 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^5}-\frac{32 c^4 (d+e x)^4 e^8}{35 (c d e+(c d-b e) e)^4 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^4}-\frac{16 c^3 (d+e x)^3 e^6}{15 (c d e+(c d-b e) e)^3 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^3}-\frac{4 c^2 (d+e x)^2 e^4}{3 (c d e+(c d-b e) e)^2 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^2}-\frac{2 c (d+e x) e^2}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}+\frac{2 \sqrt{c} \sqrt{d+e x} \sin ^{-1}\left(\frac{\sqrt{c} e \sqrt{d+e x}}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}}\right) e}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}} \sqrt{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}}\right) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^6}{4096 c^6 e^{12} (d+e x)^6 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^2}+\frac{11}{14} \left(\frac{1}{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}+\frac{1}{4 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^2}\right)\right) (d+e x)^4}{44 c e^4 \left(\frac{e}{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}\right)^{3/2} (c d-b e-c e x) \sqrt{\frac{e (c d-b e-c e x)}{c d e+(c d-b e) e}}}","\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{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{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,"-1/8*(g*(d + e*x)^4*(c*d - b*e - c*e*x)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2))/(c*e^2) - ((c*d*e + e*(c*d - b*e))*(-8*c*e^2*f - ((-5*c*d*e)/2 + (11*e*(c*d - b*e))/2)*g)*(d + e*x)^4*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(5/2)*((11*(1/(4*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^2) + (1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(-1)))/14 + (99*(c*d*e + e*(c*d - b*e))^6*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^6*((-2*c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))) - (4*c^2*e^4*(d + e*x)^2)/(3*(c*d*e + e*(c*d - b*e))^2*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^2) - (16*c^3*e^6*(d + e*x)^3)/(15*(c*d*e + e*(c*d - b*e))^3*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^3) - (32*c^4*e^8*(d + e*x)^4)/(35*(c*d*e + e*(c*d - b*e))^4*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^4) - (256*c^5*e^10*(d + e*x)^5)/(315*(c*d*e + e*(c*d - b*e))^5*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^5) + (2*Sqrt[c]*e*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*e*Sqrt[d + e*x])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))])])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))]*Sqrt[1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))])))/(4096*c^6*e^12*(d + e*x)^6*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^2)))/(44*c*e^4*(e/((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))^(3/2)*(c*d - b*e - c*e*x)*Sqrt[(e*(c*d - b*e - c*e*x))/(c*d*e + e*(c*d - b*e))])","B",1
2184,1,1329,413,6.3014858,"\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","Integrate[(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{g (c d-b e-c e x) ((d+e x) (c (d-e x)-b e))^{3/2} (d+e x)^3}{7 c e^2}-\frac{2 (c d e+(c d-b e) e) \left(-7 c f e^2-\left(\frac{9}{2} e (c d-b e)-\frac{5 c d e}{2}\right) g\right) ((d+e x) (c (d-e x)-b e))^{3/2} \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^{5/2} \left(\frac{63 (c d e+(c d-b e) e)^5 \left(-\frac{32 c^4 (d+e x)^4 e^8}{35 (c d e+(c d-b e) e)^4 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^4}-\frac{16 c^3 (d+e x)^3 e^6}{15 (c d e+(c d-b e) e)^3 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^3}-\frac{4 c^2 (d+e x)^2 e^4}{3 (c d e+(c d-b e) e)^2 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^2}-\frac{2 c (d+e x) e^2}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}+\frac{2 \sqrt{c} \sqrt{d+e x} \sin ^{-1}\left(\frac{\sqrt{c} e \sqrt{d+e x}}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}}\right) e}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}} \sqrt{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}}\right) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^5}{2048 c^5 e^{10} (d+e x)^5 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^2}+\frac{3}{4} \left(\frac{1}{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}+\frac{3}{10 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^2}\right)\right) (d+e x)^3}{63 c e^4 \left(\frac{e}{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}\right)^{3/2} (c d-b e-c e x) \sqrt{\frac{e (c d-b e-c e x)}{c d e+(c d-b e) e}}}","\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{(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{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,"-1/7*(g*(d + e*x)^3*(c*d - b*e - c*e*x)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2))/(c*e^2) - (2*(c*d*e + e*(c*d - b*e))*(-7*c*e^2*f - ((-5*c*d*e)/2 + (9*e*(c*d - b*e))/2)*g)*(d + e*x)^3*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(5/2)*((3*(3/(10*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^2) + (1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(-1)))/4 + (63*(c*d*e + e*(c*d - b*e))^5*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^5*((-2*c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))) - (4*c^2*e^4*(d + e*x)^2)/(3*(c*d*e + e*(c*d - b*e))^2*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^2) - (16*c^3*e^6*(d + e*x)^3)/(15*(c*d*e + e*(c*d - b*e))^3*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^3) - (32*c^4*e^8*(d + e*x)^4)/(35*(c*d*e + e*(c*d - b*e))^4*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^4) + (2*Sqrt[c]*e*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*e*Sqrt[d + e*x])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))])])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))]*Sqrt[1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))])))/(2048*c^5*e^10*(d + e*x)^5*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^2)))/(63*c*e^4*(e/((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))^(3/2)*(c*d - b*e - c*e*x)*Sqrt[(e*(c*d - b*e - c*e*x))/(c*d*e + e*(c*d - b*e))])","B",1
2185,1,504,297,5.7198475,"\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","Integrate[(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{(d+e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} \left(\frac{7 \sqrt{e (2 c d-b e)} \left(\frac{b e-c d+c e x}{b e-2 c d}\right)^{3/2} \left(c e (d g+6 e f)-\frac{7}{2} b e^2 g\right) \left(16 c^4 e^{12} (d+e x)^4 \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} (11 b e-14 c d+8 c e x)-e^6 (2 c d-b e)^3 \left(8 c^3 e^6 (d+e x)^3 \sqrt{e (2 c d-b e)} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}-10 c^2 e^6 (d+e x)^2 \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}+15 \sqrt{c} e^{13/2} \sqrt{d+e x} (b e-2 c d)^3 \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)+15 c e^6 (d+e x) \sqrt{e (2 c d-b e)} (b e-2 c d)^2 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}\right)\right)}{640 c^4 e^{12} (d+e x)^4 (b e-c d+c e x)^2}-7 e^2 g (b e-c d+c e x)^2\right)}{42 c e^4}","\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}",1,"((d + e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-7*e^2*g*(-(c*d) + b*e + c*e*x)^2 + (7*Sqrt[e*(2*c*d - b*e)]*((-7*b*e^2*g)/2 + c*e*(6*e*f + d*g))*((-(c*d) + b*e + c*e*x)/(-2*c*d + b*e))^(3/2)*(16*c^4*e^12*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*(d + e*x)^4*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*(-14*c*d + 11*b*e + 8*c*e*x) - e^6*(2*c*d - b*e)^3*(15*c*e^6*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*(d + e*x)*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] - 10*c^2*e^6*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*(d + e*x)^2*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + 8*c^3*e^6*Sqrt[e*(2*c*d - b*e)]*(d + e*x)^3*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + 15*Sqrt[c]*e^(13/2)*(-2*c*d + b*e)^3*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])))/(640*c^4*e^12*(d + e*x)^4*(-(c*d) + b*e + c*e*x)^2)))/(42*c*e^4)","A",1
2186,1,361,266,2.5654294,"\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","Integrate[((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{(d+e x) \sqrt{(d+e x) (c (d-e x)-b e)} \left(\frac{\sqrt{e (2 c d-b e)} \left(\frac{b e-c d+c e x}{b e-2 c d}\right)^{3/2} (-3 b e g-2 c d g+8 c e f) \left(2 c^2 e^8 (d+e x)^2 \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} (7 b e-10 c d+4 c e x)-3 e^6 (2 c d-b e)^3 \left(\sqrt{c} e^{5/2} \sqrt{d+e x} (b e-2 c d) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)+c e^2 (d+e x) \sqrt{e (2 c d-b e)} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}\right)\right)}{16 c^2 e^7 (d+e x)^2 (b e-c d+c e x)^2}-3 e^2 g (b e-c d+c e x)^2\right)}{12 c e^4}","\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{(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{\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,"((d + e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-3*e^2*g*(-(c*d) + b*e + c*e*x)^2 + (Sqrt[e*(2*c*d - b*e)]*(8*c*e*f - 2*c*d*g - 3*b*e*g)*((-(c*d) + b*e + c*e*x)/(-2*c*d + b*e))^(3/2)*(2*c^2*e^8*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*(d + e*x)^2*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*(-10*c*d + 7*b*e + 4*c*e*x) - 3*e^6*(2*c*d - b*e)^3*(c*e^2*Sqrt[e*(2*c*d - b*e)]*(d + e*x)*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + Sqrt[c]*e^(5/2)*(-2*c*d + b*e)*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])))/(16*c^2*e^7*(d + e*x)^2*(-(c*d) + b*e + c*e*x)^2)))/(12*c*e^4)","A",1
2187,1,228,278,0.8739589,"\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","Integrate[((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{\sqrt{(d+e x) (c (d-e x)-b e)} \left(-\sqrt{c} \sqrt{e} \left(3 b^2 e^2 g+2 b c e (-14 d g+15 e f+7 e g x)+4 c^2 \left(10 d^2 g-6 d e (2 f+g x)+e^2 x (3 f+2 g x)\right)\right)-\frac{3 \sqrt{e (2 c d-b e)} (b e-2 c d) (-b e g-4 c d g+6 c e f) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)}{\sqrt{d+e x} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}\right)}{24 c^{3/2} e^{5/2}}","\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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-(Sqrt[c]*Sqrt[e]*(3*b^2*e^2*g + 2*b*c*e*(15*e*f - 14*d*g + 7*e*g*x) + 4*c^2*(10*d^2*g - 6*d*e*(2*f + g*x) + e^2*x*(3*f + 2*g*x)))) - (3*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*(6*c*e*f - 4*c*d*g - b*e*g)*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])/(Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])))/(24*c^(3/2)*e^(5/2))","A",1
2188,1,208,271,0.8454112,"\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","Integrate[((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{\sqrt{(d+e x) (c (d-e x)-b e)} \left(-\frac{\sqrt{e} \left(b e (13 d g-8 e f+5 e g x)+c \left(-28 d^2 g+10 d e (2 f-g x)+2 e^2 x (2 f+g x)\right)\right)}{d+e x}-\frac{3 \sqrt{e (2 c d-b e)} (b e g-6 c d g+4 c e f) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)}{\sqrt{c} \sqrt{d+e x} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}\right)}{4 e^{5/2}}","-\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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-((Sqrt[e]*(b*e*(-8*e*f + 13*d*g + 5*e*g*x) + c*(-28*d^2*g + 10*d*e*(2*f - g*x) + 2*e^2*x*(2*f + g*x))))/(d + e*x)) - (3*Sqrt[e*(2*c*d - b*e)]*(4*c*e*f - 6*c*d*g + b*e*g)*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])/(Sqrt[c]*Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])))/(4*e^(5/2))","A",1
2189,1,150,276,0.1981421,"\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","Integrate[((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 \sqrt{(d+e x) (c (d-e x)-b e)} \left(\frac{e (d+e x) (3 b e g-8 c d g+2 c e f) \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{c (d+e x)}{2 c d-b e}\right)}{\sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}+\frac{e (e f-d g) (b e-c d+c e x)^2}{b e-2 c d}\right)}{3 e^3 (d+e x)^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,"(2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*((e*(e*f - d*g)*(-(c*d) + b*e + c*e*x)^2)/(-2*c*d + b*e) + (e*(2*c*e*f - 8*c*d*g + 3*b*e*g)*(d + e*x)*Hypergeometric2F1[-3/2, -1/2, 1/2, (c*(d + e*x))/(2*c*d - b*e)])/Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(3*e^3*(d + e*x)^2)","C",1
2190,1,150,214,0.2802454,"\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","Integrate[((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{2 \sqrt{(d+e x) (c (d-e x)-b e)} \left(\frac{g (2 c d-b e)^3 \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};\frac{c (d+e x)}{2 c d-b e}\right)}{\sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}-(b e-c d+c e x)^2 (-b e g+c d g+c e f)\right)}{5 c e^2 (d+e x)^3 (2 c d-b e)}","\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*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-((c*e*f + c*d*g - b*e*g)*(-(c*d) + b*e + c*e*x)^2) + ((2*c*d - b*e)^3*g*Hypergeometric2F1[-5/2, -5/2, -3/2, (c*(d + e*x))/(2*c*d - b*e)])/Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(5*c*e^2*(2*c*d - b*e)*(d + e*x)^3)","C",1
2191,1,104,138,0.0788285,"\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","Integrate[((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 (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} \left(2 c \left(d^2 g+6 d e (f+g x)+e^2 f x\right)-b e (2 d g+5 e f+7 e g x)\right)}{35 e^2 (d+e x)^4 (b e-2 c d)^2}","\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*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-(b*e*(5*e*f + 2*d*g + 7*e*g*x)) + 2*c*(d^2*g + e^2*f*x + 6*d*e*(f + g*x))))/(35*e^2*(-2*c*d + b*e)^2*(d + e*x)^4)","A",1
2192,1,168,210,0.1170931,"\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","Integrate[((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{2 (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} \left(5 b^2 e^2 (2 d g+7 e f+9 e g x)-2 b c e \left(19 d^2 g+d e (80 f+98 g x)+e^2 x (10 f+9 g x)\right)+4 c^2 \left(7 d^3 g+d^2 e (47 f+49 g x)+7 d e^2 x (2 f+g x)+2 e^3 f x^2\right)\right)}{315 e^2 (d+e x)^5 (b e-2 c d)^3}","-\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*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(5*b^2*e^2*(7*e*f + 2*d*g + 9*e*g*x) + 4*c^2*(7*d^3*g + 2*e^3*f*x^2 + 7*d*e^2*x*(2*f + g*x) + d^2*e*(47*f + 49*g*x)) - 2*b*c*e*(19*d^2*g + e^2*x*(10*f + 9*g*x) + d*e*(80*f + 98*g*x))))/(315*e^2*(-2*c*d + b*e)^3*(d + e*x)^5)","A",1
2193,1,249,285,0.1780699,"\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","Integrate[((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{2 (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} \left(-35 b^3 e^3 (2 d g+9 e f+11 e g x)+10 b^2 c e^2 \left(43 d^2 g+d e (210 f+254 g x)+e^2 x (21 f+22 g x)\right)-4 b c^2 e \left(212 d^3 g+d^2 e (1185 f+1391 g x)+2 d e^2 x (135 f+128 g x)+2 e^3 x^2 (15 f+11 g x)\right)+8 c^3 \left(61 d^4 g+8 d^3 e (57 f+61 g x)+d^2 e^2 x (183 f+128 g x)+16 d e^3 x^2 (3 f+g x)+6 e^4 f x^3\right)\right)}{3465 e^2 (d+e x)^6 (b e-2 c d)^4}","-\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*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-35*b^3*e^3*(9*e*f + 2*d*g + 11*e*g*x) + 8*c^3*(61*d^4*g + 6*e^4*f*x^3 + 16*d*e^3*x^2*(3*f + g*x) + 8*d^3*e*(57*f + 61*g*x) + d^2*e^2*x*(183*f + 128*g*x)) + 10*b^2*c*e^2*(43*d^2*g + e^2*x*(21*f + 22*g*x) + d*e*(210*f + 254*g*x)) - 4*b*c^2*e*(212*d^3*g + 2*e^3*x^2*(15*f + 11*g*x) + 2*d*e^2*x*(135*f + 128*g*x) + d^2*e*(1185*f + 1391*g*x))))/(3465*e^2*(-2*c*d + b*e)^4*(d + e*x)^6)","A",1
2194,1,349,360,0.2555801,"\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","Integrate[((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{2 (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} \left(105 b^4 e^4 (2 d g+11 e f+13 e g x)-70 b^3 c e^3 \left(25 d^2 g+2 d e (72 f+85 g x)+e^2 x (12 f+13 g x)\right)+20 b^2 c^2 e^2 \left(271 d^3 g+2 d^2 e (833 f+977 g x)+d e^2 x (308 f+323 g x)+2 e^3 x^2 (14 f+13 g x)\right)-8 b c^3 e \left(911 d^4 g+d^3 e (6200 f+7134 g x)+d^2 e^2 x (1940 f+1901 g x)+4 d e^3 x^2 (100 f+81 g x)+2 e^4 x^3 (20 f+13 g x)\right)+16 c^4 \left(213 d^5 g+d^4 e (1763 f+1917 g x)+3 d^3 e^2 x (284 f+231 g x)+2 d^2 e^3 x^2 (154 f+81 g x)+18 d e^4 x^3 (4 f+g x)+8 e^5 f x^4\right)\right)}{15015 e^2 (d+e x)^7 (b e-2 c d)^5}","-\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*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(105*b^4*e^4*(11*e*f + 2*d*g + 13*e*g*x) - 70*b^3*c*e^3*(25*d^2*g + e^2*x*(12*f + 13*g*x) + 2*d*e*(72*f + 85*g*x)) + 20*b^2*c^2*e^2*(271*d^3*g + 2*e^3*x^2*(14*f + 13*g*x) + d*e^2*x*(308*f + 323*g*x) + 2*d^2*e*(833*f + 977*g*x)) + 16*c^4*(213*d^5*g + 8*e^5*f*x^4 + 18*d*e^4*x^3*(4*f + g*x) + 2*d^2*e^3*x^2*(154*f + 81*g*x) + 3*d^3*e^2*x*(284*f + 231*g*x) + d^4*e*(1763*f + 1917*g*x)) - 8*b*c^3*e*(911*d^4*g + 2*e^4*x^3*(20*f + 13*g*x) + 4*d*e^3*x^2*(100*f + 81*g*x) + d^2*e^2*x*(1940*f + 1901*g*x) + d^3*e*(6200*f + 7134*g*x))))/(15015*e^2*(-2*c*d + b*e)^5*(d + e*x)^7)","A",1
2195,1,1600,562,6.777969,"\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","Integrate[(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{g (c d-b e-c e x) ((d+e x) (c (d-e x)-b e))^{5/2} (d+e x)^4}{10 c e^2}-\frac{(c d e+(c d-b e) e)^2 \left(-10 c f e^2-\left(\frac{13}{2} e (c d-b e)-\frac{7 c d e}{2}\right) g\right) ((d+e x) (c (d-e x)-b e))^{5/2} \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^{7/2} \left(\frac{715 (c d e+(c d-b e) e)^7 \left(-\frac{512 c^6 (d+e x)^6 e^{12}}{693 (c d e+(c d-b e) e)^6 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^6}-\frac{256 c^5 (d+e x)^5 e^{10}}{315 (c d e+(c d-b e) e)^5 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^5}-\frac{32 c^4 (d+e x)^4 e^8}{35 (c d e+(c d-b e) e)^4 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^4}-\frac{16 c^3 (d+e x)^3 e^6}{15 (c d e+(c d-b e) e)^3 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^3}-\frac{4 c^2 (d+e x)^2 e^4}{3 (c d e+(c d-b e) e)^2 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^2}-\frac{2 c (d+e x) e^2}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}+\frac{2 \sqrt{c} \sqrt{d+e x} \sin ^{-1}\left(\frac{\sqrt{c} e \sqrt{d+e x}}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}}\right) e}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}} \sqrt{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}}\right) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^7}{131072 c^7 e^{14} (d+e x)^7 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^3}+\frac{13}{18} \left(\frac{1}{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}+\frac{5}{16 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^2}+\frac{15}{224 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^3}\right)\right) (d+e x)^4}{65 c e^5 \left(\frac{e}{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}\right)^{5/2} (c d-b e-c e x)^2 \sqrt{\frac{e (c d-b e-c e x)}{c d e+(c d-b e) e}}}","\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{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{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,"-1/10*(g*(d + e*x)^4*(c*d - b*e - c*e*x)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2))/(c*e^2) - ((c*d*e + e*(c*d - b*e))^2*(-10*c*e^2*f - ((-7*c*d*e)/2 + (13*e*(c*d - b*e))/2)*g)*(d + e*x)^4*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(7/2)*((13*(15/(224*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^3) + 5/(16*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^2) + (1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(-1)))/18 + (715*(c*d*e + e*(c*d - b*e))^7*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^7*((-2*c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))) - (4*c^2*e^4*(d + e*x)^2)/(3*(c*d*e + e*(c*d - b*e))^2*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^2) - (16*c^3*e^6*(d + e*x)^3)/(15*(c*d*e + e*(c*d - b*e))^3*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^3) - (32*c^4*e^8*(d + e*x)^4)/(35*(c*d*e + e*(c*d - b*e))^4*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^4) - (256*c^5*e^10*(d + e*x)^5)/(315*(c*d*e + e*(c*d - b*e))^5*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^5) - (512*c^6*e^12*(d + e*x)^6)/(693*(c*d*e + e*(c*d - b*e))^6*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^6) + (2*Sqrt[c]*e*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*e*Sqrt[d + e*x])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))])])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))]*Sqrt[1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))])))/(131072*c^7*e^14*(d + e*x)^7*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^3)))/(65*c*e^5*(e/((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))^(5/2)*(c*d - b*e - c*e*x)^2*Sqrt[(e*(c*d - b*e - c*e*x))/(c*d*e + e*(c*d - b*e))])","B",1
2196,1,1511,487,6.5637434,"\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","Integrate[(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 (c d e+(c d-b e) e)^2 \left(-9 c f e^2-\left(\frac{11}{2} e (c d-b e)-\frac{7 c d e}{2}\right) g\right) (d+e x)^3 ((d+e x) (c (d-e x)-b e))^{5/2} \left(\frac{495 (c d e+(c d-b e) e)^6 \left(-\frac{256 c^5 (d+e x)^5 e^{10}}{315 (c d e+(c d-b e) e)^5 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^5}-\frac{32 c^4 (d+e x)^4 e^8}{35 (c d e+(c d-b e) e)^4 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^4}-\frac{16 c^3 (d+e x)^3 e^6}{15 (c d e+(c d-b e) e)^3 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^3}-\frac{4 c^2 (d+e x)^2 e^4}{3 (c d e+(c d-b e) e)^2 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^2}-\frac{2 c (d+e x) e^2}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}+\frac{2 \sqrt{c} \sqrt{d+e x} \sin ^{-1}\left(\frac{\sqrt{c} e \sqrt{d+e x}}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}}\right) e}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}} \sqrt{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}}\right) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^6}{65536 c^6 e^{12} (d+e x)^6 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^3}+\frac{11}{16} \left(\frac{1}{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}+\frac{5}{14 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^2}+\frac{5}{56 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^3}\right)\right) \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^{7/2}}{99 c e^5 \left(\frac{e}{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}\right)^{5/2} (c d-b e-c e x)^2 \sqrt{\frac{e (c d-b e-c e x)}{c d e+(c d-b e) e}}}-\frac{g (d+e x)^3 (c d-b e-c e x) ((d+e x) (c (d-e x)-b e))^{5/2}}{9 c 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{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{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,"-1/9*(g*(d + e*x)^3*(c*d - b*e - c*e*x)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2))/(c*e^2) - (2*(c*d*e + e*(c*d - b*e))^2*(-9*c*e^2*f - ((-7*c*d*e)/2 + (11*e*(c*d - b*e))/2)*g)*(d + e*x)^3*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(7/2)*((11*(5/(56*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^3) + 5/(14*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^2) + (1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(-1)))/16 + (495*(c*d*e + e*(c*d - b*e))^6*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^6*((-2*c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))) - (4*c^2*e^4*(d + e*x)^2)/(3*(c*d*e + e*(c*d - b*e))^2*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^2) - (16*c^3*e^6*(d + e*x)^3)/(15*(c*d*e + e*(c*d - b*e))^3*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^3) - (32*c^4*e^8*(d + e*x)^4)/(35*(c*d*e + e*(c*d - b*e))^4*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^4) - (256*c^5*e^10*(d + e*x)^5)/(315*(c*d*e + e*(c*d - b*e))^5*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^5) + (2*Sqrt[c]*e*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*e*Sqrt[d + e*x])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))])])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))]*Sqrt[1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))])))/(65536*c^6*e^12*(d + e*x)^6*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^3)))/(99*c*e^5*(e/((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))^(5/2)*(c*d - b*e - c*e*x)^2*Sqrt[(e*(c*d - b*e - c*e*x))/(c*d*e + e*(c*d - b*e))])","B",1
2197,1,1422,371,6.3785071,"\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","Integrate[(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{(c d e+(c d-b e) e)^2 \left(-8 c f e^2-\left(\frac{9}{2} e (c d-b e)-\frac{7 c d e}{2}\right) g\right) (d+e x)^2 ((d+e x) (c (d-e x)-b e))^{5/2} \left(\frac{45 (c d e+(c d-b e) e)^5 \left(-\frac{32 c^4 (d+e x)^4 e^8}{35 (c d e+(c d-b e) e)^4 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^4}-\frac{16 c^3 (d+e x)^3 e^6}{15 (c d e+(c d-b e) e)^3 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^3}-\frac{4 c^2 (d+e x)^2 e^4}{3 (c d e+(c d-b e) e)^2 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^2}-\frac{2 c (d+e x) e^2}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}+\frac{2 \sqrt{c} \sqrt{d+e x} \sin ^{-1}\left(\frac{\sqrt{c} e \sqrt{d+e x}}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}}\right) e}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}} \sqrt{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}}\right) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^5}{4096 c^5 e^{10} (d+e x)^5 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^3}+\frac{9}{14} \left(\frac{1}{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}+\frac{5}{12 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^2}+\frac{1}{8 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^3}\right)\right) \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^{7/2}}{36 c e^5 \left(\frac{e}{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}\right)^{5/2} (c d-b e-c e x)^2 \sqrt{\frac{e (c d-b e-c e x)}{c d e+(c d-b e) e}}}-\frac{g (d+e x)^2 (c d-b e-c e x) ((d+e x) (c (d-e x)-b e))^{5/2}}{8 c 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}",1,"-1/8*(g*(d + e*x)^2*(c*d - b*e - c*e*x)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2))/(c*e^2) - ((c*d*e + e*(c*d - b*e))^2*(-8*c*e^2*f - ((-7*c*d*e)/2 + (9*e*(c*d - b*e))/2)*g)*(d + e*x)^2*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(7/2)*((9*(1/(8*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^3) + 5/(12*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^2) + (1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(-1)))/14 + (45*(c*d*e + e*(c*d - b*e))^5*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^5*((-2*c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))) - (4*c^2*e^4*(d + e*x)^2)/(3*(c*d*e + e*(c*d - b*e))^2*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^2) - (16*c^3*e^6*(d + e*x)^3)/(15*(c*d*e + e*(c*d - b*e))^3*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^3) - (32*c^4*e^8*(d + e*x)^4)/(35*(c*d*e + e*(c*d - b*e))^4*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^4) + (2*Sqrt[c]*e*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*e*Sqrt[d + e*x])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))])])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))]*Sqrt[1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))])))/(4096*c^5*e^10*(d + e*x)^5*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^3)))/(36*c*e^5*(e/((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))^(5/2)*(c*d - b*e - c*e*x)^2*Sqrt[(e*(c*d - b*e - c*e*x))/(c*d*e + e*(c*d - b*e))])","B",1
2198,1,1230,346,6.2042582,"\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","Integrate[((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{(c d e+(c d-b e) e)^2 \left(-6 c f e^2-\left(\frac{5}{2} e (c d-b e)-\frac{7 c d e}{2}\right) g\right) ((d+e x) (c (d-e x)-b e))^{5/2} \left(\frac{15 (c d e+(c d-b e) e)^3 \left(-\frac{4 c^2 (d+e x)^2 e^4}{3 (c d e+(c d-b e) e)^2 \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^2}-\frac{2 c (d+e x) e^2}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}+\frac{2 \sqrt{c} \sqrt{d+e x} \sin ^{-1}\left(\frac{\sqrt{c} e \sqrt{d+e x}}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}}\right) e}{\sqrt{c d e+(c d-b e) e} \sqrt{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}} \sqrt{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}}\right) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)^3}{512 c^3 e^6 (d+e x)^3 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^3}+\frac{1}{2} \left(\frac{1}{1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}}+\frac{5}{8 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^2}+\frac{5}{16 \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^3}\right)\right) \left(1-\frac{c e^2 (d+e x)}{(c d e+(c d-b e) e) \left(\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}\right)}\right)^{7/2}}{15 c e^5 \left(\frac{e}{\frac{c d e^2}{c d e+(c d-b e) e}+\frac{(c d-b e) e^2}{c d e+(c d-b e) e}}\right)^{5/2} (c d-b e-c e x)^2 \sqrt{\frac{e (c d-b e-c e x)}{c d e+(c d-b e) e}}}-\frac{g (c d-b e-c e x) ((d+e x) (c (d-e x)-b e))^{5/2}}{6 c e^2}","-\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{(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{\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,"-1/6*(g*(c*d - b*e - c*e*x)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2))/(c*e^2) - ((c*d*e + e*(c*d - b*e))^2*(-6*c*e^2*f - ((-7*c*d*e)/2 + (5*e*(c*d - b*e))/2)*g)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(7/2)*((5/(16*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^3) + 5/(8*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^2) + (1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^(-1))/2 + (15*(c*d*e + e*(c*d - b*e))^3*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^3*((-2*c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))) - (4*c^2*e^4*(d + e*x)^2)/(3*(c*d*e + e*(c*d - b*e))^2*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))^2) + (2*Sqrt[c]*e*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*e*Sqrt[d + e*x])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))])])/(Sqrt[c*d*e + e*(c*d - b*e)]*Sqrt[(c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))]*Sqrt[1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))])))/(512*c^3*e^6*(d + e*x)^3*(1 - (c*e^2*(d + e*x))/((c*d*e + e*(c*d - b*e))*((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e)))))^3)))/(15*c*e^5*(e/((c*d*e^2)/(c*d*e + e*(c*d - b*e)) + (e^2*(c*d - b*e))/(c*d*e + e*(c*d - b*e))))^(5/2)*(c*d - b*e - c*e*x)^2*Sqrt[(e*(c*d - b*e - c*e*x))/(c*d*e + e*(c*d - b*e))])","B",1
2199,1,379,354,4.4079516,"\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","Integrate[((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 e-c d+c e x)^2 ((d+e x) (c (d-e x)-b e))^{3/2} \left(\frac{\sqrt{\frac{b e-c d+c e x}{b e-2 c d}} (-3 b e g-4 c d g+10 c e f) \left(2 c^2 e^9 (d+e x)^2 (e (2 c d-b e))^{3/2} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} \left(59 b^2 e^2+4 b c e (17 e x-42 d)+4 c^2 \left(31 d^2-22 d e x+6 e^2 x^2\right)\right)-15 e^8 (b e-2 c d)^4 \left(\sqrt{c} e^{5/2} \sqrt{d+e x} (b e-2 c d) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)+c e^2 (d+e x) \sqrt{e (2 c d-b e)} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}\right)\right)}{128 c^2 e^7 (d+e x)^2 \sqrt{e (2 c d-b e)} (b e-c d+c e x)^4}-3 e^3 g\right)}{15 c e^5}","\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) (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{(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,"((-(c*d) + b*e + c*e*x)^2*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(-3*e^3*g + ((10*c*e*f - 4*c*d*g - 3*b*e*g)*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*(2*c^2*e^9*(e*(2*c*d - b*e))^(3/2)*(d + e*x)^2*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*(59*b^2*e^2 + 4*b*c*e*(-42*d + 17*e*x) + 4*c^2*(31*d^2 - 22*d*e*x + 6*e^2*x^2)) - 15*e^8*(-2*c*d + b*e)^4*(c*e^2*Sqrt[e*(2*c*d - b*e)]*(d + e*x)*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + Sqrt[c]*e^(5/2)*(-2*c*d + b*e)*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])))/(128*c^2*e^7*Sqrt[e*(2*c*d - b*e)]*(d + e*x)^2*(-(c*d) + b*e + c*e*x)^4)))/(15*c*e^5)","A",1
2200,1,294,354,1.3659924,"\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","Integrate[((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{\sqrt{(d+e x) (c (d-e x)-b e)} \left(\sqrt{c} \sqrt{e} \left(15 b^3 e^3 g+2 b^2 c e^2 (-118 d g+132 e f+59 e g x)+4 b c^2 e \left(173 d^2 g-2 d e (106 f+51 g x)+2 e^2 x (26 f+17 g x)\right)-8 c^3 \left(72 d^3 g-d^2 e (88 f+45 g x)+12 d e^2 x (3 f+2 g x)-2 e^3 x^2 (4 f+3 g x)\right)\right)+\frac{15 \sqrt{e (2 c d-b e)} (b e-2 c d)^2 (-b e g-6 c d g+8 c e f) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)}{\sqrt{d+e x} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}\right)}{192 c^{3/2} e^{5/2}}","\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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(Sqrt[c]*Sqrt[e]*(15*b^3*e^3*g + 2*b^2*c*e^2*(132*e*f - 118*d*g + 59*e*g*x) - 8*c^3*(72*d^3*g + 12*d*e^2*x*(3*f + 2*g*x) - 2*e^3*x^2*(4*f + 3*g*x) - d^2*e*(88*f + 45*g*x)) + 4*b*c^2*e*(173*d^2*g + 2*e^2*x*(26*f + 17*g*x) - 2*d*e*(106*f + 51*g*x))) + (15*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*(8*c*e*f - 6*c*d*g - b*e*g)*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])/(Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])))/(192*c^(3/2)*e^(5/2))","A",1
2201,1,309,342,1.886826,"\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","Integrate[((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 ((d+e x) (c (d-e x)-b e))^{5/2} \left(e^3 (e f-d g) (b e-c d+c e x)^3-\frac{e^{5/2} \sqrt{d+e x} (b e g-8 c d g+6 c e f) \left(\sqrt{c} \sqrt{e} \sqrt{d+e x} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} \left(33 b^2 e^2+2 b c e (13 e x-53 d)+4 c^2 \left(22 d^2-9 d e x+2 e^2 x^2\right)\right)+15 \sqrt{e (2 c d-b e)} (b e-2 c d)^2 \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)\right)}{48 \sqrt{c} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}\right)}{e^5 (d+e x)^3 (2 c d-b e) (b e-c d+c e x)^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,"(2*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(e^3*(e*f - d*g)*(-(c*d) + b*e + c*e*x)^3 - (e^(5/2)*(6*c*e*f - 8*c*d*g + b*e*g)*Sqrt[d + e*x]*(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*(33*b^2*e^2 + 2*b*c*e*(-53*d + 13*e*x) + 4*c^2*(22*d^2 - 9*d*e*x + 2*e^2*x^2)) + 15*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]]))/(48*Sqrt[c]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])))/(e^5*(2*c*d - b*e)*(d + e*x)^3*(-(c*d) + b*e + c*e*x)^2)","A",1
2202,1,173,350,0.1970895,"\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","Integrate[((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 ((d+e x) (c (d-e x)-b e))^{5/2} \left(\frac{(d+e x) (b e-2 c d)^2 (3 b e g-10 c d g+4 c e f) \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};\frac{c (d+e x)}{2 c d-b e}\right)}{\sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}+(e f-d g) (b e-c d+c e x)^3\right)}{3 e^2 (d+e x)^4 (2 c d-b e) (b e-c d+c e x)^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,"(2*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*((e*f - d*g)*(-(c*d) + b*e + c*e*x)^3 + ((-2*c*d + b*e)^2*(4*c*e*f - 10*c*d*g + 3*b*e*g)*(d + e*x)*Hypergeometric2F1[-5/2, -1/2, 1/2, (c*(d + e*x))/(2*c*d - b*e)])/Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(3*e^2*(2*c*d - b*e)*(d + e*x)^4*(-(c*d) + b*e + c*e*x)^2)","C",1
2203,1,175,352,0.1983875,"\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","Integrate[((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{2 ((d+e x) (c (d-e x)-b e))^{5/2} \left(\frac{(d+e x) (b e-2 c d)^2 (5 b e g+2 c (e f-6 d g)) \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};\frac{c (d+e x)}{2 c d-b e}\right)}{\sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}+3 (e f-d g) (b e-c d+c e x)^3\right)}{15 e^2 (d+e x)^5 (2 c d-b e) (b e-c d+c e x)^2}","-\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{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{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,"(2*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(3*(e*f - d*g)*(-(c*d) + b*e + c*e*x)^3 + ((-2*c*d + b*e)^2*(5*b*e*g + 2*c*(e*f - 6*d*g))*(d + e*x)*Hypergeometric2F1[-5/2, -3/2, -1/2, (c*(d + e*x))/(2*c*d - b*e)])/Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(15*e^2*(2*c*d - b*e)*(d + e*x)^5*(-(c*d) + b*e + c*e*x)^2)","C",1
2204,1,162,264,0.3769652,"\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","Integrate[((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 ((d+e x) (c (d-e x)-b e))^{5/2} \left((b e-c d+c e x)^3 (-b e g+c d g+c e f)+\frac{g (b e-2 c d)^4 \, _2F_1\left(-\frac{7}{2},-\frac{7}{2};-\frac{5}{2};\frac{c (d+e x)}{2 c d-b e}\right)}{\sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}\right)}{7 c e^2 (d+e x)^6 (2 c d-b e) (b e-c d+c e x)^2}","-\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 c^2 g \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e 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}}{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*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*((c*e*f + c*d*g - b*e*g)*(-(c*d) + b*e + c*e*x)^3 + ((-2*c*d + b*e)^4*g*Hypergeometric2F1[-7/2, -7/2, -5/2, (c*(d + e*x))/(2*c*d - b*e)])/Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(7*c*e^2*(2*c*d - b*e)*(d + e*x)^6*(-(c*d) + b*e + c*e*x)^2)","C",1
2205,1,104,138,0.0992433,"\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","Integrate[((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 (b e-c d+c e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} \left(2 c \left(d^2 g+8 d e (f+g x)+e^2 f x\right)-b e (2 d g+7 e f+9 e g x)\right)}{63 e^2 (d+e x)^5 (b e-2 c d)^2}","\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*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-(b*e*(7*e*f + 2*d*g + 9*e*g*x)) + 2*c*(d^2*g + e^2*f*x + 8*d*e*(f + g*x))))/(63*e^2*(-2*c*d + b*e)^2*(d + e*x)^5)","A",1
2206,1,169,210,0.1506888,"\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","Integrate[((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{2 (b e-c d+c e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} \left(7 b^2 e^2 (2 d g+9 e f+11 e g x)-2 b c e \left(25 d^2 g+2 d e (70 f+81 g x)+e^2 x (14 f+11 g x)\right)+4 c^2 \left(9 d^3 g+d^2 e (79 f+81 g x)+9 d e^2 x (2 f+g x)+2 e^3 f x^2\right)\right)}{693 e^2 (d+e x)^6 (b e-2 c d)^3}","-\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*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(7*b^2*e^2*(9*e*f + 2*d*g + 11*e*g*x) - 2*b*c*e*(25*d^2*g + e^2*x*(14*f + 11*g*x) + 2*d*e*(70*f + 81*g*x)) + 4*c^2*(9*d^3*g + 2*e^3*f*x^2 + 9*d*e^2*x*(2*f + g*x) + d^2*e*(79*f + 81*g*x))))/(693*e^2*(-2*c*d + b*e)^3*(d + e*x)^6)","A",1
2207,1,250,285,0.2212632,"\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","Integrate[((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{2 (b e-c d+c e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} \left(-63 b^3 e^3 (2 d g+11 e f+13 e g x)+14 b^2 c e^2 \left(53 d^2 g+4 d e (81 f+94 g x)+e^2 x (27 f+26 g x)\right)-4 b c^2 e \left(348 d^3 g+d^2 e (2499 f+2801 g x)+2 d e^2 x (231 f+200 g x)+2 e^3 x^2 (21 f+13 g x)\right)+8 c^3 \left(97 d^4 g+10 d^3 e (93 f+97 g x)+d^2 e^2 x (291 f+200 g x)+20 d e^3 x^2 (3 f+g x)+6 e^4 f x^3\right)\right)}{9009 e^2 (d+e x)^7 (b e-2 c d)^4}","-\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*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-63*b^3*e^3*(11*e*f + 2*d*g + 13*e*g*x) + 14*b^2*c*e^2*(53*d^2*g + e^2*x*(27*f + 26*g*x) + 4*d*e*(81*f + 94*g*x)) + 8*c^3*(97*d^4*g + 6*e^4*f*x^3 + 20*d*e^3*x^2*(3*f + g*x) + 10*d^3*e*(93*f + 97*g*x) + d^2*e^2*x*(291*f + 200*g*x)) - 4*b*c^2*e*(348*d^3*g + 2*e^3*x^2*(21*f + 13*g*x) + 2*d*e^2*x*(231*f + 200*g*x) + d^2*e*(2499*f + 2801*g*x))))/(9009*e^2*(-2*c*d + b*e)^4*(d + e*x)^7)","A",1
2208,1,351,360,0.2977055,"\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","Integrate[((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{2 (b e-c d+c e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} \left(231 b^4 e^4 (2 d g+13 e f+15 e g x)-42 b^3 c e^3 \left(89 d^2 g+d e (616 f+706 g x)+e^2 x (44 f+45 g x)\right)+84 b^2 c^2 e^2 \left(133 d^3 g+6 d^2 e (167 f+189 g x)+3 d e^2 x (52 f+51 g x)+2 e^3 x^2 (6 f+5 g x)\right)-8 b c^3 e \left(1801 d^4 g+2 d^3 e (7672 f+8481 g x)+3 d^2 e^2 x (1316 f+1201 g x)+4 d e^3 x^2 (168 f+121 g x)+2 e^4 x^3 (28 f+15 g x)\right)+16 c^4 \left(407 d^5 g+d^4 e (4243 f+4477 g x)+11 d^3 e^2 x (148 f+117 g x)+2 d^2 e^3 x^2 (234 f+121 g x)+22 d e^4 x^3 (4 f+g x)+8 e^5 f x^4\right)\right)}{45045 e^2 (d+e x)^8 (b e-2 c d)^5}","-\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*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(231*b^4*e^4*(13*e*f + 2*d*g + 15*e*g*x) + 84*b^2*c^2*e^2*(133*d^3*g + 2*e^3*x^2*(6*f + 5*g*x) + 3*d*e^2*x*(52*f + 51*g*x) + 6*d^2*e*(167*f + 189*g*x)) - 42*b^3*c*e^3*(89*d^2*g + e^2*x*(44*f + 45*g*x) + d*e*(616*f + 706*g*x)) + 16*c^4*(407*d^5*g + 8*e^5*f*x^4 + 22*d*e^4*x^3*(4*f + g*x) + 11*d^3*e^2*x*(148*f + 117*g*x) + 2*d^2*e^3*x^2*(234*f + 121*g*x) + d^4*e*(4243*f + 4477*g*x)) - 8*b*c^3*e*(1801*d^4*g + 2*e^4*x^3*(28*f + 15*g*x) + 4*d*e^3*x^2*(168*f + 121*g*x) + 3*d^2*e^2*x*(1316*f + 1201*g*x) + 2*d^3*e*(7672*f + 8481*g*x))))/(45045*e^2*(-2*c*d + b*e)^5*(d + e*x)^8)","A",1
2209,1,375,340,1.7416153,"\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","Integrate[((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{\sqrt{(d+e x) (c (d-e x)-b e)} \left(-\frac{e^3 (-7 b e g+6 c d g+8 c e f) \left(8 c^3 e^6 (d+e x)^3 \sqrt{e (2 c d-b e)} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}-10 c^2 e^6 (d+e x)^2 \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}+15 \sqrt{c} e^{13/2} \sqrt{d+e x} (b e-2 c d)^3 \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)+15 c e^6 (d+e x) \sqrt{e (2 c d-b e)} (b e-2 c d)^2 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}\right)}{3 \sqrt{e (2 c d-b e)} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}-16 c^4 e^9 g (d+e x)^4\right)}{64 c^5 e^{11} (d+e x)}","\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{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{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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-16*c^4*e^9*g*(d + e*x)^4 - (e^3*(8*c*e*f + 6*c*d*g - 7*b*e*g)*(15*c*e^6*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)^2*(d + e*x)*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] - 10*c^2*e^6*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*(d + e*x)^2*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + 8*c^3*e^6*Sqrt[e*(2*c*d - b*e)]*(d + e*x)^3*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)] + 15*Sqrt[c]*e^(13/2)*(-2*c*d + b*e)^3*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]]))/(3*Sqrt[e*(2*c*d - b*e)]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])))/(64*c^5*e^11*(d + e*x))","A",1
2210,1,251,265,1.2777327,"\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","Integrate[((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{\sqrt{(d+e x) (c (d-e x)-b e)} \left(\frac{e^7 (-5 b e g+4 c d g+6 c e f) \left(3 \sqrt{c} \sqrt{e} \sqrt{d+e x} (b e-2 c d)^2 \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)-c (d+e x) \sqrt{e (2 c d-b e)} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} (-3 b e+8 c d+2 c e x)\right)}{\sqrt{e (2 c d-b e)} \sqrt{\frac{b e-c d+c e x}{b e-2 c d}}}-8 c^3 e^7 g (d+e x)^3\right)}{24 c^4 e^9 (d+e x)}","\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{(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{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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-8*c^3*e^7*g*(d + e*x)^3 + (e^7*(6*c*e*f + 4*c*d*g - 5*b*e*g)*(-(c*Sqrt[e*(2*c*d - b*e)]*(d + e*x)*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*(8*c*d - 3*b*e + 2*c*e*x)) + 3*Sqrt[c]*Sqrt[e]*(-2*c*d + b*e)^2*Sqrt[d + e*x]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]]))/(Sqrt[e*(2*c*d - b*e)]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])))/(24*c^4*e^9*(d + e*x))","A",1
2211,1,218,149,0.7878576,"\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","Integrate[((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{c} \sqrt{e} (d+e x) \sqrt{e (2 c d-b e)} (b e-c d+c e x) (2 c (2 d g+2 e f+e g x)-3 b e g)+e \sqrt{d+e x} (b e-2 c d)^2 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} (-3 b e g+2 c d g+4 c e f) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)}{4 c^{5/2} e^{5/2} \sqrt{e (2 c d-b e)} \sqrt{(d+e x) (c (d-e x)-b e)}}","\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}",1,"(Sqrt[c]*Sqrt[e]*Sqrt[e*(2*c*d - b*e)]*(d + e*x)*(-(c*d) + b*e + c*e*x)*(-3*b*e*g + 2*c*(2*e*f + 2*d*g + e*g*x)) + e*(-2*c*d + b*e)^2*(4*c*e*f + 2*c*d*g - 3*b*e*g)*Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])/(4*c^(5/2)*e^(5/2)*Sqrt[e*(2*c*d - b*e)]*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2212,1,189,121,0.4724351,"\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","Integrate[(f + g*x)/((d + e*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2]),x]","-\frac{2 \left(\sqrt{c} \sqrt{e (2 c d-b e)} (e f-d g) (b e-c d+c e x)+\sqrt{e} g \sqrt{d+e x} (b e-2 c d)^2 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)\right)}{\sqrt{c} e^2 \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{(d+e x) (c (d-e x)-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*(Sqrt[c]*Sqrt[e*(2*c*d - b*e)]*(e*f - d*g)*(-(c*d) + b*e + c*e*x) + Sqrt[e]*(-2*c*d + b*e)^2*g*Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]]))/(Sqrt[c]*e^2*Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2213,1,89,137,0.0719034,"\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","Integrate[(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 \sqrt{(d+e x) (c (d-e x)-b e)} \left(2 c \left(d^2 g+2 d e (f+g x)+e^2 f x\right)-b e (2 d g+e (f+3 g x))\right)}{3 e^2 (d+e x)^2 (b e-2 c d)^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*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(2*c*(d^2*g + e^2*f*x + 2*d*e*(f + g*x)) - b*e*(2*d*g + e*(f + 3*g*x))))/(3*e^2*(-2*c*d + b*e)^2*(d + e*x)^2)","A",1
2214,1,166,210,0.0977485,"\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","Integrate[(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 (b e-c d+c e x) \left(b^2 e^2 (2 d g+3 e f+5 e g x)-2 b c e \left(7 d^2 g+2 d e (4 f+9 g x)+e^2 x (2 f+5 g x)\right)+4 c^2 \left(3 d^3 g+d^2 e (7 f+9 g x)+3 d e^2 x (2 f+g x)+2 e^3 f x^2\right)\right)}{15 e^2 (d+e x)^2 (b e-2 c d)^3 \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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*(-(c*d) + b*e + c*e*x)*(b^2*e^2*(3*e*f + 2*d*g + 5*e*g*x) - 2*b*c*e*(7*d^2*g + e^2*x*(2*f + 5*g*x) + 2*d*e*(4*f + 9*g*x)) + 4*c^2*(3*d^3*g + 2*e^3*f*x^2 + 3*d*e^2*x*(2*f + g*x) + d^2*e*(7*f + 9*g*x))))/(15*e^2*(-2*c*d + b*e)^3*(d + e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2215,1,247,285,0.1444055,"\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","Integrate[(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{2 (b e-c d+c e x) \left(-3 b^3 e^3 (2 d g+5 e f+7 e g x)+2 b^2 c e^2 \left(23 d^2 g+d e (54 f+82 g x)+e^2 x (9 f+14 g x)\right)-4 b c^2 e \left(36 d^3 g+d^2 e (69 f+131 g x)+2 d e^2 x (15 f+32 g x)+2 e^3 x^2 (3 f+7 g x)\right)+8 c^3 \left(13 d^4 g+4 d^3 e (9 f+13 g x)+d^2 e^2 x (39 f+32 g x)+8 d e^3 x^2 (3 f+g x)+6 e^4 f x^3\right)\right)}{105 e^2 (d+e x)^3 (b e-2 c d)^4 \sqrt{(d+e x) (c (d-e x)-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*(-(c*d) + b*e + c*e*x)*(-3*b^3*e^3*(5*e*f + 2*d*g + 7*e*g*x) + 8*c^3*(13*d^4*g + 6*e^4*f*x^3 + 8*d*e^3*x^2*(3*f + g*x) + 4*d^3*e*(9*f + 13*g*x) + d^2*e^2*x*(39*f + 32*g*x)) + 2*b^2*c*e^2*(23*d^2*g + e^2*x*(9*f + 14*g*x) + d*e*(54*f + 82*g*x)) - 4*b*c^2*e*(36*d^3*g + 2*e^3*x^2*(3*f + 7*g*x) + 2*d*e^2*x*(15*f + 32*g*x) + d^2*e*(69*f + 131*g*x))))/(105*e^2*(-2*c*d + b*e)^4*(d + e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2216,1,348,360,0.2132588,"\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","Integrate[(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{2 (b e-c d+c e x) \left(5 b^4 e^4 (2 d g+7 e f+9 e g x)-2 b^3 c e^3 \left(47 d^2 g+2 d e (80 f+107 g x)+e^2 x (20 f+27 g x)\right)+12 b^2 c^2 e^2 \left(29 d^3 g+2 d^2 e (47 f+67 g x)+d e^2 x (28 f+41 g x)+2 e^3 x^2 (2 f+3 g x)\right)-8 b c^3 e \left(83 d^4 g+d^3 e (232 f+390 g x)+3 d^2 e^2 x (44 f+83 g x)+4 d e^3 x^2 (12 f+25 g x)+2 e^4 x^3 (4 f+9 g x)\right)+16 c^4 \left(25 d^5 g+d^4 e (83 f+125 g x)+5 d^3 e^2 x (20 f+21 g x)+2 d^2 e^3 x^2 (42 f+25 g x)+10 d e^4 x^3 (4 f+g x)+8 e^5 f x^4\right)\right)}{315 e^2 (d+e x)^4 (b e-2 c d)^5 \sqrt{(d+e x) (c (d-e x)-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*(-(c*d) + b*e + c*e*x)*(5*b^4*e^4*(7*e*f + 2*d*g + 9*e*g*x) + 12*b^2*c^2*e^2*(29*d^3*g + 2*e^3*x^2*(2*f + 3*g*x) + d*e^2*x*(28*f + 41*g*x) + 2*d^2*e*(47*f + 67*g*x)) - 2*b^3*c*e^3*(47*d^2*g + e^2*x*(20*f + 27*g*x) + 2*d*e*(80*f + 107*g*x)) + 16*c^4*(25*d^5*g + 8*e^5*f*x^4 + 10*d*e^4*x^3*(4*f + g*x) + 5*d^3*e^2*x*(20*f + 21*g*x) + 2*d^2*e^3*x^2*(42*f + 25*g*x) + d^4*e*(83*f + 125*g*x)) - 8*b*c^3*e*(83*d^4*g + 2*e^4*x^3*(4*f + 9*g*x) + 4*d*e^3*x^2*(12*f + 25*g*x) + 3*d^2*e^2*x*(44*f + 83*g*x) + d^3*e*(232*f + 390*g*x))))/(315*e^2*(-2*c*d + b*e)^5*(d + e*x)^4*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2217,1,250,287,0.8975956,"\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","Integrate[((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{\sqrt{c} \sqrt{e} (d+e x) \sqrt{e (2 c d-b e)} \left(15 b^2 e^2 g+b c e (-43 d g-12 e f+5 e g x)+2 c^2 \left(14 d^2 g+5 d e (2 f-g x)-e^2 x (2 f+g x)\right)\right)-3 e \sqrt{d+e x} (b e-2 c d)^2 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} (-5 b e g+6 c d g+4 c e f) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)}{4 c^{7/2} e^{5/2} \sqrt{e (2 c d-b e)} \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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{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{(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{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,"(Sqrt[c]*Sqrt[e]*Sqrt[e*(2*c*d - b*e)]*(d + e*x)*(15*b^2*e^2*g + b*c*e*(-12*e*f - 43*d*g + 5*e*g*x) + 2*c^2*(14*d^2*g + 5*d*e*(2*f - g*x) - e^2*x*(2*f + g*x))) - 3*e*(-2*c*d + b*e)^2*(4*c*e*f + 6*c*d*g - 5*b*e*g)*Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])/(4*c^(7/2)*e^(5/2)*Sqrt[e*(2*c*d - b*e)]*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2218,1,201,213,0.5811992,"\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","Integrate[((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{c} \sqrt{e} (d+e x) \sqrt{e (2 c d-b e)} (c (3 d g+2 e f-e g x)-3 b e g)+e \sqrt{d+e x} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} (-3 b e g+4 c d g+2 c e f) \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)}{c^{5/2} e^{5/2} \sqrt{e (2 c d-b e)} \sqrt{(d+e x) (c (d-e x)-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{\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{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,"(Sqrt[c]*Sqrt[e]*Sqrt[e*(2*c*d - b*e)]*(d + e*x)*(-3*b*e*g + c*(2*e*f + 3*d*g - e*g*x)) + e*(-2*c*d + b*e)*(2*c*e*f + 4*c*d*g - 3*b*e*g)*Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])/(c^(5/2)*e^(5/2)*Sqrt[e*(2*c*d - b*e)]*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2219,1,173,129,0.4398896,"\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","Integrate[((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(\sqrt{c} \sqrt{e} (d+e x) (-b e g+c d g+c e f)+g \sqrt{d+e x} \sqrt{e (2 c d-b e)} (b e-2 c d) \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)\right)}{c^{3/2} e^{5/2} (b e-2 c d) \sqrt{(d+e x) (c (d-e x)-b e)}}","\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*(Sqrt[c]*Sqrt[e]*(c*e*f + c*d*g - b*e*g)*(d + e*x) + Sqrt[e*(2*c*d - b*e)]*(-2*c*d + b*e)*g*Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]]))/(c^(3/2)*e^(5/2)*(-2*c*d + b*e)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2220,1,149,136,0.098216,"\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","Integrate[(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 e^2 (2 d g+e (f+3 g x))+4 b c e \left(d^2 g+d e (2 g x-4 f)+e^2 x (3 g x-2 f)\right)-8 c^2 \left(d^3 g+d^2 e (g x-f)+d e^2 x (2 f+g x)+2 e^3 f x^2\right)}{3 e^2 (d+e x) (b e-2 c d)^3 \sqrt{(d+e x) (c (d-e x)-b e)}}","\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,"(-8*c^2*(d^3*g + 2*e^3*f*x^2 + d^2*e*(-f + g*x) + d*e^2*x*(2*f + g*x)) + 4*b*c*e*(d^2*g + d*e*(-4*f + 2*g*x) + e^2*x*(-2*f + 3*g*x)) + 2*b^2*e^2*(2*d*g + e*(f + 3*g*x)))/(3*e^2*(-2*c*d + b*e)^3*(d + e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2221,1,233,209,0.1345333,"\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","Integrate[(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 \left(b^3 e^3 (2 d g+3 e f+5 e g x)-2 b^2 c e^2 \left(13 d^2 g+4 d e (3 f+8 g x)+e^2 x (3 f+10 g x)\right)+4 b c^2 e \left(4 d^3 g+7 d^2 e (3 f+g x)+2 d e^2 x (9 f-8 g x)+2 e^3 x^2 (3 f-5 g x)\right)+8 c^3 \left(d^4 g+d^3 e (2 g x-6 f)+d^2 e^2 x (3 f+8 g x)+4 d e^3 x^2 (3 f+g x)+6 e^4 f x^3\right)\right)}{15 e^2 (d+e x)^2 (b e-2 c d)^4 \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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,"(2*(b^3*e^3*(3*e*f + 2*d*g + 5*e*g*x) + 4*b*c^2*e*(4*d^3*g + 2*d*e^2*x*(9*f - 8*g*x) + 2*e^3*x^2*(3*f - 5*g*x) + 7*d^2*e*(3*f + g*x)) + 8*c^3*(d^4*g + 6*e^4*f*x^3 + 4*d*e^3*x^2*(3*f + g*x) + d^3*e*(-6*f + 2*g*x) + d^2*e^2*x*(3*f + 8*g*x)) - 2*b^2*c*e^2*(13*d^2*g + 4*d*e*(3*f + 8*g*x) + e^2*x*(3*f + 10*g*x))))/(15*e^2*(-2*c*d + b*e)^4*(d + e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2222,1,331,284,0.2019173,"\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","Integrate[(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{2 \left(b^4 e^4 (2 d g+5 e f+7 e g x)-2 b^3 c e^3 \left(11 d^2 g+d e (24 f+38 g x)+e^2 x (4 f+7 g x)\right)+4 b^2 c^2 e^2 \left(31 d^3 g+2 d^2 e (23 f+53 g x)+d e^2 x (20 f+59 g x)+2 e^3 x^2 (2 f+7 g x)\right)-8 b c^3 e \left(15 d^4 g+d^3 e (48 f+46 g x)+d^2 e^2 x (52 f-11 g x)+4 d e^3 x^2 (8 f-9 g x)+2 e^4 x^3 (4 f-7 g x)\right)+16 c^4 \left(d^5 g+d^4 e (13 f+3 g x)+d^3 e^2 x (4 f-15 g x)-2 d^2 e^3 x^2 (10 f+9 g x)-6 d e^4 x^3 (4 f+g x)-8 e^5 f x^4\right)\right)}{35 e^2 (d+e x)^3 (b e-2 c d)^5 \sqrt{(d+e x) (c (d-e x)-b e)}}","\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,"(2*(b^4*e^4*(5*e*f + 2*d*g + 7*e*g*x) + 16*c^4*(d^5*g - 8*e^5*f*x^4 + d^3*e^2*x*(4*f - 15*g*x) - 6*d*e^4*x^3*(4*f + g*x) + d^4*e*(13*f + 3*g*x) - 2*d^2*e^3*x^2*(10*f + 9*g*x)) - 2*b^3*c*e^3*(11*d^2*g + e^2*x*(4*f + 7*g*x) + d*e*(24*f + 38*g*x)) - 8*b*c^3*e*(15*d^4*g + d^2*e^2*x*(52*f - 11*g*x) + 4*d*e^3*x^2*(8*f - 9*g*x) + 2*e^4*x^3*(4*f - 7*g*x) + d^3*e*(48*f + 46*g*x)) + 4*b^2*c^2*e^2*(31*d^3*g + 2*e^3*x^2*(2*f + 7*g*x) + 2*d^2*e*(23*f + 53*g*x) + d*e^2*x*(20*f + 59*g*x))))/(35*e^2*(-2*c*d + b*e)^5*(d + e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2223,1,139,364,0.2910029,"\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","Integrate[((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)^5 \left(\left(\frac{b e-c d+c e x}{b e-2 c d}\right)^{3/2} (-7 b e g+10 c d g+4 c e f) \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};\frac{c (d+e x)}{2 c d-b e}\right)-7 (-b e g+c d g+c e f)\right)}{21 c e^2 (b e-2 c d) ((d+e x) (c (d-e x)-b e))^{3/2}}","\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{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 (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{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{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*(d + e*x)^5*(-7*(c*e*f + c*d*g - b*e*g) + (4*c*e*f + 10*c*d*g - 7*b*e*g)*((-(c*d) + b*e + c*e*x)/(-2*c*d + b*e))^(3/2)*Hypergeometric2F1[3/2, 7/2, 9/2, (c*(d + e*x))/(2*c*d - b*e)]))/(21*c*e^2*(-2*c*d + b*e)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2))","C",1
2224,1,139,291,0.2512869,"\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","Integrate[((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)^4 \left(\left(\frac{b e-c d+c e x}{b e-2 c d}\right)^{3/2} (-5 b e g+8 c d g+2 c e f) \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{c (d+e x)}{2 c d-b e}\right)-5 (-b e g+c d g+c e f)\right)}{15 c e^2 (b e-2 c d) ((d+e x) (c (d-e x)-b e))^{3/2}}","\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{\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{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{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*(d + e*x)^4*(-5*(c*e*f + c*d*g - b*e*g) + (2*c*e*f + 8*c*d*g - 5*b*e*g)*((-(c*d) + b*e + c*e*x)/(-2*c*d + b*e))^(3/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (c*(d + e*x))/(2*c*d - b*e)]))/(15*c*e^2*(-2*c*d + b*e)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2))","C",1
2225,1,228,177,1.2341914,"\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","Integrate[((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 \left(-\frac{\sqrt{c} (d+e x) \left(3 b^2 e^2 g+4 b c e g (e x-2 d)+c^2 \left(5 d^2 g-d e (f+7 g x)-e^2 f x\right)\right)}{b e-c d+c e x}-\frac{3 \sqrt{e} g \sqrt{d+e x} (b e-2 c d)^2 \sqrt{\frac{b e-c d+c e x}{b e-2 c d}} \sin ^{-1}\left(\frac{\sqrt{c} \sqrt{e} \sqrt{d+e x}}{\sqrt{e (2 c d-b e)}}\right)}{\sqrt{e (2 c d-b e)}}\right)}{3 c^{5/2} e^2 (b e-2 c d) \sqrt{(d+e x) (c (d-e x)-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)}{c^{5/2} e^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{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*(-((Sqrt[c]*(d + e*x)*(3*b^2*e^2*g + 4*b*c*e*g*(-2*d + e*x) + c^2*(5*d^2*g - e^2*f*x - d*e*(f + 7*g*x))))/(-(c*d) + b*e + c*e*x)) - (3*Sqrt[e]*(-2*c*d + b*e)^2*g*Sqrt[d + e*x]*Sqrt[(-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]*ArcSin[(Sqrt[c]*Sqrt[e]*Sqrt[d + e*x])/Sqrt[e*(2*c*d - b*e)]])/Sqrt[e*(2*c*d - b*e)]))/(3*c^(5/2)*e^2*(-2*c*d + b*e)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2226,1,100,146,0.0651854,"\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","Integrate[((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) \left(b e (-2 d g+3 e f+e g x)+2 c \left(d^2 g-2 d e (f+g x)+e^2 f x\right)\right)}{3 e^2 (b e-2 c d)^2 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","\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*(d + e*x)*(b*e*(3*e*f - 2*d*g + e*g*x) + 2*c*(d^2*g + e^2*f*x - 2*d*e*(f + g*x))))/(3*e^2*(-2*c*d + b*e)^2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2227,1,151,165,0.0920887,"\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","Integrate[((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{6 b^2 e^2 (2 d g-e f+e g x)-4 b c e \left(5 d^2 g-2 d e g x+e^2 x (6 f-g x)\right)+8 c^2 \left(d^3 g+d^2 e (f-g x)+d e^2 x (2 f+g x)-2 e^3 f x^2\right)}{3 e^2 (b e-2 c d)^3 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","\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,"(6*b^2*e^2*(-(e*f) + 2*d*g + e*g*x) - 4*b*c*e*(5*d^2*g - 2*d*e*g*x + e^2*x*(6*f - g*x)) + 8*c^2*(d^3*g - 2*e^3*f*x^2 + d^2*e*(f - g*x) + d*e^2*x*(2*f + g*x)))/(3*e^2*(-2*c*d + b*e)^3*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2228,1,345,208,0.1868643,"\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","Integrate[(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 \left(b^4 e^4 (2 d g+3 e f+5 e g x)-2 b^3 c e^3 \left(19 d^2 g+2 d e (8 f+23 g x)+e^2 x (4 f+15 g x)\right)+12 b^2 c^2 e^2 \left(d^3 g+2 d^2 e (7 f-g x)+d e^2 x (12 f-19 g x)+2 e^3 x^2 (2 f-5 g x)\right)+8 b c^3 e \left(9 d^4 g-6 d^3 e (4 f-3 g x)+3 d^2 e^2 x (4 f+9 g x)-4 d e^3 x^2 (g x-12 f)+2 e^4 x^3 (12 f-5 g x)\right)-16 c^4 \left(3 d^5 g-3 d^4 e (f-g x)+3 d^3 e^2 x (4 f+g x)-2 d^2 e^3 x^2 (g x-6 f)-2 d e^4 x^3 (4 f+g x)-8 e^5 f x^4\right)\right)}{15 e^2 (d+e x)^2 (b e-2 c d)^5 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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*(b^4*e^4*(3*e*f + 2*d*g + 5*e*g*x) + 12*b^2*c^2*e^2*(d^3*g + d*e^2*x*(12*f - 19*g*x) + 2*e^3*x^2*(2*f - 5*g*x) + 2*d^2*e*(7*f - g*x)) - 16*c^4*(3*d^5*g - 8*e^5*f*x^4 - 3*d^4*e*(f - g*x) - 2*d^2*e^3*x^2*(-6*f + g*x) + 3*d^3*e^2*x*(4*f + g*x) - 2*d*e^4*x^3*(4*f + g*x)) + 8*b*c^3*e*(9*d^4*g + 2*e^4*x^3*(12*f - 5*g*x) - 6*d^3*e*(4*f - 3*g*x) - 4*d*e^3*x^2*(-12*f + g*x) + 3*d^2*e^2*x*(4*f + 9*g*x)) - 2*b^3*c*e^3*(19*d^2*g + e^2*x*(4*f + 15*g*x) + 2*d*e*(8*f + 23*g*x))))/(15*e^2*(-2*c*d + b*e)^5*(d + e*x)^2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2229,1,468,283,0.300581,"\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","Integrate[(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{-6 b^5 e^5 (2 d g+5 e f+7 e g x)+4 b^4 c e^4 \left(43 d^2 g+2 d e (45 f+73 g x)+e^2 x (15 f+28 g x)\right)-16 b^3 c^2 e^3 \left(88 d^3 g+d^2 e (115 f+293 g x)+2 d e^2 x (25 f+86 g x)+2 e^3 x^2 (5 f+21 g x)\right)+96 b^2 c^3 e^2 \left(17 d^4 g+20 d^3 e (3 f+2 g x)+d^2 e^2 x (65 f-54 g x)+40 d e^3 x^2 (f-2 g x)+2 e^4 x^3 (5 f-14 g x)\right)+32 b c^4 e \left(6 d^5 g-39 d^4 e (5 f-g x)+12 d^3 e^2 x (24 g x-5 f)+4 d^2 e^3 x^2 (75 f+43 g x)+8 d e^4 x^3 (45 f-8 g x)+8 e^5 x^4 (15 f-7 g x)\right)-64 c^5 \left(9 d^6 g-6 d^5 e (5 f-3 g x)+3 d^4 e^2 x (15 f+16 g x)+8 d^3 e^3 x^2 (15 f+g x)+4 d^2 e^4 x^3 (5 f-8 g x)-16 d e^5 x^4 (5 f+g x)-40 e^6 f x^5\right)}{105 e^2 (d+e x)^3 (b e-2 c d)^6 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","\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,"(-6*b^5*e^5*(5*e*f + 2*d*g + 7*e*g*x) + 96*b^2*c^3*e^2*(17*d^4*g + d^2*e^2*x*(65*f - 54*g*x) + 2*e^4*x^3*(5*f - 14*g*x) + 40*d*e^3*x^2*(f - 2*g*x) + 20*d^3*e*(3*f + 2*g*x)) - 64*c^5*(9*d^6*g - 40*e^6*f*x^5 + 4*d^2*e^4*x^3*(5*f - 8*g*x) - 6*d^5*e*(5*f - 3*g*x) - 16*d*e^5*x^4*(5*f + g*x) + 8*d^3*e^3*x^2*(15*f + g*x) + 3*d^4*e^2*x*(15*f + 16*g*x)) + 32*b*c^4*e*(6*d^5*g + 8*d*e^4*x^3*(45*f - 8*g*x) + 8*e^5*x^4*(15*f - 7*g*x) - 39*d^4*e*(5*f - g*x) + 12*d^3*e^2*x*(-5*f + 24*g*x) + 4*d^2*e^3*x^2*(75*f + 43*g*x)) + 4*b^4*c*e^4*(43*d^2*g + e^2*x*(15*f + 28*g*x) + 2*d*e*(45*f + 73*g*x)) - 16*b^3*c^2*e^3*(88*d^3*g + 2*e^3*x^2*(5*f + 21*g*x) + 2*d*e^2*x*(25*f + 86*g*x) + d^2*e*(115*f + 293*g*x)))/(105*e^2*(-2*c*d + b*e)^6*(d + e*x)^3*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2230,1,598,358,0.3559698,"\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","Integrate[(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{2 (-b e+c d-c e x) (-g (c d-b e)-c e f)}{3 c e (d+e x)^2 (-e (c d-b e)-c d e) ((d+e x) (c (d-e x)-b e))^{5/2}}-\frac{2 (d+e x)^{5/2} (-b e+c d-c e x)^{5/2} \left(\frac{10 c e \left(\frac{8 c e \left(\frac{6 c e \left(\frac{4 c e \left(\frac{2}{\sqrt{d+e x} (-e (c d-b e)-c d e) \sqrt{-b e+c d-c e x}}-\frac{4 c e \sqrt{d+e x}}{(-e (c d-b e)-c d e) (e (c d-b e)+c d e) \sqrt{-b e+c d-c e x}}\right)}{3 (e (c d-b e)+c d e)}-\frac{2}{3 (d+e x)^{3/2} (e (c d-b e)+c d e) \sqrt{-b e+c d-c e x}}\right)}{5 (e (c d-b e)+c d e)}-\frac{2}{5 (d+e x)^{5/2} (e (c d-b e)+c d e) \sqrt{-b e+c d-c e x}}\right)}{7 (e (c d-b e)+c d e)}-\frac{2}{7 (d+e x)^{7/2} (e (c d-b e)+c d e) \sqrt{-b e+c d-c e x}}\right)}{9 (e (c d-b e)+c d e)}-\frac{2}{9 (d+e x)^{9/2} (e (c d-b e)+c d e) \sqrt{-b e+c d-c e x}}\right) \left(6 c e^2 f-g \left(\frac{3 c d e}{2}-\frac{9}{2} e (c d-b e)\right)\right)}{3 c e (-e (c d-b e)-c d e) ((d+e x) (c (d-e x)-b e))^{5/2}}","\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,"(2*(-(c*e*f) - (c*d - b*e)*g)*(c*d - b*e - c*e*x))/(3*c*e*(-(c*d*e) - e*(c*d - b*e))*(d + e*x)^2*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)) - (2*(6*c*e^2*f - ((3*c*d*e)/2 - (9*e*(c*d - b*e))/2)*g)*(d + e*x)^(5/2)*(c*d - b*e - c*e*x)^(5/2)*(-2/(9*(c*d*e + e*(c*d - b*e))*(d + e*x)^(9/2)*Sqrt[c*d - b*e - c*e*x]) + (10*c*e*(-2/(7*(c*d*e + e*(c*d - b*e))*(d + e*x)^(7/2)*Sqrt[c*d - b*e - c*e*x]) + (8*c*e*(-2/(5*(c*d*e + e*(c*d - b*e))*(d + e*x)^(5/2)*Sqrt[c*d - b*e - c*e*x]) + (6*c*e*(-2/(3*(c*d*e + e*(c*d - b*e))*(d + e*x)^(3/2)*Sqrt[c*d - b*e - c*e*x]) + (4*c*e*(2/((-(c*d*e) - e*(c*d - b*e))*Sqrt[d + e*x]*Sqrt[c*d - b*e - c*e*x]) - (4*c*e*Sqrt[d + e*x])/((-(c*d*e) - e*(c*d - b*e))*(c*d*e + e*(c*d - b*e))*Sqrt[c*d - b*e - c*e*x])))/(3*(c*d*e + e*(c*d - b*e)))))/(5*(c*d*e + e*(c*d - b*e)))))/(7*(c*d*e + e*(c*d - b*e)))))/(9*(c*d*e + e*(c*d - b*e)))))/(3*c*e*(-(c*d*e) - e*(c*d - b*e))*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2))","A",1
2231,1,262,347,0.2285555,"\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","Integrate[(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 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)} \left(128 b^4 e^4 g-16 b^3 c e^3 (65 d g+11 e f+12 e g x)+24 b^2 c^2 e^2 \left(131 d^2 g+d e (55 f+57 g x)+e^2 x (11 f+10 g x)\right)-2 b c^3 e \left(2071 d^3 g+3 d^2 e (583 f+558 g x)+3 d e^2 x (286 f+245 g x)+5 e^3 x^2 (33 f+28 g x)\right)+c^4 \left(1910 d^4 g+d^3 e (3509 f+2865 g x)+3 d^2 e^2 x (1177 f+905 g x)+5 d e^3 x^2 (363 f+287 g x)+35 e^4 x^3 (11 f+9 g x)\right)\right)}{3465 c^5 e^2 \sqrt{d+e 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}",1,"(2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(128*b^4*e^4*g - 16*b^3*c*e^3*(11*e*f + 65*d*g + 12*e*g*x) + 24*b^2*c^2*e^2*(131*d^2*g + e^2*x*(11*f + 10*g*x) + d*e*(55*f + 57*g*x)) - 2*b*c^3*e*(2071*d^3*g + 5*e^3*x^2*(33*f + 28*g*x) + 3*d*e^2*x*(286*f + 245*g*x) + 3*d^2*e*(583*f + 558*g*x)) + c^4*(1910*d^4*g + 35*e^4*x^3*(11*f + 9*g*x) + 5*d*e^3*x^2*(363*f + 287*g*x) + 3*d^2*e^2*x*(1177*f + 905*g*x) + d^3*e*(3509*f + 2865*g*x))))/(3465*c^5*e^2*Sqrt[d + e*x])","A",1
2232,1,179,267,0.1573297,"\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","Integrate[(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 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)} \left(-16 b^3 e^3 g+24 b^2 c e^2 (4 d g+e (f+g x))-6 b c^2 e \left(31 d^2 g+d e (22 f+20 g x)+e^2 x (6 f+5 g x)\right)+c^3 \left(106 d^3 g+3 d^2 e (71 f+53 g x)+6 d e^2 x (27 f+20 g x)+5 e^3 x^2 (9 f+7 g x)\right)\right)}{315 c^4 e^2 \sqrt{d+e 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}",1,"(2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-16*b^3*e^3*g + 24*b^2*c*e^2*(4*d*g + e*(f + g*x)) - 6*b*c^2*e*(31*d^2*g + e^2*x*(6*f + 5*g*x) + d*e*(22*f + 20*g*x)) + c^3*(106*d^3*g + 5*e^3*x^2*(9*f + 7*g*x) + 6*d*e^2*x*(27*f + 20*g*x) + 3*d^2*e*(71*f + 53*g*x))))/(315*c^4*e^2*Sqrt[d + e*x])","A",1
2233,1,119,191,0.1004065,"\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","Integrate[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 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)} \left(8 b^2 e^2 g-2 b c e (15 d g+7 e f+6 e g x)+c^2 \left(22 d^2 g+d e (49 f+33 g x)+3 e^2 x (7 f+5 g x)\right)\right)}{105 c^3 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 \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{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,"(2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(8*b^2*e^2*g - 2*b*c*e*(7*e*f + 15*d*g + 6*e*g*x) + c^2*(22*d^2*g + 3*e^2*x*(7*f + 5*g*x) + d*e*(49*f + 33*g*x))))/(105*c^3*e^2*Sqrt[d + e*x])","A",1
2234,1,76,118,0.0643332,"\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","Integrate[((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 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)} (c (2 d g+5 e f+3 e g x)-2 b e g)}{15 c^2 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*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-2*b*e*g + c*(5*e*f + 2*d*g + 3*e*g*x)))/(15*c^2*e^2*Sqrt[d + e*x])","A",1
2235,1,154,186,0.1866243,"\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","Integrate[((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 \sqrt{d+e x} \sqrt{c (d-e x)-b e} \left(\sqrt{c (d-e x)-b e} (b e g+c (-4 d g+3 e f+e g x))+3 c \sqrt{2 c d-b e} (d g-e f) \tanh ^{-1}\left(\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right)\right)}{3 c e^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","\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*Sqrt[d + e*x]*Sqrt[-(b*e) + c*(d - e*x)]*(Sqrt[-(b*e) + c*(d - e*x)]*(b*e*g + c*(3*e*f - 4*d*g + e*g*x)) + 3*c*Sqrt[2*c*d - b*e]*(-(e*f) + d*g)*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]]))/(3*c*e^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2236,1,173,223,0.2316246,"\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","Integrate[((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{\sqrt{(d+e x) (c (d-e x)-b e)} \left((d+e x) \sqrt{2 c d-b e} (-2 b e g+5 c d g-c e f) \tanh ^{-1}\left(\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right)-(2 c d-b e) \sqrt{c (d-e x)-b e} (3 d g-e f+2 e g x)\right)}{e^2 (d+e x)^{3/2} (b e-2 c d) \sqrt{c (d-e x)-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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-((2*c*d - b*e)*(-(e*f) + 3*d*g + 2*e*g*x)*Sqrt[-(b*e) + c*(d - e*x)]) + Sqrt[2*c*d - b*e]*(-(c*e*f) + 5*c*d*g - 2*b*e*g)*(d + e*x)*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]]))/(e^2*(-2*c*d + b*e)*(d + e*x)^(3/2)*Sqrt[-(b*e) + c*(d - e*x)])","A",1
2237,1,222,231,0.5978827,"\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","Integrate[((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{\sqrt{(d+e x) (c (d-e x)-b e)} \left(-2 e (e f-d g) (b e-c d+c e x)^2-\frac{e (d+e x) (-4 b e g+7 c d g+c e f) \left(c \sqrt{e} (d+e x) \sqrt{c (d-e x)-b e} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c (d-e x)-b e}}{\sqrt{e (b e-2 c d)}}\right)-\sqrt{e (b e-2 c d)} (b e-c d+c e x)\right)}{\sqrt{e (b e-2 c d)}}\right)}{4 e^3 (d+e x)^{5/2} (b e-2 c d) (b e-c d+c e 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}}",1,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-2*e*(e*f - d*g)*(-(c*d) + b*e + c*e*x)^2 - (e*(c*e*f + 7*c*d*g - 4*b*e*g)*(d + e*x)*(-(Sqrt[e*(-2*c*d + b*e)]*(-(c*d) + b*e + c*e*x)) + c*Sqrt[e]*(d + e*x)*Sqrt[-(b*e) + c*(d - e*x)]*ArcTan[(Sqrt[e]*Sqrt[-(b*e) + c*(d - e*x)])/Sqrt[e*(-2*c*d + b*e)]]))/Sqrt[e*(-2*c*d + b*e)]))/(4*e^3*(-2*c*d + b*e)*(d + e*x)^(5/2)*(-(c*d) + b*e + c*e*x))","A",1
2238,1,128,307,0.1332946,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{3/2} \left(-\frac{3 c^2 (d+e x)^3 (-2 b e g+3 c d g+c e f) \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{(2 c d-b e)^3}+3 d g-3 e f\right)}{9 e^2 (d+e x)^{9/2} (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,"(((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(-3*e*f + 3*d*g - (3*c^2*(c*e*f + 3*c*d*g - 2*b*e*g)*(d + e*x)^3*Hypergeometric2F1[3/2, 3, 5/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(2*c*d - b*e)^3))/(9*e^2*(2*c*d - b*e)*(d + e*x)^(9/2))","C",1
2239,1,128,387,0.1454198,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{3/2} \left(-\frac{c^3 (d+e x)^4 (-8 b e g+11 c d g+5 c e f) \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{(b e-2 c d)^4}+3 d g-3 e f\right)}{12 e^2 (d+e x)^{11/2} (2 c d-b e)}","\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^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 \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,"(((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(-3*e*f + 3*d*g - (c^3*(5*c*e*f + 11*c*d*g - 8*b*e*g)*(d + e*x)^4*Hypergeometric2F1[3/2, 4, 5/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(-2*c*d + b*e)^4))/(12*e^2*(2*c*d - b*e)*(d + e*x)^(11/2))","C",1
2240,1,364,419,0.3465718,"\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","Integrate[(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 (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} \left(-256 b^5 e^5 g+128 b^4 c e^4 (22 d g+3 e f+5 e g x)-32 b^3 c^2 e^3 \left(389 d^2 g+2 d e (63 f+100 g x)+5 e^2 x (6 f+7 g x)\right)+16 b^2 c^3 e^2 \left(1724 d^3 g+3 d^2 e (347 f+515 g x)+30 d e^2 x (19 f+21 g x)+105 e^3 x^2 (f+g x)\right)-2 b c^4 e \left(15191 d^4 g+4 d^3 e (4131 f+5530 g x)+30 d^2 e^2 x (542 f+553 g x)+420 d e^3 x^2 (17 f+16 g x)+105 e^4 x^3 (12 f+11 g x)\right)+c^5 \left(12686 d^5 g+d^4 e (29049 f+31715 g x)+20 d^3 e^2 x (2505 f+2212 g x)+210 d^2 e^3 x^2 (203 f+173 g x)+210 d e^4 x^3 (90 f+77 g x)+231 e^5 x^4 (15 f+13 g x)\right)\right)}{45045 c^6 e^2 \sqrt{d+e 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}",1,"(-2*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-256*b^5*e^5*g + 128*b^4*c*e^4*(3*e*f + 22*d*g + 5*e*g*x) - 32*b^3*c^2*e^3*(389*d^2*g + 5*e^2*x*(6*f + 7*g*x) + 2*d*e*(63*f + 100*g*x)) + 16*b^2*c^3*e^2*(1724*d^3*g + 105*e^3*x^2*(f + g*x) + 30*d*e^2*x*(19*f + 21*g*x) + 3*d^2*e*(347*f + 515*g*x)) - 2*b*c^4*e*(15191*d^4*g + 105*e^4*x^3*(12*f + 11*g*x) + 420*d*e^3*x^2*(17*f + 16*g*x) + 30*d^2*e^2*x*(542*f + 553*g*x) + 4*d^3*e*(4131*f + 5530*g*x)) + c^5*(12686*d^5*g + 231*e^5*x^4*(15*f + 13*g*x) + 210*d*e^4*x^3*(90*f + 77*g*x) + 210*d^2*e^3*x^2*(203*f + 173*g*x) + 20*d^3*e^2*x*(2505*f + 2212*g*x) + d^4*e*(29049*f + 31715*g*x))))/(45045*c^6*e^2*Sqrt[d + e*x])","A",1
2241,1,264,347,0.2559575,"\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","Integrate[(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 (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} \left(128 b^4 e^4 g-16 b^3 c e^3 (71 d g+13 e f+20 e g x)+8 b^2 c^2 e^2 \left(473 d^2 g+d e (221 f+315 g x)+5 e^2 x (13 f+14 g x)\right)-2 b c^3 e \left(2765 d^3 g+d^2 e (2743 f+3470 g x)+25 d e^2 x (78 f+77 g x)+35 e^3 x^2 (13 f+12 g x)\right)+c^4 \left(2754 d^4 g+d^3 e (6929 f+6885 g x)+5 d^2 e^2 x (1963 f+1659 g x)+35 d e^3 x^2 (169 f+141 g x)+105 e^4 x^3 (13 f+11 g x)\right)\right)}{15015 c^5 e^2 \sqrt{d+e 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}",1,"(-2*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(128*b^4*e^4*g - 16*b^3*c*e^3*(13*e*f + 71*d*g + 20*e*g*x) + 8*b^2*c^2*e^2*(473*d^2*g + 5*e^2*x*(13*f + 14*g*x) + d*e*(221*f + 315*g*x)) - 2*b*c^3*e*(2765*d^3*g + 35*e^3*x^2*(13*f + 12*g*x) + 25*d*e^2*x*(78*f + 77*g*x) + d^2*e*(2743*f + 3470*g*x)) + c^4*(2754*d^4*g + 105*e^4*x^3*(13*f + 11*g*x) + 35*d*e^3*x^2*(169*f + 141*g*x) + 5*d^2*e^2*x*(1963*f + 1659*g*x) + d^3*e*(6929*f + 6885*g*x))))/(15015*c^5*e^2*Sqrt[d + e*x])","A",1
2242,1,183,267,0.17407,"\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","Integrate[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 (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} \left(-48 b^3 e^3 g+8 b^2 c e^2 (40 d g+11 e f+15 e g x)-2 b c^2 e \left(347 d^2 g+d e (286 f+340 g x)+5 e^2 x (22 f+21 g x)\right)+c^3 \left(422 d^3 g+d^2 e (1177 f+1055 g x)+10 d e^2 x (121 f+98 g x)+35 e^3 x^2 (11 f+9 g x)\right)\right)}{3465 c^4 e^2 \sqrt{d+e 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)^{5/2} (-6 b e g+c d g+11 c e f)}{3465 c^4 e^2 (d+e x)^{5/2}}-\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{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{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,"(-2*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-48*b^3*e^3*g + 8*b^2*c*e^2*(11*e*f + 40*d*g + 15*e*g*x) - 2*b*c^2*e*(347*d^2*g + 5*e^2*x*(22*f + 21*g*x) + d*e*(286*f + 340*g*x)) + c^3*(422*d^3*g + 35*e^3*x^2*(11*f + 9*g*x) + 10*d*e^2*x*(121*f + 98*g*x) + d^2*e*(1177*f + 1055*g*x))))/(3465*c^4*e^2*Sqrt[d + e*x])","A",1
2243,1,121,193,0.1187146,"\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","Integrate[((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 (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} \left(8 b^2 e^2 g-2 b c e (17 d g+9 e f+10 e g x)+c^2 \left(26 d^2 g+d e (81 f+65 g x)+5 e^2 x (9 f+7 g x)\right)\right)}{315 c^3 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)^{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 \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{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,"(-2*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(8*b^2*e^2*g - 2*b*c*e*(9*e*f + 17*d*g + 10*e*g*x) + c^2*(26*d^2*g + 5*e^2*x*(9*f + 7*g*x) + d*e*(81*f + 65*g*x))))/(315*c^3*e^2*Sqrt[d + e*x])","A",1
2244,1,78,118,0.084506,"\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","Integrate[((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 (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} (c (2 d g+7 e f+5 e g x)-2 b e g)}{35 c^2 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} (-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*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-2*b*e*g + c*(7*e*f + 2*d*g + 5*e*g*x)))/(35*c^2*e^2*Sqrt[d + e*x])","A",1
2245,1,199,250,0.2773547,"\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","Integrate[((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 \sqrt{d+e x} \sqrt{c (d-e x)-b e} \left(\sqrt{c (d-e x)-b e} \left(3 b^2 e^2 g+2 b c e (-13 d g+10 e f+3 e g x)+c^2 \left(38 d^2 g-d e (35 f+11 g x)+e^2 x (5 f+3 g x)\right)\right)-15 c (2 c d-b e)^{3/2} (d g-e f) \tanh ^{-1}\left(\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right)\right)}{15 c e^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","\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*Sqrt[d + e*x]*Sqrt[-(b*e) + c*(d - e*x)]*(Sqrt[-(b*e) + c*(d - e*x)]*(3*b^2*e^2*g + 2*b*c*e*(10*e*f - 13*d*g + 3*e*g*x) + c^2*(38*d^2*g + e^2*x*(5*f + 3*g*x) - d*e*(35*f + 11*g*x))) - 15*c*(2*c*d - b*e)^(3/2)*(-(e*f) + d*g)*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]]))/(15*c*e^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2246,1,195,288,0.2559777,"\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","Integrate[((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{\sqrt{(d+e x) (c (d-e x)-b e)} \left(\sqrt{c (d-e x)-b e} \left(b e (-11 d g+3 e f-8 e g x)+2 c \left(13 d^2 g+d e (9 g x-6 f)-e^2 x (3 f+g x)\right)\right)-3 (d+e x) \sqrt{2 c d-b e} (-2 b e g+7 c d g-3 c e f) \tanh ^{-1}\left(\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right)\right)}{3 e^2 (d+e x)^{3/2} \sqrt{c (d-e x)-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}}{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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(Sqrt[-(b*e) + c*(d - e*x)]*(b*e*(3*e*f - 11*d*g - 8*e*g*x) + 2*c*(13*d^2*g - e^2*x*(3*f + g*x) + d*e*(-6*f + 9*g*x))) - 3*Sqrt[2*c*d - b*e]*(-3*c*e*f + 7*c*d*g - 2*b*e*g)*(d + e*x)*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]]))/(3*e^2*(d + e*x)^(3/2)*Sqrt[-(b*e) + c*(d - e*x)])","A",1
2247,1,129,305,0.1776824,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{5/2} \left(\frac{c (d+e x)^2 (4 b e g-9 c d g+c e f) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{e (b e-2 c d)^2}+\frac{5 d g}{e}-5 f\right)}{10 e (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)^{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,"(((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(-5*f + (5*d*g)/e + (c*(c*e*f - 9*c*d*g + 4*b*e*g)*(d + e*x)^2*Hypergeometric2F1[2, 5/2, 7/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(e*(-2*c*d + b*e)^2)))/(10*e*(2*c*d - b*e)*(d + e*x)^(9/2))","C",1
2248,1,254,307,1.2812219,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{3/2} \left(\frac{e (d+e x) (-6 b e g+11 c d g+c e f) \left(\sqrt{e (b e-2 c d)} \left(-2 b^2 e^2+b c e (d-7 e x)+c^2 \left(d^2+4 d e x-5 e^2 x^2\right)\right)+3 c^2 \sqrt{e} (d+e x)^2 \sqrt{c (d-e x)-b e} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c (d-e x)-b e}}{\sqrt{e (b e-2 c d)}}\right)\right)}{\sqrt{e (b e-2 c d)}}+8 e (e f-d g) (b e-c d+c e x)^3\right)}{24 e^3 (d+e x)^{9/2} (2 c d-b e) (b e-c d+c e x)^2}","-\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,"(((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(8*e*(e*f - d*g)*(-(c*d) + b*e + c*e*x)^3 + (e*(c*e*f + 11*c*d*g - 6*b*e*g)*(d + e*x)*(Sqrt[e*(-2*c*d + b*e)]*(-2*b^2*e^2 + b*c*e*(d - 7*e*x) + c^2*(d^2 + 4*d*e*x - 5*e^2*x^2)) + 3*c^2*Sqrt[e]*(d + e*x)^2*Sqrt[-(b*e) + c*(d - e*x)]*ArcTan[(Sqrt[e]*Sqrt[-(b*e) + c*(d - e*x)])/Sqrt[e*(-2*c*d + b*e)]]))/Sqrt[e*(-2*c*d + b*e)]))/(24*e^3*(2*c*d - b*e)*(d + e*x)^(9/2)*(-(c*d) + b*e + c*e*x)^2)","A",1
2249,1,128,387,0.2077699,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{5/2} \left(-\frac{c^3 (d+e x)^4 (-8 b e g+13 c d g+3 c e f) \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{(b e-2 c d)^4}+5 d g-5 e f\right)}{20 e^2 (d+e x)^{13/2} (2 c d-b e)}","-\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^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 \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,"(((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(-5*e*f + 5*d*g - (c^3*(3*c*e*f + 13*c*d*g - 8*b*e*g)*(d + e*x)^4*Hypergeometric2F1[5/2, 4, 7/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(-2*c*d + b*e)^4))/(20*e^2*(2*c*d - b*e)*(d + e*x)^(13/2))","C",1
2250,1,284,501,0.6976904,"\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","Integrate[(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 ((d+e x) (c (d-e x)-b e))^{7/2} \left(-171171 (b e-c d+c e x)^5 (-6 b e g+11 c d g+c e f)-969969 (2 c d-b e) (b e-c d+c e x)^4 (-3 b e g+5 c d g+c e f)-1322685 (2 c d-b e)^3 (b e-c d+c e x)^2 (-3 b e g+4 c d g+2 c e f)+2238390 (b e-2 c d)^2 (c (d-e x)-b e)^3 (-2 b e g+3 c d g+c e f)+323323 (b e-2 c d)^4 (c (d-e x)-b e) (-6 b e g+7 c d g+5 c e f)-415701 (2 c d-b e)^5 (-b e g+c d g+c e f)-153153 g (b e-c d+c e x)^6\right)}{2909907 c^7 e^2 (d+e x)^{7/2}}","-\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,"(2*((d + e*x)*(-(b*e) + c*(d - e*x)))^(7/2)*(-415701*(2*c*d - b*e)^5*(c*e*f + c*d*g - b*e*g) - 1322685*(2*c*d - b*e)^3*(2*c*e*f + 4*c*d*g - 3*b*e*g)*(-(c*d) + b*e + c*e*x)^2 - 969969*(2*c*d - b*e)*(c*e*f + 5*c*d*g - 3*b*e*g)*(-(c*d) + b*e + c*e*x)^4 - 171171*(c*e*f + 11*c*d*g - 6*b*e*g)*(-(c*d) + b*e + c*e*x)^5 - 153153*g*(-(c*d) + b*e + c*e*x)^6 + 323323*(-2*c*d + b*e)^4*(5*c*e*f + 7*c*d*g - 6*b*e*g)*(-(b*e) + c*(d - e*x)) + 2238390*(-2*c*d + b*e)^2*(c*e*f + 3*c*d*g - 2*b*e*g)*(-(b*e) + c*(d - e*x))^3))/(2909907*c^7*e^2*(d + e*x)^(7/2))","A",1
2251,1,367,424,0.3838397,"\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","Integrate[(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 (b e-c d+c e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} \left(-1280 b^5 e^5 g+128 b^4 c e^4 (118 d g+17 e f+35 e g x)-32 b^3 c^2 e^3 \left(2253 d^2 g+2 d e (391 f+756 g x)+7 e^2 x (34 f+45 g x)\right)+16 b^2 c^3 e^2 \left(10864 d^3 g+3 d^2 e (2397 f+4249 g x)+294 d e^2 x (17 f+21 g x)+21 e^3 x^2 (51 f+55 g x)\right)-2 b c^4 e \left(104843 d^4 g+4 d^3 e (32623 f+50554 g x)+42 d^2 e^2 x (3842 f+4287 g x)+84 d e^3 x^2 (969 f+968 g x)+231 e^4 x^3 (68 f+65 g x)\right)+c^5 \left(94134 d^5 g+d^4 e (278171 f+329469 g x)+28 d^3 e^2 x (21097 f+19638 g x)+126 d^2 e^3 x^2 (4471 f+3949 g x)+462 d e^4 x^3 (578 f+507 g x)+3003 e^5 x^4 (17 f+15 g x)\right)\right)}{765765 c^6 e^2 \sqrt{d+e 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}",1,"(2*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-1280*b^5*e^5*g + 128*b^4*c*e^4*(17*e*f + 118*d*g + 35*e*g*x) - 32*b^3*c^2*e^3*(2253*d^2*g + 7*e^2*x*(34*f + 45*g*x) + 2*d*e*(391*f + 756*g*x)) + 16*b^2*c^3*e^2*(10864*d^3*g + 294*d*e^2*x*(17*f + 21*g*x) + 21*e^3*x^2*(51*f + 55*g*x) + 3*d^2*e*(2397*f + 4249*g*x)) - 2*b*c^4*e*(104843*d^4*g + 231*e^4*x^3*(68*f + 65*g*x) + 84*d*e^3*x^2*(969*f + 968*g*x) + 42*d^2*e^2*x*(3842*f + 4287*g*x) + 4*d^3*e*(32623*f + 50554*g*x)) + c^5*(94134*d^5*g + 3003*e^5*x^4*(17*f + 15*g*x) + 462*d*e^4*x^3*(578*f + 507*g*x) + 126*d^2*e^3*x^2*(4471*f + 3949*g*x) + 28*d^3*e^2*x*(21097*f + 19638*g*x) + d^4*e*(278171*f + 329469*g*x))))/(765765*c^6*e^2*Sqrt[d + e*x])","A",1
2252,1,264,343,0.2872956,"\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","Integrate[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 (b e-c d+c e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} \left(128 b^4 e^4 g-16 b^3 c e^3 (77 d g+15 e f+28 e g x)+24 b^2 c^2 e^2 \left(187 d^2 g+d e (95 f+161 g x)+7 e^2 x (5 f+6 g x)\right)-2 b c^3 e \left(3611 d^3 g+d^2 e (4065 f+5922 g x)+21 d e^2 x (170 f+183 g x)+21 e^3 x^2 (45 f+44 g x)\right)+c^4 \left(3838 d^4 g+d^3 e (12525 f+13433 g x)+147 d^2 e^2 x (145 f+129 g x)+21 d e^3 x^2 (675 f+583 g x)+231 e^4 x^3 (15 f+13 g x)\right)\right)}{45045 c^5 e^2 \sqrt{d+e 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)^{7/2} (-8 b e g+c d g+15 c e f)}{45045 c^5 e^2 (d+e x)^{7/2}}-\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{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{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{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,"(2*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(128*b^4*e^4*g - 16*b^3*c*e^3*(15*e*f + 77*d*g + 28*e*g*x) + 24*b^2*c^2*e^2*(187*d^2*g + 7*e^2*x*(5*f + 6*g*x) + d*e*(95*f + 161*g*x)) - 2*b*c^3*e*(3611*d^3*g + 21*e^3*x^2*(45*f + 44*g*x) + 21*d*e^2*x*(170*f + 183*g*x) + d^2*e*(4065*f + 5922*g*x)) + c^4*(3838*d^4*g + 231*e^4*x^3*(15*f + 13*g*x) + 147*d^2*e^2*x*(145*f + 129*g*x) + 21*d*e^3*x^2*(675*f + 583*g*x) + d^3*e*(12525*f + 13433*g*x))))/(45045*c^5*e^2*Sqrt[d + e*x])","A",1
2253,1,183,270,0.2101494,"\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","Integrate[((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 (b e-c d+c e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} \left(-48 b^3 e^3 g+8 b^2 c e^2 (44 d g+13 e f+21 e g x)-2 b c^2 e \left(423 d^2 g+d e (390 f+532 g x)+7 e^2 x (26 f+27 g x)\right)+c^3 \left(542 d^3 g+d^2 e (1963 f+1897 g x)+14 d e^2 x (169 f+144 g x)+63 e^3 x^2 (13 f+11 g x)\right)\right)}{9009 c^4 e^2 \sqrt{d+e 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)^{7/2} (-6 b e g-c d g+13 c e f)}{9009 c^4 e^2 (d+e x)^{7/2}}-\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{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{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,"(2*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-48*b^3*e^3*g + 8*b^2*c*e^2*(13*e*f + 44*d*g + 21*e*g*x) - 2*b*c^2*e*(423*d^2*g + 7*e^2*x*(26*f + 27*g*x) + d*e*(390*f + 532*g*x)) + c^3*(542*d^3*g + 63*e^3*x^2*(13*f + 11*g*x) + 14*d*e^2*x*(169*f + 144*g*x) + d^2*e*(1963*f + 1897*g*x))))/(9009*c^4*e^2*Sqrt[d + e*x])","A",1
2254,1,121,193,0.1485002,"\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","Integrate[((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 (b e-c d+c e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} \left(8 b^2 e^2 g-2 b c e (19 d g+11 e f+14 e g x)+c^2 \left(30 d^2 g+d e (121 f+105 g x)+7 e^2 x (11 f+9 g x)\right)\right)}{693 c^3 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} (-4 b e g-3 c d g+11 c e f)}{693 c^3 e^2 (d+e x)^{7/2}}-\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{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,"(2*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(8*b^2*e^2*g - 2*b*c*e*(11*e*f + 19*d*g + 14*e*g*x) + c^2*(30*d^2*g + 7*e^2*x*(11*f + 9*g*x) + d*e*(121*f + 105*g*x))))/(693*c^3*e^2*Sqrt[d + e*x])","A",1
2255,1,78,118,0.1127776,"\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","Integrate[((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 (b e-c d+c e x)^3 \sqrt{(d+e x) (c (d-e x)-b e)} (c (2 d g+9 e f+7 e g x)-2 b e g)}{63 c^2 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} (-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*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-2*b*e*g + c*(9*e*f + 2*d*g + 7*e*g*x)))/(63*c^2*e^2*Sqrt[d + e*x])","A",1
2256,1,197,316,0.5718489,"\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","Integrate[((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 ((d+e x) (c (d-e x)-b e))^{5/2} \left(\frac{7 c (e f-d g) \left(\sqrt{c (d-e x)-b e} \left(23 b^2 e^2+b c e (11 e x-81 d)+c^2 \left(73 d^2-16 d e x+3 e^2 x^2\right)\right)-15 (2 c d-b e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right)\right)}{15 (c (d-e x)-b e)^{5/2}}+g (b e-c d+c e x)\right)}{7 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)^{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*((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(g*(-(c*d) + b*e + c*e*x) + (7*c*(e*f - d*g)*(Sqrt[-(b*e) + c*(d - e*x)]*(23*b^2*e^2 + b*c*e*(-81*d + 11*e*x) + c^2*(73*d^2 - 16*d*e*x + 3*e^2*x^2)) - 15*(2*c*d - b*e)^(5/2)*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]]))/(15*(-(b*e) + c*(d - e*x))^(5/2))))/(7*c*e^2*(d + e*x)^(5/2))","A",1
2257,1,221,360,0.6623139,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{5/2} \left((e f-d g) (b e-c d+c e x)-\frac{(d+e x) (2 b e g-9 c d g+5 c e f) \left(\sqrt{c (d-e x)-b e} \left(23 b^2 e^2+b c e (11 e x-81 d)+c^2 \left(73 d^2-16 d e x+3 e^2 x^2\right)\right)-15 (2 c d-b e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right)\right)}{15 (c (d-e x)-b e)^{5/2}}\right)}{e^2 (d+e x)^{7/2} (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}}{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,"(((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*((e*f - d*g)*(-(c*d) + b*e + c*e*x) - ((5*c*e*f - 9*c*d*g + 2*b*e*g)*(d + e*x)*(Sqrt[-(b*e) + c*(d - e*x)]*(23*b^2*e^2 + b*c*e*(-81*d + 11*e*x) + c^2*(73*d^2 - 16*d*e*x + 3*e^2*x^2)) - 15*(2*c*d - b*e)^(5/2)*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]]))/(15*(-(b*e) + c*(d - e*x))^(5/2))))/(e^2*(2*c*d - b*e)*(d + e*x)^(7/2))","A",1
2258,1,130,372,0.246327,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{7/2} \left(\frac{c (d+e x)^2 (4 b e g-11 c d g+3 c e f) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{e (b e-2 c d)^2}+\frac{7 d g}{e}-7 f\right)}{14 e (d+e x)^{11/2} (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}}{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,"(((d + e*x)*(-(b*e) + c*(d - e*x)))^(7/2)*(-7*f + (7*d*g)/e + (c*(3*c*e*f - 11*c*d*g + 4*b*e*g)*(d + e*x)^2*Hypergeometric2F1[2, 7/2, 9/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(e*(-2*c*d + b*e)^2)))/(14*e*(2*c*d - b*e)*(d + e*x)^(11/2))","C",1
2259,1,127,383,0.1387911,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{7/2} \left(\frac{c^2 (d+e x)^3 (6 b e g-13 c d g+c e f) \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{(2 c d-b e)^3}+7 d g-7 e f\right)}{21 e^2 (d+e x)^{13/2} (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,"(((d + e*x)*(-(b*e) + c*(d - e*x)))^(7/2)*(-7*e*f + 7*d*g + (c^2*(c*e*f - 13*c*d*g + 6*b*e*g)*(d + e*x)^3*Hypergeometric2F1[3, 7/2, 9/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(2*c*d - b*e)^3))/(21*e^2*(2*c*d - b*e)*(d + e*x)^(13/2))","C",1
2260,1,303,383,3.531195,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{5/2} \left(-\frac{e (d+e x) (-8 b e g+15 c d g+c e f) \left(15 c^3 \sqrt{e} (d+e x)^3 \sqrt{c (d-e x)-b e} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c (d-e x)-b e}}{\sqrt{e (b e-2 c d)}}\right)-\sqrt{e (b e-2 c d)} \left(8 b^3 e^3+2 b^2 c e^2 (17 e x-7 d)+b c^2 e \left(19 d^2-18 d e x+59 e^2 x^2\right)-\left(c^3 \left(13 d^3+d^2 e x+19 d e^2 x^2-33 e^3 x^3\right)\right)\right)\right)}{3 \sqrt{e (b e-2 c d)}}-16 e (e f-d g) (b e-c d+c e x)^4\right)}{64 e^3 (d+e x)^{13/2} (2 c d-b e) (b e-c d+c e x)^3}","\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{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{(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,"-1/64*(((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*(-16*e*(e*f - d*g)*(-(c*d) + b*e + c*e*x)^4 - (e*(c*e*f + 15*c*d*g - 8*b*e*g)*(d + e*x)*(-(Sqrt[e*(-2*c*d + b*e)]*(8*b^3*e^3 + 2*b^2*c*e^2*(-7*d + 17*e*x) + b*c^2*e*(19*d^2 - 18*d*e*x + 59*e^2*x^2) - c^3*(13*d^3 + d^2*e*x + 19*d*e^2*x^2 - 33*e^3*x^3))) + 15*c^3*Sqrt[e]*(d + e*x)^3*Sqrt[-(b*e) + c*(d - e*x)]*ArcTan[(Sqrt[e]*Sqrt[-(b*e) + c*(d - e*x)])/Sqrt[e*(-2*c*d + b*e)]]))/(3*Sqrt[e*(-2*c*d + b*e)])))/(e^3*(2*c*d - b*e)*(d + e*x)^(13/2)*(-(c*d) + b*e + c*e*x)^3)","A",1
2261,1,129,464,0.1633432,"\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","Integrate[((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{((d+e x) (c (d-e x)-b e))^{7/2} \left(-\frac{c^4 (d+e x)^5 (-10 b e g+17 c d g+3 c e f) \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{(2 c d-b e)^5}+7 d g-7 e f\right)}{35 e^2 (d+e x)^{17/2} (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^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 \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,"(((d + e*x)*(-(b*e) + c*(d - e*x)))^(7/2)*(-7*e*f + 7*d*g - (c^4*(3*c*e*f + 17*c*d*g - 10*b*e*g)*(d + e*x)^5*Hypergeometric2F1[7/2, 5, 9/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(2*c*d - b*e)^5))/(35*e^2*(2*c*d - b*e)*(d + e*x)^(17/2))","C",1
2262,1,181,270,0.1489512,"\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","Integrate[((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 \sqrt{d+e x} (b e-c d+c e x) \left(-48 b^3 e^3 g+8 b^2 c e^2 (32 d g+7 e f+3 e g x)-2 b c^2 e \left(219 d^2 g+2 d e (63 f+26 g x)+e^2 x (14 f+9 g x)\right)+c^3 \left(230 d^3 g+d^2 e (301 f+115 g x)+2 d e^2 x (49 f+30 g x)+3 e^3 x^2 (7 f+5 g x)\right)\right)}{105 c^4 e^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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{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{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{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,"(2*Sqrt[d + e*x]*(-(c*d) + b*e + c*e*x)*(-48*b^3*e^3*g + 8*b^2*c*e^2*(7*e*f + 32*d*g + 3*e*g*x) - 2*b*c^2*e*(219*d^2*g + e^2*x*(14*f + 9*g*x) + 2*d*e*(63*f + 26*g*x)) + c^3*(230*d^3*g + 3*e^3*x^2*(7*f + 5*g*x) + 2*d*e^2*x*(49*f + 30*g*x) + d^2*e*(301*f + 115*g*x))))/(105*c^4*e^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2263,1,118,193,0.0914528,"\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","Integrate[((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} (b e-c d+c e x) \left(8 b^2 e^2 g-2 b c e (13 d g+5 e f+2 e g x)+c^2 \left(18 d^2 g+d e (25 f+9 g x)+e^2 x (5 f+3 g x)\right)\right)}{15 c^3 e^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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 \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{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,"(2*Sqrt[d + e*x]*(-(c*d) + b*e + c*e*x)*(8*b^2*e^2*g - 2*b*c*e*(5*e*f + 13*d*g + 2*e*g*x) + c^2*(18*d^2*g + e^2*x*(5*f + 3*g*x) + d*e*(25*f + 9*g*x))))/(15*c^3*e^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2264,1,63,117,0.0652935,"\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","Integrate[(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+e x) (c (d-e x)-b e)} (c (2 d g+3 e f+e g x)-2 b e g)}{3 c^2 e^2 \sqrt{d+e 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}",1,"(-2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-2*b*e*g + c*(3*e*f + 2*d*g + e*g*x)))/(3*c^2*e^2*Sqrt[d + e*x])","A",1
2265,1,148,131,0.139685,"\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","Integrate[(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 \sqrt{d+e x} \left(g (2 c d-b e) (c (d-e x)-b e)-c \sqrt{2 c d-b e} (d g-e f) \sqrt{c (d-e x)-b e} \tanh ^{-1}\left(\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right)\right)}{c e^2 (b e-2 c d) \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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*Sqrt[d + e*x]*((2*c*d - b*e)*g*(-(b*e) + c*(d - e*x)) - c*Sqrt[2*c*d - b*e]*(-(e*f) + d*g)*Sqrt[-(b*e) + c*(d - e*x)]*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]]))/(c*e^2*(-2*c*d + b*e)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2266,1,153,153,0.1648197,"\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","Integrate[(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) (b e-c d+c e x)-\frac{(d+e x) \sqrt{c (d-e x)-b e} (-2 b e g+3 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right)}{\sqrt{2 c d-b e}}}{e^2 \sqrt{d+e x} (2 c d-b e) \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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)*(-(c*d) + b*e + c*e*x) - ((c*e*f + 3*c*d*g - 2*b*e*g)*(d + e*x)*Sqrt[-(b*e) + c*(d - e*x)]*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]])/Sqrt[2*c*d - b*e])/(e^2*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2267,1,209,233,0.5414499,"\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","Integrate[(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{\sqrt{(d+e x) (c (d-e x)-b e)} \left(-\frac{(d+e x) (-4 b e g+5 c d g+3 c e f) \left(\sqrt{e} (2 c d-b e) \sqrt{c (d-e x)-b e}+c (d+e x) \sqrt{e (b e-2 c d)} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c (d-e x)-b e}}{\sqrt{e (b e-2 c d)}}\right)\right)}{2 e^{3/2} (b e-2 c d)^2 \sqrt{c (d-e x)-b e}}+\frac{d g}{e}-f\right)}{2 e (d+e x)^{5/2} (2 c d-b e)}","-\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,"(Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-f + (d*g)/e - ((3*c*e*f + 5*c*d*g - 4*b*e*g)*(d + e*x)*(Sqrt[e]*(2*c*d - b*e)*Sqrt[-(b*e) + c*(d - e*x)] + c*Sqrt[e*(-2*c*d + b*e)]*(d + e*x)*ArcTan[(Sqrt[e]*Sqrt[-(b*e) + c*(d - e*x)])/Sqrt[e*(-2*c*d + b*e)]]))/(2*e^(3/2)*(-2*c*d + b*e)^2*Sqrt[-(b*e) + c*(d - e*x)])))/(2*e*(2*c*d - b*e)*(d + e*x)^(5/2))","A",1
2268,1,245,369,0.2182551,"\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","Integrate[((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 \sqrt{d+e x} \left(-128 b^4 e^4 g+16 b^3 c e^3 (53 d g+7 e f-4 e g x)-8 b^2 c^2 e^2 \left(257 d^2 g+d e (77 f-45 g x)-e^2 x (7 f+2 g x)\right)-2 b c^3 e \left(-1075 d^3 g+d^2 e (334 g x-553 f)+d e^2 x (126 f+37 g x)+e^3 x^2 (7 f+4 g x)\right)+c^4 \left(-814 d^4 g+d^3 e (407 g x-637 f)+d^2 e^2 x (301 f+93 g x)+d e^3 x^2 (49 f+29 g x)+e^4 x^3 (7 f+5 g x)\right)\right)}{35 c^5 e^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","\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{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{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{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{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*Sqrt[d + e*x]*(-128*b^4*e^4*g + 16*b^3*c*e^3*(7*e*f + 53*d*g - 4*e*g*x) - 8*b^2*c^2*e^2*(257*d^2*g + d*e*(77*f - 45*g*x) - e^2*x*(7*f + 2*g*x)) - 2*b*c^3*e*(-1075*d^3*g + e^3*x^2*(7*f + 4*g*x) + d*e^2*x*(126*f + 37*g*x) + d^2*e*(-553*f + 334*g*x)) + c^4*(-814*d^4*g + e^4*x^3*(7*f + 5*g*x) + d*e^3*x^2*(49*f + 29*g*x) + d^2*e^2*x*(301*f + 93*g*x) + d^3*e*(-637*f + 407*g*x))))/(35*c^5*e^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2269,1,168,292,0.1319149,"\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","Integrate[((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 \sqrt{d+e x} \left(48 b^3 e^3 g-8 b^2 c e^2 (28 d g+5 e f-3 e g x)+2 b c^2 e \left(167 d^2 g+d e (70 f-44 g x)-e^2 x (10 f+3 g x)\right)+c^3 \left(-158 d^3 g+d^2 e (79 g x-115 f)+2 d e^2 x (25 f+8 g x)+e^3 x^2 (5 f+3 g x)\right)\right)}{15 c^4 e^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","\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{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{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{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*Sqrt[d + e*x]*(48*b^3*e^3*g - 8*b^2*c*e^2*(5*e*f + 28*d*g - 3*e*g*x) + 2*b*c^2*e*(167*d^2*g + d*e*(70*f - 44*g*x) - e^2*x*(10*f + 3*g*x)) + c^3*(-158*d^3*g + e^3*x^2*(5*f + 3*g*x) + 2*d*e^2*x*(25*f + 8*g*x) + d^2*e*(-115*f + 79*g*x))))/(15*c^4*e^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2270,1,105,217,0.0778914,"\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","Integrate[((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} \left(-8 b^2 e^2 g+2 b c e (11 d g+3 e f-2 e g x)+c^2 \left(-14 d^2 g+d e (7 g x-9 f)+e^2 x (3 f+g x)\right)\right)}{3 c^3 e^2 \sqrt{(d+e x) (c (d-e x)-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 \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{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*Sqrt[d + e*x]*(-8*b^2*e^2*g + 2*b*c*e*(3*e*f + 11*d*g - 2*e*g*x) + c^2*(-14*d^2*g + e^2*x*(3*f + g*x) + d*e*(-9*f + 7*g*x))))/(3*c^3*e^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2271,1,60,148,0.049963,"\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","Integrate[((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+e x} (-2 b e g+2 c d g+c e (f-g x))}{c^2 e^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","\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*Sqrt[d + e*x]*(2*c*d*g - 2*b*e*g + c*e*(f - g*x)))/(c^2*e^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2272,1,147,155,0.1373904,"\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","Integrate[(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} \left(c \sqrt{2 c d-b e} (d g-e f) \sqrt{c (d-e x)-b e} \tanh ^{-1}\left(\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right)+(2 c d-b e) (-b e g+c d g+c e f)\right)}{c e^2 (b e-2 c d)^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","\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*Sqrt[d + e*x]*((2*c*d - b*e)*(c*e*f + c*d*g - b*e*g) + c*Sqrt[2*c*d - b*e]*(-(e*f) + d*g)*Sqrt[-(b*e) + c*(d - e*x)]*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]]))/(c*e^2*(-2*c*d + b*e)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2273,1,117,223,0.0748961,"\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","Integrate[(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{(d+e x) (-2 b e g+c d g+3 c e f) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)+(2 c d-b e) (d g-e f)}{e^2 \sqrt{d+e x} (b e-2 c d)^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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,"((2*c*d - b*e)*(-(e*f) + d*g) + (3*c*e*f + c*d*g - 2*b*e*g)*(d + e*x)*Hypergeometric2F1[-1/2, 1, 1/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(e^2*(-2*c*d + b*e)^2*Sqrt[d + e*x]*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","C",1
2274,1,129,308,0.1046573,"\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","Integrate[(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{\frac{c (d+e x)^2 (-4 b e g+3 c d g+5 c e f) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{e (b e-2 c d)^2}+\frac{d g}{e}-f}{2 e (d+e x)^{3/2} (2 c d-b e) \sqrt{(d+e x) (c (d-e x)-b e)}}","\frac{d g-e f}{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,"(-f + (d*g)/e + (c*(5*c*e*f + 3*c*d*g - 4*b*e*g)*(d + e*x)^2*Hypergeometric2F1[-1/2, 2, 1/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(e*(-2*c*d + b*e)^2))/(2*e*(2*c*d - b*e)*(d + e*x)^(3/2)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","C",1
2275,1,127,387,0.1118183,"\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","Integrate[(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{\frac{c^2 (d+e x)^3 (-6 b e g+5 c d g+7 c e f) \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{(2 c d-b e)^3}+d g-e f}{3 e^2 (d+e x)^{5/2} (2 c d-b e) \sqrt{(d+e x) (c (d-e x)-b e)}}","\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{d g-e f}{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 + (c^2*(7*c*e*f + 5*c*d*g - 6*b*e*g)*(d + e*x)^3*Hypergeometric2F1[-1/2, 3, 1/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(2*c*d - b*e)^3)/(3*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","C",1
2276,1,366,448,0.3096017,"\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","Integrate[((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 \sqrt{d+e x} \left(-1280 b^5 e^5 g+128 b^4 c e^4 (78 d g+7 e f-15 e g x)-32 b^3 c^2 e^3 \left(953 d^2 g+2 d e (91 f-204 g x)+3 e^2 x (5 g x-14 f)\right)+16 b^2 c^3 e^2 \left(2844 d^3 g+3 d^2 e (287 f-681 g x)+6 d e^2 x (29 g x-77 f)+e^3 x^2 (21 f+5 g x)\right)-2 b c^4 e \left(16563 d^4 g+12 d^3 e (581 f-1482 g x)+6 d^2 e^2 x (449 g x-1106 f)+12 d e^3 x^2 (63 f+16 g x)+e^4 x^3 (28 f+15 g x)\right)+c^5 \left(9414 d^5 g+3 d^4 e (1687 f-4707 g x)+12 d^3 e^2 x (292 g x-637 f)+2 d^2 e^3 x^2 (903 f+257 g x)+2 d e^4 x^3 (98 f+57 g x)+3 e^5 x^4 (7 f+5 g x)\right)\right)}{105 c^6 e^2 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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{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{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{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{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{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*Sqrt[d + e*x]*(-1280*b^5*e^5*g + 128*b^4*c*e^4*(7*e*f + 78*d*g - 15*e*g*x) - 32*b^3*c^2*e^3*(953*d^2*g + 2*d*e*(91*f - 204*g*x) + 3*e^2*x*(-14*f + 5*g*x)) + 16*b^2*c^3*e^2*(2844*d^3*g + 3*d^2*e*(287*f - 681*g*x) + e^3*x^2*(21*f + 5*g*x) + 6*d*e^2*x*(-77*f + 29*g*x)) + c^5*(9414*d^5*g + 3*d^4*e*(1687*f - 4707*g*x) + 3*e^5*x^4*(7*f + 5*g*x) + 2*d*e^4*x^3*(98*f + 57*g*x) + 2*d^2*e^3*x^2*(903*f + 257*g*x) + 12*d^3*e^2*x*(-637*f + 292*g*x)) - 2*b*c^4*e*(16563*d^4*g + 12*d^3*e*(581*f - 1482*g*x) + e^4*x^3*(28*f + 15*g*x) + 12*d*e^3*x^2*(63*f + 16*g*x) + 6*d^2*e^2*x*(-1106*f + 449*g*x))))/(105*c^6*e^2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2277,1,263,371,0.2030786,"\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","Integrate[((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 \sqrt{d+e x} \left(128 b^4 e^4 g-16 b^3 c e^3 (47 d g+5 e f-12 e g x)+24 b^2 c^2 e^2 \left(67 d^2 g+3 d e (5 f-13 g x)+e^2 x (2 g x-5 f)\right)-2 b c^3 e \left(741 d^3 g+3 d^2 e (85 f-246 g x)+3 d e^2 x (31 g x-70 f)+e^3 x^2 (15 f+4 g x)\right)+c^4 \left(498 d^4 g+9 d^3 e (25 f-83 g x)+3 d^2 e^2 x (61 g x-115 f)+d e^3 x^2 (75 f+23 g x)+e^4 x^3 (5 f+3 g x)\right)\right)}{15 c^5 e^2 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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{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{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{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{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*Sqrt[d + e*x]*(128*b^4*e^4*g - 16*b^3*c*e^3*(5*e*f + 47*d*g - 12*e*g*x) + 24*b^2*c^2*e^2*(67*d^2*g + 3*d*e*(5*f - 13*g*x) + e^2*x*(-5*f + 2*g*x)) - 2*b*c^3*e*(741*d^3*g + 3*d^2*e*(85*f - 246*g*x) + e^3*x^2*(15*f + 4*g*x) + 3*d*e^2*x*(-70*f + 31*g*x)) + c^4*(498*d^4*g + 9*d^3*e*(25*f - 83*g*x) + e^4*x^3*(5*f + 3*g*x) + d*e^3*x^2*(75*f + 23*g*x) + 3*d^2*e^2*x*(-115*f + 61*g*x))))/(15*c^5*e^2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2278,1,180,291,0.153145,"\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","Integrate[((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 \sqrt{d+e x} \left(-16 b^3 e^3 g+8 b^2 c e^2 (8 d g+e (f-3 g x))-2 b c^2 e \left(41 d^2 g+2 d e (5 f-18 g x)+3 e^2 x (g x-2 f)\right)+c^3 \left(34 d^3 g+d^2 e (11 f-51 g x)+6 d e^2 x (2 g x-3 f)+e^3 x^2 (3 f+g x)\right)\right)}{3 c^4 e^2 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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{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{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{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*Sqrt[d + e*x]*(-16*b^3*e^3*g + 8*b^2*c*e^2*(8*d*g + e*(f - 3*g*x)) - 2*b*c^2*e*(41*d^2*g + 2*d*e*(5*f - 18*g*x) + 3*e^2*x*(-2*f + g*x)) + c^3*(34*d^3*g + d^2*e*(11*f - 51*g*x) + e^3*x^2*(3*f + g*x) + 6*d*e^2*x*(-3*f + 2*g*x))))/(3*c^4*e^2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2279,1,117,217,0.0934548,"\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","Integrate[((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 \sqrt{d+e x} \left(8 b^2 e^2 g-2 b c e (9 d g+e (f-6 g x))+c^2 \left(10 d^2 g+d e (f-15 g x)+3 e^2 x (g x-f)\right)\right)}{3 c^3 e^2 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","-\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)^{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{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*Sqrt[d + e*x]*(8*b^2*e^2*g - 2*b*c*e*(9*d*g + e*(f - 6*g*x)) + c^2*(10*d^2*g + d*e*(f - 15*g*x) + 3*e^2*x*(-f + g*x))))/(3*c^3*e^2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2280,1,76,152,0.057812,"\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","Integrate[((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-2 c d g+c e (f+3 g x))}{3 c^2 e^2 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","\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*Sqrt[d + e*x]*(-2*c*d*g + 2*b*e*g + c*e*(f + 3*g*x)))/(3*c^2*e^2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2281,1,146,221,0.0809797,"\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","Integrate[((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 \sqrt{d+e x} \left(3 c (e f-d g) (b e-c d+c e x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)-(2 c d-b e) (-b e g+c d g+c e f)\right)}{3 c e^2 (b e-2 c d)^2 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","\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*Sqrt[d + e*x]*(-((2*c*d - b*e)*(c*e*f + c*d*g - b*e*g)) + 3*c*(e*f - d*g)*(-(c*d) + b*e + c*e*x)*Hypergeometric2F1[-1/2, 1, 1/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(3*c*e^2*(-2*c*d + b*e)^2*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","C",1
2282,1,135,313,0.0765658,"\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","Integrate[(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{(d+e x) (2 b e g+c d g-5 c e f) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)-3 (2 c d-b e) (d g-e f)}{3 e^2 \sqrt{d+e x} (b e-2 c d)^2 (b e-c d+c e x) \sqrt{(d+e x) (c (d-e x)-b e)}}","\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,"(-3*(2*c*d - b*e)*(-(e*f) + d*g) + (-5*c*e*f + c*d*g + 2*b*e*g)*(d + e*x)*Hypergeometric2F1[-3/2, 1, -1/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(3*e^2*(-2*c*d + b*e)^2*Sqrt[d + e*x]*(-(c*d) + b*e + c*e*x)*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","C",1
2283,1,129,378,0.1088457,"\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","Integrate[(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{\frac{c (d+e x)^2 (-4 b e g+c d g+7 c e f) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{e (b e-2 c d)^2}+\frac{3 d g}{e}-3 f}{6 e \sqrt{d+e x} (2 c d-b e) ((d+e x) (c (d-e x)-b e))^{3/2}}","-\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,"(-3*f + (3*d*g)/e + (c*(7*c*e*f + c*d*g - 4*b*e*g)*(d + e*x)^2*Hypergeometric2F1[-3/2, 2, -1/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(e*(-2*c*d + b*e)^2))/(6*e*(2*c*d - b*e)*Sqrt[d + e*x]*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2))","C",1
2284,1,128,457,0.1122122,"\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","Integrate[(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{\frac{3 c^2 (d+e x)^3 (-2 b e g+c d g+3 c e f) \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{(2 c d-b e)^3}+3 d g-3 e f}{9 e^2 (d+e x)^{3/2} (2 c d-b e) ((d+e x) (c (d-e x)-b e))^{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{d g-e f}{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,"(-3*e*f + 3*d*g + (3*c^2*(3*c*e*f + c*d*g - 2*b*e*g)*(d + e*x)^3*Hypergeometric2F1[-3/2, 3, -1/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/(2*c*d - b*e)^3)/(9*e^2*(2*c*d - b*e)*(d + e*x)^(3/2)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2))","C",1
2285,1,161,221,0.664183,"\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","Integrate[(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{(d+e x)^{m-3} ((d+e x) (c (d-e x)-b e))^{7/2} \left(-(b e-2 c d)^2 \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (2 c (d g m+e f (m+7))-b e g (2 m+7)) \, _2F_1\left(\frac{7}{2},-m-\frac{5}{2};\frac{9}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)-7 c^3 g (d+e x)^3\right)}{7 c^4 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,"((d + e*x)^(-3 + m)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(7/2)*(-7*c^3*g*(d + e*x)^3 - (-2*c*d + b*e)^2*(-(b*e*g*(7 + 2*m)) + 2*c*(d*g*m + e*f*(7 + m)))*((c*(d + e*x))/(2*c*d - b*e))^(-1/2 - m)*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",1
2286,1,170,219,0.5734331,"\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","Integrate[(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{(d+e x)^m (b e-c d+c e x)^2 \sqrt{(d+e x) (c (d-e x)-b e)} \left((b e-2 c d) \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (2 c (d g m+e f (m+5))-b e g (2 m+5)) \, _2F_1\left(\frac{5}{2},-m-\frac{3}{2};\frac{7}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)-5 c^2 g (d+e x)^2\right)}{5 c^3 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,"((d + e*x)^m*(-(c*d) + b*e + c*e*x)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(-5*c^2*g*(d + e*x)^2 + (-2*c*d + b*e)*(-(b*e*g*(5 + 2*m)) + 2*c*(d*g*m + e*f*(5 + m)))*((c*(d + e*x))/(2*c*d - b*e))^(-1/2 - m)*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",1
2287,1,149,208,0.3145667,"\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","Integrate[(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-1} ((d+e x) (c (d-e x)-b e))^{3/2} \left(-e \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (2 c (d g m+e f (m+3))-b e g (2 m+3)) \, _2F_1\left(\frac{3}{2},-m-\frac{1}{2};\frac{5}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)-3 c e g (d+e x)\right)}{3 c^2 e^3 (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,"((d + e*x)^(-1 + m)*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2)*(-3*c*e*g*(d + e*x) - e*(-(b*e*g*(3 + 2*m)) + 2*c*(d*g*m + e*f*(3 + m)))*((c*(d + e*x))/(2*c*d - b*e))^(-1/2 - m)*Hypergeometric2F1[3/2, -1/2 - m, 5/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(3*c^2*e^3*(3 + m))","A",1
2288,1,155,205,0.3008586,"\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","Integrate[((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{2 (d+e x)^m \sqrt{(d+e x) (c (d-e x)-b e)} \left(\frac{e \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (b e g (2 m+1)-2 c (d g m+e f (m+1))) \, _2F_1\left(\frac{1}{2},-m-\frac{1}{2};\frac{3}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)}{c}+e (e f-d g)\right)}{e^3 (2 m+1) (b e-2 c d)}","\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,"(-2*(d + e*x)^m*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(e*(e*f - d*g) + (e*(b*e*g*(1 + 2*m) - 2*c*(d*g*m + e*f*(1 + m)))*((c*(d + e*x))/(2*c*d - b*e))^(-1/2 - m)*Hypergeometric2F1[1/2, -1/2 - m, 3/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)])/c))/(e^3*(-2*c*d + b*e)*(1 + 2*m))","A",1
2289,1,176,210,0.3282645,"\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","Integrate[((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 (d+e x)^m \left(e (2 c d-b e) (-b e g+c d g+c e f)-e (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 (1-2 m)+2 c (d g m+e f (m-1))) \, _2F_1\left(\frac{1}{2},\frac{3}{2}-m;\frac{3}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)\right)}{c e^3 (b e-2 c d)^2 \sqrt{(d+e x) (c (d-e x)-b e)}}","\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,"(2*(d + e*x)^m*(e*(2*c*d - b*e)*(c*e*f + c*d*g - b*e*g) - e*(b*e*g*(1 - 2*m) + 2*c*(e*f*(-1 + m) + d*g*m))*((c*(d + e*x))/(2*c*d - b*e))^(1/2 - m)*(-(c*d) + b*e + c*e*x)*Hypergeometric2F1[1/2, 3/2 - m, 3/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(c*e^3*(-2*c*d + b*e)^2*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))])","A",1
2290,1,185,224,0.34787,"\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","Integrate[((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 (d+e x)^m \left(-e (d+e x) (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 (3-2 m)+2 c (d g m+e f (m-3))) \, _2F_1\left(-\frac{1}{2},\frac{5}{2}-m;\frac{1}{2};\frac{-c d+b e+c e x}{b e-2 c d}\right)-\frac{e (b e-2 c d)^2 (-b e g+c d g+c e f)}{c}\right)}{3 e^3 (b e-2 c d)^3 ((d+e x) (c (d-e x)-b e))^{3/2}}","\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,"(2*(d + e*x)^m*(-((e*(-2*c*d + b*e)^2*(c*e*f + c*d*g - b*e*g))/c) - e*(b*e*g*(3 - 2*m) + 2*c*(e*f*(-3 + m) + d*g*m))*(d + e*x)*((c*(d + e*x))/(2*c*d - b*e))^(1/2 - m)*(-(c*d) + b*e + c*e*x)*Hypergeometric2F1[-1/2, 5/2 - m, 1/2, (-(c*d) + b*e + c*e*x)/(-2*c*d + b*e)]))/(3*e^3*(-2*c*d + b*e)^3*((d + e*x)*(-(b*e) + c*(d - e*x)))^(3/2))","A",1
2291,1,34,42,0.137583,"\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","Integrate[(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 ((d+e x) (c (d-e x)-b e))^{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 + e*x)*(-(b*e) + c*(d - e*x)))^(1 + p))/e","A",1
2292,1,48,64,0.1337355,"\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","Integrate[(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} ((d+e x) (d g (p+1)+e (f+g (p+2) x)))^{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*x)*(d*g*(1 + p) + e*(f + g*(2 + p)*x)))^(1 + p))/(e^2*(2 + p)))","A",1
2293,1,153,143,0.1268578,"\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","Integrate[((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{\frac{\left(b^2 e^2 g^2-4 b c e^2 f g+c^2 \left(-d^2 g^2+2 d e f g+3 e^2 f^2\right)\right) \log (-b g+c f-c g x)}{c^2 (b g-2 c f)^2}+\frac{(-b e g+c d g+c e f)^2}{c^2 (2 c f-b g) (c (f-g x)-b g)}+\frac{(e f-d g)^2 \log (f+g x)}{(b g-2 c f)^2}}{g^3}","\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*(2*c*f - b*g)*(-(b*g) + c*(f - g*x))) + ((e*f - d*g)^2*Log[f + g*x])/(-2*c*f + b*g)^2 + ((-4*b*c*e^2*f*g + b^2*e^2*g^2 + c^2*(3*e^2*f^2 + 2*d*e*f*g - d^2*g^2))*Log[c*f - b*g - c*g*x])/(c^2*(-2*c*f + b*g)^2))/g^3","A",1
2294,1,73,73,0.0024567,"\int (1+x)^4 (a+b x) \left(1-x+x^2\right)^4 \, dx","Integrate[(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",1
2295,1,60,60,0.0023227,"\int (1+x)^3 (a+b x) \left(1-x+x^2\right)^3 \, dx","Integrate[(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",1
2296,1,44,44,0.0020557,"\int (1+x)^2 (a+b x) \left(1-x+x^2\right)^2 \, dx","Integrate[(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",1
2297,1,28,28,0.0016271,"\int (1+x) (a+b x) \left(1-x+x^2\right) \, dx","Integrate[(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",1
2298,1,49,54,0.0272188,"\int \frac{a+b x}{(1+x) \left(1-x+x^2\right)} \, dx","Integrate[(a + b*x)/((1 + x)*(1 - x + x^2)),x]","\frac{1}{6} (a-b) \left(2 \log (x+1)-\log \left(x^2-x+1\right)\right)+\frac{(a+b) \tan ^{-1}\left(\frac{2 x-1}{\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)*(2*Log[1 + x] - Log[1 - x + x^2]))/6","A",1
2299,1,72,79,0.0434047,"\int \frac{a+b x}{(1+x)^2 \left(1-x+x^2\right)^2} \, dx","Integrate[(a + b*x)/((1 + x)^2*(1 - x + x^2)^2),x]","\frac{1}{18} \left(\frac{6 x (a+b x)}{x^3+1}+(b-2 a) \log \left(x^2-x+1\right)+2 (2 a-b) \log (x+1)+2 \sqrt{3} (2 a+b) \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)\right)","\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,"((6*x*(a + b*x))/(1 + x^3) + 2*Sqrt[3]*(2*a + b)*ArcTan[(-1 + 2*x)/Sqrt[3]] + 2*(2*a - b)*Log[1 + x] + (-2*a + b)*Log[1 - x + x^2])/18","A",1
2300,1,94,101,0.0612573,"\int \frac{a+b x}{(1+x)^3 \left(1-x+x^2\right)^3} \, dx","Integrate[(a + b*x)/((1 + x)^3*(1 - x + x^2)^3),x]","\frac{1}{54} \left(\frac{9 x (a+b x)}{\left(x^3+1\right)^2}+\frac{3 x (5 a+4 b x)}{x^3+1}+(2 b-5 a) \log \left(x^2-x+1\right)+2 (5 a-2 b) \log (x+1)+2 \sqrt{3} (5 a+2 b) \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)\right)","\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,"((9*x*(a + b*x))/(1 + x^3)^2 + (3*x*(5*a + 4*b*x))/(1 + x^3) + 2*Sqrt[3]*(5*a + 2*b)*ArcTan[(-1 + 2*x)/Sqrt[3]] + 2*(5*a - 2*b)*Log[1 + x] + (-5*a + 2*b)*Log[1 - x + x^2])/54","A",1
2301,1,437,365,1.8349762,"\int (1+x)^{3/2} (a+b x) \left(1-x+x^2\right)^{3/2} \, dx","Integrate[(1 + x)^(3/2)*(a + b*x)*(1 - x + x^2)^(3/2),x]","\frac{2 x \sqrt{x+1} \sqrt{x^2-x+1} \left(91 a \left(5 x^3+14\right)+55 b x \left(7 x^3+16\right)\right)}{5005}-\frac{9 (x+1)^{3/2} \left(\frac{\sqrt{2} \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{\sqrt{3}-3 i}} \left(55 \left(3-i \sqrt{3}\right) b-182 i \sqrt{3} a\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{\sqrt{x+1}}-\frac{660 \sqrt{-\frac{i}{\sqrt{3}+3 i}} b \left(x^2-x+1\right)}{(x+1)^2}+\frac{165 i \sqrt{2} \left(\sqrt{3}+i\right) b \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{\sqrt{3}-3 i}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{\sqrt{x+1}}\right)}{10010 \sqrt{-\frac{i}{\sqrt{3}+3 i}} \sqrt{x^2-x+1}}","\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,"(2*x*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(91*a*(14 + 5*x^3) + 55*b*x*(16 + 7*x^3)))/5005 - (9*(1 + x)^(3/2)*((-660*Sqrt[(-I)/(3*I + Sqrt[3])]*b*(1 - x + x^2))/(1 + x)^2 + ((165*I)*Sqrt[2]*(I + Sqrt[3])*b*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[(-3*I + Sqrt[3] + (6*I)/(1 + x))/(-3*I + Sqrt[3])]*EllipticE[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])])/Sqrt[1 + x] + (Sqrt[2]*((-182*I)*Sqrt[3]*a + 55*(3 - I*Sqrt[3])*b)*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[(-3*I + Sqrt[3] + (6*I)/(1 + x))/(-3*I + Sqrt[3])]*EllipticF[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])])/Sqrt[1 + x]))/(10010*Sqrt[(-I)/(3*I + Sqrt[3])]*Sqrt[1 - x + x^2])","C",1
2302,1,423,326,1.6034038,"\int \sqrt{1+x} (a+b x) \sqrt{1-x+x^2} \, dx","Integrate[Sqrt[1 + x]*(a + b*x)*Sqrt[1 - x + x^2],x]","\frac{2}{35} x \sqrt{x+1} \sqrt{x^2-x+1} (7 a+5 b x)-\frac{(x+1)^{3/2} \left(\frac{\sqrt{2} \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{\sqrt{3}-3 i}} \left(5 \left(3-i \sqrt{3}\right) b-14 i \sqrt{3} a\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{\sqrt{x+1}}-\frac{60 \sqrt{-\frac{i}{\sqrt{3}+3 i}} b \left(x^2-x+1\right)}{(x+1)^2}+\frac{15 i \sqrt{2} \left(\sqrt{3}+i\right) b \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{\sqrt{3}-3 i}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{\sqrt{x+1}}\right)}{70 \sqrt{-\frac{i}{\sqrt{3}+3 i}} \sqrt{x^2-x+1}}","\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,"(2*x*Sqrt[1 + x]*(7*a + 5*b*x)*Sqrt[1 - x + x^2])/35 - ((1 + x)^(3/2)*((-60*Sqrt[(-I)/(3*I + Sqrt[3])]*b*(1 - x + x^2))/(1 + x)^2 + ((15*I)*Sqrt[2]*(I + Sqrt[3])*b*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[(-3*I + Sqrt[3] + (6*I)/(1 + x))/(-3*I + Sqrt[3])]*EllipticE[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])])/Sqrt[1 + x] + (Sqrt[2]*((-14*I)*Sqrt[3]*a + 5*(3 - I*Sqrt[3])*b)*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[(-3*I + Sqrt[3] + (6*I)/(1 + x))/(-3*I + Sqrt[3])]*EllipticF[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])])/Sqrt[1 + x]))/(70*Sqrt[(-I)/(3*I + Sqrt[3])]*Sqrt[1 - x + x^2])","C",1
2303,1,389,275,1.1065878,"\int \frac{a+b x}{\sqrt{1+x} \sqrt{1-x+x^2}} \, dx","Integrate[(a + b*x)/(Sqrt[1 + x]*Sqrt[1 - x + x^2]),x]","-\frac{(x+1)^{3/2} \left(\frac{\sqrt{2} \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{\sqrt{3}-3 i}} \left(\left(3-i \sqrt{3}\right) b-2 i \sqrt{3} a\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{\sqrt{x+1}}-\frac{12 \sqrt{-\frac{i}{\sqrt{3}+3 i}} b \left(x^2-x+1\right)}{(x+1)^2}+\frac{3 i \sqrt{2} \left(\sqrt{3}+i\right) b \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{\sqrt{3}-3 i}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{\sqrt{x+1}}\right)}{6 \sqrt{-\frac{i}{\sqrt{3}+3 i}} \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{\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 b \left(x^3+1\right)}{\sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}",1,"-1/6*((1 + x)^(3/2)*((-12*Sqrt[(-I)/(3*I + Sqrt[3])]*b*(1 - x + x^2))/(1 + x)^2 + ((3*I)*Sqrt[2]*(I + Sqrt[3])*b*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[(-3*I + Sqrt[3] + (6*I)/(1 + x))/(-3*I + Sqrt[3])]*EllipticE[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])])/Sqrt[1 + x] + (Sqrt[2]*((-2*I)*Sqrt[3]*a + (3 - I*Sqrt[3])*b)*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[(-3*I + Sqrt[3] + (6*I)/(1 + x))/(-3*I + Sqrt[3])]*EllipticF[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])])/Sqrt[1 + x]))/(Sqrt[(-I)/(3*I + Sqrt[3])]*Sqrt[1 - x + x^2])","C",1
2304,1,417,304,0.9849555,"\int \frac{a+b x}{(1+x)^{3/2} \left(1-x+x^2\right)^{3/2}} \, dx","Integrate[(a + b*x)/((1 + x)^(3/2)*(1 - x + x^2)^(3/2)),x]","\frac{12 \sqrt{-\frac{i}{\sqrt{3}+3 i}} x (a+b x)+\sqrt{2} \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{-\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{-\sqrt{3}+3 i}} (x+1)^{3/2} \left(2 i \sqrt{3} a+\left(3-i \sqrt{3}\right) b\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)-12 \sqrt{-\frac{i}{\sqrt{3}+3 i}} b \left(x^2-x+1\right)+3 i \sqrt{2} \left(\sqrt{3}+i\right) b \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{-\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{-\sqrt{3}+3 i}} (x+1)^{3/2} E\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{18 \sqrt{-\frac{i}{\sqrt{3}+3 i}} \sqrt{x+1} \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{\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 b \left(x^3+1\right)}{3 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}",1,"(12*Sqrt[(-I)/(3*I + Sqrt[3])]*x*(a + b*x) - 12*Sqrt[(-I)/(3*I + Sqrt[3])]*b*(1 - x + x^2) + (3*I)*Sqrt[2]*(I + Sqrt[3])*b*(1 + x)^(3/2)*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[-((-3*I + Sqrt[3] + (6*I)/(1 + x))/(3*I - Sqrt[3]))]*EllipticE[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])] + Sqrt[2]*((2*I)*Sqrt[3]*a + (3 - I*Sqrt[3])*b)*(1 + x)^(3/2)*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[-((-3*I + Sqrt[3] + (6*I)/(1 + x))/(3*I - Sqrt[3]))]*EllipticF[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])])/(18*Sqrt[(-I)/(3*I + Sqrt[3])]*Sqrt[1 + x]*Sqrt[1 - x + x^2])","C",1
2305,1,435,351,1.6986215,"\int \frac{a+b x}{(1+x)^{5/2} \left(1-x+x^2\right)^{5/2}} \, dx","Integrate[(a + b*x)/((1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]","\frac{2 x \left(a \left(7 x^3+10\right)+b x \left(5 x^3+8\right)\right)}{27 \left(x^2-x+1\right)^{3/2} (x+1)^{3/2}}+\frac{(x+1)^{3/2} \left(\frac{\sqrt{2} \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{\sqrt{3}-3 i}} \left(14 i \sqrt{3} a+5 \left(3-i \sqrt{3}\right) b\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{\sqrt{x+1}}-\frac{60 \sqrt{-\frac{i}{\sqrt{3}+3 i}} b \left(x^2-x+1\right)}{(x+1)^2}+\frac{15 i \sqrt{2} \left(\sqrt{3}+i\right) b \sqrt{\frac{-\frac{6 i}{x+1}+\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt{\frac{\frac{6 i}{x+1}+\sqrt{3}-3 i}{\sqrt{3}-3 i}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{6 i}{3 i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{\sqrt{x+1}}\right)}{162 \sqrt{-\frac{i}{\sqrt{3}+3 i}} \sqrt{x^2-x+1}}","\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{2 x (a+b x)}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}+\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{10 b \left(x^3+1\right)}{27 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}",1,"(2*x*(b*x*(8 + 5*x^3) + a*(10 + 7*x^3)))/(27*(1 + x)^(3/2)*(1 - x + x^2)^(3/2)) + ((1 + x)^(3/2)*((-60*Sqrt[(-I)/(3*I + Sqrt[3])]*b*(1 - x + x^2))/(1 + x)^2 + ((15*I)*Sqrt[2]*(I + Sqrt[3])*b*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[(-3*I + Sqrt[3] + (6*I)/(1 + x))/(-3*I + Sqrt[3])]*EllipticE[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])])/Sqrt[1 + x] + (Sqrt[2]*((14*I)*Sqrt[3]*a + 5*(3 - I*Sqrt[3])*b)*Sqrt[(3*I + Sqrt[3] - (6*I)/(1 + x))/(3*I + Sqrt[3])]*Sqrt[(-3*I + Sqrt[3] + (6*I)/(1 + x))/(-3*I + Sqrt[3])]*EllipticF[I*ArcSinh[Sqrt[(-6*I)/(3*I + Sqrt[3])]/Sqrt[1 + x]], (3*I + Sqrt[3])/(3*I - Sqrt[3])])/Sqrt[1 + x]))/(162*Sqrt[(-I)/(3*I + Sqrt[3])]*Sqrt[1 - x + x^2])","C",1
2306,1,251,134,0.1371883,"\int (A+B x) (d+e x)^4 \left(a+b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a + b*x + c*x^2),x]","\frac{1}{6} e^2 x^6 \left(B e (a e+4 b d)+A e (b e+4 c d)+6 B c d^2\right)+\frac{1}{4} d x^4 \left(2 A e \left(e (2 a e+3 b d)+2 c d^2\right)+B d \left(6 a e^2+4 b d e+c d^2\right)\right)+\frac{1}{3} d^2 x^3 \left(6 a A e^2+4 a B d e+b d (4 A e+B d)+A c d^2\right)+\frac{1}{5} e x^5 \left(A e \left(e (a e+4 b d)+6 c d^2\right)+B \left(2 d e (2 a e+3 b d)+4 c d^3\right)\right)+\frac{1}{2} d^3 x^2 (4 a A e+a B d+A b d)+a A d^4 x+\frac{1}{7} e^3 x^7 (A c e+b B e+4 B c d)+\frac{1}{8} B c e^4 x^8","-\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,"a*A*d^4*x + (d^3*(A*b*d + a*B*d + 4*a*A*e)*x^2)/2 + (d^2*(A*c*d^2 + 4*a*B*d*e + 6*a*A*e^2 + b*d*(B*d + 4*A*e))*x^3)/3 + (d*(B*d*(c*d^2 + 4*b*d*e + 6*a*e^2) + 2*A*e*(2*c*d^2 + e*(3*b*d + 2*a*e)))*x^4)/4 + (e*(A*e*(6*c*d^2 + e*(4*b*d + a*e)) + B*(4*c*d^3 + 2*d*e*(3*b*d + 2*a*e)))*x^5)/5 + (e^2*(6*B*c*d^2 + B*e*(4*b*d + a*e) + A*e*(4*c*d + b*e))*x^6)/6 + (e^3*(4*B*c*d + b*B*e + A*c*e)*x^7)/7 + (B*c*e^4*x^8)/8","A",1
2307,1,192,134,0.0861427,"\int (A+B x) (d+e x)^3 \left(a+b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a + b*x + c*x^2),x]","\frac{1}{3} d x^3 \left(3 a A e^2+3 a B d e+b d (3 A e+B d)+A c d^2\right)+\frac{1}{5} e x^5 \left(B e (a e+3 b d)+A e (b e+3 c d)+3 B c d^2\right)+\frac{1}{4} x^4 \left(A e \left(e (a e+3 b d)+3 c d^2\right)+B \left(3 d e (a e+b d)+c d^3\right)\right)+\frac{1}{2} d^2 x^2 (3 a A e+a B d+A b d)+a A d^3 x+\frac{1}{6} e^2 x^6 (A c e+b B e+3 B c d)+\frac{1}{7} B c e^3 x^7","-\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,"a*A*d^3*x + (d^2*(A*b*d + a*B*d + 3*a*A*e)*x^2)/2 + (d*(A*c*d^2 + 3*a*B*d*e + 3*a*A*e^2 + b*d*(B*d + 3*A*e))*x^3)/3 + ((B*(c*d^3 + 3*d*e*(b*d + a*e)) + A*e*(3*c*d^2 + e*(3*b*d + a*e)))*x^4)/4 + (e*(3*B*c*d^2 + B*e*(3*b*d + a*e) + A*e*(3*c*d + b*e))*x^5)/5 + (e^2*(3*B*c*d + b*B*e + A*c*e)*x^6)/6 + (B*c*e^3*x^7)/7","A",1
2308,1,137,134,0.059527,"\int (A+B x) (d+e x)^2 \left(a+b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a + b*x + c*x^2),x]","\frac{1}{3} x^3 \left(a A e^2+2 a B d e+b d (2 A e+B d)+A c d^2\right)+\frac{1}{4} x^4 \left(B e (a e+2 b d)+A e (b e+2 c d)+B c d^2\right)+\frac{1}{2} d x^2 (2 a A e+a B d+A b d)+a A d^2 x+\frac{1}{5} e x^5 (A c e+b B e+2 B c d)+\frac{1}{6} B c e^2 x^6","-\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,"a*A*d^2*x + (d*(A*b*d + a*B*d + 2*a*A*e)*x^2)/2 + ((A*c*d^2 + 2*a*B*d*e + a*A*e^2 + b*d*(B*d + 2*A*e))*x^3)/3 + ((B*c*d^2 + B*e*(2*b*d + a*e) + A*e*(2*c*d + 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",1
2309,1,80,80,0.0290984,"\int (A+B x) (d+e x) \left(a+b x+c x^2\right) \, dx","Integrate[(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",1
2310,1,42,42,0.013555,"\int (A+B x) \left(a+b x+c x^2\right) \, dx","Integrate[(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",1
2311,1,100,111,0.0513777,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{d+e x} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/(d + e*x),x]","\frac{e x \left(3 B e (2 a e-2 b d+b e x)+3 A e (2 b e-2 c d+c e x)+B c \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)-6 (B d-A e) \log (d+e x) \left(e (a e-b d)+c d^2\right)}{6 e^4}","-\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,"(e*x*(3*B*e*(-2*b*d + 2*a*e + b*e*x) + 3*A*e*(-2*c*d + 2*b*e + c*e*x) + B*c*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) - 6*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))*Log[d + e*x])/(6*e^4)","A",1
2312,1,106,116,0.0740897,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^2,x]","\frac{\frac{2 (B d-A e) \left(e (a e-b d)+c d^2\right)}{d+e x}+2 \log (d+e x) \left(B e (a e-2 b d)+A e (b e-2 c d)+3 B c d^2\right)+2 e x (A c e+b B e-2 B c d)+B c e^2 x^2}{2 e^4}","-\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{(B d-A e) \left(a e^2-b d e+c d^2\right)}{e^4 (d+e x)}-\frac{x (-A c e-b B e+2 B c d)}{e^3}+\frac{B c x^2}{2 e^2}",1,"(2*e*(-2*B*c*d + b*B*e + A*c*e)*x + B*c*e^2*x^2 + (2*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e)))/(d + e*x) + 2*(3*B*c*d^2 + B*e*(-2*b*d + a*e) + A*e*(-2*c*d + b*e))*Log[d + e*x])/(2*e^4)","A",1
2313,1,135,119,0.0682612,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^3,x]","\frac{-a B e^2-A b e^2+2 A c d e+2 b B d e-3 B c d^2}{e^4 (d+e x)}+\frac{-a A e^3+a B d e^2+A b d e^2-A c d^2 e-b B d^2 e+B c d^3}{2 e^4 (d+e x)^2}+\frac{\log (d+e x) (A c e+b B e-3 B c d)}{e^4}+\frac{B c x}{e^3}","\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{(B d-A e) \left(a e^2-b d e+c d^2\right)}{2 e^4 (d+e x)^2}-\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*c*d^3 - b*B*d^2*e - A*c*d^2*e + A*b*d*e^2 + a*B*d*e^2 - a*A*e^3)/(2*e^4*(d + e*x)^2) + (-3*B*c*d^2 + 2*b*B*d*e + 2*A*c*d*e - A*b*e^2 - a*B*e^2)/(e^4*(d + e*x)) + ((-3*B*c*d + b*B*e + A*c*e)*Log[d + e*x])/e^4","A",1
2314,1,130,127,0.0704832,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^4,x]","\frac{-A e \left(e (2 a e+b d+3 b e x)+2 c \left(d^2+3 d e x+3 e^2 x^2\right)\right)+B \left(c d \left(11 d^2+27 d e x+18 e^2 x^2\right)-e \left(a e (d+3 e x)+2 b \left(d^2+3 d e x+3 e^2 x^2\right)\right)\right)+6 B c (d+e x)^3 \log (d+e x)}{6 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)}{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,"(-(A*e*(e*(b*d + 2*a*e + 3*b*e*x) + 2*c*(d^2 + 3*d*e*x + 3*e^2*x^2))) + B*(c*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2) - e*(a*e*(d + 3*e*x) + 2*b*(d^2 + 3*d*e*x + 3*e^2*x^2))) + 6*B*c*(d + e*x)^3*Log[d + e*x])/(6*e^4*(d + e*x)^3)","A",1
2315,1,118,132,0.0558769,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^5,x]","-\frac{A e \left(e (3 a e+b d+4 b e x)+c \left(d^2+4 d e x+6 e^2 x^2\right)\right)+B \left(e \left(a e (d+4 e x)+b \left(d^2+4 d e x+6 e^2 x^2\right)\right)+3 c \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)}{12 e^4 (d+e x)^4}","\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,"-1/12*(A*e*(e*(b*d + 3*a*e + 4*b*e*x) + c*(d^2 + 4*d*e*x + 6*e^2*x^2)) + B*(3*c*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) + e*(a*e*(d + 4*e*x) + b*(d^2 + 4*d*e*x + 6*e^2*x^2))))/(e^4*(d + e*x)^4)","A",1
2316,1,122,134,0.0610235,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^6,x]","-\frac{A e \left(3 e (4 a e+b d+5 b e x)+2 c \left(d^2+5 d e x+10 e^2 x^2\right)\right)+B \left(e \left(3 a e (d+5 e x)+2 b \left(d^2+5 d e x+10 e^2 x^2\right)\right)+3 c \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)}{60 e^4 (d+e x)^5}","\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,"-1/60*(A*e*(3*e*(b*d + 4*a*e + 5*b*e*x) + 2*c*(d^2 + 5*d*e*x + 10*e^2*x^2)) + B*(3*c*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + e*(3*a*e*(d + 5*e*x) + 2*b*(d^2 + 5*d*e*x + 10*e^2*x^2))))/(e^4*(d + e*x)^5)","A",1
2317,1,119,134,0.0588761,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^7,x]","-\frac{A e \left(2 e (5 a e+b d+6 b e x)+c \left(d^2+6 d e x+15 e^2 x^2\right)\right)+B \left(e \left(2 a e (d+6 e x)+b \left(d^2+6 d e x+15 e^2 x^2\right)\right)+c \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)}{60 e^4 (d+e x)^6}","\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,"-1/60*(A*e*(2*e*(b*d + 5*a*e + 6*b*e*x) + c*(d^2 + 6*d*e*x + 15*e^2*x^2)) + B*(c*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + e*(2*a*e*(d + 6*e*x) + b*(d^2 + 6*d*e*x + 15*e^2*x^2))))/(e^4*(d + e*x)^6)","A",1
2318,1,665,304,0.300149,"\int (A+B x) (d+e x)^5 \left(a+b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^5*(a + b*x + c*x^2)^2,x]","\frac{1}{7} e x^7 \left(B \left(e^2 \left(a^2 e^2+10 a b d e+10 b^2 d^2\right)+20 c d^2 e (a e+b d)+5 c^2 d^4\right)+A e \left(10 c d e (a e+2 b d)+b e^2 (2 a e+5 b d)+10 c^2 d^3\right)\right)+\frac{1}{5} d x^5 \left(A \left(5 a^2 e^4+20 a c d^2 e^2+c^2 d^4\right)+2 b d \left(10 a A e^3+10 a B d e^2+5 A c d^2 e+B c d^3\right)+10 a B d e \left(a e^2+c d^2\right)+5 b^2 d^2 e (2 A e+B d)\right)+\frac{1}{6} x^6 \left(A e \left(e^2 \left(a^2 e^2+10 a b d e+10 b^2 d^2\right)+20 c d^2 e (a e+b d)+5 c^2 d^4\right)+B \left(5 d e^2 \left(a^2 e^2+4 a b d e+2 b^2 d^2\right)+10 c d^3 e (2 a e+b d)+c^2 d^5\right)\right)+a^2 A d^5 x+\frac{1}{9} e^3 x^9 \left(B \left(2 c e (a e+5 b d)+b^2 e^2+10 c^2 d^2\right)+A c e (2 b e+5 c d)\right)+\frac{1}{8} e^2 x^8 \left(A e \left(2 c e (a e+5 b d)+b^2 e^2+10 c^2 d^2\right)+B \left(10 c d e (a e+2 b d)+b e^2 (2 a e+5 b d)+10 c^2 d^3\right)\right)+\frac{1}{3} d^3 x^3 \left(A \left(10 a b d e+2 a \left(5 a e^2+c d^2\right)+b^2 d^2\right)+a B d (5 a e+2 b d)\right)+\frac{1}{4} d^2 x^4 \left(2 b d \left(10 a A e^2+5 a B d e+A c d^2\right)+2 a \left(5 a A e^3+5 a B d e^2+5 A c d^2 e+B c d^3\right)+b^2 d^2 (5 A e+B d)\right)+\frac{1}{2} a d^4 x^2 (5 a A e+a B d+2 A b d)+\frac{1}{10} c e^4 x^{10} (A c e+2 b B e+5 B c d)+\frac{1}{11} B c^2 e^5 x^{11}","-\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,"a^2*A*d^5*x + (a*d^4*(2*A*b*d + a*B*d + 5*a*A*e)*x^2)/2 + (d^3*(a*B*d*(2*b*d + 5*a*e) + A*(b^2*d^2 + 10*a*b*d*e + 2*a*(c*d^2 + 5*a*e^2)))*x^3)/3 + (d^2*(b^2*d^2*(B*d + 5*A*e) + 2*b*d*(A*c*d^2 + 5*a*B*d*e + 10*a*A*e^2) + 2*a*(B*c*d^3 + 5*A*c*d^2*e + 5*a*B*d*e^2 + 5*a*A*e^3))*x^4)/4 + (d*(5*b^2*d^2*e*(B*d + 2*A*e) + 10*a*B*d*e*(c*d^2 + a*e^2) + 2*b*d*(B*c*d^3 + 5*A*c*d^2*e + 10*a*B*d*e^2 + 10*a*A*e^3) + A*(c^2*d^4 + 20*a*c*d^2*e^2 + 5*a^2*e^4))*x^5)/5 + ((B*(c^2*d^5 + 10*c*d^3*e*(b*d + 2*a*e) + 5*d*e^2*(2*b^2*d^2 + 4*a*b*d*e + a^2*e^2)) + A*e*(5*c^2*d^4 + 20*c*d^2*e*(b*d + a*e) + e^2*(10*b^2*d^2 + 10*a*b*d*e + a^2*e^2)))*x^6)/6 + (e*(A*e*(10*c^2*d^3 + 10*c*d*e*(2*b*d + a*e) + b*e^2*(5*b*d + 2*a*e)) + B*(5*c^2*d^4 + 20*c*d^2*e*(b*d + a*e) + e^2*(10*b^2*d^2 + 10*a*b*d*e + a^2*e^2)))*x^7)/7 + (e^2*(A*e*(10*c^2*d^2 + b^2*e^2 + 2*c*e*(5*b*d + a*e)) + B*(10*c^2*d^3 + 10*c*d*e*(2*b*d + a*e) + b*e^2*(5*b*d + 2*a*e)))*x^8)/8 + (e^3*(A*c*e*(5*c*d + 2*b*e) + B*(10*c^2*d^2 + b^2*e^2 + 2*c*e*(5*b*d + a*e)))*x^9)/9 + (c*e^4*(5*B*c*d + 2*b*B*e + A*c*e)*x^10)/10 + (B*c^2*e^5*x^11)/11","B",1
2319,1,550,304,0.2444017,"\int (A+B x) (d+e x)^4 \left(a+b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a + b*x + c*x^2)^2,x]","\frac{1}{6} x^6 \left(B \left(e^2 \left(a^2 e^2+8 a b d e+6 b^2 d^2\right)+4 c d^2 e (3 a e+2 b d)+c^2 d^4\right)+2 A e \left(2 c d e (2 a e+3 b d)+b e^2 (a e+2 b d)+2 c^2 d^3\right)\right)+\frac{1}{5} x^5 \left(A \left(a^2 e^4+12 a c d^2 e^2+c^2 d^4\right)+2 b d \left(4 a A e^3+6 a B d e^2+4 A c d^2 e+B c d^3\right)+4 a B d e \left(a e^2+2 c d^2\right)+2 b^2 d^2 e (3 A e+2 B d)\right)+a^2 A d^4 x+\frac{1}{8} e^2 x^8 \left(B \left(2 c e (a e+4 b d)+b^2 e^2+6 c^2 d^2\right)+2 A c e (b e+2 c d)\right)+\frac{1}{7} e x^7 \left(A e \left(2 c e (a e+4 b d)+b^2 e^2+6 c^2 d^2\right)+2 B \left(2 c d e (2 a e+3 b d)+b e^2 (a e+2 b d)+2 c^2 d^3\right)\right)+\frac{1}{3} d^2 x^3 \left(A \left(8 a b d e+2 a \left(3 a e^2+c d^2\right)+b^2 d^2\right)+2 a B d (2 a e+b d)\right)+\frac{1}{4} d x^4 \left(2 b d \left(6 a A e^2+4 a B d e+A c d^2\right)+2 a \left(2 a A e^3+3 a B d e^2+4 A c d^2 e+B c d^3\right)+b^2 d^2 (4 A e+B d)\right)+\frac{1}{2} a d^3 x^2 (4 a A e+a B d+2 A b d)+\frac{1}{9} c e^3 x^9 (A c e+2 b B e+4 B c d)+\frac{1}{10} B c^2 e^4 x^{10}","-\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,"a^2*A*d^4*x + (a*d^3*(2*A*b*d + a*B*d + 4*a*A*e)*x^2)/2 + (d^2*(2*a*B*d*(b*d + 2*a*e) + A*(b^2*d^2 + 8*a*b*d*e + 2*a*(c*d^2 + 3*a*e^2)))*x^3)/3 + (d*(b^2*d^2*(B*d + 4*A*e) + 2*b*d*(A*c*d^2 + 4*a*B*d*e + 6*a*A*e^2) + 2*a*(B*c*d^3 + 4*A*c*d^2*e + 3*a*B*d*e^2 + 2*a*A*e^3))*x^4)/4 + ((2*b^2*d^2*e*(2*B*d + 3*A*e) + 4*a*B*d*e*(2*c*d^2 + a*e^2) + 2*b*d*(B*c*d^3 + 4*A*c*d^2*e + 6*a*B*d*e^2 + 4*a*A*e^3) + A*(c^2*d^4 + 12*a*c*d^2*e^2 + a^2*e^4))*x^5)/5 + ((2*A*e*(2*c^2*d^3 + b*e^2*(2*b*d + a*e) + 2*c*d*e*(3*b*d + 2*a*e)) + B*(c^2*d^4 + 4*c*d^2*e*(2*b*d + 3*a*e) + e^2*(6*b^2*d^2 + 8*a*b*d*e + a^2*e^2)))*x^6)/6 + (e*(A*e*(6*c^2*d^2 + b^2*e^2 + 2*c*e*(4*b*d + a*e)) + 2*B*(2*c^2*d^3 + b*e^2*(2*b*d + a*e) + 2*c*d*e*(3*b*d + 2*a*e)))*x^7)/7 + (e^2*(2*A*c*e*(2*c*d + b*e) + B*(6*c^2*d^2 + b^2*e^2 + 2*c*e*(4*b*d + a*e)))*x^8)/8 + (c*e^3*(4*B*c*d + 2*b*B*e + A*c*e)*x^9)/9 + (B*c^2*e^4*x^10)/10","A",1
2320,1,421,304,0.1891932,"\int (A+B x) (d+e x)^3 \left(a+b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a + b*x + c*x^2)^2,x]","a^2 A d^3 x+\frac{1}{7} e x^7 \left(B \left(2 c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+A c e (2 b e+3 c d)\right)+\frac{1}{6} x^6 \left(A e \left(2 c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+B \left(6 c d e (a e+b d)+b e^2 (2 a e+3 b d)+c^2 d^3\right)\right)+\frac{1}{3} d x^3 \left(A \left(6 a b d e+a \left(3 a e^2+2 c d^2\right)+b^2 d^2\right)+a B d (3 a e+2 b d)\right)+\frac{1}{5} x^5 \left(2 b \left(a A e^3+3 a B d e^2+3 A c d^2 e+B c d^3\right)+A c d \left(6 a e^2+c d^2\right)+a B e \left(a e^2+6 c d^2\right)+3 b^2 d e (A e+B d)\right)+\frac{1}{4} x^4 \left(2 b d \left(3 a A e^2+3 a B d e+A c d^2\right)+a \left(a A e^3+3 a B d e^2+6 A c d^2 e+2 B c d^3\right)+b^2 d^2 (3 A e+B d)\right)+\frac{1}{2} a d^2 x^2 (3 a A e+a B d+2 A 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{(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,"a^2*A*d^3*x + (a*d^2*(2*A*b*d + a*B*d + 3*a*A*e)*x^2)/2 + (d*(a*B*d*(2*b*d + 3*a*e) + A*(b^2*d^2 + 6*a*b*d*e + a*(2*c*d^2 + 3*a*e^2)))*x^3)/3 + ((b^2*d^2*(B*d + 3*A*e) + 2*b*d*(A*c*d^2 + 3*a*B*d*e + 3*a*A*e^2) + a*(2*B*c*d^3 + 6*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3))*x^4)/4 + ((3*b^2*d*e*(B*d + A*e) + a*B*e*(6*c*d^2 + a*e^2) + A*c*d*(c*d^2 + 6*a*e^2) + 2*b*(B*c*d^3 + 3*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3))*x^5)/5 + ((A*e*(3*c^2*d^2 + b^2*e^2 + 2*c*e*(3*b*d + a*e)) + B*(c^2*d^3 + 6*c*d*e*(b*d + a*e) + b*e^2*(3*b*d + 2*a*e)))*x^6)/6 + (e*(A*c*e*(3*c*d + 2*b*e) + B*(3*c^2*d^2 + b^2*e^2 + 2*c*e*(3*b*d + a*e)))*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",1
2321,1,301,304,0.1431704,"\int (A+B x) (d+e x)^2 \left(a+b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a + b*x + c*x^2)^2,x]","a^2 A d^2 x+\frac{1}{6} x^6 \left(B \left(2 c e (a e+2 b d)+b^2 e^2+c^2 d^2\right)+2 A c e (b e+c d)\right)+\frac{1}{5} x^5 \left(2 b \left(a B e^2+2 A c d e+B c d^2\right)+c \left(2 a A e^2+4 a B d e+A c d^2\right)+b^2 e (A e+2 B d)\right)+\frac{1}{4} x^4 \left(2 b \left(a A e^2+2 a B d e+A c d^2\right)+a \left(a B e^2+4 A c d e+2 B c d^2\right)+b^2 d (2 A e+B d)\right)+\frac{1}{3} x^3 \left(A \left(4 a b d e+a \left(a e^2+2 c d^2\right)+b^2 d^2\right)+2 a B d (a e+b d)\right)+\frac{1}{2} a d x^2 (2 A (a e+b d)+a B d)+\frac{1}{7} c e x^7 (A c e+2 B (b e+c d))+\frac{1}{8} B c^2 e^2 x^8","-\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,"a^2*A*d^2*x + (a*d*(a*B*d + 2*A*(b*d + a*e))*x^2)/2 + ((2*a*B*d*(b*d + a*e) + A*(b^2*d^2 + 4*a*b*d*e + a*(2*c*d^2 + a*e^2)))*x^3)/3 + ((b^2*d*(B*d + 2*A*e) + 2*b*(A*c*d^2 + 2*a*B*d*e + a*A*e^2) + a*(2*B*c*d^2 + 4*A*c*d*e + a*B*e^2))*x^4)/4 + ((b^2*e*(2*B*d + A*e) + c*(A*c*d^2 + 4*a*B*d*e + 2*a*A*e^2) + 2*b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2))*x^5)/5 + ((2*A*c*e*(c*d + b*e) + B*(c^2*d^2 + b^2*e^2 + 2*c*e*(2*b*d + a*e)))*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",1
2322,1,180,180,0.0783533,"\int (A+B x) (d+e x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[(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",1
2323,1,96,96,0.0239057,"\int (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[(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(2 a A c+2 a b B+A b^2\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 + ((A*b^2 + 2*a*b*B + 2*a*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",1
2324,1,298,257,0.1790686,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{d+e x} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x),x]","\frac{e x \left(B \left(10 e^2 \left(6 a^2 e^2+6 a b e (e x-2 d)+b^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+10 c e \left(2 a e \left(6 d^2-3 d e x+2 e^2 x^2\right)+b \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)+c^2 \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)+5 A e \left(4 c e \left(3 a e (e x-2 d)+b \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+6 b e^2 (4 a e-2 b d+b e x)+c^2 \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)\right)-60 (B d-A e) \log (d+e x) \left(e (a e-b d)+c d^2\right)^2}{60 e^6}","-\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^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 \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,"(e*x*(5*A*e*(6*b*e^2*(-2*b*d + 4*a*e + b*e*x) + c^2*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + 4*c*e*(3*a*e*(-2*d + e*x) + b*(6*d^2 - 3*d*e*x + 2*e^2*x^2))) + B*(c^2*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + 10*e^2*(6*a^2*e^2 + 6*a*b*e*(-2*d + e*x) + b^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + 10*c*e*(2*a*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + b*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)))) - 60*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))^2*Log[d + e*x])/(60*e^6)","A",1
2325,1,250,267,0.1129204,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^2,x]","\frac{6 e^2 x^2 \left(B \left(2 c e (a e-2 b d)+b^2 e^2+3 c^2 d^2\right)+2 A c e (b e-c d)\right)+12 e x \left(A e \left(2 c e (a e-2 b d)+b^2 e^2+3 c^2 d^2\right)-2 B (2 c d-b e) \left(e (a e-b d)+c d^2\right)\right)+\frac{12 (B d-A e) \left(e (a e-b d)+c d^2\right)^2}{d+e x}+12 \log (d+e x) \left(e (a e-b d)+c d^2\right) \left(B e (a e-3 b d)+2 A e (b e-2 c d)+5 B c d^2\right)+4 c e^3 x^3 (A c e+2 b B e-2 B c d)+3 B c^2 e^4 x^4}{12 e^6}","-\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{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{(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,"(12*e*(A*e*(3*c^2*d^2 + b^2*e^2 + 2*c*e*(-2*b*d + a*e)) - 2*B*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e)))*x + 6*e^2*(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 + 4*c*e^3*(-2*B*c*d + 2*b*B*e + A*c*e)*x^3 + 3*B*c^2*e^4*x^4 + (12*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))^2)/(d + e*x) + 12*(c*d^2 + e*(-(b*d) + a*e))*(5*B*c*d^2 + B*e*(-3*b*d + a*e) + 2*A*e*(-2*c*d + b*e))*Log[d + e*x])/(12*e^6)","A",1
2326,1,262,281,0.1241019,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^3,x]","\frac{6 e x \left(B \left(2 c e (a e-3 b d)+b^2 e^2+6 c^2 d^2\right)+A c e (2 b e-3 c d)\right)+6 \log (d+e x) \left(A e \left(2 c e (a e-3 b d)+b^2 e^2+6 c^2 d^2\right)+B \left(6 c d e (2 b d-a e)+b e^2 (2 a e-3 b d)-10 c^2 d^3\right)\right)-\frac{6 \left(e (a e-b d)+c d^2\right) \left(B e (a e-3 b d)+2 A e (b e-2 c d)+5 B c d^2\right)}{d+e x}+\frac{3 (B d-A e) \left(e (a e-b d)+c d^2\right)^2}{(d+e x)^2}+3 c e^2 x^2 (A c e+2 b B e-3 B c d)+2 B c^2 e^3 x^3}{6 e^6}","-\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,"(6*e*(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 + 3*c*e^2*(-3*B*c*d + 2*b*B*e + A*c*e)*x^2 + 2*B*c^2*e^3*x^3 + (3*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))^2)/(d + e*x)^2 - (6*(c*d^2 + e*(-(b*d) + a*e))*(5*B*c*d^2 + B*e*(-3*b*d + a*e) + 2*A*e*(-2*c*d + b*e)))/(d + e*x) + 6*(A*e*(6*c^2*d^2 + b^2*e^2 + 2*c*e*(-3*b*d + a*e)) + B*(-10*c^2*d^3 + 6*c*d*e*(2*b*d - a*e) + b*e^2*(-3*b*d + 2*a*e)))*Log[d + e*x])/(6*e^6)","A",1
2327,1,263,286,0.1136878,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^4,x]","\frac{6 \log (d+e x) \left(B \left(2 c e (a e-4 b d)+b^2 e^2+10 c^2 d^2\right)+2 A c e (b e-2 c d)\right)-\frac{6 \left(A e \left(2 c e (a e-3 b d)+b^2 e^2+6 c^2 d^2\right)+B \left(6 c d e (2 b d-a e)+b e^2 (2 a e-3 b d)-10 c^2 d^3\right)\right)}{d+e x}+\frac{2 (B d-A e) \left(e (a e-b d)+c d^2\right)^2}{(d+e x)^3}-\frac{3 \left(e (a e-b d)+c d^2\right) \left(B e (a e-3 b d)+2 A e (b e-2 c d)+5 B c d^2\right)}{(d+e x)^2}+6 c e x (A c e+2 b B e-4 B c d)+3 B c^2 e^2 x^2}{6 e^6}","-\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 \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{(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,"(6*c*e*(-4*B*c*d + 2*b*B*e + A*c*e)*x + 3*B*c^2*e^2*x^2 + (2*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))^2)/(d + e*x)^3 - (3*(c*d^2 + e*(-(b*d) + a*e))*(5*B*c*d^2 + B*e*(-3*b*d + a*e) + 2*A*e*(-2*c*d + b*e)))/(d + e*x)^2 - (6*(A*e*(6*c^2*d^2 + b^2*e^2 + 2*c*e*(-3*b*d + a*e)) + B*(-10*c^2*d^3 + 6*c*d*e*(2*b*d - a*e) + b*e^2*(-3*b*d + 2*a*e))))/(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)))*Log[d + e*x])/(6*e^6)","A",1
2328,1,391,289,0.2643248,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^5,x]","-\frac{A e \left(e^2 \left(3 a^2 e^2+2 a b e (d+4 e x)+b^2 \left(d^2+4 d e x+6 e^2 x^2\right)\right)+2 c e \left(a e \left(d^2+4 d e x+6 e^2 x^2\right)+3 b \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+c^2 (-d) \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)\right)+B \left(e^2 \left(a^2 e^2 (d+4 e x)+2 a b e \left(d^2+4 d e x+6 e^2 x^2\right)+3 b^2 \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+2 c e \left(3 a e \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)-b d \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)\right)+c^2 \left(77 d^5+248 d^4 e x+252 d^3 e^2 x^2+48 d^2 e^3 x^3-48 d e^4 x^4-12 e^5 x^5\right)\right)+12 c (d+e x)^4 \log (d+e x) (-A c e-2 b B e+5 B c d)}{12 e^6 (d+e x)^4}","\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,"-1/12*(A*e*(-(c^2*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) + e^2*(3*a^2*e^2 + 2*a*b*e*(d + 4*e*x) + b^2*(d^2 + 4*d*e*x + 6*e^2*x^2)) + 2*c*e*(a*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*b*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3))) + B*(c^2*(77*d^5 + 248*d^4*e*x + 252*d^3*e^2*x^2 + 48*d^2*e^3*x^3 - 48*d*e^4*x^4 - 12*e^5*x^5) + e^2*(a^2*e^2*(d + 4*e*x) + 2*a*b*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*b^2*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)) + 2*c*e*(3*a*e*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) - b*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3))) + 12*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^4*Log[d + e*x])/(e^6*(d + e*x)^4)","A",1
2329,1,386,297,0.2065117,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^6,x]","\frac{-2 A e \left(e^2 \left(6 a^2 e^2+3 a b e (d+5 e x)+b^2 \left(d^2+5 d e x+10 e^2 x^2\right)\right)+c e \left(2 a e \left(d^2+5 d e x+10 e^2 x^2\right)+3 b \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)+6 c^2 \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)+B \left(-e^2 \left(3 a^2 e^2 (d+5 e x)+4 a b e \left(d^2+5 d e x+10 e^2 x^2\right)+3 b^2 \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)-6 c e \left(a e \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+4 b \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)+c^2 d \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)\right)+60 B c^2 (d+e x)^5 \log (d+e x)}{60 e^6 (d+e x)^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)}{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,"(-2*A*e*(6*c^2*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4) + e^2*(6*a^2*e^2 + 3*a*b*e*(d + 5*e*x) + b^2*(d^2 + 5*d*e*x + 10*e^2*x^2)) + c*e*(2*a*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*b*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3))) + B*(c^2*d*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4) - e^2*(3*a^2*e^2*(d + 5*e*x) + 4*a*b*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*b^2*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)) - 6*c*e*(a*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 4*b*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4))) + 60*B*c^2*(d + e*x)^5*Log[d + e*x])/(60*e^6*(d + e*x)^5)","A",1
2330,1,372,302,0.1820722,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^7,x]","-\frac{A e \left(e^2 \left(10 a^2 e^2+4 a b e (d+6 e x)+b^2 \left(d^2+6 d e x+15 e^2 x^2\right)\right)+2 c e \left(a e \left(d^2+6 d e x+15 e^2 x^2\right)+b \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)+2 c^2 \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)+B \left(e^2 \left(2 a^2 e^2 (d+6 e x)+2 a b e \left(d^2+6 d e x+15 e^2 x^2\right)+b^2 \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)+2 c e \left(a e \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+2 b \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)+10 c^2 \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right)\right)}{60 e^6 (d+e x)^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)}{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,"-1/60*(A*e*(2*c^2*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4) + e^2*(10*a^2*e^2 + 4*a*b*e*(d + 6*e*x) + b^2*(d^2 + 6*d*e*x + 15*e^2*x^2)) + 2*c*e*(a*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + b*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3))) + B*(10*c^2*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5) + e^2*(2*a^2*e^2*(d + 6*e*x) + 2*a*b*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + b^2*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)) + 2*c*e*(a*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 2*b*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4))))/(e^6*(d + e*x)^6)","A",1
2331,1,377,304,0.2012863,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^8,x]","-\frac{2 A e \left(2 e^2 \left(15 a^2 e^2+5 a b e (d+7 e x)+b^2 \left(d^2+7 d e x+21 e^2 x^2\right)\right)+c e \left(4 a e \left(d^2+7 d e x+21 e^2 x^2\right)+3 b \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)\right)+2 c^2 \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)+B \left(e^2 \left(10 a^2 e^2 (d+7 e x)+8 a b e \left(d^2+7 d e x+21 e^2 x^2\right)+3 b^2 \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)\right)+2 c e \left(3 a e \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+4 b \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)+10 c^2 \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)\right)}{420 e^6 (d+e x)^7}","\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,"-1/420*(2*A*e*(2*c^2*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4) + 2*e^2*(15*a^2*e^2 + 5*a*b*e*(d + 7*e*x) + b^2*(d^2 + 7*d*e*x + 21*e^2*x^2)) + c*e*(4*a*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*b*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3))) + B*(10*c^2*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5) + e^2*(10*a^2*e^2*(d + 7*e*x) + 8*a*b*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*b^2*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3)) + 2*c*e*(3*a*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 4*b*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4))))/(e^6*(d + e*x)^7)","A",1
2332,1,375,304,0.1887763,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^9} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^9,x]","-\frac{A e \left(5 e^2 \left(21 a^2 e^2+6 a b e (d+8 e x)+b^2 \left(d^2+8 d e x+28 e^2 x^2\right)\right)+2 c e \left(5 a e \left(d^2+8 d e x+28 e^2 x^2\right)+3 b \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)\right)+3 c^2 \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)\right)+B \left(e^2 \left(15 a^2 e^2 (d+8 e x)+10 a b e \left(d^2+8 d e x+28 e^2 x^2\right)+3 b^2 \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)\right)+6 c e \left(a e \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+b \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)\right)+5 c^2 \left(d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right)\right)}{840 e^6 (d+e x)^8}","\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,"-1/840*(A*e*(3*c^2*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4) + 5*e^2*(21*a^2*e^2 + 6*a*b*e*(d + 8*e*x) + b^2*(d^2 + 8*d*e*x + 28*e^2*x^2)) + 2*c*e*(5*a*e*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*b*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3))) + B*(5*c^2*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5) + e^2*(15*a^2*e^2*(d + 8*e*x) + 10*a*b*e*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*b^2*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3)) + 6*c*e*(a*e*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + b*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4))))/(e^6*(d + e*x)^8)","A",1
2333,1,1178,555,0.5985732,"\int (A+B x) (d+e x)^5 \left(a+b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^5*(a + b*x + c*x^2)^3,x]","\frac{1}{13} B c^3 e^5 x^{13}+\frac{1}{12} c^2 e^4 (5 B c d+3 b B e+A c e) x^{12}+\frac{1}{11} c e^3 \left(A c e (5 c d+3 b e)+B \left(10 c^2 d^2+3 b^2 e^2+3 c e (5 b d+a e)\right)\right) x^{11}+\frac{1}{10} e^2 \left(A c e \left(10 c^2 d^2+3 b^2 e^2+3 c e (5 b d+a e)\right)+B \left(10 c^3 d^3+15 c^2 e (2 b d+a e) d+b^3 e^3+3 b c e^2 (5 b d+2 a e)\right)\right) x^{10}+\frac{1}{9} e \left(A e \left(10 c^3 d^3+15 c^2 e (2 b d+a e) d+b^3 e^3+3 b c e^2 (5 b d+2 a e)\right)+B \left(5 c^3 d^4+30 c^2 e (b d+a e) d^2+b^2 e^3 (5 b d+3 a e)+3 c e^2 \left(10 b^2 d^2+10 a b e d+a^2 e^2\right)\right)\right) x^9+\frac{1}{8} \left(A e \left(5 c^3 d^4+30 c^2 e (b d+a e) d^2+b^2 e^3 (5 b d+3 a e)+3 c e^2 \left(10 b^2 d^2+10 a b e d+a^2 e^2\right)\right)+B \left(c^3 d^5+15 c^2 e (b d+2 a e) d^3+15 c e^2 \left(2 b^2 d^2+4 a b e d+a^2 e^2\right) d+b e^3 \left(10 b^2 d^2+15 a b e d+3 a^2 e^2\right)\right)\right) x^8+\frac{1}{7} \left(10 d^2 e^2 (B d+A e) b^3+15 d e \left(B c d^3+2 A c e d^2+2 a B e^2 d+a A e^3\right) b^2+3 \left(A e \left(5 c^2 d^4+20 a c e^2 d^2+a^2 e^4\right)+B \left(c^2 d^5+20 a c e^2 d^3+5 a^2 e^4 d\right)\right) b+a B e \left(15 c^2 d^4+30 a c e^2 d^2+a^2 e^4\right)+A c d \left(c^2 d^4+30 a c e^2 d^2+15 a^2 e^4\right)\right) x^7+\frac{1}{6} \left(5 b^3 e (B d+2 A e) d^3+3 b^2 \left(B c d^3+5 A c e d^2+10 a B e^2 d+10 a A e^3\right) d^2+3 b \left(10 a B d e \left(c d^2+a e^2\right)+A \left(c^2 d^4+20 a c e^2 d^2+5 a^2 e^4\right)\right) d+a \left(A e \left(15 c^2 d^4+30 a c e^2 d^2+a^2 e^4\right)+B \left(3 c^2 d^5+30 a c e^2 d^3+5 a^2 e^4 d\right)\right)\right) x^6+\frac{1}{5} d \left(b^3 (B d+5 A e) d^3+3 b^2 \left(A c d^2+5 a B e d+10 a A e^2\right) d^2+6 a b \left(B c d^3+5 A c e d^2+5 a B e^2 d+5 a A e^3\right) d+a \left(5 a B d e \left(3 c d^2+2 a e^2\right)+A \left(3 c^2 d^4+30 a c e^2 d^2+5 a^2 e^4\right)\right)\right) x^5+\frac{1}{4} d^2 \left(A \left(b^3 d^3+15 a b^2 e d^2+6 a b \left(c d^2+5 a e^2\right) d+5 a^2 e \left(3 c d^2+2 a e^2\right)\right)+a B d \left(3 b^2 d^2+15 a b e d+a \left(3 c d^2+10 a e^2\right)\right)\right) x^4+\frac{1}{3} a d^3 \left(a B d (3 b d+5 a e)+A \left(3 b^2 d^2+15 a b e d+a \left(3 c d^2+10 a e^2\right)\right)\right) x^3+\frac{1}{2} a^2 d^4 (3 A b d+a B d+5 a A e) x^2+a^3 A d^5 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{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)^{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{(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,"a^3*A*d^5*x + (a^2*d^4*(3*A*b*d + a*B*d + 5*a*A*e)*x^2)/2 + (a*d^3*(a*B*d*(3*b*d + 5*a*e) + A*(3*b^2*d^2 + 15*a*b*d*e + a*(3*c*d^2 + 10*a*e^2)))*x^3)/3 + (d^2*(A*(b^3*d^3 + 15*a*b^2*d^2*e + 5*a^2*e*(3*c*d^2 + 2*a*e^2) + 6*a*b*d*(c*d^2 + 5*a*e^2)) + a*B*d*(3*b^2*d^2 + 15*a*b*d*e + a*(3*c*d^2 + 10*a*e^2)))*x^4)/4 + (d*(b^3*d^3*(B*d + 5*A*e) + 3*b^2*d^2*(A*c*d^2 + 5*a*B*d*e + 10*a*A*e^2) + 6*a*b*d*(B*c*d^3 + 5*A*c*d^2*e + 5*a*B*d*e^2 + 5*a*A*e^3) + a*(5*a*B*d*e*(3*c*d^2 + 2*a*e^2) + A*(3*c^2*d^4 + 30*a*c*d^2*e^2 + 5*a^2*e^4)))*x^5)/5 + ((5*b^3*d^3*e*(B*d + 2*A*e) + 3*b^2*d^2*(B*c*d^3 + 5*A*c*d^2*e + 10*a*B*d*e^2 + 10*a*A*e^3) + 3*b*d*(10*a*B*d*e*(c*d^2 + a*e^2) + A*(c^2*d^4 + 20*a*c*d^2*e^2 + 5*a^2*e^4)) + a*(A*e*(15*c^2*d^4 + 30*a*c*d^2*e^2 + a^2*e^4) + B*(3*c^2*d^5 + 30*a*c*d^3*e^2 + 5*a^2*d*e^4)))*x^6)/6 + ((10*b^3*d^2*e^2*(B*d + A*e) + 15*b^2*d*e*(B*c*d^3 + 2*A*c*d^2*e + 2*a*B*d*e^2 + a*A*e^3) + a*B*e*(15*c^2*d^4 + 30*a*c*d^2*e^2 + a^2*e^4) + A*c*d*(c^2*d^4 + 30*a*c*d^2*e^2 + 15*a^2*e^4) + 3*b*(A*e*(5*c^2*d^4 + 20*a*c*d^2*e^2 + a^2*e^4) + B*(c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4)))*x^7)/7 + ((A*e*(5*c^3*d^4 + 30*c^2*d^2*e*(b*d + a*e) + b^2*e^3*(5*b*d + 3*a*e) + 3*c*e^2*(10*b^2*d^2 + 10*a*b*d*e + a^2*e^2)) + B*(c^3*d^5 + 15*c^2*d^3*e*(b*d + 2*a*e) + 15*c*d*e^2*(2*b^2*d^2 + 4*a*b*d*e + a^2*e^2) + b*e^3*(10*b^2*d^2 + 15*a*b*d*e + 3*a^2*e^2)))*x^8)/8 + (e*(A*e*(10*c^3*d^3 + b^3*e^3 + 15*c^2*d*e*(2*b*d + a*e) + 3*b*c*e^2*(5*b*d + 2*a*e)) + B*(5*c^3*d^4 + 30*c^2*d^2*e*(b*d + a*e) + b^2*e^3*(5*b*d + 3*a*e) + 3*c*e^2*(10*b^2*d^2 + 10*a*b*d*e + a^2*e^2)))*x^9)/9 + (e^2*(A*c*e*(10*c^2*d^2 + 3*b^2*e^2 + 3*c*e*(5*b*d + a*e)) + B*(10*c^3*d^3 + b^3*e^3 + 15*c^2*d*e*(2*b*d + a*e) + 3*b*c*e^2*(5*b*d + 2*a*e)))*x^10)/10 + (c*e^3*(A*c*e*(5*c*d + 3*b*e) + B*(10*c^2*d^2 + 3*b^2*e^2 + 3*c*e*(5*b*d + a*e)))*x^11)/11 + (c^2*e^4*(5*B*c*d + 3*b*B*e + A*c*e)*x^12)/12 + (B*c^3*e^5*x^13)/13","B",1
2334,1,957,555,0.4731012,"\int (A+B x) (d+e x)^4 \left(a+b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^4*(a + b*x + c*x^2)^3,x]","\frac{1}{12} B c^3 e^4 x^{12}+\frac{1}{11} c^2 e^3 (4 B c d+3 b B e+A c e) x^{11}+\frac{1}{10} c e^2 \left(A c e (4 c d+3 b e)+3 B \left(2 c^2 d^2+b^2 e^2+c e (4 b d+a e)\right)\right) x^{10}+\frac{1}{9} e \left(3 A c e \left(2 c^2 d^2+b^2 e^2+c e (4 b d+a e)\right)+B \left(4 c^3 d^3+6 c^2 e (3 b d+2 a e) d+b^3 e^3+6 b c e^2 (2 b d+a e)\right)\right) x^9+\frac{1}{8} \left(A e \left(4 c^3 d^3+6 c^2 e (3 b d+2 a e) d+b^3 e^3+6 b c e^2 (2 b d+a e)\right)+B \left(c^3 d^4+6 c^2 e (2 b d+3 a e) d^2+b^2 e^3 (4 b d+3 a e)+3 c e^2 \left(6 b^2 d^2+8 a b e d+a^2 e^2\right)\right)\right) x^8+\frac{1}{7} \left(2 d e^2 (3 B d+2 A e) b^3+3 e \left(4 B c d^3+6 A c e d^2+4 a B e^2 d+a A e^3\right) b^2+12 A c d e \left(c d^2+2 a e^2\right) b+3 B \left(c^2 d^4+12 a c e^2 d^2+a^2 e^4\right) b+12 a B c d e \left(c d^2+a e^2\right)+A c \left(c^2 d^4+18 a c e^2 d^2+3 a^2 e^4\right)\right) x^7+\frac{1}{6} \left(2 d^2 e (2 B d+3 A e) b^3+3 d \left(B c d^3+4 A c e d^2+6 a B e^2 d+4 a A e^3\right) b^2+12 a B d e \left(2 c d^2+a e^2\right) b+3 A \left(c^2 d^4+12 a c e^2 d^2+a^2 e^4\right) b+12 a A c d e \left(c d^2+a e^2\right)+a B \left(3 c^2 d^4+18 a c e^2 d^2+a^2 e^4\right)\right) x^6+\frac{1}{5} \left(b^3 (B d+4 A e) d^3+3 b^2 \left(A c d^2+4 a B e d+6 a A e^2\right) d^2+6 a b \left(B c d^3+4 A c e d^2+3 a B e^2 d+2 a A e^3\right) d+a \left(4 a B d e \left(3 c d^2+a e^2\right)+A \left(3 c^2 d^4+18 a c e^2 d^2+a^2 e^4\right)\right)\right) x^5+\frac{1}{4} d \left(3 a B d \left(b^2 d^2+4 a b e d+a \left(c d^2+2 a e^2\right)\right)+A \left(b^3 d^3+12 a b^2 e d^2+6 a b \left(c d^2+3 a e^2\right) d+4 a^2 e \left(3 c d^2+a e^2\right)\right)\right) x^4+\frac{1}{3} a d^2 \left(a B d (3 b d+4 a e)+3 A \left(b^2 d^2+4 a b e d+a \left(c d^2+2 a e^2\right)\right)\right) x^3+\frac{1}{2} a^2 d^3 (3 A b d+a B d+4 a A e) x^2+a^3 A d^4 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{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)^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{(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,"a^3*A*d^4*x + (a^2*d^3*(3*A*b*d + a*B*d + 4*a*A*e)*x^2)/2 + (a*d^2*(a*B*d*(3*b*d + 4*a*e) + 3*A*(b^2*d^2 + 4*a*b*d*e + a*(c*d^2 + 2*a*e^2)))*x^3)/3 + (d*(3*a*B*d*(b^2*d^2 + 4*a*b*d*e + a*(c*d^2 + 2*a*e^2)) + A*(b^3*d^3 + 12*a*b^2*d^2*e + 4*a^2*e*(3*c*d^2 + a*e^2) + 6*a*b*d*(c*d^2 + 3*a*e^2)))*x^4)/4 + ((b^3*d^3*(B*d + 4*A*e) + 3*b^2*d^2*(A*c*d^2 + 4*a*B*d*e + 6*a*A*e^2) + 6*a*b*d*(B*c*d^3 + 4*A*c*d^2*e + 3*a*B*d*e^2 + 2*a*A*e^3) + a*(4*a*B*d*e*(3*c*d^2 + a*e^2) + A*(3*c^2*d^4 + 18*a*c*d^2*e^2 + a^2*e^4)))*x^5)/5 + ((2*b^3*d^2*e*(2*B*d + 3*A*e) + 12*a*A*c*d*e*(c*d^2 + a*e^2) + 12*a*b*B*d*e*(2*c*d^2 + a*e^2) + 3*b^2*d*(B*c*d^3 + 4*A*c*d^2*e + 6*a*B*d*e^2 + 4*a*A*e^3) + 3*A*b*(c^2*d^4 + 12*a*c*d^2*e^2 + a^2*e^4) + a*B*(3*c^2*d^4 + 18*a*c*d^2*e^2 + a^2*e^4))*x^6)/6 + ((2*b^3*d*e^2*(3*B*d + 2*A*e) + 12*a*B*c*d*e*(c*d^2 + a*e^2) + 12*A*b*c*d*e*(c*d^2 + 2*a*e^2) + 3*b^2*e*(4*B*c*d^3 + 6*A*c*d^2*e + 4*a*B*d*e^2 + a*A*e^3) + 3*b*B*(c^2*d^4 + 12*a*c*d^2*e^2 + a^2*e^4) + A*c*(c^2*d^4 + 18*a*c*d^2*e^2 + 3*a^2*e^4))*x^7)/7 + ((A*e*(4*c^3*d^3 + b^3*e^3 + 6*b*c*e^2*(2*b*d + a*e) + 6*c^2*d*e*(3*b*d + 2*a*e)) + B*(c^3*d^4 + 6*c^2*d^2*e*(2*b*d + 3*a*e) + b^2*e^3*(4*b*d + 3*a*e) + 3*c*e^2*(6*b^2*d^2 + 8*a*b*d*e + a^2*e^2)))*x^8)/8 + (e*(3*A*c*e*(2*c^2*d^2 + b^2*e^2 + c*e*(4*b*d + a*e)) + B*(4*c^3*d^3 + b^3*e^3 + 6*b*c*e^2*(2*b*d + a*e) + 6*c^2*d*e*(3*b*d + 2*a*e)))*x^9)/9 + (c*e^2*(A*c*e*(4*c*d + 3*b*e) + 3*B*(2*c^2*d^2 + b^2*e^2 + c*e*(4*b*d + a*e)))*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",1
2335,1,715,555,0.3528264,"\int (A+B x) (d+e x)^3 \left(a+b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^3*(a + b*x + c*x^2)^3,x]","a^3 A d^3 x+\frac{1}{4} x^4 \left(A \left(a^2 e \left(a e^2+9 c d^2\right)+9 a b^2 d^2 e+3 a b d \left(3 a e^2+2 c d^2\right)+b^3 d^3\right)+3 a B d \left(3 a b d e+a \left(a e^2+c d^2\right)+b^2 d^2\right)\right)+\frac{1}{2} a^2 d^2 x^2 (3 A (a e+b d)+a B d)+\frac{1}{3} c e x^9 \left(B \left(c e (a e+3 b d)+b^2 e^2+c^2 d^2\right)+A c e (b e+c d)\right)+a d x^3 \left(A \left(3 a b d e+a \left(a e^2+c d^2\right)+b^2 d^2\right)+a B d (a e+b d)\right)+\frac{1}{8} x^8 \left(3 A c e \left(c e (a e+3 b d)+b^2 e^2+c^2 d^2\right)+B \left(9 c^2 d e (a e+b d)+3 b c e^2 (2 a e+3 b d)+b^3 e^3+c^3 d^3\right)\right)+\frac{1}{7} x^7 \left(3 b^2 e \left(a B e^2+3 A c d e+3 B c d^2\right)+3 b c \left(2 a A e^3+6 a B d e^2+3 A c d^2 e+B c d^3\right)+c \left(A c d \left(9 a e^2+c d^2\right)+3 a B e \left(a e^2+3 c d^2\right)\right)+b^3 e^2 (A e+3 B d)\right)+\frac{1}{2} x^6 \left(b^2 \left(a A e^3+3 a B d e^2+3 A c d^2 e+B c d^3\right)+A b c d \left(6 a e^2+c d^2\right)+a c \left(a A e^3+3 a B d e^2+3 A c d^2 e+B c d^3\right)+a b B e \left(a e^2+6 c d^2\right)+b^3 d e (A e+B d)\right)+\frac{1}{5} x^5 \left(3 b^2 d \left(3 a A e^2+3 a B d e+A c d^2\right)+3 a b \left(a A e^3+3 a B d e^2+6 A c d^2 e+2 B c d^3\right)+a \left(3 A c d \left(3 a e^2+c d^2\right)+a B e \left(a e^2+9 c d^2\right)\right)+b^3 d^2 (3 A e+B d)\right)+\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{(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)^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)^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)^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,"a^3*A*d^3*x + (a^2*d^2*(a*B*d + 3*A*(b*d + a*e))*x^2)/2 + a*d*(a*B*d*(b*d + a*e) + A*(b^2*d^2 + 3*a*b*d*e + a*(c*d^2 + a*e^2)))*x^3 + ((3*a*B*d*(b^2*d^2 + 3*a*b*d*e + a*(c*d^2 + a*e^2)) + A*(b^3*d^3 + 9*a*b^2*d^2*e + a^2*e*(9*c*d^2 + a*e^2) + 3*a*b*d*(2*c*d^2 + 3*a*e^2)))*x^4)/4 + ((b^3*d^2*(B*d + 3*A*e) + 3*b^2*d*(A*c*d^2 + 3*a*B*d*e + 3*a*A*e^2) + 3*a*b*(2*B*c*d^3 + 6*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3) + a*(a*B*e*(9*c*d^2 + a*e^2) + 3*A*c*d*(c*d^2 + 3*a*e^2)))*x^5)/5 + ((b^3*d*e*(B*d + A*e) + a*b*B*e*(6*c*d^2 + a*e^2) + A*b*c*d*(c*d^2 + 6*a*e^2) + b^2*(B*c*d^3 + 3*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3) + a*c*(B*c*d^3 + 3*A*c*d^2*e + 3*a*B*d*e^2 + a*A*e^3))*x^6)/2 + ((b^3*e^2*(3*B*d + A*e) + 3*b^2*e*(3*B*c*d^2 + 3*A*c*d*e + a*B*e^2) + 3*b*c*(B*c*d^3 + 3*A*c*d^2*e + 6*a*B*d*e^2 + 2*a*A*e^3) + c*(3*a*B*e*(3*c*d^2 + a*e^2) + A*c*d*(c*d^2 + 9*a*e^2)))*x^7)/7 + ((3*A*c*e*(c^2*d^2 + b^2*e^2 + c*e*(3*b*d + a*e)) + B*(c^3*d^3 + b^3*e^3 + 9*c^2*d*e*(b*d + a*e) + 3*b*c*e^2*(3*b*d + 2*a*e)))*x^8)/8 + (c*e*(A*c*e*(c*d + b*e) + B*(c^2*d^2 + b^2*e^2 + c*e*(3*b*d + a*e)))*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",1
2336,1,526,555,0.2745645,"\int (A+B x) (d+e x)^2 \left(a+b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^2*(a + b*x + c*x^2)^3,x]","a^3 A d^2 x+\frac{1}{4} x^4 \left(A \left(6 a^2 c d e+6 a b^2 d e+3 a b \left(a e^2+2 c d^2\right)+b^3 d^2\right)+a B \left(6 a b d e+a \left(a e^2+3 c d^2\right)+3 b^2 d^2\right)\right)+\frac{1}{2} a^2 d x^2 (2 a A e+a B d+3 A b d)+\frac{1}{8} c x^8 \left(B \left(3 c e (a e+2 b d)+3 b^2 e^2+c^2 d^2\right)+A c e (3 b e+2 c d)\right)+\frac{1}{3} a x^3 \left(A \left(6 a b d e+a \left(a e^2+3 c d^2\right)+3 b^2 d^2\right)+a B d (2 a e+3 b d)\right)+\frac{1}{7} x^7 \left(3 b c \left(2 a B e^2+2 A c d e+B c d^2\right)+c^2 \left(3 a A e^2+6 a B d e+A c d^2\right)+3 b^2 c e (A e+2 B d)+b^3 B e^2\right)+\frac{1}{6} x^6 \left(3 b^2 \left(a B e^2+2 A c d e+B c d^2\right)+3 b c \left(2 a A e^2+4 a B d e+A c d^2\right)+3 a c \left(a B e^2+2 A c d e+B c d^2\right)+b^3 e (A e+2 B d)\right)+\frac{1}{5} x^5 \left(3 b^2 \left(a A e^2+2 a B d e+A c d^2\right)+3 a b \left(a B e^2+4 A c d e+2 B c d^2\right)+3 a c \left(a A e^2+2 a B d e+A c d^2\right)+b^3 d (2 A e+B d)\right)+\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{(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{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)^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{(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,"a^3*A*d^2*x + (a^2*d*(3*A*b*d + a*B*d + 2*a*A*e)*x^2)/2 + (a*(a*B*d*(3*b*d + 2*a*e) + A*(3*b^2*d^2 + 6*a*b*d*e + a*(3*c*d^2 + a*e^2)))*x^3)/3 + ((A*(b^3*d^2 + 6*a*b^2*d*e + 6*a^2*c*d*e + 3*a*b*(2*c*d^2 + a*e^2)) + a*B*(3*b^2*d^2 + 6*a*b*d*e + a*(3*c*d^2 + a*e^2)))*x^4)/4 + ((b^3*d*(B*d + 2*A*e) + 3*b^2*(A*c*d^2 + 2*a*B*d*e + a*A*e^2) + 3*a*c*(A*c*d^2 + 2*a*B*d*e + a*A*e^2) + 3*a*b*(2*B*c*d^2 + 4*A*c*d*e + a*B*e^2))*x^5)/5 + ((b^3*e*(2*B*d + A*e) + 3*b*c*(A*c*d^2 + 4*a*B*d*e + 2*a*A*e^2) + 3*b^2*(B*c*d^2 + 2*A*c*d*e + a*B*e^2) + 3*a*c*(B*c*d^2 + 2*A*c*d*e + a*B*e^2))*x^6)/6 + ((b^3*B*e^2 + 3*b^2*c*e*(2*B*d + A*e) + c^2*(A*c*d^2 + 6*a*B*d*e + 3*a*A*e^2) + 3*b*c*(B*c*d^2 + 2*A*c*d*e + 2*a*B*e^2))*x^7)/7 + (c*(A*c*e*(2*c*d + 3*b*e) + B*(c^2*d^2 + 3*b^2*e^2 + 3*c*e*(2*b*d + a*e)))*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",1
2337,1,310,310,0.1605883,"\int (A+B x) (d+e x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)*(a + b*x + c*x^2)^3,x]","a^3 A d 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)+\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}{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}{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}{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}{8} c^2 x^8 (A c e+3 b B e+B c d)+\frac{1}{9} B c^3 e x^9","a^3 A d 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)+\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}{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}{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}{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}{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",1
2338,1,158,158,0.0443448,"\int (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(a + b*x + c*x^2)^3,x]","a^3 A x+\frac{1}{2} a^2 x^2 (a B+3 A b)+\frac{1}{2} c x^6 \left(a B c+A b c+b^2 B\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\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}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{8} B c^3 x^8","a^3 A x+\frac{1}{2} a^2 x^2 (a B+3 A b)+\frac{1}{2} c x^6 \left(a B c+A b c+b^2 B\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\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}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\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",1
2339,1,700,544,0.4565011,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{d+e x} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x),x]","\frac{e x \left(7 A e \left(15 c e^2 \left(6 a^2 e^2 (e x-2 d)+4 a b e \left(6 d^2-3 d e x+2 e^2 x^2\right)+b^2 \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)+10 b e^3 \left(18 a^2 e^2+9 a b e (e x-2 d)+b^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+3 c^2 e \left(5 a e \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+b \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)+c^3 \left(-60 d^5+30 d^4 e x-20 d^3 e^2 x^2+15 d^2 e^3 x^3-12 d e^4 x^4+10 e^5 x^5\right)\right)+B \left(21 c e^2 \left(10 a^2 e^2 \left(6 d^2-3 d e x+2 e^2 x^2\right)+10 a b e \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+b^2 \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)+35 e^3 \left(12 a^3 e^3+18 a^2 b e^2 (e x-2 d)+6 a b^2 e \left(6 d^2-3 d e x+2 e^2 x^2\right)+b^3 \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)+21 c^2 e \left(a e \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)+b \left(-60 d^5+30 d^4 e x-20 d^3 e^2 x^2+15 d^2 e^3 x^3-12 d e^4 x^4+10 e^5 x^5\right)\right)+c^3 \left(420 d^6-210 d^5 e x+140 d^4 e^2 x^2-105 d^3 e^3 x^3+84 d^2 e^4 x^4-70 d e^5 x^5+60 e^6 x^6\right)\right)\right)-420 (B d-A e) \log (d+e x) \left(e (a e-b d)+c d^2\right)^3}{420 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{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{(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{(B d-A e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{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{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,"(e*x*(7*A*e*(c^3*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5) + 10*b*e^3*(18*a^2*e^2 + 9*a*b*e*(-2*d + e*x) + b^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + 15*c*e^2*(6*a^2*e^2*(-2*d + e*x) + 4*a*b*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + b^2*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)) + 3*c^2*e*(5*a*e*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + b*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4))) + B*(c^3*(420*d^6 - 210*d^5*e*x + 140*d^4*e^2*x^2 - 105*d^3*e^3*x^3 + 84*d^2*e^4*x^4 - 70*d*e^5*x^5 + 60*e^6*x^6) + 35*e^3*(12*a^3*e^3 + 18*a^2*b*e^2*(-2*d + e*x) + 6*a*b^2*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + b^3*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)) + 21*c*e^2*(10*a^2*e^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + 10*a*b*e*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + b^2*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4)) + 21*c^2*e*(a*e*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + b*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5)))) - 420*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))^3*Log[d + e*x])/(420*e^8)","A",1
2340,1,922,525,0.5710756,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^2} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^2,x]","\frac{60 \left(7 B c d^2+B e (a e-4 b d)+3 A e (b e-2 c d)\right) (d+e x) \log (d+e x) \left(c d^2+e (a e-b d)\right)^2+3 A e \left(\left(-20 d^6+100 e x d^5+60 e^2 x^2 d^4-20 e^3 x^3 d^3+10 e^4 x^4 d^2-6 e^5 x^5 d+4 e^6 x^6\right) c^3+5 e \left(4 a e \left(-3 d^4+9 e x d^3+6 e^2 x^2 d^2-2 e^3 x^3 d+e^4 x^4\right)+b \left(12 d^5-48 e x d^4-30 e^2 x^2 d^3+10 e^3 x^3 d^2-5 e^4 x^4 d+3 e^5 x^5\right)\right) c^2+20 e^2 \left(\left(-3 d^4+9 e x d^3+6 e^2 x^2 d^2-2 e^3 x^3 d+e^4 x^4\right) b^2+3 a e \left(2 d^3-4 e x d^2-3 e^2 x^2 d+e^3 x^3\right) b+3 a^2 e^2 \left(-d^2+e x d+e^2 x^2\right)\right) c+10 e^3 \left(\left(2 d^3-4 e x d^2-3 e^2 x^2 d+e^3 x^3\right) b^3+6 a e \left(-d^2+e x d+e^2 x^2\right) b^2+6 a^2 d e^2 b-2 a^3 e^3\right)\right)+B \left(\left(60 d^7-360 e x d^6-210 e^2 x^2 d^5+70 e^3 x^3 d^4-35 e^4 x^4 d^3+21 e^5 x^5 d^2-14 e^6 x^6 d+10 e^7 x^7\right) c^3+3 e \left(5 a e \left(12 d^5-48 e x d^4-30 e^2 x^2 d^3+10 e^3 x^3 d^2-5 e^4 x^4 d+3 e^5 x^5\right)-6 b \left(10 d^6-50 e x d^5-30 e^2 x^2 d^4+10 e^3 x^3 d^3-5 e^4 x^4 d^2+3 e^5 x^5 d-2 e^6 x^6\right)\right) c^2+15 e^2 \left(\left(12 d^5-48 e x d^4-30 e^2 x^2 d^3+10 e^3 x^3 d^2-5 e^4 x^4 d+3 e^5 x^5\right) b^2+8 a e \left(-3 d^4+9 e x d^3+6 e^2 x^2 d^2-2 e^3 x^3 d+e^4 x^4\right) b+6 a^2 e^2 \left(2 d^3-4 e x d^2-3 e^2 x^2 d+e^3 x^3\right)\right) c+10 e^3 \left(2 \left(-3 d^4+9 e x d^3+6 e^2 x^2 d^2-2 e^3 x^3 d+e^4 x^4\right) b^3+9 a e \left(2 d^3-4 e x d^2-3 e^2 x^2 d+e^3 x^3\right) b^2+18 a^2 e^2 \left(-d^2+e x d+e^2 x^2\right) b+6 a^3 d e^3\right)\right)}{60 e^8 (d+e x)}","-\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{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^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{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{(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*A*e*(c^3*(-20*d^6 + 100*d^5*e*x + 60*d^4*e^2*x^2 - 20*d^3*e^3*x^3 + 10*d^2*e^4*x^4 - 6*d*e^5*x^5 + 4*e^6*x^6) + 10*e^3*(6*a^2*b*d*e^2 - 2*a^3*e^3 + 6*a*b^2*e*(-d^2 + d*e*x + e^2*x^2) + b^3*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3)) + 20*c*e^2*(3*a^2*e^2*(-d^2 + d*e*x + e^2*x^2) + 3*a*b*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + b^2*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4)) + 5*c^2*e*(4*a*e*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + b*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5))) + B*(c^3*(60*d^7 - 360*d^6*e*x - 210*d^5*e^2*x^2 + 70*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 - 14*d*e^6*x^6 + 10*e^7*x^7) + 10*e^3*(6*a^3*d*e^3 + 18*a^2*b*e^2*(-d^2 + d*e*x + e^2*x^2) + 9*a*b^2*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 2*b^3*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4)) + 15*c*e^2*(6*a^2*e^2*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 8*a*b*e*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + b^2*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5)) + 3*c^2*e*(5*a*e*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5) - 6*b*(10*d^6 - 50*d^5*e*x - 30*d^4*e^2*x^2 + 10*d^3*e^3*x^3 - 5*d^2*e^4*x^4 + 3*d*e^5*x^5 - 2*e^6*x^6))) + 60*(c*d^2 + e*(-(b*d) + a*e))^2*(7*B*c*d^2 + B*e*(-4*b*d + a*e) + 3*A*e*(-2*c*d + b*e))*(d + e*x)*Log[d + e*x])/(60*e^8*(d + e*x))","A",1
2341,1,503,531,0.2773164,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^3} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^3,x]","\frac{20 e x \left(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 (a e-b d)+2 c^2 d^2 e (3 a e-5 b d)+5 c^3 d^4\right)+A e \left(9 c^2 d e (2 b d-a e)+3 b c e^2 (2 a e-3 b d)+b^3 e^3-10 c^3 d^3\right)\right)+20 c e^3 x^3 \left(B \left(c e (a e-3 b d)+b^2 e^2+2 c^2 d^2\right)+A c e (b e-c d)\right)-60 \log (d+e x) \left(e (a e-b d)+c d^2\right) \left(B \left(c d e (3 a e-8 b d)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(c e (a e-5 b d)+b^2 e^2+5 c^2 d^2\right)\right)+10 e^2 x^2 \left(3 A c e \left(c e (a e-3 b d)+b^2 e^2+2 c^2 d^2\right)+B \left(9 c^2 d e (2 b d-a e)+3 b c e^2 (2 a e-3 b d)+b^3 e^3-10 c^3 d^3\right)\right)-\frac{20 \left(e (a e-b d)+c d^2\right)^2 \left(B e (a e-4 b d)+3 A e (b e-2 c d)+7 B c d^2\right)}{d+e x}+\frac{10 (B d-A e) \left(e (a e-b d)+c d^2\right)^3}{(d+e x)^2}+5 c^2 e^4 x^4 (A c e+3 b B e-3 B c d)+4 B c^3 e^5 x^5}{20 e^8}","-\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{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{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{\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,"(20*e*(A*e*(-10*c^3*d^3 + b^3*e^3 + 9*c^2*d*e*(2*b*d - a*e) + 3*b*c*e^2*(-3*b*d + 2*a*e)) + 3*B*(5*c^3*d^4 + b^2*e^3*(-(b*d) + a*e) + 2*c^2*d^2*e*(-5*b*d + 3*a*e) + c*e^2*(6*b^2*d^2 - 6*a*b*d*e + a^2*e^2)))*x + 10*e^2*(3*A*c*e*(2*c^2*d^2 + b^2*e^2 + c*e*(-3*b*d + a*e)) + B*(-10*c^3*d^3 + b^3*e^3 + 9*c^2*d*e*(2*b*d - a*e) + 3*b*c*e^2*(-3*b*d + 2*a*e)))*x^2 + 20*c*e^3*(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 + 5*c^2*e^4*(-3*B*c*d + 3*b*B*e + A*c*e)*x^4 + 4*B*c^3*e^5*x^5 + (10*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))^3)/(d + e*x)^2 - (20*(c*d^2 + e*(-(b*d) + a*e))^2*(7*B*c*d^2 + B*e*(-4*b*d + a*e) + 3*A*e*(-2*c*d + b*e)))/(d + e*x) - 60*(c*d^2 + e*(-(b*d) + a*e))*(-(A*e*(5*c^2*d^2 + b^2*e^2 + c*e*(-5*b*d + a*e))) + B*(7*c^2*d^3 + b*e^2*(2*b*d - a*e) + c*d*e*(-8*b*d + 3*a*e)))*Log[d + e*x])/(20*e^8)","A",1
2342,1,488,521,0.2611835,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^4} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^4,x]","\frac{12 \log (d+e x) \left(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 (3 a e-4 b d)+30 c^2 d^2 e (a e-2 b d)+35 c^3 d^4\right)+A e (b e-2 c d) \left(2 c e (3 a e-5 b d)+b^2 e^2+10 c^2 d^2\right)\right)+6 c e^2 x^2 \left(B \left(3 c e (a e-4 b d)+3 b^2 e^2+10 c^2 d^2\right)+A c e (3 b e-4 c d)\right)+12 e x \left(A c e \left(3 c e (a e-4 b d)+3 b^2 e^2+10 c^2 d^2\right)-B (2 c d-b e) \left(2 c e (3 a e-5 b d)+b^2 e^2+10 c^2 d^2\right)\right)+\frac{36 \left(e (a e-b d)+c d^2\right) \left(B \left(c d e (3 a e-8 b d)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(c e (a e-5 b d)+b^2 e^2+5 c^2 d^2\right)\right)}{d+e x}-\frac{6 \left(e (a e-b d)+c d^2\right)^2 \left(B e (a e-4 b d)+3 A e (b e-2 c d)+7 B c d^2\right)}{(d+e x)^2}+\frac{4 (B d-A e) \left(e (a e-b d)+c d^2\right)^3}{(d+e x)^3}+4 c^2 e^3 x^3 (A c e+3 b B e-4 B c d)+3 B c^3 e^4 x^4}{12 e^8}","-\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{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{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{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,"(12*e*(A*c*e*(10*c^2*d^2 + 3*b^2*e^2 + 3*c*e*(-4*b*d + a*e)) - B*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 + 2*c*e*(-5*b*d + 3*a*e)))*x + 6*c*e^2*(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 + 4*c^2*e^3*(-4*B*c*d + 3*b*B*e + A*c*e)*x^3 + 3*B*c^3*e^4*x^4 + (4*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))^3)/(d + e*x)^3 - (6*(c*d^2 + e*(-(b*d) + a*e))^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 + (36*(c*d^2 + e*(-(b*d) + a*e))*(-(A*e*(5*c^2*d^2 + b^2*e^2 + c*e*(-5*b*d + a*e))) + B*(7*c^2*d^3 + b*e^2*(2*b*d - a*e) + c*d*e*(-8*b*d + 3*a*e))))/(d + e*x) + 12*(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 + 30*c^2*d^2*e*(-2*b*d + a*e) + b^2*e^3*(-4*b*d + 3*a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*Log[d + e*x])/(12*e^8)","A",1
2343,1,496,533,0.2544209,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^5} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^5,x]","\frac{-\frac{12 \left(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 (3 a e-4 b d)+30 c^2 d^2 e (a e-2 b d)+35 c^3 d^4\right)+A e (b e-2 c d) \left(2 c e (3 a e-5 b d)+b^2 e^2+10 c^2 d^2\right)\right)}{d+e x}+12 c e x \left(3 B \left(c e (a e-5 b d)+b^2 e^2+5 c^2 d^2\right)+A c e (3 b e-5 c d)\right)+\frac{18 \left(e (a e-b d)+c d^2\right) \left(B \left(c d e (3 a e-8 b d)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(c e (a e-5 b d)+b^2 e^2+5 c^2 d^2\right)\right)}{(d+e x)^2}+12 \log (d+e x) \left(3 A c e \left(c e (a e-5 b d)+b^2 e^2+5 c^2 d^2\right)+B \left(15 c^2 d e (3 b d-a e)+3 b c e^2 (2 a e-5 b d)+b^3 e^3-35 c^3 d^3\right)\right)+\frac{3 (B d-A e) \left(e (a e-b d)+c d^2\right)^3}{(d+e x)^4}-\frac{4 \left(e (a e-b d)+c d^2\right)^2 \left(B e (a e-4 b d)+3 A e (b e-2 c d)+7 B c d^2\right)}{(d+e x)^3}+6 c^2 e^2 x^2 (A c e+3 b B e-5 B c d)+4 B c^3 e^3 x^3}{12 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)}{e^8 (d+e x)}-\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{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{\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,"(12*c*e*(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 + 6*c^2*e^2*(-5*B*c*d + 3*b*B*e + A*c*e)*x^2 + 4*B*c^3*e^3*x^3 + (3*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))^3)/(d + e*x)^4 - (4*(c*d^2 + e*(-(b*d) + a*e))^2*(7*B*c*d^2 + B*e*(-4*b*d + a*e) + 3*A*e*(-2*c*d + b*e)))/(d + e*x)^3 + (18*(c*d^2 + e*(-(b*d) + a*e))*(-(A*e*(5*c^2*d^2 + b^2*e^2 + c*e*(-5*b*d + a*e))) + B*(7*c^2*d^3 + b*e^2*(2*b*d - a*e) + c*d*e*(-8*b*d + 3*a*e))))/(d + e*x)^2 - (12*(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 + 30*c^2*d^2*e*(-2*b*d + a*e) + b^2*e^3*(-4*b*d + 3*a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2))))/(d + e*x) + 12*(3*A*c*e*(5*c^2*d^2 + b^2*e^2 + c*e*(-5*b*d + a*e)) + B*(-35*c^3*d^3 + b^3*e^3 + 15*c^2*d*e*(3*b*d - a*e) + 3*b*c*e^2*(-5*b*d + 2*a*e)))*Log[d + e*x])/(12*e^8)","A",1
2344,1,885,534,0.5601698,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^6} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^6,x]","\frac{60 c \left(A c e (b e-2 c d)+B \left(7 c^2 d^2+b^2 e^2+c e (a e-6 b d)\right)\right) \log (d+e x) (d+e x)^5+A e \left(-2 \left(87 d^6+375 e x d^5+600 e^2 x^2 d^4+400 e^3 x^3 d^3+50 e^4 x^4 d^2-50 e^5 x^5 d-10 e^6 x^6\right) c^3+e \left(b d \left(137 d^4+625 e x d^3+1100 e^2 x^2 d^2+900 e^3 x^3 d+300 e^4 x^4\right)-12 a e \left(d^4+5 e x d^3+10 e^2 x^2 d^2+10 e^3 x^3 d+5 e^4 x^4\right)\right) c^2-2 e^2 \left(6 \left(d^4+5 e x d^3+10 e^2 x^2 d^2+10 e^3 x^3 d+5 e^4 x^4\right) b^2+3 a e \left(d^3+5 e x d^2+10 e^2 x^2 d+10 e^3 x^3\right) b+a^2 e^2 \left(d^2+5 e x d+10 e^2 x^2\right)\right) c-e^3 \left(\left(d^3+5 e x d^2+10 e^2 x^2 d+10 e^3 x^3\right) b^3+2 a e \left(d^2+5 e x d+10 e^2 x^2\right) b^2+3 a^2 e^2 (d+5 e x) b+4 a^3 e^3\right)\right)+B \left(\left(459 d^7+1875 e x d^6+2700 e^2 x^2 d^5+1300 e^3 x^3 d^4-400 e^4 x^4 d^3-500 e^5 x^5 d^2-70 e^6 x^6 d+10 e^7 x^7\right) c^3+e \left(a d e \left(137 d^4+625 e x d^3+1100 e^2 x^2 d^2+900 e^3 x^3 d+300 e^4 x^4\right)-6 b \left(87 d^6+375 e x d^5+600 e^2 x^2 d^4+400 e^3 x^3 d^3+50 e^4 x^4 d^2-50 e^5 x^5 d-10 e^6 x^6\right)\right) c^2+e^2 \left(d \left(137 d^4+625 e x d^3+1100 e^2 x^2 d^2+900 e^3 x^3 d+300 e^4 x^4\right) b^2-24 a e \left(d^4+5 e x d^3+10 e^2 x^2 d^2+10 e^3 x^3 d+5 e^4 x^4\right) b-3 a^2 e^2 \left(d^3+5 e x d^2+10 e^2 x^2 d+10 e^3 x^3\right)\right) c-e^3 \left(4 \left(d^4+5 e x d^3+10 e^2 x^2 d^2+10 e^3 x^3 d+5 e^4 x^4\right) b^3+3 a e \left(d^3+5 e x d^2+10 e^2 x^2 d+10 e^3 x^3\right) b^2+2 a^2 e^2 \left(d^2+5 e x d+10 e^2 x^2\right) b+a^3 e^3 (d+5 e x)\right)\right)}{20 e^8 (d+e x)^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)}{2 e^8 (d+e x)^2}-\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) \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{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)^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,"(A*e*(-2*c^3*(87*d^6 + 375*d^5*e*x + 600*d^4*e^2*x^2 + 400*d^3*e^3*x^3 + 50*d^2*e^4*x^4 - 50*d*e^5*x^5 - 10*e^6*x^6) - e^3*(4*a^3*e^3 + 3*a^2*b*e^2*(d + 5*e*x) + 2*a*b^2*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + b^3*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)) - 2*c*e^2*(a^2*e^2*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*a*b*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 6*b^2*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4)) + c^2*e*(-12*a*e*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4) + b*d*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4))) + B*(c^3*(459*d^7 + 1875*d^6*e*x + 2700*d^5*e^2*x^2 + 1300*d^4*e^3*x^3 - 400*d^3*e^4*x^4 - 500*d^2*e^5*x^5 - 70*d*e^6*x^6 + 10*e^7*x^7) - e^3*(a^3*e^3*(d + 5*e*x) + 2*a^2*b*e^2*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*a*b^2*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 4*b^3*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4)) + c*e^2*(-3*a^2*e^2*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) - 24*a*b*e*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4) + b^2*d*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4)) + c^2*e*(a*d*e*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4) - 6*b*(87*d^6 + 375*d^5*e*x + 600*d^4*e^2*x^2 + 400*d^3*e^3*x^3 + 50*d^2*e^4*x^4 - 50*d*e^5*x^5 - 10*e^6*x^6))) + 60*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*Log[d + e*x])/(20*e^8*(d + e*x)^5)","A",1
2345,1,868,541,0.6545824,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^7} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^7,x]","-\frac{60 c^2 (7 B c d-3 b B e-A c e) \log (d+e x) (d+e x)^6+A e \left(-d \left(147 d^5+822 e x d^4+1875 e^2 x^2 d^3+2200 e^3 x^3 d^2+1350 e^4 x^4 d+360 e^5 x^5\right) c^3+6 e \left(a e \left(d^4+6 e x d^3+15 e^2 x^2 d^2+20 e^3 x^3 d+15 e^4 x^4\right)+5 b \left(d^5+6 e x d^4+15 e^2 x^2 d^3+20 e^3 x^3 d^2+15 e^4 x^4 d+6 e^5 x^5\right)\right) c^2+3 e^2 \left(2 \left(d^4+6 e x d^3+15 e^2 x^2 d^2+20 e^3 x^3 d+15 e^4 x^4\right) b^2+2 a e \left(d^3+6 e x d^2+15 e^2 x^2 d+20 e^3 x^3\right) b+a^2 e^2 \left(d^2+6 e x d+15 e^2 x^2\right)\right) c+e^3 \left(\left(d^3+6 e x d^2+15 e^2 x^2 d+20 e^3 x^3\right) b^3+3 a e \left(d^2+6 e x d+15 e^2 x^2\right) b^2+6 a^2 e^2 (d+6 e x) b+10 a^3 e^3\right)\right)+B \left(\left(669 d^7+3594 e x d^6+7725 e^2 x^2 d^5+8200 e^3 x^3 d^4+4050 e^4 x^4 d^3+360 e^5 x^5 d^2-360 e^6 x^6 d-60 e^7 x^7\right) c^3+3 e \left(10 a e \left(d^5+6 e x d^4+15 e^2 x^2 d^3+20 e^3 x^3 d^2+15 e^4 x^4 d+6 e^5 x^5\right)-b d \left(147 d^5+822 e x d^4+1875 e^2 x^2 d^3+2200 e^3 x^3 d^2+1350 e^4 x^4 d+360 e^5 x^5\right)\right) c^2+3 e^2 \left(10 \left(d^5+6 e x d^4+15 e^2 x^2 d^3+20 e^3 x^3 d^2+15 e^4 x^4 d+6 e^5 x^5\right) b^2+4 a e \left(d^4+6 e x d^3+15 e^2 x^2 d^2+20 e^3 x^3 d+15 e^4 x^4\right) b+a^2 e^2 \left(d^3+6 e x d^2+15 e^2 x^2 d+20 e^3 x^3\right)\right) c+e^3 \left(2 \left(d^4+6 e x d^3+15 e^2 x^2 d^2+20 e^3 x^3 d+15 e^4 x^4\right) b^3+3 a e \left(d^3+6 e x d^2+15 e^2 x^2 d+20 e^3 x^3\right) b^2+3 a^2 e^2 \left(d^2+6 e x d+15 e^2 x^2\right) b+2 a^3 e^3 (d+6 e x)\right)\right)}{60 e^8 (d+e x)^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)}{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{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{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{\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,"-1/60*(A*e*(-(c^3*d*(147*d^5 + 822*d^4*e*x + 1875*d^3*e^2*x^2 + 2200*d^2*e^3*x^3 + 1350*d*e^4*x^4 + 360*e^5*x^5)) + e^3*(10*a^3*e^3 + 6*a^2*b*e^2*(d + 6*e*x) + 3*a*b^2*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + b^3*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)) + 3*c*e^2*(a^2*e^2*(d^2 + 6*d*e*x + 15*e^2*x^2) + 2*a*b*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 2*b^2*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)) + 6*c^2*e*(a*e*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4) + 5*b*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5))) + B*(c^3*(669*d^7 + 3594*d^6*e*x + 7725*d^5*e^2*x^2 + 8200*d^4*e^3*x^3 + 4050*d^3*e^4*x^4 + 360*d^2*e^5*x^5 - 360*d*e^6*x^6 - 60*e^7*x^7) + e^3*(2*a^3*e^3*(d + 6*e*x) + 3*a^2*b*e^2*(d^2 + 6*d*e*x + 15*e^2*x^2) + 3*a*b^2*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 2*b^3*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)) + 3*c*e^2*(a^2*e^2*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 4*a*b*e*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4) + 10*b^2*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5)) + 3*c^2*e*(10*a*e*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5) - b*d*(147*d^5 + 822*d^4*e*x + 1875*d^3*e^2*x^2 + 2200*d^2*e^3*x^3 + 1350*d*e^4*x^4 + 360*e^5*x^5))) + 60*c^2*(7*B*c*d - 3*b*B*e - A*c*e)*(d + e*x)^6*Log[d + e*x])/(e^8*(d + e*x)^6)","A",1
2346,1,863,548,0.4870302,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^8} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^8,x]","\frac{420 B c^3 \log (d+e x) (d+e x)^7-3 A e \left(20 \left(d^6+7 e x d^5+21 e^2 x^2 d^4+35 e^3 x^3 d^3+35 e^4 x^4 d^2+21 e^5 x^5 d+7 e^6 x^6\right) c^3+2 e \left(2 a e \left(d^4+7 e x d^3+21 e^2 x^2 d^2+35 e^3 x^3 d+35 e^4 x^4\right)+5 b \left(d^5+7 e x d^4+21 e^2 x^2 d^3+35 e^3 x^3 d^2+35 e^4 x^4 d+21 e^5 x^5\right)\right) c^2+2 e^2 \left(2 \left(d^4+7 e x d^3+21 e^2 x^2 d^2+35 e^3 x^3 d+35 e^4 x^4\right) b^2+3 a e \left(d^3+7 e x d^2+21 e^2 x^2 d+35 e^3 x^3\right) b+2 a^2 e^2 \left(d^2+7 e x d+21 e^2 x^2\right)\right) c+e^3 \left(\left(d^3+7 e x d^2+21 e^2 x^2 d+35 e^3 x^3\right) b^3+4 a e \left(d^2+7 e x d+21 e^2 x^2\right) b^2+10 a^2 e^2 (d+7 e x) b+20 a^3 e^3\right)\right)+B \left(d \left(1089 d^6+7203 e x d^5+20139 e^2 x^2 d^4+30625 e^3 x^3 d^3+26950 e^4 x^4 d^2+13230 e^5 x^5 d+2940 e^6 x^6\right) c^3-30 e \left(a e \left(d^5+7 e x d^4+21 e^2 x^2 d^3+35 e^3 x^3 d^2+35 e^4 x^4 d+21 e^5 x^5\right)+6 b \left(d^6+7 e x d^5+21 e^2 x^2 d^4+35 e^3 x^3 d^3+35 e^4 x^4 d^2+21 e^5 x^5 d+7 e^6 x^6\right)\right) c^2-3 e^2 \left(10 \left(d^5+7 e x d^4+21 e^2 x^2 d^3+35 e^3 x^3 d^2+35 e^4 x^4 d+21 e^5 x^5\right) b^2+8 a e \left(d^4+7 e x d^3+21 e^2 x^2 d^2+35 e^3 x^3 d+35 e^4 x^4\right) b+3 a^2 e^2 \left(d^3+7 e x d^2+21 e^2 x^2 d+35 e^3 x^3\right)\right) c-e^3 \left(4 \left(d^4+7 e x d^3+21 e^2 x^2 d^2+35 e^3 x^3 d+35 e^4 x^4\right) b^3+9 a e \left(d^3+7 e x d^2+21 e^2 x^2 d+35 e^3 x^3\right) b^2+12 a^2 e^2 \left(d^2+7 e x d+21 e^2 x^2\right) b+10 a^3 e^3 (d+7 e x)\right)\right)}{420 e^8 (d+e x)^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)}{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{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{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{\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,"(-3*A*e*(20*c^3*(d^6 + 7*d^5*e*x + 21*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 35*d^2*e^4*x^4 + 21*d*e^5*x^5 + 7*e^6*x^6) + e^3*(20*a^3*e^3 + 10*a^2*b*e^2*(d + 7*e*x) + 4*a*b^2*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + b^3*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3)) + 2*c*e^2*(2*a^2*e^2*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*a*b*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 2*b^2*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)) + 2*c^2*e*(2*a*e*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4) + 5*b*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5))) + B*(c^3*d*(1089*d^6 + 7203*d^5*e*x + 20139*d^4*e^2*x^2 + 30625*d^3*e^3*x^3 + 26950*d^2*e^4*x^4 + 13230*d*e^5*x^5 + 2940*e^6*x^6) - e^3*(10*a^3*e^3*(d + 7*e*x) + 12*a^2*b*e^2*(d^2 + 7*d*e*x + 21*e^2*x^2) + 9*a*b^2*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 4*b^3*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)) - 3*c*e^2*(3*a^2*e^2*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 8*a*b*e*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4) + 10*b^2*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5)) - 30*c^2*e*(a*e*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5) + 6*b*(d^6 + 7*d^5*e*x + 21*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 35*d^2*e^4*x^4 + 21*d*e^5*x^5 + 7*e^6*x^6))) + 420*B*c^3*(d + e*x)^7*Log[d + e*x])/(420*e^8*(d + e*x)^7)","A",1
2347,1,847,550,0.4695716,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^9} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^9,x]","-\frac{A e \left(5 \left(d^6+8 e x d^5+28 e^2 x^2 d^4+56 e^3 x^3 d^3+70 e^4 x^4 d^2+56 e^5 x^5 d+28 e^6 x^6\right) c^3+e \left(3 a e \left(d^4+8 e x d^3+28 e^2 x^2 d^2+56 e^3 x^3 d+70 e^4 x^4\right)+5 b \left(d^5+8 e x d^4+28 e^2 x^2 d^3+56 e^3 x^3 d^2+70 e^4 x^4 d+56 e^5 x^5\right)\right) c^2+e^2 \left(3 \left(d^4+8 e x d^3+28 e^2 x^2 d^2+56 e^3 x^3 d+70 e^4 x^4\right) b^2+6 a e \left(d^3+8 e x d^2+28 e^2 x^2 d+56 e^3 x^3\right) b+5 a^2 e^2 \left(d^2+8 e x d+28 e^2 x^2\right)\right) c+e^3 \left(\left(d^3+8 e x d^2+28 e^2 x^2 d+56 e^3 x^3\right) b^3+5 a e \left(d^2+8 e x d+28 e^2 x^2\right) b^2+15 a^2 e^2 (d+8 e x) b+35 a^3 e^3\right)\right)+B \left(35 \left(d^7+8 e x d^6+28 e^2 x^2 d^5+56 e^3 x^3 d^4+70 e^4 x^4 d^3+56 e^5 x^5 d^2+28 e^6 x^6 d+8 e^7 x^7\right) c^3+5 e \left(a e \left(d^5+8 e x d^4+28 e^2 x^2 d^3+56 e^3 x^3 d^2+70 e^4 x^4 d+56 e^5 x^5\right)+3 b \left(d^6+8 e x d^5+28 e^2 x^2 d^4+56 e^3 x^3 d^3+70 e^4 x^4 d^2+56 e^5 x^5 d+28 e^6 x^6\right)\right) c^2+e^2 \left(5 \left(d^5+8 e x d^4+28 e^2 x^2 d^3+56 e^3 x^3 d^2+70 e^4 x^4 d+56 e^5 x^5\right) b^2+6 a e \left(d^4+8 e x d^3+28 e^2 x^2 d^2+56 e^3 x^3 d+70 e^4 x^4\right) b+3 a^2 e^2 \left(d^3+8 e x d^2+28 e^2 x^2 d+56 e^3 x^3\right)\right) c+e^3 \left(\left(d^4+8 e x d^3+28 e^2 x^2 d^2+56 e^3 x^3 d+70 e^4 x^4\right) b^3+3 a e \left(d^3+8 e x d^2+28 e^2 x^2 d+56 e^3 x^3\right) b^2+5 a^2 e^2 \left(d^2+8 e x d+28 e^2 x^2\right) b+5 a^3 e^3 (d+8 e x)\right)\right)}{280 e^8 (d+e x)^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)}{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{\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{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)^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,"-1/280*(A*e*(5*c^3*(d^6 + 8*d^5*e*x + 28*d^4*e^2*x^2 + 56*d^3*e^3*x^3 + 70*d^2*e^4*x^4 + 56*d*e^5*x^5 + 28*e^6*x^6) + e^3*(35*a^3*e^3 + 15*a^2*b*e^2*(d + 8*e*x) + 5*a*b^2*e*(d^2 + 8*d*e*x + 28*e^2*x^2) + b^3*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3)) + c*e^2*(5*a^2*e^2*(d^2 + 8*d*e*x + 28*e^2*x^2) + 6*a*b*e*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + 3*b^2*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4)) + c^2*e*(3*a*e*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4) + 5*b*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5))) + B*(35*c^3*(d^7 + 8*d^6*e*x + 28*d^5*e^2*x^2 + 56*d^4*e^3*x^3 + 70*d^3*e^4*x^4 + 56*d^2*e^5*x^5 + 28*d*e^6*x^6 + 8*e^7*x^7) + e^3*(5*a^3*e^3*(d + 8*e*x) + 5*a^2*b*e^2*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*a*b^2*e*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + b^3*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4)) + c*e^2*(3*a^2*e^2*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + 6*a*b*e*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4) + 5*b^2*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5)) + 5*c^2*e*(a*e*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5) + 3*b*(d^6 + 8*d^5*e*x + 28*d^4*e^2*x^2 + 56*d^3*e^3*x^3 + 70*d^2*e^4*x^4 + 56*d*e^5*x^5 + 28*e^6*x^6))))/(e^8*(d + e*x)^8)","A",1
2348,1,852,555,0.4879162,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^{10}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^10,x]","-\frac{A e \left(10 \left(d^6+9 e x d^5+36 e^2 x^2 d^4+84 e^3 x^3 d^3+126 e^4 x^4 d^2+126 e^5 x^5 d+84 e^6 x^6\right) c^3+3 e \left(4 a e \left(d^4+9 e x d^3+36 e^2 x^2 d^2+84 e^3 x^3 d+126 e^4 x^4\right)+5 b \left(d^5+9 e x d^4+36 e^2 x^2 d^3+84 e^3 x^3 d^2+126 e^4 x^4 d+126 e^5 x^5\right)\right) c^2+6 e^2 \left(2 \left(d^4+9 e x d^3+36 e^2 x^2 d^2+84 e^3 x^3 d+126 e^4 x^4\right) b^2+5 a e \left(d^3+9 e x d^2+36 e^2 x^2 d+84 e^3 x^3\right) b+5 a^2 e^2 \left(d^2+9 e x d+36 e^2 x^2\right)\right) c+5 e^3 \left(\left(d^3+9 e x d^2+36 e^2 x^2 d+84 e^3 x^3\right) b^3+6 a e \left(d^2+9 e x d+36 e^2 x^2\right) b^2+21 a^2 e^2 (d+9 e x) b+56 a^3 e^3\right)\right)+B \left(35 \left(d^7+9 e x d^6+36 e^2 x^2 d^5+84 e^3 x^3 d^4+126 e^4 x^4 d^3+126 e^5 x^5 d^2+84 e^6 x^6 d+36 e^7 x^7\right) c^3+15 e \left(a e \left(d^5+9 e x d^4+36 e^2 x^2 d^3+84 e^3 x^3 d^2+126 e^4 x^4 d+126 e^5 x^5\right)+2 b \left(d^6+9 e x d^5+36 e^2 x^2 d^4+84 e^3 x^3 d^3+126 e^4 x^4 d^2+126 e^5 x^5 d+84 e^6 x^6\right)\right) c^2+3 e^2 \left(5 \left(d^5+9 e x d^4+36 e^2 x^2 d^3+84 e^3 x^3 d^2+126 e^4 x^4 d+126 e^5 x^5\right) b^2+8 a e \left(d^4+9 e x d^3+36 e^2 x^2 d^2+84 e^3 x^3 d+126 e^4 x^4\right) b+5 a^2 e^2 \left(d^3+9 e x d^2+36 e^2 x^2 d+84 e^3 x^3\right)\right) c+e^3 \left(4 \left(d^4+9 e x d^3+36 e^2 x^2 d^2+84 e^3 x^3 d+126 e^4 x^4\right) b^3+15 a e \left(d^3+9 e x d^2+36 e^2 x^2 d+84 e^3 x^3\right) b^2+30 a^2 e^2 \left(d^2+9 e x d+36 e^2 x^2\right) b+35 a^3 e^3 (d+9 e x)\right)\right)}{2520 e^8 (d+e x)^9}","\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{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{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{\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,"-1/2520*(A*e*(10*c^3*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6) + 5*e^3*(56*a^3*e^3 + 21*a^2*b*e^2*(d + 9*e*x) + 6*a*b^2*e*(d^2 + 9*d*e*x + 36*e^2*x^2) + b^3*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3)) + 6*c*e^2*(5*a^2*e^2*(d^2 + 9*d*e*x + 36*e^2*x^2) + 5*a*b*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 2*b^2*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4)) + 3*c^2*e*(4*a*e*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4) + 5*b*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5))) + B*(35*c^3*(d^7 + 9*d^6*e*x + 36*d^5*e^2*x^2 + 84*d^4*e^3*x^3 + 126*d^3*e^4*x^4 + 126*d^2*e^5*x^5 + 84*d*e^6*x^6 + 36*e^7*x^7) + e^3*(35*a^3*e^3*(d + 9*e*x) + 30*a^2*b*e^2*(d^2 + 9*d*e*x + 36*e^2*x^2) + 15*a*b^2*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 4*b^3*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4)) + 3*c*e^2*(5*a^2*e^2*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 8*a*b*e*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4) + 5*b^2*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5)) + 15*c^2*e*(a*e*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5) + 2*b*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6))))/(e^8*(d + e*x)^9)","A",1
2349,1,849,555,0.5043269,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^{11}} \, dx","Integrate[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^11,x]","-\frac{3 A e \left(\left(d^6+10 e x d^5+45 e^2 x^2 d^4+120 e^3 x^3 d^3+210 e^4 x^4 d^2+252 e^5 x^5 d+210 e^6 x^6\right) c^3+2 e \left(a e \left(d^4+10 e x d^3+45 e^2 x^2 d^2+120 e^3 x^3 d+210 e^4 x^4\right)+b \left(d^5+10 e x d^4+45 e^2 x^2 d^3+120 e^3 x^3 d^2+210 e^4 x^4 d+252 e^5 x^5\right)\right) c^2+e^2 \left(2 \left(d^4+10 e x d^3+45 e^2 x^2 d^2+120 e^3 x^3 d+210 e^4 x^4\right) b^2+6 a e \left(d^3+10 e x d^2+45 e^2 x^2 d+120 e^3 x^3\right) b+7 a^2 e^2 \left(d^2+10 e x d+45 e^2 x^2\right)\right) c+e^3 \left(\left(d^3+10 e x d^2+45 e^2 x^2 d+120 e^3 x^3\right) b^3+7 a e \left(d^2+10 e x d+45 e^2 x^2\right) b^2+28 a^2 e^2 (d+10 e x) b+84 a^3 e^3\right)\right)+B \left(7 \left(d^7+10 e x d^6+45 e^2 x^2 d^5+120 e^3 x^3 d^4+210 e^4 x^4 d^3+252 e^5 x^5 d^2+210 e^6 x^6 d+120 e^7 x^7\right) c^3+3 e \left(2 a e \left(d^5+10 e x d^4+45 e^2 x^2 d^3+120 e^3 x^3 d^2+210 e^4 x^4 d+252 e^5 x^5\right)+3 b \left(d^6+10 e x d^5+45 e^2 x^2 d^4+120 e^3 x^3 d^3+210 e^4 x^4 d^2+252 e^5 x^5 d+210 e^6 x^6\right)\right) c^2+3 e^2 \left(2 \left(d^5+10 e x d^4+45 e^2 x^2 d^3+120 e^3 x^3 d^2+210 e^4 x^4 d+252 e^5 x^5\right) b^2+4 a e \left(d^4+10 e x d^3+45 e^2 x^2 d^2+120 e^3 x^3 d+210 e^4 x^4\right) b+3 a^2 e^2 \left(d^3+10 e x d^2+45 e^2 x^2 d+120 e^3 x^3\right)\right) c+e^3 \left(2 \left(d^4+10 e x d^3+45 e^2 x^2 d^2+120 e^3 x^3 d+210 e^4 x^4\right) b^3+9 a e \left(d^3+10 e x d^2+45 e^2 x^2 d+120 e^3 x^3\right) b^2+21 a^2 e^2 \left(d^2+10 e x d+45 e^2 x^2\right) b+28 a^3 e^3 (d+10 e x)\right)\right)}{2520 e^8 (d+e x)^{10}}","\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{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{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{\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,"-1/2520*(3*A*e*(c^3*(d^6 + 10*d^5*e*x + 45*d^4*e^2*x^2 + 120*d^3*e^3*x^3 + 210*d^2*e^4*x^4 + 252*d*e^5*x^5 + 210*e^6*x^6) + e^3*(84*a^3*e^3 + 28*a^2*b*e^2*(d + 10*e*x) + 7*a*b^2*e*(d^2 + 10*d*e*x + 45*e^2*x^2) + b^3*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3)) + c*e^2*(7*a^2*e^2*(d^2 + 10*d*e*x + 45*e^2*x^2) + 6*a*b*e*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 2*b^2*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4)) + 2*c^2*e*(a*e*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4) + b*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5))) + B*(7*c^3*(d^7 + 10*d^6*e*x + 45*d^5*e^2*x^2 + 120*d^4*e^3*x^3 + 210*d^3*e^4*x^4 + 252*d^2*e^5*x^5 + 210*d*e^6*x^6 + 120*e^7*x^7) + e^3*(28*a^3*e^3*(d + 10*e*x) + 21*a^2*b*e^2*(d^2 + 10*d*e*x + 45*e^2*x^2) + 9*a*b^2*e*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 2*b^3*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4)) + 3*c*e^2*(3*a^2*e^2*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 4*a*b*e*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4) + 2*b^2*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5)) + 3*c^2*e*(2*a*e*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5) + 3*b*(d^6 + 10*d^5*e*x + 45*d^4*e^2*x^2 + 120*d^3*e^3*x^3 + 210*d^2*e^4*x^4 + 252*d*e^5*x^5 + 210*e^6*x^6))))/(e^8*(d + e*x)^10)","A",1
2350,1,142,121,0.2435491,"\int x (d+e x)^m \left(a+b x+c x^2\right) \, dx","Integrate[x*(d + e*x)^m*(a + b*x + c*x^2),x]","\frac{(d+e x)^{m+1} \left(e (m+4) \left(a e (m+3) (e (m+1) x-d)+b \left(2 d^2-2 d e (m+1) x+e^2 \left(m^2+3 m+2\right) x^2\right)\right)+c \left(-6 d^3+6 d^2 e (m+1) x-3 d e^2 \left(m^2+3 m+2\right) x^2+e^3 \left(m^3+6 m^2+11 m+6\right) x^3\right)\right)}{e^4 (m+1) (m+2) (m+3) (m+4)}","\frac{(d+e x)^{m+2} \left(3 c d^2-e (2 b d-a e)\right)}{e^4 (m+2)}-\frac{d (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^4 (m+1)}-\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 + e*x)^(1 + m)*(c*(-6*d^3 + 6*d^2*e*(1 + m)*x - 3*d*e^2*(2 + 3*m + m^2)*x^2 + e^3*(6 + 11*m + 6*m^2 + m^3)*x^3) + e*(4 + m)*(a*e*(3 + m)*(-d + e*(1 + m)*x) + b*(2*d^2 - 2*d*e*(1 + m)*x + e^2*(2 + 3*m + m^2)*x^2))))/(e^4*(1 + m)*(2 + m)*(3 + m)*(4 + m))","A",1
2351,1,166,103,0.0399078,"\int x (d+e x)^5 \left(a+b x+c x^2\right) \, dx","Integrate[x*(d + e*x)^5*(a + b*x + c*x^2),x]","\frac{5}{6} d e^2 x^6 \left(a e^2+2 b d e+2 c d^2\right)+d^2 e x^5 \left(2 a e^2+2 b d e+c d^2\right)+\frac{1}{7} e^3 x^7 \left(a e^2+5 b d e+10 c d^2\right)+\frac{1}{4} d^3 x^4 \left(10 a e^2+5 b d e+c d^2\right)+\frac{1}{3} d^4 x^3 (5 a e+b d)+\frac{1}{2} a d^5 x^2+\frac{1}{8} e^4 x^8 (b e+5 c d)+\frac{1}{9} c e^5 x^9","\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,"(a*d^5*x^2)/2 + (d^4*(b*d + 5*a*e)*x^3)/3 + (d^3*(c*d^2 + 5*b*d*e + 10*a*e^2)*x^4)/4 + d^2*e*(c*d^2 + 2*b*d*e + 2*a*e^2)*x^5 + (5*d*e^2*(2*c*d^2 + 2*b*d*e + a*e^2)*x^6)/6 + (e^3*(10*c*d^2 + 5*b*d*e + a*e^2)*x^7)/7 + (e^4*(5*c*d + b*e)*x^8)/8 + (c*e^5*x^9)/9","A",1
2352,1,140,103,0.0309044,"\int x (d+e x)^4 \left(a+b x+c x^2\right) \, dx","Integrate[x*(d + e*x)^4*(a + b*x + c*x^2),x]","\frac{1}{6} e^2 x^6 \left(a e^2+4 b d e+6 c d^2\right)+\frac{2}{5} d e x^5 \left(2 a e^2+3 b d e+2 c d^2\right)+\frac{1}{4} d^2 x^4 \left(6 a e^2+4 b d e+c d^2\right)+\frac{1}{3} d^3 x^3 (4 a e+b d)+\frac{1}{2} a d^4 x^2+\frac{1}{7} e^3 x^7 (b e+4 c d)+\frac{1}{8} c e^4 x^8","\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,"(a*d^4*x^2)/2 + (d^3*(b*d + 4*a*e)*x^3)/3 + (d^2*(c*d^2 + 4*b*d*e + 6*a*e^2)*x^4)/4 + (2*d*e*(2*c*d^2 + 3*b*d*e + 2*a*e^2)*x^5)/5 + (e^2*(6*c*d^2 + 4*b*d*e + a*e^2)*x^6)/6 + (e^3*(4*c*d + b*e)*x^7)/7 + (c*e^4*x^8)/8","A",1
2353,1,109,103,0.0267816,"\int x (d+e x)^3 \left(a+b x+c x^2\right) \, dx","Integrate[x*(d + e*x)^3*(a + b*x + c*x^2),x]","\frac{1}{5} e x^5 \left(a e^2+3 b d e+3 c d^2\right)+\frac{1}{4} d x^4 \left(3 a e^2+3 b d e+c d^2\right)+\frac{1}{3} d^2 x^3 (3 a e+b d)+\frac{1}{2} a d^3 x^2+\frac{1}{6} e^2 x^6 (b e+3 c d)+\frac{1}{7} c e^3 x^7","\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,"(a*d^3*x^2)/2 + (d^2*(b*d + 3*a*e)*x^3)/3 + (d*(c*d^2 + 3*b*d*e + 3*a*e^2)*x^4)/4 + (e*(3*c*d^2 + 3*b*d*e + a*e^2)*x^5)/5 + (e^2*(3*c*d + b*e)*x^6)/6 + (c*e^3*x^7)/7","A",1
2354,1,70,78,0.0231943,"\int x (d+e x)^2 \left(a+b x+c x^2\right) \, dx","Integrate[x*(d + e*x)^2*(a + b*x + c*x^2),x]","\frac{1}{60} x^2 \left(15 x^2 \left(e (a e+2 b d)+c d^2\right)+20 d x (2 a e+b d)+30 a d^2+12 e x^3 (b e+2 c d)+10 c e^2 x^4\right)","\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,"(x^2*(30*a*d^2 + 20*d*(b*d + 2*a*e)*x + 15*(c*d^2 + e*(2*b*d + a*e))*x^2 + 12*e*(2*c*d + b*e)*x^3 + 10*c*e^2*x^4))/60","A",1
2355,1,41,47,0.0135912,"\int x (d+e x) \left(a+b x+c x^2\right) \, dx","Integrate[x*(d + e*x)*(a + b*x + c*x^2),x]","\frac{1}{60} x^2 \left(20 x (a e+b d)+30 a d+15 x^2 (b e+c d)+12 c e x^3\right)","\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,"(x^2*(30*a*d + 20*(b*d + a*e)*x + 15*(c*d + b*e)*x^2 + 12*c*e*x^3))/60","A",1
2356,1,25,25,0.0012918,"\int x \left(a+b x+c x^2\right) \, dx","Integrate[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",1
2357,1,74,79,0.0275788,"\int \frac{x \left(a+b x+c x^2\right)}{d+e x} \, dx","Integrate[(x*(a + b*x + c*x^2))/(d + e*x),x]","\frac{e x \left(3 e (2 a e-2 b d+b e x)+c \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)-6 \log (d+e x) \left(d e (a e-b d)+c d^3\right)}{6 e^4}","-\frac{d \log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^4}+\frac{x \left(a e^2-b d e+c d^2\right)}{e^3}-\frac{x^2 (c d-b e)}{2 e^2}+\frac{c x^3}{3 e}",1,"(e*x*(3*e*(-2*b*d + 2*a*e + b*e*x) + c*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) - 6*(c*d^3 + d*e*(-(b*d) + a*e))*Log[d + e*x])/(6*e^4)","A",1
2358,1,79,84,0.0565125,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^2} \, dx","Integrate[(x*(a + b*x + c*x^2))/(d + e*x)^2,x]","\frac{\frac{2 \left(d e (a e-b d)+c d^3\right)}{d+e x}+2 \log (d+e x) \left(e (a e-2 b d)+3 c d^2\right)+2 e x (b e-2 c d)+c e^2 x^2}{2 e^4}","\frac{\log (d+e x) \left(3 c d^2-e (2 b d-a e)\right)}{e^4}+\frac{d \left(a e^2-b d e+c d^2\right)}{e^4 (d+e x)}-\frac{x (2 c d-b e)}{e^3}+\frac{c x^2}{2 e^2}",1,"(2*e*(-2*c*d + b*e)*x + c*e^2*x^2 + (2*(c*d^3 + d*e*(-(b*d) + a*e)))/(d + e*x) + 2*(3*c*d^2 + e*(-2*b*d + a*e))*Log[d + e*x])/(2*e^4)","A",1
2359,1,80,89,0.0518672,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^3} \, dx","Integrate[(x*(a + b*x + c*x^2))/(d + e*x)^3,x]","\frac{\frac{d e (a e-b d)+c d^3}{(d+e x)^2}-\frac{2 \left(e (a e-2 b d)+3 c d^2\right)}{d+e x}+2 (b e-3 c d) \log (d+e x)+2 c e x}{2 e^4}","-\frac{3 c d^2-e (2 b d-a e)}{e^4 (d+e 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-b e) \log (d+e x)}{e^4}+\frac{c x}{e^3}",1,"(2*c*e*x + (c*d^3 + d*e*(-(b*d) + a*e))/(d + e*x)^2 - (2*(3*c*d^2 + e*(-2*b*d + a*e)))/(d + e*x) + 2*(-3*c*d + b*e)*Log[d + e*x])/(2*e^4)","A",1
2360,1,86,96,0.0335542,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^4} \, dx","Integrate[(x*(a + b*x + c*x^2))/(d + e*x)^4,x]","\frac{-e \left(a e (d+3 e x)+2 b \left(d^2+3 d e x+3 e^2 x^2\right)\right)+c d \left(11 d^2+27 d e x+18 e^2 x^2\right)+6 c (d+e x)^3 \log (d+e x)}{6 e^4 (d+e x)^3}","-\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,"(c*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2) - e*(a*e*(d + 3*e*x) + 2*b*(d^2 + 3*d*e*x + 3*e^2*x^2)) + 6*c*(d + e*x)^3*Log[d + e*x])/(6*e^4*(d + e*x)^3)","A",1
2361,1,77,101,0.0266758,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^5} \, dx","Integrate[(x*(a + b*x + c*x^2))/(d + e*x)^5,x]","-\frac{e \left(a e (d+4 e x)+b \left(d^2+4 d e x+6 e^2 x^2\right)\right)+3 c \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)}{12 e^4 (d+e x)^4}","-\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,"-1/12*(3*c*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) + e*(a*e*(d + 4*e*x) + b*(d^2 + 4*d*e*x + 6*e^2*x^2)))/(e^4*(d + e*x)^4)","A",1
2362,1,79,103,0.0287059,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^6} \, dx","Integrate[(x*(a + b*x + c*x^2))/(d + e*x)^6,x]","-\frac{e \left(3 a e (d+5 e x)+2 b \left(d^2+5 d e x+10 e^2 x^2\right)\right)+3 c \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)}{60 e^4 (d+e x)^5}","-\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,"-1/60*(3*c*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + e*(3*a*e*(d + 5*e*x) + 2*b*(d^2 + 5*d*e*x + 10*e^2*x^2)))/(e^4*(d + e*x)^5)","A",1
2363,1,77,103,0.0280039,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^7} \, dx","Integrate[(x*(a + b*x + c*x^2))/(d + e*x)^7,x]","-\frac{e \left(2 a e (d+6 e x)+b \left(d^2+6 d e x+15 e^2 x^2\right)\right)+c \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)}{60 e^4 (d+e x)^6}","-\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,"-1/60*(c*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + e*(2*a*e*(d + 6*e*x) + b*(d^2 + 6*d*e*x + 15*e^2*x^2)))/(e^4*(d + e*x)^6)","A",1
2364,1,352,357,0.2927581,"\int \frac{(A+B x) (d+e x)^3}{a+b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a + b*x + c*x^2),x]","\frac{6 c 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)+3 \log (a+x (b+c x)) \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)+\frac{6 \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\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(a e^2-3 c d^2\right)\right)-b^3 c e^2 (A e+3 B d)+b^4 B e^3\right)}{\sqrt{4 a c-b^2}}+3 c^2 e^2 x^2 (A c e-b B e+3 B c d)+2 B c^3 e^3 x^3}{6 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{\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{\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,"(6*c*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 + 3*c^2*e^2*(3*B*c*d - b*B*e + A*c*e)*x^2 + 2*B*c^3*e^3*x^3 + (6*(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)))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + 3*(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 + x*(b + c*x)])/(6*c^4)","A",1
2365,1,203,205,0.1653389,"\int \frac{(A+B x) (d+e x)^2}{a+b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a + b*x + c*x^2),x]","\frac{\log (a+x (b+c x)) \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)-\frac{2 \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\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)}{\sqrt{4 a c-b^2}}+2 c e x (A c e-b B e+2 B c d)+B c^2 e^2 x^2}{2 c^3}","\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,"(2*c*e*(2*B*c*d - b*B*e + A*c*e)*x + B*c^2*e^2*x^2 - (2*(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))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/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 + x*(b + c*x)])/(2*c^3)","A",1
2366,1,108,108,0.089107,"\int \frac{(A+B x) (d+e x)}{a+b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x))/(a + b*x + c*x^2),x]","\frac{\frac{2 \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right) \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)}{\sqrt{4 a c-b^2}}+\log (a+x (b+c x)) (A c e-b B e+B c d)+2 B c e x}{2 c^2}","-\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,"(2*B*c*e*x + (2*(b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + (B*c*d - b*B*e + A*c*e)*Log[a + x*(b + c*x)])/(2*c^2)","A",1
2367,1,66,64,0.0524906,"\int \frac{A+B x}{a+b x+c x^2} \, dx","Integrate[(A + B*x)/(a + b*x + c*x^2),x]","\frac{B \log (a+x (b+c x))-\frac{2 (b B-2 A c) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}}{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,"((-2*(b*B - 2*A*c)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + B*Log[a + x*(b + c*x)])/(2*c)","A",1
2368,1,125,146,0.1239041,"\int \frac{A+B x}{(d+e x) \left(a+b x+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)*(a + b*x + c*x^2)),x]","\frac{\sqrt{4 a c-b^2} (B d-A e) (2 \log (d+e x)-\log (a+x (b+c x)))+2 \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right) (-2 a B e+A b e-2 A c d+b B d)}{2 \sqrt{4 a c-b^2} \left(e (b d-a e)-c d^2\right)}","\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,"(2*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]] + Sqrt[-b^2 + 4*a*c]*(B*d - A*e)*(2*Log[d + e*x] - Log[a + x*(b + c*x)]))/(2*Sqrt[-b^2 + 4*a*c]*(-(c*d^2) + e*(b*d - a*e)))","A",1
2369,1,219,255,0.3432632,"\int \frac{A+B x}{(d+e x)^2 \left(a+b x+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(a + b*x + c*x^2)),x]","\frac{\frac{2 \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\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{4 a c-b^2}}-2 \log (d+e x) \left(B \left(c d^2-a e^2\right)+A e (b e-2 c d)\right)+\log (a+x (b+c x)) \left(B \left(c d^2-a e^2\right)+A e (b e-2 c d)\right)+\frac{2 (B d-A e) \left(e (a e-b d)+c d^2\right)}{d+e x}}{2 \left(e (a e-b d)+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,"((2*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e)))/(d + e*x) + (2*(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))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] - 2*(A*e*(-2*c*d + b*e) + B*(c*d^2 - a*e^2))*Log[d + e*x] + (A*e*(-2*c*d + b*e) + B*(c*d^2 - a*e^2))*Log[a + x*(b + c*x)])/(2*(c*d^2 + e*(-(b*d) + a*e))^2)","A",1
2370,1,413,414,0.4723016,"\int \frac{A+B x}{(d+e x)^3 \left(a+b x+c x^2\right)} \, dx","Integrate[(A + B*x)/((d + e*x)^3*(a + b*x + c*x^2)),x]","-\frac{\log (d+e x) \left(A e \left(c e (a e+3 b d)-b^2 e^2-3 c^2 d^2\right)+B \left(a b e^3-3 a c d e^2+c^2 d^3\right)\right)}{\left(e (a e-b d)+c d^2\right)^3}+\frac{\log (a+x (b+c x)) \left(A e \left(c e (a e+3 b d)-b^2 e^2-3 c^2 d^2\right)+B \left(a b e^3-3 a c d e^2+c^2 d^3\right)\right)}{2 \left(e (a e-b d)+c d^2\right)^3}+\frac{\tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\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(3 a e^2-c d^2\right)+a B e \left(a e^2-3 c d^2\right)\right)+A b^3 e^3\right)}{\sqrt{4 a c-b^2} \left(e (b d-a e)-c d^2\right)^3}+\frac{B \left(c d^2-a e^2\right)+A e (b e-2 c d)}{(d+e x) \left(e (a e-b d)+c d^2\right)^2}+\frac{B d-A e}{2 (d+e x)^2 \left(e (a e-b d)+c d^2\right)}","\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 + e*(-(b*d) + a*e))*(d + e*x)^2) + (A*e*(-2*c*d + b*e) + B*(c*d^2 - a*e^2))/((c*d^2 + e*(-(b*d) + a*e))^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*B*e*(-3*c*d^2 + a*e^2) + A*c*d*(-(c*d^2) + 3*a*e^2)))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(Sqrt[-b^2 + 4*a*c]*(-(c*d^2) + e*(b*d - a*e))^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 + e*(-(b*d) + a*e))^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 + x*(b + c*x)])/(2*(c*d^2 + e*(-(b*d) + a*e))^3)","A",1
2371,1,897,543,1.8566293,"\int \frac{(d+e x)^4 (f+g x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((d + e*x)^4*(f + g*x))/(a + b*x + c*x^2)^3,x]","\frac{c g \log (a+x (b+c x)) e^4+\frac{e^4 g x b^5+e^3 (a e g-c (e f+4 d g) x) b^4-c e^2 (a e (e f+4 d g+5 e g x)-2 c d (2 e f+3 d g) x) b^3+2 c e \left(-2 a^2 g e^3+a c \left(3 g d^2+2 e (f+4 g x) d+2 e^2 f x\right) e-c^2 d^2 (3 e f+2 d g) x\right) b^2+c^2 \left(c^2 (-d f+4 e x f+d g x) d^3-2 a c e \left(2 g d^2+3 e (f+3 g x) d+6 e^2 f x\right) d+a^2 e^3 (3 e f+12 d g+5 e g x)\right) b+2 c^2 \left(-c^3 f x d^4+a c^2 \left(g d^2+4 e (f+g x) d+6 e^2 f x\right) d^2+a^3 e^4 g-a^2 c e^2 \left(6 g d^2+4 e (f+g x) d+e^2 f x\right)\right)}{\left(b^2-4 a c\right) (a+x (b+c x))^2}+\frac{-e^4 g b^6+c e^3 (4 d g+e (f+4 g x)) b^5-c e^2 \left(2 c \left(3 g d^2+2 e (f+2 g x) d+e^2 f x\right)-11 a e^2 g\right) b^4+2 c^2 e \left(c d^2 (3 e f+2 d g)-a e^2 (4 e f+16 d g+15 e g x)\right) b^3+c^2 \left(-39 a^2 g e^4+2 a c \left(15 g d^2+10 e f d+32 e g x d+8 e^2 f x\right) e^2+c^2 d^2 \left(-3 g d^2-12 e f d+8 e g x d+12 e^2 f x\right)\right) b^2+2 c^3 \left(3 c^2 (d (f-g x)-4 e f x) d^3+2 a c e \left(2 g d^2+3 e (f-3 g x) d-6 e^2 f x\right) d+a^2 e^3 (11 e f+44 d g+25 e g x)\right) b+4 c^3 \left(3 c^3 f x d^4+2 a c^2 e (3 e f+2 d g) x d^2+8 a^3 e^4 g-a^2 c e^2 \left(24 g d^2+4 e (4 f+5 g x) d+5 e^2 f x\right)\right)}{\left(b^2-4 a c\right)^2 (a+x (b+c x))}+\frac{2 c \left(-e^4 g b^5+10 a c e^4 g b^3-30 a^2 c^2 e^4 g b+12 c^5 d^4 f+2 c^4 d^2 (4 a e (3 e f+2 d g)-3 b d (4 e f+d g))+4 c^3 e \left(b^2 (3 e f+2 d g) d^2-3 a b e (2 e f+3 d g) d+3 a^2 e^2 (e f+4 d g)\right)\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(4 a c-b^2\right)^{5/2}}}{2 c^4}","-\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) \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{(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,"((b^5*e^4*g*x + b^4*e^3*(a*e*g - c*(e*f + 4*d*g)*x) - b^3*c*e^2*(-2*c*d*(2*e*f + 3*d*g)*x + a*e*(e*f + 4*d*g + 5*e*g*x)) + 2*c^2*(a^3*e^4*g - c^3*d^4*f*x - a^2*c*e^2*(6*d^2*g + e^2*f*x + 4*d*e*(f + g*x)) + a*c^2*d^2*(d^2*g + 6*e^2*f*x + 4*d*e*(f + g*x))) + b*c^2*(c^2*d^3*(-(d*f) + 4*e*f*x + d*g*x) + a^2*e^3*(3*e*f + 12*d*g + 5*e*g*x) - 2*a*c*d*e*(2*d^2*g + 6*e^2*f*x + 3*d*e*(f + 3*g*x))) + 2*b^2*c*e*(-2*a^2*e^3*g - c^2*d^2*(3*e*f + 2*d*g)*x + a*c*e*(3*d^2*g + 2*e^2*f*x + 2*d*e*(f + 4*g*x))))/((b^2 - 4*a*c)*(a + x*(b + c*x))^2) + (-(b^6*e^4*g) + b^5*c*e^3*(4*d*g + e*(f + 4*g*x)) + 2*b^3*c^2*e*(c*d^2*(3*e*f + 2*d*g) - a*e^2*(4*e*f + 16*d*g + 15*e*g*x)) + b^2*c^2*(-39*a^2*e^4*g + c^2*d^2*(-12*d*e*f - 3*d^2*g + 12*e^2*f*x + 8*d*e*g*x) + 2*a*c*e^2*(10*d*e*f + 15*d^2*g + 8*e^2*f*x + 32*d*e*g*x)) + 2*b*c^3*(a^2*e^3*(11*e*f + 44*d*g + 25*e*g*x) + 2*a*c*d*e*(2*d^2*g - 6*e^2*f*x + 3*d*e*(f - 3*g*x)) + 3*c^2*d^3*(-4*e*f*x + d*(f - g*x))) - b^4*c*e^2*(-11*a*e^2*g + 2*c*(3*d^2*g + e^2*f*x + 2*d*e*(f + 2*g*x))) + 4*c^3*(8*a^3*e^4*g + 3*c^3*d^4*f*x + 2*a*c^2*d^2*e*(3*e*f + 2*d*g)*x - a^2*c*e^2*(24*d^2*g + 5*e^2*f*x + 4*d*e*(4*f + 5*g*x))))/((b^2 - 4*a*c)^2*(a + x*(b + c*x))) + (2*c*(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)))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(5/2) + c*e^4*g*Log[a + x*(b + c*x)])/(2*c^4)","A",1
2372,1,550,195,0.9781212,"\int \frac{(d+e x)^3 (f+g x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((d + e*x)^3*(f + g*x))/(a + b*x + c*x^2)^3,x]","\frac{1}{2} \left(\frac{b c \left(-3 a^2 e^3 g+3 a c e \left(d^2 g+d e (f+3 g x)+e^2 f x\right)+c^2 d^2 (d (f-g x)-3 e f x)\right)+2 c^2 \left(a^2 e^2 (3 d g+e (f+g x))-a c d \left(d^2 g+3 d e (f+g x)+3 e^2 f x\right)+c^2 d^3 f x\right)+b^3 e^2 (a e g-c x (3 d g+e f))-b^2 c e (a e (3 d g+e f+4 e g x)-3 c d x (d g+e f))+b^4 e^3 g x}{c^3 \left(4 a c-b^2\right) (a+x (b+c x))^2}+\frac{2 b c^2 \left(11 a^2 e^3 g+3 a c e \left(d^2 g+d e (f-3 g x)-e^2 f x\right)+3 c^2 d^2 (d (f-g x)-3 e f x)\right)-4 c^3 \left(a^2 e^2 (12 d g+4 e f+5 e g x)-3 a c d e x (d g+e f)-3 c^2 d^3 f x\right)+b^3 c e \left(3 c d (d g+e f)-8 a e^2 g\right)+b^2 c^2 \left(a e^2 (15 d g+5 e f+16 e g x)-3 c d \left(d^2 g+3 d e f-2 d e g x-2 e^2 f x\right)\right)+b^5 e^3 g-b^4 c e^2 (3 d g+e (f+2 g x))}{c^3 \left(b^2-4 a c\right)^2 (a+x (b+c x))}+\frac{12 \left(e (a e-b d)+c d^2\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right) (2 a e g-b (d g+e f)+2 c d f)}{\left(4 a c-b^2\right)^{5/2}}\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,"((b^5*e^3*g + b^3*c*e*(-8*a*e^2*g + 3*c*d*(e*f + d*g)) - b^4*c*e^2*(3*d*g + e*(f + 2*g*x)) - 4*c^3*(-3*c^2*d^3*f*x - 3*a*c*d*e*(e*f + d*g)*x + a^2*e^2*(4*e*f + 12*d*g + 5*e*g*x)) + b^2*c^2*(a*e^2*(5*e*f + 15*d*g + 16*e*g*x) - 3*c*d*(3*d*e*f + d^2*g - 2*e^2*f*x - 2*d*e*g*x)) + 2*b*c^2*(11*a^2*e^3*g + 3*a*c*e*(d^2*g - e^2*f*x + d*e*(f - 3*g*x)) + 3*c^2*d^2*(-3*e*f*x + d*(f - g*x))))/(c^3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))) + (b^4*e^3*g*x + b^3*e^2*(a*e*g - c*(e*f + 3*d*g)*x) - b^2*c*e*(-3*c*d*(e*f + d*g)*x + a*e*(e*f + 3*d*g + 4*e*g*x)) + 2*c^2*(c^2*d^3*f*x + a^2*e^2*(3*d*g + e*(f + g*x)) - a*c*d*(d^2*g + 3*e^2*f*x + 3*d*e*(f + g*x))) + b*c*(-3*a^2*e^3*g + c^2*d^2*(-3*e*f*x + d*(f - g*x)) + 3*a*c*e*(d^2*g + e^2*f*x + d*e*(f + 3*g*x))))/(c^3*(-b^2 + 4*a*c)*(a + x*(b + c*x))^2) + (12*(c*d^2 + e*(-(b*d) + a*e))*(2*c*d*f + 2*a*e*g - b*(e*f + d*g))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(5/2))/2","B",1
2373,1,408,305,0.6675601,"\int \frac{(d+e x)^2 (f+g x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((d + e*x)^2*(f + g*x))/(a + b*x + c*x^2)^3,x]","\frac{1}{2} \left(\frac{2 c \left(a^2 e^2 g-a c \left(d^2 g+2 d e (f+g x)+e^2 f x\right)+c^2 d^2 f x\right)+b^2 e (c x (2 d g+e f)-a e g)+b c (a e (2 d g+e f+3 e g x)+c d (d f-d g x-2 e f x))+b^3 \left(-e^2\right) g x}{c^2 \left(4 a c-b^2\right) (a+x (b+c x))^2}+\frac{4 c^2 \left(-4 a^2 e^2 g+a c e x (2 d g+e f)+3 c^2 d^2 f x\right)+b^2 c \left(5 a e^2 g+c \left(-3 d^2 g-6 d e f+4 d e g x+2 e^2 f x\right)\right)+2 b c^2 (a e (2 d g+e f-3 e g x)+3 c d (d f-d g x-2 e f x))+b^4 \left(-e^2\right) g+b^3 c e (2 d g+e f)}{c^2 \left(b^2-4 a c\right)^2 (a+x (b+c x))}+\frac{4 \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\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(4 a c-b^2\right)^{5/2}}\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}-\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)}",1,"((-(b^4*e^2*g) + b^3*c*e*(e*f + 2*d*g) + 4*c^2*(-4*a^2*e^2*g + 3*c^2*d^2*f*x + a*c*e*(e*f + 2*d*g)*x) + 2*b*c^2*(3*c*d*(d*f - 2*e*f*x - d*g*x) + a*e*(e*f + 2*d*g - 3*e*g*x)) + b^2*c*(5*a*e^2*g + c*(-6*d*e*f - 3*d^2*g + 2*e^2*f*x + 4*d*e*g*x)))/(c^2*(b^2 - 4*a*c)^2*(a + x*(b + c*x))) + (-(b^3*e^2*g*x) + b^2*e*(-(a*e*g) + c*(e*f + 2*d*g)*x) + b*c*(c*d*(d*f - 2*e*f*x - d*g*x) + a*e*(e*f + 2*d*g + 3*e*g*x)) + 2*c*(a^2*e^2*g + c^2*d^2*f*x - a*c*(d^2*g + e^2*f*x + 2*d*e*(f + g*x))))/(c^2*(-b^2 + 4*a*c)*(a + x*(b + c*x))^2) + (4*(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))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(5/2))/2","A",1
2374,1,216,221,0.4018745,"\int \frac{(d+e x) (f+g x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[((d + e*x)*(f + g*x))/(a + b*x + c*x^2)^3,x]","\frac{1}{2} \left(\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)}{c \left(b^2-4 a c\right)^2 (a+x (b+c x))}+\frac{a b e g-2 a c (d g+e (f+g x))+b^2 e g x+b c (d (f-g x)-e f x)+2 c^2 d f x}{c \left(4 a c-b^2\right) (a+x (b+c x))^2}+\frac{4 \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\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(4 a c-b^2\right)^{5/2}}\right)","\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,"(((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))/(c*(b^2 - 4*a*c)^2*(a + x*(b + c*x))) + (a*b*e*g + 2*c^2*d*f*x + b^2*e*g*x + b*c*(-(e*f*x) + d*(f - g*x)) - 2*a*c*(d*g + e*(f + g*x)))/(c*(-b^2 + 4*a*c)*(a + x*(b + c*x))^2) + (4*(6*c^2*d*f + b^2*e*g + 2*a*c*e*g - 3*b*c*(e*f + d*g))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(5/2))/2","A",1
2375,1,128,131,0.1272634,"\int \frac{f+g x}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[(f + g*x)/(a + b*x + c*x^2)^3,x]","\frac{\frac{\left(b^2-4 a c\right) (2 a g-b f+b g x-2 c f x)}{(a+x (b+c x))^2}-\frac{12 c (b g-2 c f) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+\frac{3 (b+2 c x) (2 c f-b g)}{a+x (b+c x)}}{2 \left(b^2-4 a c\right)^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^2 - 4*a*c)*(-(b*f) + 2*a*g - 2*c*f*x + b*g*x))/(a + x*(b + c*x))^2 + (3*(2*c*f - b*g)*(b + 2*c*x))/(a + x*(b + c*x)) - (12*c*(-2*c*f + b*g)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c])/(2*(b^2 - 4*a*c)^2)","A",1
2376,1,668,666,2.822205,"\int \frac{f+g x}{(d+e x) \left(a+b x+c x^2\right)^3} \, dx","Integrate[(f + g*x)/((d + e*x)*(a + b*x + c*x^2)^3),x]","\frac{1}{2} \left(\frac{2 b c \left(3 a^2 e^3 g-a c e \left(d^2 g-7 d e f+5 d e g x+7 e^2 f x\right)+3 c^2 d^2 (d f-d g x-3 e f x)\right)-4 c^2 \left(a^2 e^2 (4 d g-4 e f-3 e g x)+a c d e x (d g-7 e f)-3 c^2 d^3 f x\right)+b^2 c \left(3 a e^2 (d g-5 e f)+c d \left(-3 d^2 g-9 d e f+10 d e g x+2 e^2 f x\right)\right)+2 b^4 e^2 (e f-d g)+b^3 c e \left(5 d^2 g+d e (f-2 g x)+2 e^2 f x\right)}{\left(b^2-4 a c\right)^2 (a+x (b+c x)) \left(e (a e-b d)+c d^2\right)^2}-\frac{2 \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right) \left(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)+6 c^2 e^2 \left(2 a^3 e^3 g-a^2 b e^2 (d g+5 e f)+6 a b^2 d^2 e g-2 b^3 d^3 g\right)+10 a b^3 c e^4 (e f-d g)-2 c^4 d^3 (2 a e (d g-10 e f)+3 b d (d g+5 e f))+b^5 e^4 (d g-e f)+12 c^5 d^5 f\right)}{\left(4 a c-b^2\right)^{5/2} \left(e (b d-a e)-c d^2\right)^3}+\frac{b (a e g+c d (f-g x)-c e f x)+2 c (-a d g+a e (f+g x)+c d f x)+b^2 (-e) f}{\left(b^2-4 a c\right) (a+x (b+c x))^2 \left(e (b d-a e)-c d^2\right)}+\frac{2 e^4 (e f-d g) \log (d+e x)}{\left(e (a e-b d)+c d^2\right)^3}+\frac{e^4 (d g-e f) \log (a+x (b+c x))}{\left(e (a e-b d)+c d^2\right)^3}\right)","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(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)-6 c^2 e^2 \left(-2 a^3 e^3 g+a^2 b e^2 (d g+5 e f)-6 a b^2 d^2 e g+2 b^3 d^3 g\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^2*e*f) + b*(a*e*g - c*e*f*x + c*d*(f - g*x)) + 2*c*(-(a*d*g) + c*d*f*x + a*e*(f + g*x)))/((b^2 - 4*a*c)*(-(c*d^2) + e*(b*d - a*e))*(a + x*(b + c*x))^2) + (2*b^4*e^2*(e*f - d*g) + b^3*c*e*(5*d^2*g + 2*e^2*f*x + d*e*(f - 2*g*x)) - 4*c^2*(-3*c^2*d^3*f*x + a*c*d*e*(-7*e*f + d*g)*x + a^2*e^2*(-4*e*f + 4*d*g - 3*e*g*x)) + 2*b*c*(3*a^2*e^3*g + 3*c^2*d^2*(d*f - 3*e*f*x - d*g*x) - a*c*e*(-7*d*e*f + d^2*g + 7*e^2*f*x + 5*d*e*g*x)) + b^2*c*(3*a*e^2*(-5*e*f + d*g) + c*d*(-9*d*e*f - 3*d^2*g + 2*e^2*f*x + 10*d*e*g*x)))/((b^2 - 4*a*c)^2*(c*d^2 + e*(-(b*d) + a*e))^2*(a + x*(b + c*x))) - (2*(12*c^5*d^5*f + 10*a*b^3*c*e^4*(e*f - d*g) + b^5*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)))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/((-b^2 + 4*a*c)^(5/2)*(-(c*d^2) + e*(b*d - a*e))^3) + (2*e^4*(e*f - d*g)*Log[d + e*x])/(c*d^2 + e*(-(b*d) + a*e))^3 + (e^4*(-(e*f) + d*g)*Log[a + x*(b + c*x)])/(c*d^2 + e*(-(b*d) + a*e))^3)/2","A",1
2377,1,1409,1043,6.7488568,"\int \frac{f+g x}{(d+e x)^2 \left(a+b x+c x^2\right)^3} \, dx","Integrate[(f + g*x)/((d + e*x)^2*(a + b*x + c*x^2)^3),x]","-\frac{(e f-d g) e^4}{\left(c d^2-b e d+a e^2\right)^3 (d+e x)}+\frac{\left(3 e^6 f b^6-2 d e^5 g b^6-6 c d e^5 f b^5-a e^6 g b^5+5 c d^2 e^4 g b^5-30 a c e^6 f b^4+20 a c d e^5 g b^4+60 a c^2 d e^5 f b^3+10 a^2 c e^6 g b^3-50 a c^2 d^2 e^4 g b^3-20 c^3 d^4 e^2 g b^3+90 a^2 c^2 e^6 f b^2+30 c^4 d^4 e^2 f b^2-60 a^2 c^2 d e^5 g b^2+80 a c^3 d^3 e^3 g b^2+20 c^4 d^5 e g b^2-180 a^2 c^3 d e^5 f b-120 a c^4 d^3 e^3 f b-36 c^5 d^5 e f b-6 c^5 d^6 g b-30 a^3 c^2 e^6 g b+30 a^2 c^3 d^2 e^4 g b-10 a c^4 d^4 e^2 g b+12 c^6 d^6 f-60 a^3 c^3 e^6 f+180 a^2 c^4 d^2 e^4 f+60 a c^5 d^4 e^2 f+120 a^3 c^3 d e^5 g-80 a^2 c^4 d^3 e^3 g-8 a c^5 d^5 e g\right) \tan ^{-1}\left(\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right)}{\left(b^2-4 a c\right)^2 \sqrt{4 a c-b^2} \left(-c d^2+b e d-a e^2\right)^4}+\frac{\left(-3 b f e^6+a g e^6+6 c d f e^5+2 b d g e^5-5 c d^2 g e^4\right) \log (d+e x)}{\left(c d^2-b e d+a e^2\right)^4}+\frac{\left(3 b f e^6-a g e^6-6 c d f e^5-2 b d g e^5+5 c d^2 g e^4\right) \log \left(c x^2+b x+a\right)}{2 \left(c d^2-b e d+a e^2\right)^4}+\frac{-4 e^4 f b^5+2 d e^3 g b^5+7 c d e^3 f b^4+2 a e^4 g b^4-6 c d^2 e^2 g b^4-4 c e^4 f x b^4+2 c d e^3 g x b^4+29 a c e^4 f b^3+3 c^2 d^2 e^2 f b^3-13 a c d e^3 g b^3+7 c^2 d^3 e g b^3+6 c^2 d e^3 f x b^3+2 a c e^4 g x b^3-6 c^2 d^2 e^2 g x b^3-56 a c^2 d e^3 f b^2-12 c^3 d^3 e f b^2-3 c^3 d^4 g b^2-15 a^2 c e^4 g b^2+18 a c^2 d^2 e^2 g b^2+26 a c^2 e^4 f x b^2+6 c^3 d^2 e^2 f x b^2-10 a c^2 d e^3 g x b^2+14 c^3 d^3 e g x b^2+6 c^4 d^4 f b-46 a^2 c^2 e^4 f b+24 a c^3 d^2 e^2 f b+44 a^2 c^2 d e^3 g b-4 a c^3 d^3 e g b-48 a c^3 d e^3 f x b-24 c^4 d^3 e f x b-6 c^4 d^4 g x b-14 a^2 c^2 e^4 g x b-12 a c^3 d^2 e^2 g x b+64 a^2 c^3 d e^3 f+16 a^3 c^2 e^4 g-48 a^2 c^3 d^2 e^2 g+12 c^5 d^4 f x-28 a^2 c^3 e^4 f x+48 a c^4 d^2 e^2 f x+56 a^2 c^3 d e^3 g x-8 a c^4 d^3 e g x}{2 \left(4 a c-b^2\right)^2 \left(c d^2-b e d+a e^2\right)^3 \left(c x^2+b x+a\right)}+\frac{e^2 f b^3-2 c d e f b^2-a e^2 g b^2+c e^2 f x b^2+c^2 d^2 f b-3 a c e^2 f b+2 a c d e g b-2 c^2 d e f x b-c^2 d^2 g x b-a c e^2 g x b+4 a c^2 d e f-2 a c^2 d^2 g+2 a^2 c e^2 g+2 c^3 d^2 f x-2 a c^2 e^2 f x+4 a c^2 d e g x}{2 \left(4 a c-b^2\right) \left(c d^2-b e d+a e^2\right)^2 \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^4*(e*f - d*g))/((c*d^2 - b*d*e + a*e^2)^3*(d + e*x))) + (b*c^2*d^2*f - 2*b^2*c*d*e*f + 4*a*c^2*d*e*f + b^3*e^2*f - 3*a*b*c*e^2*f - 2*a*c^2*d^2*g + 2*a*b*c*d*e*g - a*b^2*e^2*g + 2*a^2*c*e^2*g + 2*c^3*d^2*f*x - 2*b*c^2*d*e*f*x + b^2*c*e^2*f*x - 2*a*c^2*e^2*f*x - b*c^2*d^2*g*x + 4*a*c^2*d*e*g*x - a*b*c*e^2*g*x)/(2*(-b^2 + 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)^2) + (6*b*c^4*d^4*f - 12*b^2*c^3*d^3*e*f + 3*b^3*c^2*d^2*e^2*f + 24*a*b*c^3*d^2*e^2*f + 7*b^4*c*d*e^3*f - 56*a*b^2*c^2*d*e^3*f + 64*a^2*c^3*d*e^3*f - 4*b^5*e^4*f + 29*a*b^3*c*e^4*f - 46*a^2*b*c^2*e^4*f - 3*b^2*c^3*d^4*g + 7*b^3*c^2*d^3*e*g - 4*a*b*c^3*d^3*e*g - 6*b^4*c*d^2*e^2*g + 18*a*b^2*c^2*d^2*e^2*g - 48*a^2*c^3*d^2*e^2*g + 2*b^5*d*e^3*g - 13*a*b^3*c*d*e^3*g + 44*a^2*b*c^2*d*e^3*g + 2*a*b^4*e^4*g - 15*a^2*b^2*c*e^4*g + 16*a^3*c^2*e^4*g + 12*c^5*d^4*f*x - 24*b*c^4*d^3*e*f*x + 6*b^2*c^3*d^2*e^2*f*x + 48*a*c^4*d^2*e^2*f*x + 6*b^3*c^2*d*e^3*f*x - 48*a*b*c^3*d*e^3*f*x - 4*b^4*c*e^4*f*x + 26*a*b^2*c^2*e^4*f*x - 28*a^2*c^3*e^4*f*x - 6*b*c^4*d^4*g*x + 14*b^2*c^3*d^3*e*g*x - 8*a*c^4*d^3*e*g*x - 6*b^3*c^2*d^2*e^2*g*x - 12*a*b*c^3*d^2*e^2*g*x + 2*b^4*c*d*e^3*g*x - 10*a*b^2*c^2*d*e^3*g*x + 56*a^2*c^3*d*e^3*g*x + 2*a*b^3*c*e^4*g*x - 14*a^2*b*c^2*e^4*g*x)/(2*(-b^2 + 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(a + b*x + c*x^2)) + ((12*c^6*d^6*f - 36*b*c^5*d^5*e*f + 30*b^2*c^4*d^4*e^2*f + 60*a*c^5*d^4*e^2*f - 120*a*b*c^4*d^3*e^3*f + 180*a^2*c^4*d^2*e^4*f - 6*b^5*c*d*e^5*f + 60*a*b^3*c^2*d*e^5*f - 180*a^2*b*c^3*d*e^5*f + 3*b^6*e^6*f - 30*a*b^4*c*e^6*f + 90*a^2*b^2*c^2*e^6*f - 60*a^3*c^3*e^6*f - 6*b*c^5*d^6*g + 20*b^2*c^4*d^5*e*g - 8*a*c^5*d^5*e*g - 20*b^3*c^3*d^4*e^2*g - 10*a*b*c^4*d^4*e^2*g + 80*a*b^2*c^3*d^3*e^3*g - 80*a^2*c^4*d^3*e^3*g + 5*b^5*c*d^2*e^4*g - 50*a*b^3*c^2*d^2*e^4*g + 30*a^2*b*c^3*d^2*e^4*g - 2*b^6*d*e^5*g + 20*a*b^4*c*d*e^5*g - 60*a^2*b^2*c^2*d*e^5*g + 120*a^3*c^3*d*e^5*g - a*b^5*e^6*g + 10*a^2*b^3*c*e^6*g - 30*a^3*b*c^2*e^6*g)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/((b^2 - 4*a*c)^2*Sqrt[-b^2 + 4*a*c]*(-(c*d^2) + b*d*e - a*e^2)^4) + ((6*c*d*e^5*f - 3*b*e^6*f - 5*c*d^2*e^4*g + 2*b*d*e^5*g + a*e^6*g)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^4 + ((-6*c*d*e^5*f + 3*b*e^6*f + 5*c*d^2*e^4*g - 2*b*d*e^5*g - a*e^6*g)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^4)","A",1
2378,1,43,43,0.0213149,"\int \frac{(5-x) (3+2 x)^4}{2+5 x+3 x^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2),x]","\frac{1}{972} \left(42500 \log (-6 x-4)-3 \left(432 x^4-384 x^3-13872 x^2-46304 x+1944 \log (-2 (x+1))-41727\right)\right)","-\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,"(42500*Log[-4 - 6*x] - 3*(-41727 - 46304*x - 13872*x^2 - 384*x^3 + 432*x^4 + 1944*Log[-2*(1 + x)]))/972","A",1
2379,1,35,36,0.014738,"\int \frac{(5-x) (3+2 x)^3}{2+5 x+3 x^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2),x]","\frac{1}{162} \left(-144 x^3+468 x^2+5532 x+4250 \log (-6 x-4)-972 \log (-2 (x+1))+6759\right)","-\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,"(6759 + 5532*x + 468*x^2 - 144*x^3 + 4250*Log[-4 - 6*x] - 972*Log[-2*(1 + x)])/162","A",1
2380,1,34,29,0.0142802,"\int \frac{(5-x) (3+2 x)^2}{2+5 x+3 x^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2),x]","-\frac{2 x^2}{3}+\frac{44 x}{9}+\frac{425}{27} \log (-6 x-4)-6 \log (-2 (x+1))+\frac{53}{6}","-\frac{2 x^2}{3}+\frac{44 x}{9}-6 \log (x+1)+\frac{425}{27} \log (3 x+2)",1,"53/6 + (44*x)/9 - (2*x^2)/3 + (425*Log[-4 - 6*x])/27 - 6*Log[-2*(1 + x)]","A",1
2381,1,22,22,0.0065576,"\int \frac{(5-x) (3+2 x)}{2+5 x+3 x^2} \, dx","Integrate[((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",1
2382,1,17,17,0.0038227,"\int \frac{5-x}{2+5 x+3 x^2} \, dx","Integrate[(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",1
2383,1,27,27,0.0077379,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)} \, dx","Integrate[(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",1
2384,1,38,38,0.0259514,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)} \, dx","Integrate[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)),x]","\frac{1}{25} \left(-\frac{65}{2 x+3}+51 \log (-6 x-4)-150 \log (-2 (x+1))+99 \log (2 x+3)\right)","-\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,"(-65/(3 + 2*x) + 51*Log[-4 - 6*x] - 150*Log[-2*(1 + x)] + 99*Log[3 + 2*x])/25","A",1
2385,1,47,49,0.0269809,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)} \, dx","Integrate[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)),x]","\frac{1}{250} \left(-\frac{990}{2 x+3}-\frac{325}{(2 x+3)^2}+306 \log (-6 x-4)-1500 \log (-2 (x+1))+1194 \log (2 x+3)\right)","-\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,"(-325/(3 + 2*x)^2 - 990/(3 + 2*x) + 306*Log[-4 - 6*x] - 1500*Log[-2*(1 + x)] + 1194*Log[3 + 2*x])/250","A",1
2386,1,62,60,0.0328523,"\int \frac{5-x}{(3+2 x)^4 \left(2+5 x+3 x^2\right)} \, dx","Integrate[(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}+\frac{459}{625} \log (-6 x-4)-6 \log (-2 (x+1))+\frac{3291}{625} \log (2 x+3)","-\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)) + (459*Log[-4 - 6*x])/625 - 6*Log[-2*(1 + x)] + (3291*Log[3 + 2*x])/625","A",1
2387,1,56,50,0.0355655,"\int \frac{(5-x) (3+2 x)^4}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^2,x]","\frac{1}{81} \left(-\frac{12083 x+11597}{3 x^2+5 x+2}-18 (2 x+3)^2+276 (2 x+3)-4875 \log (-6 x-4)+6723 \log (-2 (x+1))\right)","-\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,"(276*(3 + 2*x) - 18*(3 + 2*x)^2 - (11597 + 12083*x)/(2 + 5*x + 3*x^2) - 4875*Log[-4 - 6*x] + 6723*Log[-2*(1 + x)])/81","A",1
2388,1,47,43,0.0309604,"\int \frac{(5-x) (3+2 x)^3}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^2,x]","-\frac{2611 x+2449}{81 x^2+135 x+54}-\frac{4}{9} (2 x+3)-\frac{1825}{27} \log (-6 x-4)+71 \log (-2 (x+1))","-\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,"(-4*(3 + 2*x))/9 - (2449 + 2611*x)/(54 + 135*x + 81*x^2) - (1825*Log[-4 - 6*x])/27 + 71*Log[-2*(1 + x)]","A",1
2389,1,38,38,0.0266882,"\int \frac{(5-x) (3+2 x)^2}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2)^2,x]","-\frac{587 x+533}{27 x^2+45 x+18}-\frac{535}{9} \log (-6 x-4)+59 \log (-2 (x+1))","-\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)/(18 + 45*x + 27*x^2)) - (535*Log[-4 - 6*x])/9 + 59*Log[-2*(1 + x)]","A",1
2390,1,34,36,0.0165476,"\int \frac{(5-x) (3+2 x)}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^2,x]","-\frac{139 x+121}{9 x^2+15 x+6}+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)/(6 + 15*x + 9*x^2)) + 47*Log[1 + x] - 47*Log[2 + 3*x]","A",1
2391,1,33,34,0.0142258,"\int \frac{5-x}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(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",1
2392,1,48,48,0.0306632,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(5 - x)/((3 + 2*x)*(2 + 5*x + 3*x^2)^2),x]","\frac{1}{25} \left(-\frac{15 (47 x+37)}{3 x^2+5 x+2}-627 \log (-6 x-4)+575 \log (-2 (x+1))+52 \log (2 x+3)\right)","-\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,"((-15*(37 + 47*x))/(2 + 5*x + 3*x^2) - 627*Log[-4 - 6*x] + 575*Log[-2*(1 + x)] + 52*Log[3 + 2*x])/25","A",1
2393,1,57,66,0.0321872,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^2),x]","\frac{1}{125} \left(-\frac{15 (201 x+151)}{3 x^2+5 x+2}-\frac{260}{2 x+3}-2187 \log (-6 x-4)+1375 \log (-2 (x+1))+812 \log (2 x+3)\right)","-\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,"(-260/(3 + 2*x) - (15*(151 + 201*x))/(2 + 5*x + 3*x^2) - 2187*Log[-4 - 6*x] + 1375*Log[-2*(1 + x)] + 812*Log[3 + 2*x])/125","A",1
2394,1,66,77,0.0324163,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^2),x]","\frac{1}{625} \left(-\frac{15 (903 x+653)}{3 x^2+5 x+2}-\frac{4060}{2 x+3}-\frac{650}{(2 x+3)^2}-7479 \log (-6 x-4)-625 \log (-2 (x+1))+8104 \log (2 x+3)\right)","-\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,"(-650/(3 + 2*x)^2 - 4060/(3 + 2*x) - (15*(653 + 903*x))/(2 + 5*x + 3*x^2) - 7479*Log[-4 - 6*x] - 625*Log[-2*(1 + x)] + 8104*Log[3 + 2*x])/625","A",1
2395,1,75,88,0.0434729,"\int \frac{5-x}{(3+2 x)^4 \left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(5 - x)/((3 + 2*x)^4*(2 + 5*x + 3*x^2)^2),x]","\frac{-\frac{45 (4209 x+2959)}{3 x^2+5 x+2}-\frac{121560}{2 x+3}-\frac{30450}{(2 x+3)^2}-\frac{6500}{(2 x+3)^3}-75573 \log (-6 x-4)-121875 \log (-2 (x+1))+197448 \log (2 x+3)}{9375}","-\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,"(-6500/(3 + 2*x)^3 - 30450/(3 + 2*x)^2 - 121560/(3 + 2*x) - (45*(2959 + 4209*x))/(2 + 5*x + 3*x^2) - 75573*Log[-4 - 6*x] - 121875*Log[-2*(1 + x)] + 197448*Log[3 + 2*x])/9375","A",1
2396,1,81,64,0.0324656,"\int \frac{(5-x) (3+2 x)^5}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((5 - x)*(3 + 2*x)^5)/(2 + 5*x + 3*x^2)^3,x]","\frac{-1728 x^5-8352 x^4+486510 x^3+1221179 x^2+176250 \left(3 x^2+5 x+2\right)^2 \log (-6 x-4)-175770 \left(3 x^2+5 x+2\right)^2 \log (-2 (x+1))+973450 x+245891}{162 \left(3 x^2+5 x+2\right)^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,"(245891 + 973450*x + 1221179*x^2 + 486510*x^3 - 8352*x^4 - 1728*x^5 + 176250*(2 + 5*x + 3*x^2)^2*Log[-4 - 6*x] - 175770*(2 + 5*x + 3*x^2)^2*Log[-2*(1 + x)])/(162*(2 + 5*x + 3*x^2)^2)","A",1
2397,1,62,59,0.0354895,"\int \frac{(5-x) (3+2 x)^4}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^3,x]","\frac{1}{54} \left(47650 \log (-6 x-4)-\frac{3 \left(-47362 x^3-117789 x^2+15894 \left(3 x^2+5 x+2\right)^2 \log (-2 (x+1))-94986 x-24613\right)}{\left(3 x^2+5 x+2\right)^2}\right)","-\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,"(47650*Log[-4 - 6*x] - (3*(-24613 - 94986*x - 117789*x^2 - 47362*x^3 + 15894*(2 + 5*x + 3*x^2)^2*Log[-2*(1 + x)]))/(2 + 5*x + 3*x^2)^2)/54","A",1
2398,1,59,69,0.0281735,"\int \frac{(5-x) (3+2 x)^3}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^3,x]","-\frac{2611 x+2449}{54 \left(3 x^2+5 x+2\right)^2}+\frac{38118 x+31673}{54 \left(3 x^2+5 x+2\right)}+705 \log (-6 x-4)-705 \log (-2 (x+1))","-\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,"-1/54*(2449 + 2611*x)/(2 + 5*x + 3*x^2)^2 + (31673 + 38118*x)/(54*(2 + 5*x + 3*x^2)) + 705*Log[-4 - 6*x] - 705*Log[-2*(1 + x)]","A",1
2399,1,56,57,0.0294365,"\int \frac{(5-x) (3+2 x)^2}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((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}{54 x^2+90 x+36}+551 \log (-6 x-4)-551 \log (-2 (x+1))","-\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,"-1/18*(533 + 587*x)/(2 + 5*x + 3*x^2)^2 + (8269 + 9918*x)/(36 + 90*x + 54*x^2) + 551*Log[-4 - 6*x] - 551*Log[-2*(1 + x)]","A",1
2400,1,57,57,0.0182194,"\int \frac{(5-x) (3+2 x)}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((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,"-1/6*(121 + 139*x)/(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",1
2401,1,57,57,0.0144112,"\int \frac{5-x}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[(5 - x)/(2 + 5*x + 3*x^2)^3,x]","\frac{-35 x-29}{2 \left(3 x^2+5 x+2\right)^2}+\frac{105 (6 x+5)}{2 \left(3 x^2+5 x+2\right)}-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",1
2402,1,68,69,0.0458768,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)^3} \, dx","Integrate[(5 - x)/((3 + 2*x)*(2 + 5*x + 3*x^2)^3),x]","\frac{1}{125} \left(-\frac{75 (47 x+37)}{2 \left(3 x^2+5 x+2\right)^2}+\frac{57210 x+47935}{6 x^2+10 x+4}+28917 \log (-6 x-4)-29125 \log (-2 (x+1))+208 \log (2 x+3)\right)","-\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,"((-75*(37 + 47*x))/(2*(2 + 5*x + 3*x^2)^2) + (47935 + 57210*x)/(4 + 10*x + 6*x^2) + 28917*Log[-4 - 6*x] - 29125*Log[-2*(1 + x)] + 208*Log[3 + 2*x])/125","A",1
2403,1,78,94,0.0446842,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)^3} \, dx","Integrate[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^3),x]","\frac{1}{625} \left(-\frac{75 (201 x+151)}{2 \left(3 x^2+5 x+2\right)^2}+\frac{5 (39462 x+33697)}{6 x^2+10 x+4}-\frac{1040}{2 x+3}+104463 \log (-6 x-4)-109375 \log (-2 (x+1))+4912 \log (2 x+3)\right)","-\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,"(-1040/(3 + 2*x) - (75*(151 + 201*x))/(2*(2 + 5*x + 3*x^2)^2) + (5*(33697 + 39462*x))/(4 + 10*x + 6*x^2) + 104463*Log[-4 - 6*x] - 109375*Log[-2*(1 + x)] + 4912*Log[3 + 2*x])/625","A",1
2404,1,86,105,0.0512029,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)^3} \, dx","Integrate[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^3),x]","\frac{-\frac{75 (903 x+653)}{2 \left(3 x^2+5 x+2\right)^2}+\frac{611970 x+550495}{6 x^2+10 x+4}-\frac{24560}{2 x+3}-\frac{2600}{(2 x+3)^2}+372033 \log (-6 x-4)-440625 \log (-2 (x+1))+68592 \log (2 x+3)}{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,"(-2600/(3 + 2*x)^2 - 24560/(3 + 2*x) - (75*(653 + 903*x))/(2*(2 + 5*x + 3*x^2)^2) + (550495 + 611970*x)/(4 + 10*x + 6*x^2) + 372033*Log[-4 - 6*x] - 440625*Log[-2*(1 + x)] + 68592*Log[3 + 2*x])/3125","A",1
2405,1,22,33,0.0082539,"\int \frac{x (1+x)^2}{\left(1+x+x^2\right)^3} \, dx","Integrate[(x*(1 + x)^2)/(1 + x + x^2)^3,x]","-\frac{3 x^2+4 x+2}{6 \left(x^2+x+1\right)^2}","-\frac{(x+1) (2 x+1)}{6 \left(x^2+x+1\right)^2}-\frac{1}{6 \left(x^2+x+1\right)}",1,"-1/6*(2 + 4*x + 3*x^2)/(1 + x + x^2)^2","A",1
2406,1,82,160,0.059561,"\int (5-x) (3+2 x)^4 \sqrt{2+5 x+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)^4*Sqrt[2 + 5*x + 3*x^2],x]","\frac{-908915 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(1244160 x^6+1624320 x^5-28649088 x^4-123633360 x^3-208601544 x^2-161915450 x-47009103\right)}{3265920}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-47009103 - 161915450*x - 208601544*x^2 - 123633360*x^3 - 28649088*x^4 + 1624320*x^5 + 1244160*x^6) - 908915*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/3265920","A",1
2407,1,77,135,0.0430634,"\int (5-x) (3+2 x)^3 \sqrt{2+5 x+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)^3*Sqrt[2 + 5*x + 3*x^2],x]","\frac{-31105 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(34560 x^5-14976 x^4-825840 x^3-2317848 x^2-2432350 x-859701\right)}{155520}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-859701 - 2432350*x - 2317848*x^2 - 825840*x^3 - 14976*x^4 + 34560*x^5) - 31105*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/155520","A",1
2408,1,72,110,0.0346882,"\int (5-x) (3+2 x)^2 \sqrt{2+5 x+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2],x]","\frac{-11335 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(10368 x^4-23760 x^3-229416 x^2-375250 x-168627\right)}{77760}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-168627 - 375250*x - 229416*x^2 - 23760*x^3 + 10368*x^4) - 11335*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/77760","A",1
2409,1,67,85,0.0285885,"\int (5-x) (3+2 x) \sqrt{2+5 x+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)*Sqrt[2 + 5*x + 3*x^2],x]","\frac{-559 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(432 x^3-1896 x^2-7426 x-4539\right)}{5184}","\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-4539 - 7426*x - 1896*x^2 + 432*x^3) - 559*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/5184","A",1
2410,1,62,80,0.0488044,"\int (5-x) \sqrt{2+5 x+3 x^2} \, dx","Integrate[(5 - x)*Sqrt[2 + 5*x + 3*x^2],x]","\frac{1}{432} \left(-6 \sqrt{3 x^2+5 x+2} \left(24 x^2-170 x-159\right)-35 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)\right)","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-159 - 170*x + 24*x^2) - 35*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/432","A",1
2411,1,93,100,0.0415839,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{3+2 x} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x),x]","\frac{1}{144} \left(-6 \sqrt{3 x^2+5 x+2} (6 x-73)-234 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-311 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)\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,"(-6*(-73 + 6*x)*Sqrt[2 + 5*x + 3*x^2] - 234*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 311*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/144","A",1
2412,1,98,105,0.0669059,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^2} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2,x]","-\frac{\sqrt{3 x^2+5 x+2} (x+8)}{4 x+6}+\frac{57 \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{8 \sqrt{5}}+\frac{43 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)}{8 \sqrt{3}}","-\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])/(6 + 4*x)) + (57*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(8*Sqrt[5]) + (43*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/(8*Sqrt[3])","A",1
2413,1,100,107,0.0803628,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^3} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^3,x]","\frac{1}{400} \left(\frac{10 \sqrt{3 x^2+5 x+2} (124 x+121)}{(2 x+3)^2}-27 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-50 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)\right)","\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,"((10*(121 + 124*x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2 - 27*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 50*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/400","A",1
2414,1,74,94,0.0331989,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^4} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^4,x]","\frac{\sqrt{3 x^2+5 x+2} \left(696 x^2+2758 x+1921\right)}{600 (2 x+3)^3}+\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,"(Sqrt[2 + 5*x + 3*x^2]*(1921 + 2758*x + 696*x^2))/(600*(3 + 2*x)^3) + (47*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(400*Sqrt[5])","A",1
2415,1,119,119,0.0456984,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^5} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^5,x]","\frac{1}{20} \left(-\frac{16 \left(3 x^2+5 x+2\right)^{3/2}}{(2 x+3)^3}-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{(2 x+3)^4}+\frac{153 (8 x+7) \sqrt{3 x^2+5 x+2}}{40 (2 x+3)^2}+\frac{153 \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{80 \sqrt{5}}\right)","-\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])/(40*(3 + 2*x)^2) - (13*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^4 - (16*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^3 + (153*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(80*Sqrt[5]))/20","A",1
2416,1,146,144,0.1066781,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^6} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^6,x]","\frac{1}{25} \left(-\frac{87 \left(3 x^2+5 x+2\right)^{3/2}}{5 (2 x+3)^3}-\frac{339 \left(3 x^2+5 x+2\right)^{3/2}}{20 (2 x+3)^4}-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{(2 x+3)^5}+\frac{3159 \left(\frac{10 \sqrt{3 x^2+5 x+2} (8 x+7)}{(2 x+3)^2}+\sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)}{8000}\right)","-\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,"((-13*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^5 - (339*(2 + 5*x + 3*x^2)^(3/2))/(20*(3 + 2*x)^4) - (87*(2 + 5*x + 3*x^2)^(3/2))/(5*(3 + 2*x)^3) + (3159*((10*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2 + Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/8000)/25","A",1
2417,1,169,169,0.0907369,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^7} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^7,x]","\frac{1}{750} \left(-\frac{2237 \left(3 x^2+5 x+2\right)^{3/2}}{5 (2 x+3)^3}-\frac{9339 \left(3 x^2+5 x+2\right)^{3/2}}{20 (2 x+3)^4}-\frac{438 \left(3 x^2+5 x+2\right)^{3/2}}{(2 x+3)^5}-\frac{325 \left(3 x^2+5 x+2\right)^{3/2}}{(2 x+3)^6}+\frac{79359 \left(\frac{10 \sqrt{3 x^2+5 x+2} (8 x+7)}{(2 x+3)^2}+\sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)}{8000}\right)","-\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,"((-325*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^6 - (438*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^5 - (9339*(2 + 5*x + 3*x^2)^(3/2))/(20*(3 + 2*x)^4) - (2237*(2 + 5*x + 3*x^2)^(3/2))/(5*(3 + 2*x)^3) + (79359*((10*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2 + Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/8000)/750","A",1
2418,1,92,183,0.0623012,"\int (5-x) (3+2 x)^4 \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^4*(2 + 5*x + 3*x^2)^(3/2),x]","\frac{2274845 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(119439360 x^8+370759680 x^7-2143687680 x^6-14811482880 x^5-37262745216 x^4-49917376080 x^3-37650690888 x^2-15049298650 x-2471988351\right)}{134369280}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-2471988351 - 15049298650*x - 37650690888*x^2 - 49917376080*x^3 - 37262745216*x^4 - 14811482880*x^5 - 2143687680*x^6 + 370759680*x^7 + 119439360*x^8) + 2274845*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/134369280","A",1
2419,1,87,158,0.0525644,"\int (5-x) (3+2 x)^3 \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(3/2),x]","\frac{429695 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(17418240 x^7+25297920 x^6-368236800 x^5-1650151296 x^4-2993047920 x^3-2762417688 x^2-1276112350 x-233137461\right)}{34836480}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-233137461 - 1276112350*x - 2762417688*x^2 - 2993047920*x^3 - 1650151296*x^4 - 368236800*x^5 + 25297920*x^6 + 17418240*x^7) + 429695*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/34836480","A",1
2420,1,82,133,0.0548172,"\int (5-x) (3+2 x)^2 \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(3/2),x]","\frac{39515 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(1244160 x^6-311040 x^5-27084672 x^4-79049520 x^3-94861176 x^2-51971350 x-10669737\right)}{4354560}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-10669737 - 51971350*x - 94861176*x^2 - 79049520*x^3 - 27084672*x^4 - 311040*x^5 + 1244160*x^6) + 39515*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/4354560","A",1
2421,1,77,108,0.0372584,"\int (5-x) (3+2 x) \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)*(2 + 5*x + 3*x^2)^(3/2),x]","\frac{4195 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(103680 x^5-210816 x^4-2032560 x^3-3567288 x^2-2406950 x-561921\right)}{622080}","\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-561921 - 2406950*x - 3567288*x^2 - 2032560*x^3 - 210816*x^4 + 103680*x^5) + 4195*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/622080","A",1
2422,1,72,103,0.0586366,"\int (5-x) \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(2 + 5*x + 3*x^2)^(3/2),x]","\frac{175 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(3456 x^4-13680 x^3-48792 x^2-43070 x-11589\right)}{34560}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-11589 - 43070*x - 48792*x^2 - 13680*x^3 + 3456*x^4) + 175*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/34560","A",1
2423,1,103,123,0.0441798,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{3+2 x} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x),x]","\frac{1}{768} \left(-1560 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-2011 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-2 \sqrt{3 x^2+5 x+2} \left(144 x^3-888 x^2-542 x-1277\right)\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,"(-2*Sqrt[2 + 5*x + 3*x^2]*(-1277 - 542*x - 888*x^2 + 144*x^3) - 1560*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 2011*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/768","A",1
2424,1,110,128,0.0726713,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^2} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^2,x]","\frac{1}{576} \left(2898 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+3743 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{6 \sqrt{3 x^2+5 x+2} \left(48 x^3-364 x^2+256 x+1755\right)}{2 x+3}\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,"((-6*Sqrt[2 + 5*x + 3*x^2]*(1755 + 256*x - 364*x^2 + 48*x^3))/(3 + 2*x) + 2898*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] + 3743*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/576","A",1
2425,1,110,135,0.0941419,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^3} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^3,x]","\frac{1}{320} \left(-1329 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-1715 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{20 \sqrt{3 x^2+5 x+2} \left(12 x^3-142 x^2-777 x-773\right)}{(2 x+3)^2}\right)","-\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,"((-20*Sqrt[2 + 5*x + 3*x^2]*(-773 - 777*x - 142*x^2 + 12*x^3))/(3 + 2*x)^2 - 1329*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 1715*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/320","A",1
2426,1,110,137,0.0996693,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^4} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^4,x]","\frac{5919 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+7650 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{10 \sqrt{3 x^2+5 x+2} \left(720 x^3+13176 x^2+30878 x+19751\right)}{(2 x+3)^3}}{4800}","\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,"((-10*Sqrt[2 + 5*x + 3*x^2]*(19751 + 30878*x + 13176*x^2 + 720*x^3))/(3 + 2*x)^3 + 5919*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] + 7650*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/4800","A",1
2427,1,110,137,0.111074,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^5} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^5,x]","\frac{-7077 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-9000 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+\frac{10 \sqrt{3 x^2+5 x+2} \left(60576 x^3+190412 x^2+211148 x+82989\right)}{(2 x+3)^4}}{96000}","\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,"((10*Sqrt[2 + 5*x + 3*x^2]*(82989 + 211148*x + 190412*x^2 + 60576*x^3))/(3 + 2*x)^4 - 7077*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 9000*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/96000","A",1
2428,1,128,124,0.0763041,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^6} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^6,x]","-\frac{83200 \left(3 x^2+5 x+2\right)^{5/2}-47 (2 x+3) \left(-30 (8 x+7) \sqrt{3 x^2+5 x+2} (2 x+3)^2+400 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}-3 \sqrt{5} (2 x+3)^4 \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)}{160000 (2 x+3)^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,"-1/160000*(83200*(2 + 5*x + 3*x^2)^(5/2) - 47*(3 + 2*x)*(-30*(3 + 2*x)^2*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2] + 400*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2) - 3*Sqrt[5]*(3 + 2*x)^4*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/(3 + 2*x)^5","A",1
2429,1,151,149,0.0910002,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^7} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^7,x]","\frac{1}{30} \left(-\frac{334 \left(3 x^2+5 x+2\right)^{5/2}}{25 (2 x+3)^5}-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{(2 x+3)^6}+\frac{1141 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{400 (2 x+3)^4}-\frac{3423 \left(\frac{10 \sqrt{3 x^2+5 x+2} (8 x+7)}{(2 x+3)^2}+\sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)}{160000}\right)","-\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)*(2 + 5*x + 3*x^2)^(3/2))/(400*(3 + 2*x)^4) - (13*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^6 - (334*(2 + 5*x + 3*x^2)^(5/2))/(25*(3 + 2*x)^5) - (3423*((10*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2 + Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/160000)/30","A",1
2430,1,157,174,0.1475121,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^8} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^8,x]","\frac{1}{35} \left(-\frac{4892 \left(3 x^2+5 x+2\right)^{5/2}}{375 (2 x+3)^5}-\frac{433 \left(3 x^2+5 x+2\right)^{5/2}}{30 (2 x+3)^6}-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{(2 x+3)^7}+\frac{32641 \left(\frac{10 \sqrt{3 x^2+5 x+2} \left(864 x^3+2068 x^2+1572 x+371\right)}{(2 x+3)^4}-3 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)}{4800000}\right)","-\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,"((-13*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^7 - (433*(2 + 5*x + 3*x^2)^(5/2))/(30*(3 + 2*x)^6) - (4892*(2 + 5*x + 3*x^2)^(5/2))/(375*(3 + 2*x)^5) + (32641*((10*Sqrt[2 + 5*x + 3*x^2]*(371 + 1572*x + 2068*x^2 + 864*x^3))/(3 + 2*x)^4 - 3*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/4800000)/35","A",1
2431,1,182,199,0.1251072,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^9} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^9,x]","\frac{1}{40} \left(-\frac{7758 \left(3 x^2+5 x+2\right)^{5/2}}{625 (2 x+3)^5}-\frac{717 \left(3 x^2+5 x+2\right)^{5/2}}{50 (2 x+3)^6}-\frac{76 \left(3 x^2+5 x+2\right)^{5/2}}{5 (2 x+3)^7}-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{(2 x+3)^8}+\frac{51309 \left(\frac{10 \sqrt{3 x^2+5 x+2} \left(864 x^3+2068 x^2+1572 x+371\right)}{(2 x+3)^4}-3 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)}{8000000}\right)","-\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,"((-13*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^8 - (76*(2 + 5*x + 3*x^2)^(5/2))/(5*(3 + 2*x)^7) - (717*(2 + 5*x + 3*x^2)^(5/2))/(50*(3 + 2*x)^6) - (7758*(2 + 5*x + 3*x^2)^(5/2))/(625*(3 + 2*x)^5) + (51309*((10*Sqrt[2 + 5*x + 3*x^2]*(371 + 1572*x + 2068*x^2 + 864*x^3))/(3 + 2*x)^4 - 3*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/8000000)/40","A",1
2432,1,102,206,0.0710568,"\int (5-x) (3+2 x)^4 \left(2+5 x+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^4*(2 + 5*x + 3*x^2)^(5/2),x]","\frac{-95980115 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(180592312320 x^{10}+875872714752 x^9-1932170526720 x^8-25759323039744 x^7-90095929758720 x^6-172473366866688 x^5-204855126595200 x^4-155155370878800 x^3-73069860056520 x^2-19521700361210 x-2261297826735\right)}{82771476480}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-2261297826735 - 19521700361210*x - 73069860056520*x^2 - 155155370878800*x^3 - 204855126595200*x^4 - 172473366866688*x^5 - 90095929758720*x^6 - 25759323039744*x^7 - 1932170526720*x^8 + 875872714752*x^9 + 180592312320*x^10) - 95980115*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/82771476480","A",1
2433,1,97,181,0.0622148,"\int (5-x) (3+2 x)^3 \left(2+5 x+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(5/2),x]","\frac{-6402095 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(9029615616 x^9+29262643200 x^8-147947046912 x^7-1086687912960 x^6-2893044950784 x^5-4253933381760 x^4-3762746217360 x^3-1995914277480 x^2-585749416130 x-73178684475\right)}{7524679680}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-73178684475 - 585749416130*x - 1995914277480*x^2 - 3762746217360*x^3 - 4253933381760*x^4 - 2893044950784*x^5 - 1086687912960*x^6 - 147947046912*x^7 + 29262643200*x^8 + 9029615616*x^9) - 6402095*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/7524679680","A",1
2434,1,92,156,0.0544309,"\int (5-x) (3+2 x)^2 \left(2+5 x+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(5/2),x]","\frac{-157745 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(167215104 x^8+268240896 x^7-3275873280 x^6-15455860992 x^5-30355761024 x^4-32476001904 x^3-19762157208 x^2-6434937470 x-871825317\right)}{250822656}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-871825317 - 6434937470*x - 19762157208*x^2 - 32476001904*x^3 - 30355761024*x^4 - 15455860992*x^5 - 3275873280*x^6 + 268240896*x^7 + 167215104*x^8) - 157745*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/250822656","A",1
2435,1,101,131,0.0785279,"\int (5-x) (3+2 x) \left(2+5 x+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)*(2 + 5*x + 3*x^2)^(5/2),x]","\frac{373 \left(6 \sqrt{3 x^2+5 x+2} \left(20736 x^5+86400 x^4+142128 x^3+115320 x^2+46166 x+7305\right)-5 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)\right)}{3981312}-\frac{1}{168} (14 x-71) \left(3 x^2+5 x+2\right)^{7/2}","\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,"-1/168*((-71 + 14*x)*(2 + 5*x + 3*x^2)^(7/2)) + (373*(6*Sqrt[2 + 5*x + 3*x^2]*(7305 + 46166*x + 115320*x^2 + 142128*x^3 + 86400*x^4 + 20736*x^5) - 5*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])]))/3981312","A",1
2436,1,108,126,0.0635732,"\int (5-x) \left(2+5 x+3 x^2\right)^{5/2} \, dx","Integrate[(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 \left(\sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+6 \sqrt{3 x^2+5 x+2} \left(144 x^3+360 x^2+290 x+75\right)\right)}{497664}","-\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,"(35*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/216 - (2 + 5*x + 3*x^2)^(7/2)/21 - (175*(6*Sqrt[2 + 5*x + 3*x^2]*(75 + 290*x + 360*x^2 + 144*x^3) + Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])]))/497664","A",1
2437,1,113,146,0.0606712,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{3+2 x} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x),x]","\frac{-2106000 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-2719055 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(103680 x^5-376704 x^4-1311120 x^3-1624872 x^2-583490 x-580299\right)}{829440}","\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-580299 - 583490*x - 1624872*x^2 - 1311120*x^3 - 376704*x^4 + 103680*x^5) - 2106000*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 2719055*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/829440","A",1
2438,1,120,151,0.0882888,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^2} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^2,x]","\frac{159000 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+205265 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{2 \sqrt{3 x^2+5 x+2} \left(6912 x^5-28512 x^4-80064 x^3-118996 x^2+40412 x+293973\right)}{2 x+3}}{15360}","-\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,"((-2*Sqrt[2 + 5*x + 3*x^2]*(293973 + 40412*x - 118996*x^2 - 80064*x^3 - 28512*x^4 + 6912*x^5))/(3 + 2*x) + 159000*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] + 205265*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/15360","A",1
2439,1,120,160,0.0937654,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^3} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^3,x]","\frac{-154620 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-199615 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{6 \sqrt{3 x^2+5 x+2} \left(1728 x^5-8544 x^4-14456 x^3-57292 x^2-290742 x-295719\right)}{(2 x+3)^2}}{9216}","-\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,"((-6*Sqrt[2 + 5*x + 3*x^2]*(-295719 - 290742*x - 57292*x^2 - 14456*x^3 - 8544*x^4 + 1728*x^5))/(3 + 2*x)^2 - 154620*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 199615*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/9216","A",1
2440,1,120,165,0.0981616,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^4} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^4,x]","\frac{1}{768} \left(10461 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+13505 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{4 \sqrt{3 x^2+5 x+2} \left(288 x^5-1896 x^4+1944 x^3+64332 x^2+143533 x+89224\right)}{(2 x+3)^3}\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,"((-4*Sqrt[2 + 5*x + 3*x^2]*(89224 + 143533*x + 64332*x^2 + 1944*x^3 - 1896*x^4 + 288*x^5))/(3 + 2*x)^3 + 10461*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] + 13505*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/768","A",1
2441,1,120,167,0.1291239,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^5} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^5,x]","\frac{-87141 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-112500 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{10 \sqrt{3 x^2+5 x+2} \left(3456 x^5-39744 x^4-533280 x^3-1672268 x^2-2059268 x-896721\right)}{(2 x+3)^4}}{15360}","-\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,"((-10*Sqrt[2 + 5*x + 3*x^2]*(-896721 - 2059268*x - 1672268*x^2 - 533280*x^3 - 39744*x^4 + 3456*x^5))/(3 + 2*x)^4 - 87141*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 112500*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/15360","A",1
2442,1,120,167,0.1438363,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^6} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^6,x]","\frac{411333 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+531000 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{10 \sqrt{3 x^2+5 x+2} \left(172800 x^5+4630848 x^4+21586808 x^3+41641148 x^2+37019838 x+12600183\right)}{(2 x+3)^5}}{384000}","\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,"((-10*Sqrt[2 + 5*x + 3*x^2]*(12600183 + 37019838*x + 41641148*x^2 + 21586808*x^3 + 4630848*x^4 + 172800*x^5))/(3 + 2*x)^5 + 411333*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] + 531000*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/384000","A",1
2443,1,120,167,0.1492212,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^7} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^7,x]","\frac{-41793 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-54000 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+\frac{10 \sqrt{3 x^2+5 x+2} \left(1351296 x^5+7629680 x^4+18217760 x^3+22854480 x^2+14921560 x+4015849\right)}{(2 x+3)^6}}{768000}","\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,"((10*Sqrt[2 + 5*x + 3*x^2]*(4015849 + 14921560*x + 22854480*x^2 + 18217760*x^3 + 7629680*x^4 + 1351296*x^5))/(3 + 2*x)^6 - 41793*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 54000*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/768000","A",1
2444,1,154,154,0.0781135,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^8} \, dx","Integrate[((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 \left(\frac{10 \sqrt{3 x^2+5 x+2} (8 x+7)}{(2 x+3)^2}+\sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)}{1280000}","-\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)*(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*((10*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2 + Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/1280000","A",1
2445,1,182,179,0.1759418,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^9} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^9,x]","\frac{1}{40} \left(-\frac{428 \left(3 x^2+5 x+2\right)^{7/2}}{35 (2 x+3)^7}-\frac{13 \left(3 x^2+5 x+2\right)^{7/2}}{(2 x+3)^8}+\frac{1517 \left(\frac{32 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{(2 x+3)^6}-\frac{2 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{(2 x+3)^4}+\frac{3 (8 x+7) \sqrt{3 x^2+5 x+2}}{20 (2 x+3)^2}+\frac{3 \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40 \sqrt{5}}\right)}{19200}\right)","-\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,"((-13*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^8 - (428*(2 + 5*x + 3*x^2)^(7/2))/(35*(3 + 2*x)^7) + (1517*((3*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(20*(3 + 2*x)^2) - (2*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^4 + (32*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^6 + (3*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(40*Sqrt[5])))/19200)/40","A",1
2446,1,207,204,0.1497923,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{10}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^10,x]","\frac{1}{45} \left(-\frac{3963 \left(3 x^2+5 x+2\right)^{7/2}}{350 (2 x+3)^7}-\frac{527 \left(3 x^2+5 x+2\right)^{7/2}}{40 (2 x+3)^8}-\frac{13 \left(3 x^2+5 x+2\right)^{7/2}}{(2 x+3)^9}+\frac{18501 \left(\frac{32 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{(2 x+3)^6}-\frac{2 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{(2 x+3)^4}+\frac{3 (8 x+7) \sqrt{3 x^2+5 x+2}}{20 (2 x+3)^2}+\frac{3 \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40 \sqrt{5}}\right)}{256000}\right)","-\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,"((-13*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^9 - (527*(2 + 5*x + 3*x^2)^(7/2))/(40*(3 + 2*x)^8) - (3963*(2 + 5*x + 3*x^2)^(7/2))/(350*(3 + 2*x)^7) + (18501*((3*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(20*(3 + 2*x)^2) - (2*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^4 + (32*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^6 + (3*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(40*Sqrt[5])))/256000)/45","A",1
2447,1,184,229,0.2194079,"\int (5-x) (3+2 x)^4 \left(2+5 x+3 x^2\right)^{7/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^4*(2 + 5*x + 3*x^2)^(7/2),x]","\frac{-36 (2 x+3)^4 \left(3 x^2+5 x+2\right)^{9/2}+439 (2 x+3)^3 \left(3 x^2+5 x+2\right)^{9/2}+820 (2 x+3)^2 \left(3 x^2+5 x+2\right)^{9/2}+\frac{1}{162} (389394 x+852175) \left(3 x^2+5 x+2\right)^{9/2}+\frac{964171 \left(35 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+6 \sqrt{3 x^2+5 x+2} \left(4478976 x^7+26127360 x^6+64800000 x^5+88560000 x^4+72023472 x^3+34858680 x^2+9298342 x+1054785\right)\right)}{286654464}}{1404}","-\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,"(820*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(9/2) + 439*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(9/2) - 36*(3 + 2*x)^4*(2 + 5*x + 3*x^2)^(9/2) + ((852175 + 389394*x)*(2 + 5*x + 3*x^2)^(9/2))/162 + (964171*(6*Sqrt[2 + 5*x + 3*x^2]*(1054785 + 9298342*x + 34858680*x^2 + 72023472*x^3 + 88560000*x^4 + 64800000*x^5 + 26127360*x^6 + 4478976*x^7) + 35*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])]))/286654464)/1404","A",1
2448,1,163,204,0.1477041,"\int (5-x) (3+2 x)^3 \left(2+5 x+3 x^2\right)^{7/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(7/2),x]","\frac{1}{36} \left(-(2 x+3)^3 \left(3 x^2+5 x+2\right)^{9/2}+\frac{136}{11} (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}}{8910}+\frac{91087 \left(35 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+6 \sqrt{3 x^2+5 x+2} \left(4478976 x^7+26127360 x^6+64800000 x^5+88560000 x^4+72023472 x^3+34858680 x^2+9298342 x+1054785\right)\right)}{1433272320}\right)","-\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,"((136*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(9/2))/11 - (3 + 2*x)^3*(2 + 5*x + 3*x^2)^(9/2) + ((863825 + 390798*x)*(2 + 5*x + 3*x^2)^(9/2))/8910 + (91087*(6*Sqrt[2 + 5*x + 3*x^2]*(1054785 + 9298342*x + 34858680*x^2 + 72023472*x^3 + 88560000*x^4 + 64800000*x^5 + 26127360*x^6 + 4478976*x^7) + 35*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])]))/1433272320)/36","A",1
2449,1,138,179,0.1427043,"\int (5-x) (3+2 x)^2 \left(2+5 x+3 x^2\right)^{7/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(7/2),x]","\frac{1}{33} \left(-(2 x+3)^2 \left(3 x^2+5 x+2\right)^{9/2}+\frac{1}{810} (20358 x+47425) \left(3 x^2+5 x+2\right)^{9/2}+\frac{61897 \left(35 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+6 \sqrt{3 x^2+5 x+2} \left(4478976 x^7+26127360 x^6+64800000 x^5+88560000 x^4+72023472 x^3+34858680 x^2+9298342 x+1054785\right)\right)}{1433272320}\right)","-\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,"(-((3 + 2*x)^2*(2 + 5*x + 3*x^2)^(9/2)) + ((47425 + 20358*x)*(2 + 5*x + 3*x^2)^(9/2))/810 + (61897*(6*Sqrt[2 + 5*x + 3*x^2]*(1054785 + 9298342*x + 34858680*x^2 + 72023472*x^3 + 88560000*x^4 + 64800000*x^5 + 26127360*x^6 + 4478976*x^7) + 35*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])]))/1433272320)/33","A",1
2450,1,111,154,0.0552192,"\int (5-x) (3+2 x) \left(2+5 x+3 x^2\right)^{7/2} \, dx","Integrate[(5 - x)*(3 + 2*x)*(2 + 5*x + 3*x^2)^(7/2),x]","\frac{1399 \left(35 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+6 \sqrt{3 x^2+5 x+2} \left(4478976 x^7+26127360 x^6+64800000 x^5+88560000 x^4+72023472 x^3+34858680 x^2+9298342 x+1054785\right)\right)}{1433272320}-\frac{1}{810} (54 x-265) \left(3 x^2+5 x+2\right)^{9/2}","\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,"-1/810*((-265 + 54*x)*(2 + 5*x + 3*x^2)^(9/2)) + (1399*(6*Sqrt[2 + 5*x + 3*x^2]*(1054785 + 9298342*x + 34858680*x^2 + 72023472*x^3 + 88560000*x^4 + 64800000*x^5 + 26127360*x^6 + 4478976*x^7) + 35*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])]))/1433272320","A",1
2451,1,119,149,0.1205145,"\int (5-x) \left(2+5 x+3 x^2\right)^{7/2} \, dx","Integrate[(5 - x)*(2 + 5*x + 3*x^2)^(7/2),x]","\frac{-64 \left(3 x^2+5 x+2\right)^{9/2}+210 (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}-\frac{245 \left(6 \sqrt{3 x^2+5 x+2} \left(20736 x^5+86400 x^4+142128 x^3+115320 x^2+46166 x+7305\right)-5 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)\right)}{27648}}{1728}","-\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,"(210*(5 + 6*x)*(2 + 5*x + 3*x^2)^(7/2) - 64*(2 + 5*x + 3*x^2)^(9/2) - (245*(6*Sqrt[2 + 5*x + 3*x^2]*(7305 + 46166*x + 115320*x^2 + 142128*x^3 + 86400*x^4 + 20736*x^5) - 5*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])]))/27648)/1728","A",1
2452,1,123,169,0.0776309,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{3+2 x} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x),x]","\frac{-353808000 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-456762005 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(31352832 x^7-50015232 x^6-529784064 x^5-1167854976 x^4-1224844848 x^3-722869752 x^2-185981750 x-101435865\right)}{111476736}","\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-101435865 - 185981750*x - 722869752*x^2 - 1224844848*x^3 - 1167854976*x^4 - 529784064*x^5 - 50015232*x^6 + 31352832*x^7) - 353808000*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 456762005*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/111476736","A",1
2453,1,130,174,0.1066961,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^2} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^2,x]","\frac{418446000 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+540211805 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{6 \sqrt{3 x^2+5 x+2} \left(7464960 x^7-13893120 x^6-125632512 x^5-273531168 x^4-275126016 x^3-179819084 x^2+28017108 x+259165107\right)}{2 x+3}}{23224320}","-\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,"((-6*Sqrt[2 + 5*x + 3*x^2]*(259165107 + 28017108*x - 179819084*x^2 - 275126016*x^3 - 273531168*x^4 - 125632512*x^5 - 13893120*x^6 + 7464960*x^7))/(3 + 2*x) + 418446000*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] + 540211805*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/23224320","A",1
2454,1,130,181,0.1080899,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^3} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^3,x]","\frac{-48195000 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-62219465 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{6 \sqrt{3 x^2+5 x+2} \left(414720 x^7-926208 x^6-6830784 x^5-15112992 x^4-12848072 x^3-19284852 x^2-89867034 x-91912653\right)}{(2 x+3)^2}}{1105920}","-\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,"((-6*Sqrt[2 + 5*x + 3*x^2]*(-91912653 - 89867034*x - 19284852*x^2 - 12848072*x^3 - 15112992*x^4 - 6830784*x^5 - 926208*x^6 + 414720*x^7))/(3 + 2*x)^2 - 48195000*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 62219465*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/1105920","A",1
2455,1,130,190,0.1102824,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^4} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^4,x]","\frac{10754100 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+13883485 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{6 \sqrt{3 x^2+5 x+2} \left(82944 x^7-231552 x^6-1266816 x^5-3277520 x^4+746240 x^3+44770416 x^2+98927312 x+61268351\right)}{(2 x+3)^3}}{184320}","-\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,"((-6*Sqrt[2 + 5*x + 3*x^2]*(61268351 + 98927312*x + 44770416*x^2 + 746240*x^3 - 3277520*x^4 - 1266816*x^5 - 231552*x^6 + 82944*x^7))/(3 + 2*x)^3 + 10754100*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] + 13883485*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/184320","A",1
2456,1,130,195,0.1197582,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^5} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^5,x]","\frac{-576513 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-744275 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{12 \sqrt{3 x^2+5 x+2} \left(3456 x^7-12864 x^6-38288 x^5-253688 x^4-2869312 x^3-9107922 x^2-11295211 x-4933171\right)}{(2 x+3)^4}}{12288}","-\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,"((-12*Sqrt[2 + 5*x + 3*x^2]*(-4933171 - 11295211*x - 9107922*x^2 - 2869312*x^3 - 253688*x^4 - 38288*x^5 - 12864*x^6 + 3456*x^7))/(3 + 2*x)^4 - 576513*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 744275*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/12288","A",1
2457,1,130,197,0.1535496,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^6} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^6,x]","\frac{2345091 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+3027500 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{10 \sqrt{3 x^2+5 x+2} \left(46080 x^7-257280 x^6+483840 x^5+27897856 x^4+127665096 x^3+242016116 x^2+213122626 x+72189541\right)}{(2 x+3)^5}}{102400}","-\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,"((-10*Sqrt[2 + 5*x + 3*x^2]*(72189541 + 213122626*x + 242016116*x^2 + 127665096*x^3 + 27897856*x^4 + 483840*x^5 - 257280*x^6 + 46080*x^7))/(3 + 2*x)^5 + 2345091*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] + 3027500*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/102400","A",1
2458,1,130,197,0.1716678,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^7} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^7,x]","\frac{-19861443 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-25641000 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{10 \sqrt{3 x^2+5 x+2} \left(2073600 x^7-23155200 x^6-550079616 x^5-2968126160 x^4-7425343520 x^3-9799959120 x^2-6648875480 x-1835461379\right)}{(2 x+3)^6}}{3072000}","-\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,"((-10*Sqrt[2 + 5*x + 3*x^2]*(-1835461379 - 6648875480*x - 9799959120*x^2 - 7425343520*x^3 - 2968126160*x^4 - 550079616*x^5 - 23155200*x^6 + 2073600*x^7))/(3 + 2*x)^6 - 19861443*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 25641000*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/3072000","A",1
2459,1,130,197,0.1815706,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^8} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^8,x]","\frac{6539127 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+8442000 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-\frac{10 \sqrt{3 x^2+5 x+2} \left(9676800 x^7+338443008 x^6+2361590432 x^5+7622049520 x^4+13619671040 x^3+13975079520 x^2+7753535702 x+1810375853\right)}{(2 x+3)^7}}{7168000}","\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,"((-10*Sqrt[2 + 5*x + 3*x^2]*(1810375853 + 7753535702*x + 13975079520*x^2 + 13619671040*x^3 + 7622049520*x^4 + 2361590432*x^5 + 338443008*x^6 + 9676800*x^7))/(3 + 2*x)^7 + 6539127*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] + 8442000*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/7168000","A",1
2460,1,130,197,0.1902858,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^9} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^9,x]","\frac{-11712477 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-15120000 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+\frac{10 \sqrt{3 x^2+5 x+2} \left(1478785536 x^7+12182619328 x^6+45214440256 x^5+97176896240 x^4+129405924160 x^3+105874603844 x^2+48950756372 x+9818427389\right)}{(2 x+3)^8}}{286720000}","\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,"((10*Sqrt[2 + 5*x + 3*x^2]*(9818427389 + 48950756372*x + 105874603844*x^2 + 129405924160*x^3 + 97176896240*x^4 + 45214440256*x^5 + 12182619328*x^6 + 1478785536*x^7))/(3 + 2*x)^8 - 11712477*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 15120000*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/286720000","A",1
2461,1,185,184,0.1367298,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^{10}} \, dx","Integrate[((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 \left(\frac{32 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{(2 x+3)^6}-\frac{2 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{(2 x+3)^4}+\frac{3 (8 x+7) \sqrt{3 x^2+5 x+2}}{20 (2 x+3)^2}+\frac{3 \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40 \sqrt{5}}\right)}{3072000}","-\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,"(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*((3*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(20*(3 + 2*x)^2) - (2*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^4 + (32*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^6 + (3*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(40*Sqrt[5])))/3072000","A",1
2462,1,212,209,0.1612295,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^{11}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^11,x]","\frac{1}{50} \left(-\frac{58 \left(3 x^2+5 x+2\right)^{9/2}}{5 (2 x+3)^9}-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{(2 x+3)^{10}}+\frac{1893 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{800 (2 x+3)^8}-\frac{4417 \left(\frac{32 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{(2 x+3)^6}-\frac{2 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{(2 x+3)^4}+\frac{3 (8 x+7) \sqrt{3 x^2+5 x+2}}{20 (2 x+3)^2}+\frac{3 \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40 \sqrt{5}}\right)}{1024000}\right)","-\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,"((1893*(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))/(3 + 2*x)^10 - (58*(2 + 5*x + 3*x^2)^(9/2))/(5*(3 + 2*x)^9) - (4417*((3*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(20*(3 + 2*x)^2) - (2*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^4 + (32*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^6 + (3*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(40*Sqrt[5])))/1024000)/50","A",1
2463,1,239,234,0.3078916,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^{12}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^12,x]","\frac{1}{55} \left(-\frac{3904 \left(3 x^2+5 x+2\right)^{9/2}}{375 (2 x+3)^9}-\frac{621 \left(3 x^2+5 x+2\right)^{9/2}}{50 (2 x+3)^{10}}-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{(2 x+3)^{11}}+\frac{84381 \left(\frac{2 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{(2 x+3)^8}-\frac{7 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{60 (2 x+3)^6}+\frac{7 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{960 (2 x+3)^4}-\frac{7 \left(\frac{10 \sqrt{3 x^2+5 x+2} (8 x+7)}{(2 x+3)^2}+\sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)}{128000}\right)}{80000}\right)","-\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,"((-13*(2 + 5*x + 3*x^2)^(9/2))/(3 + 2*x)^11 - (621*(2 + 5*x + 3*x^2)^(9/2))/(50*(3 + 2*x)^10) - (3904*(2 + 5*x + 3*x^2)^(9/2))/(375*(3 + 2*x)^9) + (84381*((7*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(960*(3 + 2*x)^4) - (7*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(60*(3 + 2*x)^6) + (2*(7 + 8*x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^8 - (7*((10*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2 + Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/128000))/80000)/55","A",1
2464,1,262,259,0.2406254,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^{13}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^13,x]","\frac{-\frac{12758 \left(3 x^2+5 x+2\right)^{9/2}}{25 (2 x+3)^9}-\frac{6201 \left(3 x^2+5 x+2\right)^{9/2}}{10 (2 x+3)^{10}}-\frac{720 \left(3 x^2+5 x+2\right)^{9/2}}{(2 x+3)^{11}}-\frac{715 \left(3 x^2+5 x+2\right)^{9/2}}{(2 x+3)^{12}}+\frac{825561 \left(\frac{2 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{(2 x+3)^8}-\frac{7 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{60 (2 x+3)^6}+\frac{7 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{960 (2 x+3)^4}-\frac{7 \left(\frac{10 \sqrt{3 x^2+5 x+2} (8 x+7)}{(2 x+3)^2}+\sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)}{128000}\right)}{16000}}{3300}","-\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,"((-715*(2 + 5*x + 3*x^2)^(9/2))/(3 + 2*x)^12 - (720*(2 + 5*x + 3*x^2)^(9/2))/(3 + 2*x)^11 - (6201*(2 + 5*x + 3*x^2)^(9/2))/(10*(3 + 2*x)^10) - (12758*(2 + 5*x + 3*x^2)^(9/2))/(25*(3 + 2*x)^9) + (825561*((7*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(960*(3 + 2*x)^4) - (7*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(60*(3 + 2*x)^6) + (2*(7 + 8*x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^8 - (7*((10*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2 + Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/128000))/16000)/3300","A",1
2465,1,357,407,0.5275743,"\int \frac{(A+B x) (d+e x)^3}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{c} \sqrt{a+x (b+c x)} \left(8 A c e \left(-2 c e (8 a e+27 b d+5 b e x)+15 b^2 e^2+4 c^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+B \left(-8 c^2 e \left(3 a e (16 d+3 e x)+b \left(54 d^2+30 d e x+7 e^2 x^2\right)\right)+10 b c e^2 (22 a e+36 b d+7 b e x)-105 b^3 e^3+48 c^3 \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)\right)\right)+3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\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(a e^2-4 c d^2\right)\right)-40 b^3 c e^2 (A e+3 B d)+35 b^4 B e^3\right)}{384 c^{9/2}}","\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,"(2*Sqrt[c]*Sqrt[a + x*(b + c*x)]*(8*A*c*e*(15*b^2*e^2 - 2*c*e*(27*b*d + 8*a*e + 5*b*e*x) + 4*c^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2)) + B*(-105*b^3*e^3 + 10*b*c*e^2*(36*b*d + 22*a*e + 7*b*e*x) + 48*c^3*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) - 8*c^2*e*(3*a*e*(16*d + 3*e*x) + b*(54*d^2 + 30*d*e*x + 7*e^2*x^2)))) + 3*(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 + x*(b + c*x)])])/(384*c^(9/2))","A",1
2466,1,225,234,0.1979531,"\int \frac{(A+B x) (d+e x)^2}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/Sqrt[a + b*x + c*x^2],x]","\frac{\frac{\sqrt{a+x (b+c x)} \left(B \left(-2 c e (8 a e+18 b d+5 b e x)+15 b^2 e^2+8 c^2 d (2 d+e x)\right)+6 A c e (-3 b e+8 c d+2 c e x)\right)}{8 c^2}-\frac{3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\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^{5/2}}+B (d+e x)^2 \sqrt{a+x (b+c x)}}{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 + x*(b + c*x)] + (Sqrt[a + x*(b + c*x)]*(6*A*c*e*(8*c*d - 3*b*e + 2*c*e*x) + B*(15*b^2*e^2 + 8*c^2*d*(2*d + e*x) - 2*c*e*(18*b*d + 8*a*e + 5*b*e*x))))/(8*c^2) - (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 + x*(b + c*x)])])/(16*c^(5/2)))/(3*c)","A",1
2467,1,115,116,0.0711875,"\int \frac{(A+B x) (d+e x)}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((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+x (b+c x)}}\right) \left(-2 a B c e-2 b c (A e+B d)+4 A c^2 d+\frac{3}{2} b^2 B e\right)+\sqrt{c} \sqrt{a+x (b+c x)} (4 A c e+B (-3 b e+4 c d+2 c e x))}{4 c^{5/2}}","\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,"(Sqrt[c]*Sqrt[a + x*(b + c*x)]*(4*A*c*e + B*(4*c*d - 3*b*e + 2*c*e*x)) + (4*A*c^2*d + (3*b^2*B*e)/2 - 2*a*B*c*e - 2*b*c*(B*d + A*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(4*c^(5/2))","A",1
2468,1,66,67,0.0896203,"\int \frac{A+B x}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/Sqrt[a + b*x + c*x^2],x]","\frac{(2 A c-b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{2 c^{3/2}}+\frac{B \sqrt{a+x (b+c x)}}{c}","\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 + x*(b + c*x)])/c + ((-(b*B) + 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(2*c^(3/2))","A",1
2469,1,126,132,0.1533378,"\int \frac{A+B x}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{\frac{(B d-A e) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{\sqrt{e (a e-b d)+c d^2}}+\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{\sqrt{c}}}{e}","\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 + x*(b + c*x)])])/Sqrt[c] + ((B*d - A*e)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/Sqrt[c*d^2 + e*(-(b*d) + a*e)])/e","A",1
2470,1,147,150,0.090629,"\int \frac{A+B x}{(d+e x)^2 \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^2*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+x (b+c x)} (B d-A e)}{(d+e x) \left(e (a e-b d)+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-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{2 \left(e (a e-b d)+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 + x*(b + c*x)])/((c*d^2 + e*(-(b*d) + a*e))*(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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(2*(c*d^2 + e*(-(b*d) + a*e))^(3/2))","A",1
2471,1,264,271,0.4572489,"\int \frac{A+B x}{(d+e x)^3 \sqrt{a+b x+c x^2}} \, dx","Integrate[(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-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{8 \left(e (a e-b d)+c d^2\right)^{5/2}}+\frac{\sqrt{a+x (b+c x)} (B d-A e)}{2 (d+e x)^2 \left(e (a e-b d)+c d^2\right)}+\frac{\sqrt{a+x (b+c x)} \left(B e (b d-4 a e)+3 A e (b e-2 c d)+2 B c d^2\right)}{4 (d+e x) \left(e (a e-b d)+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 + x*(b + c*x)])/(2*(c*d^2 + e*(-(b*d) + a*e))*(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 + x*(b + c*x)])/(4*(c*d^2 + e*(-(b*d) + a*e))^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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(8*(c*d^2 + e*(-(b*d) + a*e))^(5/2))","A",1
2472,1,434,444,0.9291824,"\int \frac{A+B x}{(d+e x)^4 \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^4*Sqrt[a + b*x + c*x^2]),x]","\frac{\frac{\sqrt{a+x (b+c x)} \left(A e \left(4 c e (4 a e+11 b d)-15 b^2 e^2-44 c^2 d^2\right)+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)\right)}{4 (d+e x) \left(e (a e-b d)+c d^2\right)}+\frac{3 \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(3 a e^2-2 c d^2\right)+a B e \left(a e^2-4 c d^2\right)\right)+b^3 e^2 (5 A e+B d)\right) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{8 \left(e (a e-b d)+c d^2\right)^{3/2}}+\frac{2 \sqrt{a+x (b+c x)} (B d-A e) \left(e (a e-b d)+c d^2\right)}{(d+e x)^3}+\frac{\sqrt{a+x (b+c x)} \left(B e (b d-6 a e)+5 A e (b e-2 c d)+4 B c d^2\right)}{2 (d+e x)^2}}{6 \left(e (a e-b d)+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,"((2*(B*d - A*e)*(c*d^2 + e*(-(b*d) + a*e))*Sqrt[a + x*(b + c*x)])/(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 + x*(b + c*x)])/(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 + x*(b + c*x)])/(4*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)) + (3*(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*B*e*(-4*c*d^2 + a*e^2) + A*c*d*(-2*c*d^2 + 3*a*e^2)))*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(8*(c*d^2 + e*(-(b*d) + a*e))^(3/2)))/(6*(c*d^2 + e*(-(b*d) + a*e))^2)","A",1
2473,1,426,325,0.6401243,"\int \frac{(A+B x) (d+e x)^3}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a + b*x + c*x^2)^(3/2),x]","\frac{-2 \sqrt{c} \left(4 A c \left(-4 c \left(2 a^2 e^3+a c e \left(-3 d^2-3 d e x+e^2 x^2\right)+c^2 d^3 x\right)+b^2 e^2 (3 a e+c x (e x-6 d))-2 b c \left(a e^2 (3 d+5 e x)+c d^2 (d-3 e x)\right)+3 b^3 e^3 x\right)+B \left(-4 a^2 c e^2 (6 c (4 d+e x)-13 b e)+a \left(-15 b^3 e^3+2 b^2 c e^2 (18 d+31 e x)+4 b c^2 e \left(-6 d^2-30 d e x+5 e^2 x^2\right)+8 c^3 \left(2 d^3+6 d^2 e x-6 d e^2 x^2-e^3 x^3\right)\right)+b x \left(-15 b^3 e^3+b^2 c e^2 (36 d-5 e x)+2 b c^2 e \left(-12 d^2+6 d e x+e^2 x^2\right)+8 c^3 d^3\right)\right)\right)-3 e \left(b^2-4 a c\right) \sqrt{a+x (b+c x)} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\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} \left(4 a c-b^2\right) \sqrt{a+x (b+c x)}}","\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)}",1,"(-2*Sqrt[c]*(4*A*c*(3*b^3*e^3*x + b^2*e^2*(3*a*e + c*x*(-6*d + e*x)) - 2*b*c*(c*d^2*(d - 3*e*x) + a*e^2*(3*d + 5*e*x)) - 4*c*(2*a^2*e^3 + c^2*d^3*x + a*c*e*(-3*d^2 - 3*d*e*x + e^2*x^2))) + B*(-4*a^2*c*e^2*(-13*b*e + 6*c*(4*d + e*x)) + b*x*(8*c^3*d^3 - 15*b^3*e^3 + b^2*c*e^2*(36*d - 5*e*x) + 2*b*c^2*e*(-12*d^2 + 6*d*e*x + e^2*x^2)) + a*(-15*b^3*e^3 + 2*b^2*c*e^2*(18*d + 31*e*x) + 4*b*c^2*e*(-6*d^2 - 30*d*e*x + 5*e^2*x^2) + 8*c^3*(2*d^3 + 6*d^2*e*x - 6*d*e^2*x^2 - e^3*x^3)))) - 3*(b^2 - 4*a*c)*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)))*Sqrt[a + x*(b + c*x)]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(8*c^(7/2)*(-b^2 + 4*a*c)*Sqrt[a + x*(b + c*x)])","A",1
2474,1,238,210,0.4479412,"\int \frac{(A+B x) (d+e x)^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a + b*x + c*x^2)^(3/2),x]","\frac{\frac{2 \sqrt{c} \left(B \left(8 a^2 c e^2+a \left(-3 b^2 e^2+2 b c e (2 d+5 e x)-4 c^2 \left(d^2+2 d e x-e^2 x^2\right)\right)-b x \left(3 b^2 e^2+b c e (e x-4 d)+2 c^2 d^2\right)\right)+2 A c \left(a b e^2-2 a c e (2 d+e x)+b^2 e^2 x+b c d (d-2 e x)+2 c^2 d^2 x\right)\right)}{\sqrt{a+x (b+c x)}}+e \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right) (-2 A c e+3 b B e-4 B c d)}{2 c^{5/2} \left(4 a c-b^2\right)}","\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*Sqrt[c]*(2*A*c*(a*b*e^2 + 2*c^2*d^2*x + b^2*e^2*x + b*c*d*(d - 2*e*x) - 2*a*c*e*(2*d + e*x)) + B*(8*a^2*c*e^2 - b*x*(2*c^2*d^2 + 3*b^2*e^2 + b*c*e*(-4*d + e*x)) + a*(-3*b^2*e^2 + 2*b*c*e*(2*d + 5*e*x) - 4*c^2*(d^2 + 2*d*e*x - e^2*x^2)))))/Sqrt[a + x*(b + c*x)] + (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 + x*(b + c*x)])])/(2*c^(5/2)*(-b^2 + 4*a*c))","A",1
2475,1,127,126,0.366062,"\int \frac{(A+B x) (d+e x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{\frac{2 \sqrt{c} (A c (-2 a e+b (d-e x)+2 c d x)+B (a b e-2 a c (d+e x)+b x (b e-c d)))}{\sqrt{a+x (b+c x)}}-B e \left(b^2-4 a c\right) \log \left(2 \sqrt{c} \sqrt{a+x (b+c x)}+b+2 c x\right)}{c^{3/2} \left(4 a c-b^2\right)}","\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*Sqrt[c]*(A*c*(-2*a*e + 2*c*d*x + b*(d - e*x)) + B*(a*b*e + b*(-(c*d) + b*e)*x - 2*a*c*(d + e*x))))/Sqrt[a + x*(b + c*x)] - B*(b^2 - 4*a*c)*e*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/(c^(3/2)*(-b^2 + 4*a*c))","A",1
2476,1,44,45,0.1568041,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(a + b*x + c*x^2)^(3/2),x]","\frac{2 B (2 a+b x)-2 A (b+2 c x)}{\left(b^2-4 a c\right) \sqrt{a+x (b+c 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}}",1,"(2*B*(2*a + b*x) - 2*A*(b + 2*c*x))/((b^2 - 4*a*c)*Sqrt[a + x*(b + c*x)])","A",1
2477,1,184,188,0.1585049,"\int \frac{A+B x}{(d+e x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \left(2 A c (a e+c d x)+a B (b e-2 c d+2 c e x)-A b^2 e+A b c (d-e x)-b B c d x\right)}{\left(b^2-4 a c\right) \sqrt{a+x (b+c x)} \left(e (b d-a e)-c d^2\right)}+\frac{e (B d-A e) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{\left(e (a e-b d)+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*e) - b*B*c*d*x + 2*A*c*(a*e + c*d*x) + A*b*c*(d - e*x) + a*B*(-2*c*d + b*e + 2*c*e*x)))/((b^2 - 4*a*c)*(-(c*d^2) + e*(b*d - a*e))*Sqrt[a + x*(b + c*x)]) + (e*(B*d - A*e)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(c*d^2 + e*(-(b*d) + a*e))^(3/2)","A",1
2478,1,326,334,0.8466792,"\int \frac{A+B x}{(d+e x)^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(a + b*x + c*x^2)^(3/2)),x]","\frac{e \sqrt{a+x (b+c x)} \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(e (a e-b d)+c d^2\right)^2}+\frac{2 \left(-2 A c (a e+c d x)+a B (2 c (d-e x)-b e)+A b^2 e+A b c (e x-d)+b B c d x\right)}{\left(b^2-4 a c\right) (d+e x) \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right)}+\frac{e \left(-B e (2 a e+b d)+3 A e (b e-2 c d)+4 B c d^2\right) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{2 \left(e (a e-b d)+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,"(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 + x*(b + c*x)])/((b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e))^2*(d + e*x)) + (2*(A*b^2*e + b*B*c*d*x - 2*A*c*(a*e + c*d*x) + A*b*c*(-d + e*x) + a*B*(-(b*e) + 2*c*(d - e*x))))/((b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)*Sqrt[a + x*(b + c*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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(2*(c*d^2 + e*(-(b*d) + a*e))^(5/2))","A",1
2479,1,527,545,3.3494825,"\int \frac{A+B x}{(d+e x)^3 \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^3*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \left(\frac{3 e \left(b^2-4 a c\right) \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-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{16 \left(e (a e-b d)+c d^2\right)^{5/2}}+\frac{e \sqrt{a+x (b+c x)} \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)}{4 (d+e x)^2 \left(e (a e-b d)+c d^2\right)}+\frac{-2 A c (a e+c d x)+a B (2 c (d-e x)-b e)+A b^2 e+A b c (e x-d)+b B c d x}{(d+e x)^2 \sqrt{a+x (b+c x)}}-\frac{e \sqrt{a+x (b+c x)} \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)}{8 (d+e x) \left(e (a e-b d)+c d^2\right)^2}\right)}{\left(b^2-4 a c\right) \left(e (a e-b d)+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{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{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}",1,"(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 + x*(b + c*x)])/(4*(c*d^2 + e*(-(b*d) + a*e))*(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 + x*(b + c*x)])/(8*(c*d^2 + e*(-(b*d) + a*e))^2*(d + e*x)) + (A*b^2*e + b*B*c*d*x - 2*A*c*(a*e + c*d*x) + A*b*c*(-d + e*x) + a*B*(-(b*e) + 2*c*(d - e*x)))/((d + e*x)^2*Sqrt[a + x*(b + c*x)]) + (3*(b^2 - 4*a*c)*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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(16*(c*d^2 + e*(-(b*d) + a*e))^(5/2))))/((b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e)))","A",1
2480,1,849,608,2.3964348,"\int \frac{(A+B x) (d+e x)^4}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a + b*x + c*x^2)^(5/2),x]","\frac{(8 B c d-5 b B e+2 A c e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right) e^3}{2 c^{7/2}}+\frac{B \left(128 a^4 c^2 e^4+4 a^3 c \left(-48 \left(d^2+e x d-e^2 x^2\right) c^2+2 b e (20 d+39 e x) c-25 b^2 e^2\right) e^2+b x \left(15 e^4 x b^5+4 c e^3 x (5 e x-6 d) b^4+c^2 e^3 x^2 (3 e x-32 d) b^3-6 c^3 d^2 \left(d^2-4 e x d-2 e^2 x^2\right) b^2+8 c^4 d^3 x (2 e x-3 d) b-16 c^5 d^4 x^2\right)+a^2 \left(-16 \left(d^4+18 e^2 x^2 d^2+16 e^3 x^3 d-3 e^4 x^4\right) c^4+32 b e \left(2 d^3-9 e x d^2+8 e^3 x^3\right) c^3+48 b^2 e^3 x (7 d+e x) c^2-6 b^3 e^3 (4 d+35 e x) c+15 b^4 e^4\right)+2 a \left(15 e^4 x b^5-3 c e^3 x (8 d+15 e x) b^4+2 c^2 e^3 x^2 (36 d-37 e x) b^3-2 c^3 \left(d^4-24 e x d^3+18 e^2 x^2 d^2-56 e^3 x^3 d+6 e^4 x^4\right) b^2-12 c^4 d^2 x \left(d^2-4 e x d+6 e^2 x^2\right) b+32 c^5 d^3 e x^3\right)\right)-2 A c \left(3 e^4 x^2 b^5+2 e^4 x \left(2 c x^2+3 a\right) b^4+\left(3 a^2 e^4-18 a c x^2 e^4+c^2 d \left(d^3+12 e x d^2-18 e^2 x^2 d-4 e^3 x^3\right)\right) b^3-2 c \left(21 a^2 x e^4+2 a c \left(-2 d^3+18 e x d^2-6 e^2 x^2 d+7 e^3 x^3\right) e+3 c^2 d^2 x \left(d^2-8 e x d+2 e^2 x^2\right)\right) b^2-4 c \left(5 a^3 e^4+12 a^2 c d (d-2 e x) e^2+2 c^3 d^3 x^2 (3 d-4 e x)+3 a c^2 d \left(d^3-4 e x d^2+6 e^2 x^2 d-4 e^3 x^3\right)\right) b+8 c^2 \left(-2 c^3 x^3 d^4-3 a c^2 x \left(d^2+2 e^2 x^2\right) d^2+a^3 e^3 (8 d+3 e x)+4 a^2 c e \left(d^3+3 e^2 x^2 d+e^3 x^3\right)\right)\right)}{3 c^3 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{3/2}}","\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{2 (d+e x) \left(-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)-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)+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{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{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*A*c*(3*b^5*e^4*x^2 + 2*b^4*e^4*x*(3*a + 2*c*x^2) + b^3*(3*a^2*e^4 - 18*a*c*e^4*x^2 + c^2*d*(d^3 + 12*d^2*e*x - 18*d*e^2*x^2 - 4*e^3*x^3)) - 4*b*c*(5*a^3*e^4 + 2*c^3*d^3*x^2*(3*d - 4*e*x) + 12*a^2*c*d*e^2*(d - 2*e*x) + 3*a*c^2*d*(d^3 - 4*d^2*e*x + 6*d*e^2*x^2 - 4*e^3*x^3)) + 8*c^2*(-2*c^3*d^4*x^3 + a^3*e^3*(8*d + 3*e*x) - 3*a*c^2*d^2*x*(d^2 + 2*e^2*x^2) + 4*a^2*c*e*(d^3 + 3*d*e^2*x^2 + e^3*x^3)) - 2*b^2*c*(21*a^2*e^4*x + 3*c^2*d^2*x*(d^2 - 8*d*e*x + 2*e^2*x^2) + 2*a*c*e*(-2*d^3 + 18*d^2*e*x - 6*d*e^2*x^2 + 7*e^3*x^3))) + B*(128*a^4*c^2*e^4 + b*x*(15*b^5*e^4*x - 16*c^5*d^4*x^2 + 8*b*c^4*d^3*x*(-3*d + 2*e*x) + b^3*c^2*e^3*x^2*(-32*d + 3*e*x) + 4*b^4*c*e^3*x*(-6*d + 5*e*x) - 6*b^2*c^3*d^2*(d^2 - 4*d*e*x - 2*e^2*x^2)) + 4*a^3*c*e^2*(-25*b^2*e^2 + 2*b*c*e*(20*d + 39*e*x) - 48*c^2*(d^2 + d*e*x - e^2*x^2)) + a^2*(15*b^4*e^4 + 48*b^2*c^2*e^3*x*(7*d + e*x) - 6*b^3*c*e^3*(4*d + 35*e*x) + 32*b*c^3*e*(2*d^3 - 9*d^2*e*x + 8*e^3*x^3) - 16*c^4*(d^4 + 18*d^2*e^2*x^2 + 16*d*e^3*x^3 - 3*e^4*x^4)) + 2*a*(15*b^5*e^4*x + 32*c^5*d^3*e*x^3 + 2*b^3*c^2*e^3*x^2*(36*d - 37*e*x) - 3*b^4*c*e^3*x*(8*d + 15*e*x) - 12*b*c^4*d^2*x*(d^2 - 4*d*e*x + 6*e^2*x^2) - 2*b^2*c^3*(d^4 - 24*d^3*e*x + 18*d^2*e^2*x^2 - 56*d*e^3*x^3 + 6*e^4*x^4))))/(3*c^3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2)) + (e^3*(8*B*c*d - 5*b*B*e + 2*A*c*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(2*c^(7/2))","A",1
2481,1,505,397,1.3415249,"\int \frac{(A+B x) (d+e x)^3}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a + b*x + c*x^2)^(5/2),x]","\frac{B e^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{c^{5/2}}-\frac{2 \left(A c^2 \left(-12 b (d-e x) \left(2 a^2 e^2+a c (d-e x)^2+2 c^2 d^2 x^2\right)+8 \left(2 a^3 e^3+3 a^2 c e \left(d^2+e^2 x^2\right)-3 a c^2 d x \left(d^2+e^2 x^2\right)-2 c^3 d^3 x^3\right)+6 b^2 \left(d^2-6 d e x+e^2 x^2\right) (a e-c d x)+b^3 \left(d^3+9 d^2 e x-9 d e^2 x^2-e^3 x^3\right)\right)+B \left(4 a^3 c e^2 (6 c (2 d+e x)-5 b e)+a^2 \left(3 b^3 e^3-42 b^2 c e^3 x-24 b c^2 d e (d-3 e x)+8 c^3 \left(d^3+9 d e^2 x^2+4 e^3 x^3\right)\right)+2 a \left(3 b^4 e^3 x-9 b^3 c e^3 x^2+b^2 c^2 \left(d^3-18 d^2 e x+9 d e^2 x^2-14 e^3 x^3\right)+6 b c^3 d x \left(d^2-3 d e x+3 e^2 x^2\right)-12 c^4 d^2 e x^3\right)+b x \left(3 b^4 e^3 x+4 b^3 c e^3 x^2+3 b^2 c^2 d \left(d^2-3 d e x-e^2 x^2\right)+6 b c^3 d^2 x (2 d-e x)+8 c^4 d^3 x^2\right)\right)\right)}{3 c^2 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{3/2}}","\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{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)-3 b^4 B e^3+2 b^3 B c d e^2\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{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*(A*c^2*(6*b^2*(a*e - c*d*x)*(d^2 - 6*d*e*x + e^2*x^2) + b^3*(d^3 + 9*d^2*e*x - 9*d*e^2*x^2 - e^3*x^3) - 12*b*(d - e*x)*(2*a^2*e^2 + 2*c^2*d^2*x^2 + a*c*(d - e*x)^2) + 8*(2*a^3*e^3 - 2*c^3*d^3*x^3 + 3*a^2*c*e*(d^2 + e^2*x^2) - 3*a*c^2*d*x*(d^2 + e^2*x^2))) + B*(4*a^3*c*e^2*(-5*b*e + 6*c*(2*d + e*x)) + b*x*(3*b^4*e^3*x + 8*c^4*d^3*x^2 + 4*b^3*c*e^3*x^2 + 6*b*c^3*d^2*x*(2*d - e*x) + 3*b^2*c^2*d*(d^2 - 3*d*e*x - e^2*x^2)) + 2*a*(3*b^4*e^3*x - 9*b^3*c*e^3*x^2 - 12*c^4*d^2*e*x^3 + 6*b*c^3*d*x*(d^2 - 3*d*e*x + 3*e^2*x^2) + b^2*c^2*(d^3 - 18*d^2*e*x + 9*d*e^2*x^2 - 14*e^3*x^3)) + a^2*(3*b^3*e^3 - 42*b^2*c*e^3*x - 24*b*c^2*d*e*(d - 3*e*x) + 8*c^3*(d^3 + 9*d*e^2*x^2 + 4*e^3*x^3)))))/(3*c^2*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2)) + (B*e^3*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/c^(5/2)","A",1
2482,1,314,121,0.9548934,"\int \frac{(A+B x) (d+e x)^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a + b*x + c*x^2)^(5/2),x]","\frac{2 A \left(4 b \left(2 a^2 e^2+3 a c (d-e x)^2+2 c^2 d x^2 (3 d-2 e x)\right)+8 c \left(-2 a^2 d e+a c x \left(3 d^2+e^2 x^2\right)+2 c^2 d^2 x^3\right)+b^2 \left(2 c x \left(3 d^2-12 d e x+e^2 x^2\right)-4 a e (d-3 e x)\right)-\left(b^3 \left(d^2+6 d e x-3 e^2 x^2\right)\right)\right)-2 B \left(16 a^3 e^2+8 a^2 \left(b e (3 e x-2 d)+c \left(d^2+3 e^2 x^2\right)\right)+2 a \left(b^2 \left(d^2-12 d e x+3 e^2 x^2\right)+6 b c x (d-e x)^2-8 c^2 d e x^3\right)+b x \left(b^2 \left(3 d^2-6 d e x-e^2 x^2\right)+4 b c d x (3 d-e x)+8 c^2 d^2 x^2\right)\right)}{3 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{3/2}}","-\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^3*(d^2 + 6*d*e*x - 3*e^2*x^2)) + 4*b*(2*a^2*e^2 + 2*c^2*d*x^2*(3*d - 2*e*x) + 3*a*c*(d - e*x)^2) + 8*c*(-2*a^2*d*e + 2*c^2*d^2*x^3 + a*c*x*(3*d^2 + e^2*x^2)) + b^2*(-4*a*e*(d - 3*e*x) + 2*c*x*(3*d^2 - 12*d*e*x + e^2*x^2))) - 2*B*(16*a^3*e^2 + b*x*(8*c^2*d^2*x^2 + 4*b*c*d*x*(3*d - e*x) + b^2*(3*d^2 - 6*d*e*x - e^2*x^2)) + 8*a^2*(b*e*(-2*d + 3*e*x) + c*(d^2 + 3*e^2*x^2)) + 2*a*(-8*c^2*d*e*x^3 + 6*b*c*x*(d - e*x)^2 + b^2*(d^2 - 12*d*e*x + 3*e^2*x^2))))/(3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2))","B",1
2483,1,200,158,0.3077185,"\int \frac{(A+B x) (d+e x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x))/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \left(A \left(8 c \left(a^2 e-3 a c d x-2 c^2 d x^3\right)+2 b^2 \left(a e-3 c d x+6 c e x^2\right)+4 b c \left(-3 a d+3 a e x-6 c d x^2+2 c e x^3\right)+b^3 (d+3 e x)\right)+B \left(8 a^2 (c d-b e)+2 a \left(b^2 (d-6 e x)+6 b c x (d-e x)-4 c^2 e x^3\right)+b x \left(3 b^2 (d-e x)-2 b c x (e x-6 d)+8 c^2 d x^2\right)\right)\right)}{3 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{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*(A*(b^3*(d + 3*e*x) + 2*b^2*(a*e - 3*c*d*x + 6*c*e*x^2) + 8*c*(a^2*e - 3*a*c*d*x - 2*c^2*d*x^3) + 4*b*c*(-3*a*d + 3*a*e*x - 6*c*d*x^2 + 2*c*e*x^3)) + B*(8*a^2*(c*d - b*e) + 2*a*(-4*c^2*e*x^3 + b^2*(d - 6*e*x) + 6*b*c*x*(d - e*x)) + b*x*(8*c^2*d*x^2 + 3*b^2*(d - e*x) - 2*b*c*x*(-6*d + e*x)))))/(3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2))","A",1
2484,1,99,90,0.0986532,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \left(B \left(8 a^2 c+2 a b (b+6 c x)+b x \left(3 b^2+12 b c x+8 c^2 x^2\right)\right)+A (b+2 c x) \left(-4 c \left(3 a+2 c x^2\right)+b^2-8 b c x\right)\right)}{3 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{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*c*x)*(b^2 - 8*b*c*x - 4*c*(3*a + 2*c*x^2)) + B*(8*a^2*c + 2*a*b*(b + 6*c*x) + b*x*(3*b^2 + 12*b*c*x + 8*c^2*x^2))))/(3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2))","A",1
2485,1,437,436,1.0397592,"\int \frac{A+B x}{(d+e x) \left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((d + e*x)*(a + b*x + c*x^2)^(5/2)),x]","\frac{4 \left(c x \left(\frac{1}{2} (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)+2 c e (b d-2 a e) (-2 a B e+A b e-2 A c d+b B d)\right)+\frac{1}{2} \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)+2 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+x (b+c x)} \left(e (a e-b d)+c d^2\right)^2}+\frac{2 \left(2 A c (a e+c d x)+a B (b e-2 c d+2 c e x)-A b^2 e+A b c (d-e x)-b B c d x\right)}{3 \left(b^2-4 a c\right) (a+x (b+c x))^{3/2} \left(e (b d-a e)-c d^2\right)}+\frac{e^3 (B d-A e) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{\left(e (a e-b d)+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,"(4*(2*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)))/2 + c*(2*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)))/2)*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 + e*(-(b*d) + a*e))^2*Sqrt[a + x*(b + c*x)]) + (2*(-(A*b^2*e) - b*B*c*d*x + 2*A*c*(a*e + c*d*x) + A*b*c*(d - e*x) + a*B*(-2*c*d + b*e + 2*c*e*x)))/(3*(b^2 - 4*a*c)*(-(c*d^2) + e*(b*d - a*e))*(a + x*(b + c*x))^(3/2)) + (e^3*(B*d - A*e)*ArcTanh[(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(c*d^2 + e*(-(b*d) + a*e))^(5/2)","A",1
2486,1,754,746,4.712557,"\int \frac{A+B x}{(d+e x)^2 \left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^2*(a + b*x + c*x^2)^(5/2)),x]","\frac{2 \left(\frac{-4 b c \left(A c \left(a e^2 (9 d-7 e x)+2 c d^2 (d-3 e x)\right)-B \left(-4 a^2 e^3+a c d e (d+3 e x)+2 c^2 d^3 x\right)\right)-8 c^2 \left(a^2 e^2 (4 A e-5 B d+3 B e x)-a c d e (A d-7 A e x+2 B d x)+2 A c^2 d^3 x\right)+b^3 e \left(2 a B e^2+A c e (3 d-5 e x)+B c d (3 e x-7 d)\right)+2 b^2 c \left(16 a A e^3+a B e^2 (e x-5 d)+A c d e (5 d+e x)+2 B c d^2 (d-4 e x)\right)+b^4 e^2 (3 B d-5 A e)}{\left(b^2-4 a c\right) (d+e x) \sqrt{a+x (b+c x)} \left(e (b d-a e)-c d^2\right)}+\frac{e \sqrt{a+x (b+c x)} \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 \left(-8 a^2 e^4+9 a c d^2 e^2+2 c^2 d^4\right)+a B d e \left(13 a e^2-2 c d^2\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)}{2 \left(b^2-4 a c\right) (d+e x) \left(e (a e-b d)+c d^2\right)^2}+\frac{3 e^3 \left(b^2-4 a c\right) \left(-B e (2 a e+3 b d)+5 A e (b e-2 c d)+8 B c d^2\right) \tanh ^{-1}\left(\frac{2 a e-b d+b e x-2 c d x}{2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}}\right)}{4 \left(e (a e-b d)+c d^2\right)^{5/2}}+\frac{-2 A c (a e+c d x)+a B (2 c (d-e x)-b e)+A b^2 e+A b c (e x-d)+b B c d x}{(d+e x) (a+x (b+c x))^{3/2}}\right)}{3 \left(b^2-4 a c\right) \left(e (a e-b d)+c d^2\right)}","\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*((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 + x*(b + c*x)])/(2*(b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e))^2*(d + e*x)) + (A*b^2*e + b*B*c*d*x - 2*A*c*(a*e + c*d*x) + A*b*c*(-d + e*x) + a*B*(-(b*e) + 2*c*(d - e*x)))/((d + e*x)*(a + x*(b + c*x))^(3/2)) + (b^4*e^2*(3*B*d - 5*A*e) + 2*b^2*c*(16*a*A*e^3 + 2*B*c*d^2*(d - 4*e*x) + a*B*e^2*(-5*d + e*x) + A*c*d*e*(5*d + e*x)) + b^3*e*(2*a*B*e^2 + A*c*e*(3*d - 5*e*x) + B*c*d*(-7*d + 3*e*x)) - 8*c^2*(2*A*c^2*d^3*x - a*c*d*e*(A*d + 2*B*d*x - 7*A*e*x) + a^2*e^2*(-5*B*d + 4*A*e + 3*B*e*x)) - 4*b*c*(A*c*(a*e^2*(9*d - 7*e*x) + 2*c*d^2*(d - 3*e*x)) - B*(-4*a^2*e^3 + 2*c^2*d^3*x + a*c*d*e*(d + 3*e*x))))/((b^2 - 4*a*c)*(-(c*d^2) + e*(b*d - a*e))*(d + e*x)*Sqrt[a + x*(b + c*x)]) + (3*(b^2 - 4*a*c)*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*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(4*(c*d^2 + e*(-(b*d) + a*e))^(5/2))))/(3*(b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e)))","A",1
2487,1,2369,1401,11.2484231,"\int \frac{(A+B x) (d+e x)^6}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^6)/(a + b*x + c*x^2)^(7/2),x]","\text{Result too large to show}","\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*A*c*(15*b^8*e^6*x^3 + 5*b^7*e^6*x^2*(9*a + 7*c*x^2) + b^6*e^6*x*(45*a^2 - 100*a*c*x^2 + 23*c^2*x^4) - 2*b^4*c*(245*a^3*e^6*x + 75*a^2*c*e^6*x^3 + 5*c^3*d^2*x*(d^4 + 24*d^3*e*x - 135*d^2*e^2*x^2 + 40*d*e^3*x^3 + 3*e^4*x^4) - 3*a*c^2*e*(2*d^5 + 50*d^4*e*x - 300*d^3*e^2*x^2 + 100*d^2*e^3*x^3 + 10*d*e^4*x^4 - 43*e^5*x^5)) + 40*b^3*c*(-4*a^4*e^6 + 35*a^3*c*e^6*x^2 + c^4*d^3*x^2*(2*d^3 - 36*d^2*e*x + 45*d*e^2*x^2 - 4*e^3*x^3) + 3*a^2*c^2*e^2*(d^4 - 20*d^3*e*x + 30*d^2*e^2*x^2 - 4*d*e^3*x^3 + 10*e^4*x^4) - a*c^3*d*(d^5 + 18*d^4*e*x - 75*d^3*e^2*x^2 + 100*d^2*e^3*x^3 - 45*d*e^4*x^4 - 6*e^5*x^5)) + 3*b^5*(5*a^3*e^6 - 155*a^2*c*e^6*x^2 - 125*a*c^2*e^6*x^4 + c^3*d*(d^5 + 10*d^4*e*x + 75*d^3*e^2*x^2 - 100*d^2*e^3*x^3 - 25*d*e^4*x^4 - 6*e^5*x^5)) + 16*b*c^2*(33*a^5*e^6 + 8*c^5*d^5*x^4*(5*d - 6*e*x) + 15*a^4*c*e^4*(8*d^2 - 16*d*e*x + e^2*x^2) + 30*a*c^4*d^3*x^2*(2*d^3 - 4*d^2*e*x + 5*d*e^2*x^2 - 4*e^3*x^3) - 5*a^3*c^2*e^2*(-18*d^4 + 40*d^3*e*x - 60*d^2*e^2*x^2 + 72*d*e^3*x^3 + 5*e^4*x^4) + 15*a^2*c^3*d*(d^5 - 6*d^4*e*x + 15*d^3*e^2*x^2 - 20*d^2*e^3*x^3 + 15*d*e^4*x^4 - 6*e^5*x^5)) + 48*b^2*c^2*(35*a^4*e^6*x + 5*c^4*d^4*x^3*(2*d^2 - 8*d*e*x + 3*e^2*x^2) + 5*a^3*c*e^3*(-4*d^3 + 20*d^2*e*x - 12*d*e^2*x^2 + 9*e^3*x^3) + 5*a*c^3*d^2*x*(d^4 - 12*d^3*e*x + 15*d^2*e^2*x^2 - 20*d*e^3*x^3 + 3*e^4*x^4) + a^2*c^2*e*(-6*d^5 + 75*d^4*e*x - 100*d^3*e^2*x^2 + 150*d^2*e^3*x^3 - 30*d*e^4*x^4 + 19*e^5*x^5)) - 32*c^3*(-8*c^5*d^6*x^5 + 3*a^5*e^5*(16*d + 5*e*x) - 10*a*c^4*d^4*x^3*(2*d^2 + 3*e^2*x^2) + 5*a^4*c*e^3*(8*d^3 + 24*d*e^2*x^2 + 7*e^3*x^3) - 15*a^2*c^3*d^2*x*(d^4 + 5*d^2*e^2*x^2 + 3*e^4*x^4) + a^3*c^2*e*(18*d^5 + 100*d^3*e^2*x^2 + 90*d*e^4*x^4 + 23*e^5*x^5))) + B*(3072*a^6*c^3*e^6 + 48*a^5*c^2*e^4*(-77*b^2*e^2 + 2*b*c*e*(66*d + 115*e*x) - 40*c^2*(4*d^2 + 3*d*e*x - 4*e^2*x^2)) - b*x*(105*b^8*e^6*x^2 + 256*c^8*d^6*x^4 + 64*b*c^7*d^5*x^3*(10*d - 9*e*x) + 3*b^5*c^3*e^5*x^4*(-92*d + 5*e*x) + 7*b^6*c^2*e^5*x^3*(-60*d + 23*e*x) + 5*b^7*c*e^5*x^2*(-36*d + 49*e*x) + 240*b^2*c^6*d^4*x^2*(2*d^2 - 6*d*e*x + e^2*x^2) + 40*b^3*c^5*d^3*x*(2*d^3 - 27*d^2*e*x + 15*d*e^2*x^2 + 2*e^3*x^3) - 10*b^4*c^4*d^2*(d^4 + 18*d^3*e*x - 45*d^2*e^2*x^2 - 20*d*e^3*x^3 - 9*e^4*x^4)) + 80*a^4*c*e^2*(14*b^4*e^4 + 3*b^2*c^2*e^3*x*(84*d + 17*e*x) - 3*b^3*c*e^3*(8*d + 49*e*x) + 2*b*c^3*e*(32*d^3 - 120*d^2*e*x + 18*d*e^2*x^2 + 121*e^3*x^3) - 24*c^4*(d^4 + 10*d^2*e^2*x^2 + 7*d*e^3*x^3 - 3*e^4*x^4)) - a^3*(105*b^6*e^6 + 1960*b^4*c^2*e^5*x*(3*d + 5*e*x) + 240*b^3*c^3*e^5*x^2*(-70*d + 59*e*x) - 10*b^5*c*e^5*(18*d + 343*e*x) - 80*b^2*c^4*e^2*(-18*d^4 + 160*d^3*e*x - 180*d^2*e^2*x^2 + 324*d*e^3*x^3 + 71*e^4*x^4) - 32*b*c^5*e*(36*d^5 - 150*d^4*e*x + 400*d^3*e^2*x^2 - 900*d^2*e^3*x^3 - 150*d*e^4*x^4 + 251*e^5*x^5) + 192*c^6*(d^6 + 25*d^4*e^2*x^2 + 75*d^2*e^4*x^4 + 46*d*e^5*x^5 - 5*e^6*x^6)) - 3*a^2*(105*b^7*e^6*x + 10*b^5*c^2*e^5*x^2*(186*d - 35*e*x) + 40*b^4*c^3*e^5*x^3*(15*d + 71*e*x) - 5*b^6*c*e^5*x*(36*d + 217*e*x) - 640*c^7*d^3*e*x^3*(d^2 + 2*e^2*x^2) + 160*b*c^6*d^2*x*(d^4 - 6*d^3*e*x + 15*d^2*e^2*x^2 - 20*d*e^3*x^3 + 15*e^4*x^4) + 16*b^3*c^4*e*(-2*d^5 + 75*d^4*e*x - 200*d^3*e^2*x^2 + 50*d^2*e^3*x^3 - 300*d*e^4*x^4 + 143*e^5*x^5) + 16*b^2*c^5*(2*d^6 - 60*d^5*e*x + 150*d^4*e^2*x^2 - 400*d^3*e^3*x^3 + 150*d^2*e^4*x^4 - 228*d*e^5*x^5 + 15*e^6*x^6)) + a*(-315*b^8*e^6*x^2 + 768*c^8*d^5*e*x^5 + 75*b^6*c^2*e^5*x^3*(-16*d + 35*e*x) + 20*b^7*c*e^5*x^2*(27*d + 35*e*x) + 6*b^5*c^3*e^5*x^4*(-750*d + 307*e*x) - 320*b*c^7*d^4*x^3*(2*d^2 - 6*d*e*x + 9*e^2*x^2) + 480*b^2*c^6*d^3*x^2*(-2*d^3 + 6*d^2*e*x - 15*d*e^2*x^2 + 4*e^3*x^3) - 240*b^3*c^5*d^2*x*(d^4 - 10*d^3*e*x + 25*d^2*e^2*x^2 - 20*d*e^3*x^3 - 5*e^4*x^4) + 4*b^4*c^4*(d^6 + 60*d^5*e*x - 675*d^4*e^2*x^2 + 400*d^3*e^3*x^3 + 75*d^2*e^4*x^4 - 774*d*e^5*x^5 + 45*e^6*x^6))))/(15*c^4*(-b^2 + 4*a*c)^3*(a + x*(b + c*x))^(5/2)) + (e^5*(12*B*c*d - 7*b*B*e + 2*A*c*e)*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/(2*c^(9/2))","A",1
2488,1,1608,942,9.1911504,"\int \frac{(A+B x) (d+e x)^5}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^5)/(a + b*x + c*x^2)^(7/2),x]","\frac{\frac{2 \sqrt{c} \left(A \left(\left(3 d^5+25 e x d^4+150 e^2 x^2 d^3-150 e^3 x^3 d^2-25 e^4 x^4 d-3 e^5 x^5\right) b^5+10 (a e-c d x) \left(d^4+20 e x d^3-90 e^2 x^2 d^2+20 e^3 x^3 d+e^4 x^4\right) b^4+40 (d-e x) \left(2 a^2 \left(d^2-14 e x d+e^2 x^2\right) e^2+2 c^2 d^2 x^2 \left(d^2-14 e x d+e^2 x^2\right)-a c (d-e x)^2 \left(d^2+18 e x d+e^2 x^2\right)\right) b^3+80 \left(-2 a^3 \left(3 d^2-10 e x d+3 e^2 x^2\right) e^3-3 a^2 c \left(d^4-10 e x d^3+10 e^2 x^2 d^2-10 e^3 x^3 d+e^4 x^4\right) e+2 c^3 d^3 x^3 \left(3 d^2-10 e x d+3 e^2 x^2\right)+3 a c^2 d x \left(d^4-10 e x d^3+10 e^2 x^2 d^2-10 e^3 x^3 d+e^4 x^4\right)\right) b^2+80 (d-e x) \left(8 a^4 e^4+4 a^3 c \left(3 d^2-2 e x d+3 e^2 x^2\right) e^2+8 c^4 d^4 x^4+3 a^2 c^2 (d-e x)^4+4 a c^3 d^2 x^2 \left(3 d^2-2 e x d+3 e^2 x^2\right)\right) b+32 \left(-8 a^5 e^5-20 a^4 c \left(d^2+e^2 x^2\right) e^3-5 a^3 c^2 \left(3 d^4+10 e^2 x^2 d^2+3 e^4 x^4\right) e+8 c^5 d^5 x^5+20 a c^4 d^3 x^3 \left(d^2+e^2 x^2\right)+5 a^2 c^3 d x \left(3 d^4+10 e^2 x^2 d^2+3 e^4 x^4\right)\right)\right) c^3+B \left(-16 c^2 e^4 (80 c d-33 b e+30 c e x) a^5-80 c e^2 \left(2 \left(4 d^3+20 e^2 x^2 d+7 e^3 x^3\right) c^3+b e \left(-16 d^2+40 e x d-3 e^2 x^2\right) c^2-21 b^2 e^3 x c+2 b^3 e^3\right) a^4-\left(32 \left(3 d^5+50 e^2 x^2 d^3+75 e^4 x^4 d+23 e^5 x^5\right) c^5+80 b e \left(-6 d^4+20 e x d^3-40 e^2 x^2 d^2+60 e^3 x^3 d+5 e^4 x^4\right) c^4+80 b^2 e^2 \left(6 d^3-40 e x d^2+30 e^2 x^2 d-27 e^3 x^3\right) c^3-1400 b^3 e^5 x^2 c^2+490 b^4 e^5 x c-15 b^5 e^5\right) a^3+\left(45 e^5 x b^6-465 c e^5 x^2 b^5-150 c^2 e^5 x^3 b^4+40 c^3 e \left(d^4-30 e x d^3+60 e^2 x^2 d^2-10 e^3 x^3 d+30 e^4 x^4\right) b^3-48 c^4 \left(d^5-25 e x d^4+50 e^2 x^2 d^3-100 e^3 x^3 d^2+25 e^4 x^4 d-19 e^5 x^5\right) b^2-240 c^5 d x \left(d^4-5 e x d^3+10 e^2 x^2 d^2-10 e^3 x^3 d+5 e^4 x^4\right) b+160 c^6 d^2 e x^3 \left(5 d^2+6 e^2 x^2\right)\right) a^2+\left(45 e^5 x^2 b^7-100 c e^5 x^3 b^6-375 c^2 e^5 x^4 b^5+2 c^3 \left(d^5+50 e x d^4-450 e^2 x^2 d^3+200 e^3 x^3 d^2+25 e^4 x^4 d-129 e^5 x^5\right) b^4+40 c^4 d x \left(-3 d^4+25 e x d^3-50 e^2 x^2 d^2+30 e^3 x^3 d+5 e^4 x^4\right) b^3+240 c^5 d^2 x^2 \left(-2 d^3+5 e x d^2-10 e^2 x^2 d+2 e^3 x^3\right) b^2-160 c^6 d^3 x^3 \left(2 d^2-5 e x d+6 e^2 x^2\right) b+320 c^7 d^4 e x^5\right) a+b x \left(15 e^5 x^2 b^7+35 c e^5 x^3 b^6+23 c^2 e^5 x^4 b^5+5 c^3 d \left(d^4+15 e x d^3-30 e^2 x^2 d^2-10 e^3 x^3 d-3 e^4 x^4\right) b^4-10 c^4 d^2 x \left(4 d^3-45 e x d^2+20 e^2 x^2 d+2 e^3 x^3\right) b^3-40 c^5 d^3 x^2 \left(6 d^2-15 e x d+2 e^2 x^2\right) b^2+80 c^6 d^4 x^3 (3 e x-4 d) b-128 c^7 d^5 x^4\right)\right)\right)}{(a+x (b+c x))^{5/2}}-15 B \left(b^2-4 a c\right)^3 e^5 \log \left(b+2 c x+2 \sqrt{c} \sqrt{a+x (b+c x)}\right)}{15 c^{7/2} \left(4 a c-b^2\right)^3}","\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*Sqrt[c]*(A*c^3*(10*b^4*(a*e - c*d*x)*(d^4 + 20*d^3*e*x - 90*d^2*e^2*x^2 + 20*d*e^3*x^3 + e^4*x^4) + b^5*(3*d^5 + 25*d^4*e*x + 150*d^3*e^2*x^2 - 150*d^2*e^3*x^3 - 25*d*e^4*x^4 - 3*e^5*x^5) + 40*b^3*(d - e*x)*(2*a^2*e^2*(d^2 - 14*d*e*x + e^2*x^2) + 2*c^2*d^2*x^2*(d^2 - 14*d*e*x + e^2*x^2) - a*c*(d - e*x)^2*(d^2 + 18*d*e*x + e^2*x^2)) + 80*b*(d - e*x)*(8*a^4*e^4 + 8*c^4*d^4*x^4 + 3*a^2*c^2*(d - e*x)^4 + 4*a^3*c*e^2*(3*d^2 - 2*d*e*x + 3*e^2*x^2) + 4*a*c^3*d^2*x^2*(3*d^2 - 2*d*e*x + 3*e^2*x^2)) + 80*b^2*(-2*a^3*e^3*(3*d^2 - 10*d*e*x + 3*e^2*x^2) + 2*c^3*d^3*x^3*(3*d^2 - 10*d*e*x + 3*e^2*x^2) - 3*a^2*c*e*(d^4 - 10*d^3*e*x + 10*d^2*e^2*x^2 - 10*d*e^3*x^3 + e^4*x^4) + 3*a*c^2*d*x*(d^4 - 10*d^3*e*x + 10*d^2*e^2*x^2 - 10*d*e^3*x^3 + e^4*x^4)) + 32*(-8*a^5*e^5 + 8*c^5*d^5*x^5 - 20*a^4*c*e^3*(d^2 + e^2*x^2) + 20*a*c^4*d^3*x^3*(d^2 + e^2*x^2) - 5*a^3*c^2*e*(3*d^4 + 10*d^2*e^2*x^2 + 3*e^4*x^4) + 5*a^2*c^3*d*x*(3*d^4 + 10*d^2*e^2*x^2 + 3*e^4*x^4))) + B*(-16*a^5*c^2*e^4*(80*c*d - 33*b*e + 30*c*e*x) - 80*a^4*c*e^2*(2*b^3*e^3 - 21*b^2*c*e^3*x + b*c^2*e*(-16*d^2 + 40*d*e*x - 3*e^2*x^2) + 2*c^3*(4*d^3 + 20*d*e^2*x^2 + 7*e^3*x^3)) + b*x*(15*b^7*e^5*x^2 + 35*b^6*c*e^5*x^3 - 128*c^7*d^5*x^4 + 23*b^5*c^2*e^5*x^4 + 80*b*c^6*d^4*x^3*(-4*d + 3*e*x) - 40*b^2*c^5*d^3*x^2*(6*d^2 - 15*d*e*x + 2*e^2*x^2) - 10*b^3*c^4*d^2*x*(4*d^3 - 45*d^2*e*x + 20*d*e^2*x^2 + 2*e^3*x^3) + 5*b^4*c^3*d*(d^4 + 15*d^3*e*x - 30*d^2*e^2*x^2 - 10*d*e^3*x^3 - 3*e^4*x^4)) + a*(45*b^7*e^5*x^2 - 100*b^6*c*e^5*x^3 - 375*b^5*c^2*e^5*x^4 + 320*c^7*d^4*e*x^5 - 160*b*c^6*d^3*x^3*(2*d^2 - 5*d*e*x + 6*e^2*x^2) + 240*b^2*c^5*d^2*x^2*(-2*d^3 + 5*d^2*e*x - 10*d*e^2*x^2 + 2*e^3*x^3) + 40*b^3*c^4*d*x*(-3*d^4 + 25*d^3*e*x - 50*d^2*e^2*x^2 + 30*d*e^3*x^3 + 5*e^4*x^4) + 2*b^4*c^3*(d^5 + 50*d^4*e*x - 450*d^3*e^2*x^2 + 200*d^2*e^3*x^3 + 25*d*e^4*x^4 - 129*e^5*x^5)) + a^2*(45*b^6*e^5*x - 465*b^5*c*e^5*x^2 - 150*b^4*c^2*e^5*x^3 + 160*c^6*d^2*e*x^3*(5*d^2 + 6*e^2*x^2) - 240*b*c^5*d*x*(d^4 - 5*d^3*e*x + 10*d^2*e^2*x^2 - 10*d*e^3*x^3 + 5*e^4*x^4) + 40*b^3*c^3*e*(d^4 - 30*d^3*e*x + 60*d^2*e^2*x^2 - 10*d*e^3*x^3 + 30*e^4*x^4) - 48*b^2*c^4*(d^5 - 25*d^4*e*x + 50*d^3*e^2*x^2 - 100*d^2*e^3*x^3 + 25*d*e^4*x^4 - 19*e^5*x^5)) - a^3*(-15*b^5*e^5 + 490*b^4*c*e^5*x - 1400*b^3*c^2*e^5*x^2 + 80*b^2*c^3*e^2*(6*d^3 - 40*d^2*e*x + 30*d*e^2*x^2 - 27*e^3*x^3) + 80*b*c^4*e*(-6*d^4 + 20*d^3*e*x - 40*d^2*e^2*x^2 + 60*d*e^3*x^3 + 5*e^4*x^4) + 32*c^5*(3*d^5 + 50*d^3*e^2*x^2 + 75*d*e^4*x^4 + 23*e^5*x^5)))))/(a + x*(b + c*x))^(5/2) - 15*B*(b^2 - 4*a*c)^3*e^5*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/(15*c^(7/2)*(-b^2 + 4*a*c)^3)","A",1
2489,1,1196,210,6.303947,"\int \frac{(A+B x) (d+e x)^4}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a + b*x + c*x^2)^(7/2),x]","\frac{2 B \left(256 e^4 a^5+128 e^2 \left(b e (5 e x-4 d)+c \left(3 d^2+5 e^2 x^2\right)\right) a^4+32 \left(3 \left(d^4+10 e^2 x^2 d^2+5 e^4 x^4\right) c^2+2 b e \left(-6 d^3+15 e x d^2-20 e^2 x^2 d+15 e^3 x^3\right) c+b^2 e^2 \left(9 d^2-40 e x d+15 e^2 x^2\right)\right) a^3-16 \left(-15 b c^2 x (d-e x)^4+8 c^3 d e x^3 \left(5 d^2+3 e^2 x^2\right)+b^3 e \left(2 d^3-45 e x d^2+60 e^2 x^2 d-5 e^3 x^3\right)-3 b^2 c \left(d^4-20 e x d^3+30 e^2 x^2 d^2-40 e^3 x^3 d+5 e^4 x^4\right)\right) a^2-2 \left(128 c^4 d^3 e x^5-32 b c^3 d^2 \left(5 d^2-10 e x d+9 e^2 x^2\right) x^3+48 b^2 c^2 d \left(-5 d^3+10 e x d^2-15 e^2 x^2 d+2 e^3 x^3\right) x^2+20 b^3 c (d-e x)^2 \left(-3 d^2+14 e x d+e^2 x^2\right) x+b^4 \left(d^4+40 e x d^3-270 e^2 x^2 d^2+80 e^3 x^3 d+5 e^4 x^4\right)\right) a+b x \left(\left(-5 d^4-60 e x d^3+90 e^2 x^2 d^2+20 e^3 x^3 d+3 e^4 x^4\right) b^4+8 c d x \left(5 d^3-45 e x d^2+15 e^2 x^2 d+e^3 x^3\right) b^3+48 c^2 d^2 x^2 \left(5 d^2-10 e x d+e^2 x^2\right) b^2+64 c^3 d^3 x^3 (5 d-3 e x) b+128 c^4 d^4 x^4\right)\right)-2 A \left(\left(3 d^4+20 e x d^3+90 e^2 x^2 d^2-60 e^3 x^3 d-5 e^4 x^4\right) b^5+2 \left(4 a e \left(d^3+15 e x d^2-45 e^2 x^2 d+5 e^3 x^3\right)-c x \left(5 d^4+80 e x d^3-270 e^2 x^2 d^2+40 e^3 x^3 d+e^4 x^4\right)\right) b^4+8 \left(6 a^2 \left(d^2-10 e x d+5 e^2 x^2\right) e^2-5 a c (d-e x)^2 \left(d^2+14 e x d-3 e^2 x^2\right)+2 c^2 d x^2 \left(5 d^3-60 e x d^2+45 e^2 x^2 d-2 e^3 x^3\right)\right) b^3+16 \left(4 a^3 (5 e x-3 d) e^3+6 a^2 c \left(-2 d^3+15 e x d^2-10 e^2 x^2 d+5 e^3 x^3\right) e+2 c^3 d^2 x^3 \left(15 d^2-40 e x d+9 e^2 x^2\right)+3 a c^2 x \left(5 d^4-40 e x d^3+30 e^2 x^2 d^2-20 e^3 x^3 d+e^4 x^4\right)\right) b^2+16 \left(8 a^4 e^4+4 a^3 c \left(9 d^2-10 e x d+5 e^2 x^2\right) e^2+15 a^2 c^2 (d-e x)^4+8 c^4 d^3 x^4 (5 d-4 e x)+4 a c^3 d x^2 \left(15 d^3-20 e x d^2+15 e^2 x^2 d-6 e^3 x^3\right)\right) b+32 c \left(8 c^4 d^4 x^5+4 a c^3 d^2 \left(5 d^2+3 e^2 x^2\right) x^3+3 a^2 c^2 \left(5 d^4+10 e^2 x^2 d^2+e^4 x^4\right) x-8 a^4 d e^3-4 a^3 c d e \left(3 d^2+5 e^2 x^2\right)\right)\right)}{15 \left(b^2-4 a c\right)^3 (a+x (b+c x))^{5/2}}","\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^5*(3*d^4 + 20*d^3*e*x + 90*d^2*e^2*x^2 - 60*d*e^3*x^3 - 5*e^4*x^4) + 16*b*(8*a^4*e^4 + 8*c^4*d^3*x^4*(5*d - 4*e*x) + 15*a^2*c^2*(d - e*x)^4 + 4*a^3*c*e^2*(9*d^2 - 10*d*e*x + 5*e^2*x^2) + 4*a*c^3*d*x^2*(15*d^3 - 20*d^2*e*x + 15*d*e^2*x^2 - 6*e^3*x^3)) + 8*b^3*(-5*a*c*(d - e*x)^2*(d^2 + 14*d*e*x - 3*e^2*x^2) + 6*a^2*e^2*(d^2 - 10*d*e*x + 5*e^2*x^2) + 2*c^2*d*x^2*(5*d^3 - 60*d^2*e*x + 45*d*e^2*x^2 - 2*e^3*x^3)) + 32*c*(-8*a^4*d*e^3 + 8*c^4*d^4*x^5 + 4*a*c^3*d^2*x^3*(5*d^2 + 3*e^2*x^2) - 4*a^3*c*d*e*(3*d^2 + 5*e^2*x^2) + 3*a^2*c^2*x*(5*d^4 + 10*d^2*e^2*x^2 + e^4*x^4)) + 16*b^2*(4*a^3*e^3*(-3*d + 5*e*x) + 2*c^3*d^2*x^3*(15*d^2 - 40*d*e*x + 9*e^2*x^2) + 6*a^2*c*e*(-2*d^3 + 15*d^2*e*x - 10*d*e^2*x^2 + 5*e^3*x^3) + 3*a*c^2*x*(5*d^4 - 40*d^3*e*x + 30*d^2*e^2*x^2 - 20*d*e^3*x^3 + e^4*x^4)) + 2*b^4*(4*a*e*(d^3 + 15*d^2*e*x - 45*d*e^2*x^2 + 5*e^3*x^3) - c*x*(5*d^4 + 80*d^3*e*x - 270*d^2*e^2*x^2 + 40*d*e^3*x^3 + e^4*x^4))) + 2*B*(256*a^5*e^4 + 128*a^4*e^2*(b*e*(-4*d + 5*e*x) + c*(3*d^2 + 5*e^2*x^2)) + b*x*(128*c^4*d^4*x^4 + 64*b*c^3*d^3*x^3*(5*d - 3*e*x) + 48*b^2*c^2*d^2*x^2*(5*d^2 - 10*d*e*x + e^2*x^2) + 8*b^3*c*d*x*(5*d^3 - 45*d^2*e*x + 15*d*e^2*x^2 + e^3*x^3) + b^4*(-5*d^4 - 60*d^3*e*x + 90*d^2*e^2*x^2 + 20*d*e^3*x^3 + 3*e^4*x^4)) + 32*a^3*(b^2*e^2*(9*d^2 - 40*d*e*x + 15*e^2*x^2) + 2*b*c*e*(-6*d^3 + 15*d^2*e*x - 20*d*e^2*x^2 + 15*e^3*x^3) + 3*c^2*(d^4 + 10*d^2*e^2*x^2 + 5*e^4*x^4)) - 16*a^2*(-15*b*c^2*x*(d - e*x)^4 + 8*c^3*d*e*x^3*(5*d^2 + 3*e^2*x^2) + b^3*e*(2*d^3 - 45*d^2*e*x + 60*d*e^2*x^2 - 5*e^3*x^3) - 3*b^2*c*(d^4 - 20*d^3*e*x + 30*d^2*e^2*x^2 - 40*d*e^3*x^3 + 5*e^4*x^4)) - 2*a*(128*c^4*d^3*e*x^5 + 20*b^3*c*x*(d - e*x)^2*(-3*d^2 + 14*d*e*x + e^2*x^2) - 32*b*c^3*d^2*x^3*(5*d^2 - 10*d*e*x + 9*e^2*x^2) + 48*b^2*c^2*d*x^2*(-5*d^3 + 10*d^2*e*x - 15*d*e^2*x^2 + 2*e^3*x^3) + b^4*(d^4 + 40*d^3*e*x - 270*d^2*e^2*x^2 + 80*d*e^3*x^3 + 5*e^4*x^4))))/(15*(b^2 - 4*a*c)^3*(a + x*(b + c*x))^(5/2))","B",1
2490,1,963,264,1.6204448,"\int \frac{(A+B x) (d+e x)^3}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a + b*x + c*x^2)^(7/2),x]","\frac{2 \left(A \left(-3 \left(d^3+5 e x d^2+15 e^2 x^2 d-5 e^3 x^3\right) b^5+\left(10 c x \left(d^3+12 e x d^2-27 e^2 x^2 d+2 e^3 x^3\right)-6 a e \left(d^2+10 e x d-15 e^2 x^2\right)\right) b^4-8 \left(3 a^2 (d-5 e x) e^2+c^2 x^2 \left(10 d^3-90 e x d^2+45 e^2 x^2 d-e^3 x^3\right)-5 a c \left(d^3+9 e x d^2-15 e^2 x^2 d+5 e^3 x^3\right)\right) b^3+48 \left(a^3 e^3+a^2 c \left(3 d^2-15 e x d+5 e^2 x^2\right) e+c^3 d x^3 \left(-10 d^2+20 e x d-3 e^2 x^2\right)+5 a c^2 x \left(-d^3+6 e x d^2-3 e^2 x^2 d+e^3 x^3\right)\right) b^2+16 c \left(8 c^3 d^2 (3 e x-5 d) x^4+6 a c^2 \left(-10 d^3+10 e x d^2-5 e^2 x^2 d+e^3 x^3\right) x^2-15 a^2 c (d-e x)^3+2 a^3 e^2 (5 e x-9 d)\right) b-32 c \left(8 c^4 d^3 x^5+2 a c^3 d \left(10 d^2+3 e^2 x^2\right) x^3+15 a^2 c^2 d \left(d^2+e^2 x^2\right) x-2 a^4 e^3-a^3 c e \left(9 d^2+5 e^2 x^2\right)\right)\right)+B \left(64 e^2 (3 c d-2 b e) a^4+16 \left(6 \left(d^3+5 e^2 x^2 d\right) c^2-2 b e \left(9 d^2-15 e x d+10 e^2 x^2\right) c+b^2 e^2 (9 d-20 e x)\right) a^3-24 \left(e \left(d^2-15 e x d+10 e^2 x^2\right) b^3-2 c \left(d^3-15 e x d^2+15 e^2 x^2 d-10 e^3 x^3\right) b^2+10 c^2 x (e x-d)^3 b+4 c^3 e x^3 \left(5 d^2+e^2 x^2\right)\right) a^2-2 \left(96 c^4 d^2 e x^5-16 b c^3 d \left(10 d^2-15 e x d+9 e^2 x^2\right) x^3+24 b^2 c^2 \left(-10 d^3+15 e x d^2-15 e^2 x^2 d+e^3 x^3\right) x^2+60 b^3 c \left(-d^3+5 e x d^2-5 e^2 x^2 d+e^3 x^3\right) x+b^4 \left(d^3+30 e x d^2-135 e^2 x^2 d+20 e^3 x^3\right)\right) a+b x \left(-5 \left(d^3+9 e x d^2-9 e^2 x^2 d-e^3 x^3\right) b^4+2 c x \left(20 d^3-135 e x d^2+30 e^2 x^2 d+e^3 x^3\right) b^3+24 c^2 d x^2 \left(10 d^2-15 e x d+e^2 x^2\right) b^2+16 c^3 d^2 x^3 (20 d-9 e x) b+128 c^4 d^3 x^4\right)\right)\right)}{15 \left(b^2-4 a c\right)^3 (a+x (b+c x))^{5/2}}","-\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*(-3*b^5*(d^3 + 5*d^2*e*x + 15*d*e^2*x^2 - 5*e^3*x^3) - 32*c*(-2*a^4*e^3 + 8*c^4*d^3*x^5 + 15*a^2*c^2*d*x*(d^2 + e^2*x^2) + 2*a*c^3*d*x^3*(10*d^2 + 3*e^2*x^2) - a^3*c*e*(9*d^2 + 5*e^2*x^2)) + 16*b*c*(-15*a^2*c*(d - e*x)^3 + 8*c^3*d^2*x^4*(-5*d + 3*e*x) + 2*a^3*e^2*(-9*d + 5*e*x) + 6*a*c^2*x^2*(-10*d^3 + 10*d^2*e*x - 5*d*e^2*x^2 + e^3*x^3)) + 48*b^2*(a^3*e^3 + c^3*d*x^3*(-10*d^2 + 20*d*e*x - 3*e^2*x^2) + a^2*c*e*(3*d^2 - 15*d*e*x + 5*e^2*x^2) + 5*a*c^2*x*(-d^3 + 6*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3)) + b^4*(-6*a*e*(d^2 + 10*d*e*x - 15*e^2*x^2) + 10*c*x*(d^3 + 12*d^2*e*x - 27*d*e^2*x^2 + 2*e^3*x^3)) - 8*b^3*(3*a^2*e^2*(d - 5*e*x) + c^2*x^2*(10*d^3 - 90*d^2*e*x + 45*d*e^2*x^2 - e^3*x^3) - 5*a*c*(d^3 + 9*d^2*e*x - 15*d*e^2*x^2 + 5*e^3*x^3))) + B*(64*a^4*e^2*(3*c*d - 2*b*e) + 16*a^3*(b^2*e^2*(9*d - 20*e*x) - 2*b*c*e*(9*d^2 - 15*d*e*x + 10*e^2*x^2) + 6*c^2*(d^3 + 5*d*e^2*x^2)) - 24*a^2*(10*b*c^2*x*(-d + e*x)^3 + 4*c^3*e*x^3*(5*d^2 + e^2*x^2) + b^3*e*(d^2 - 15*d*e*x + 10*e^2*x^2) - 2*b^2*c*(d^3 - 15*d^2*e*x + 15*d*e^2*x^2 - 10*e^3*x^3)) + b*x*(128*c^4*d^3*x^4 + 16*b*c^3*d^2*x^3*(20*d - 9*e*x) + 24*b^2*c^2*d*x^2*(10*d^2 - 15*d*e*x + e^2*x^2) - 5*b^4*(d^3 + 9*d^2*e*x - 9*d*e^2*x^2 - e^3*x^3) + 2*b^3*c*x*(20*d^3 - 135*d^2*e*x + 30*d*e^2*x^2 + e^3*x^3)) - 2*a*(96*c^4*d^2*e*x^5 - 16*b*c^3*d*x^3*(10*d^2 - 15*d*e*x + 9*e^2*x^2) + 24*b^2*c^2*x^2*(-10*d^3 + 15*d^2*e*x - 15*d*e^2*x^2 + e^3*x^3) + 60*b^3*c*x*(-d^3 + 5*d^2*e*x - 5*d*e^2*x^2 + e^3*x^3) + b^4*(d^3 + 30*d^2*e*x - 135*d*e^2*x^2 + 20*e^3*x^3)))))/(15*(b^2 - 4*a*c)^3*(a + x*(b + c*x))^(5/2))","B",1
2491,1,711,324,1.4050511,"\int \frac{(A+B x) (d+e x)^2}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a + b*x + c*x^2)^(7/2),x]","\frac{2 B \left(64 a^4 c e^2+16 a^3 \left(3 b^2 e^2+2 b c e (5 e x-6 d)+2 c^2 \left(3 d^2+5 e^2 x^2\right)\right)-8 a^2 \left(b^3 e (2 d-15 e x)-6 b^2 c \left(d^2-10 d e x+5 e^2 x^2\right)-30 b c^2 x (d-e x)^2+40 c^3 d e x^3\right)-2 a \left(b^4 \left(d^2+20 d e x-45 e^2 x^2\right)-20 b^3 c x \left(3 d^2-10 d e x+5 e^2 x^2\right)-120 b^2 c^2 x^2 \left(2 d^2-2 d e x+e^2 x^2\right)-16 b c^3 x^3 \left(10 d^2-10 d e x+3 e^2 x^2\right)+64 c^4 d e x^5\right)+b x \left(-5 b^4 \left(d^2+6 d e x-3 e^2 x^2\right)+20 b^3 c x \left(2 d^2-9 d e x+e^2 x^2\right)+8 b^2 c^2 x^2 \left(30 d^2-30 d e x+e^2 x^2\right)+32 b c^3 d x^3 (10 d-3 e x)+128 c^4 d^2 x^4\right)\right)-2 A \left(8 b^3 \left(a^2 e^2-5 a c \left(d^2+6 d e x-5 e^2 x^2\right)+5 c^2 x^2 \left(2 d^2-12 d e x+3 e^2 x^2\right)\right)+16 b^2 c \left(3 a^2 e (5 e x-2 d)+15 a c x \left(d^2-4 d e x+e^2 x^2\right)+c^2 x^3 \left(30 d^2-40 d e x+3 e^2 x^2\right)\right)+16 b c \left(6 a^3 e^2+15 a^2 c (d-e x)^2+10 a c^2 x^2 \left(6 d^2-4 d e x+e^2 x^2\right)+8 c^3 d x^4 (5 d-2 e x)\right)+32 c^2 \left(-6 a^3 d e+5 a^2 c x \left(3 d^2+e^2 x^2\right)+2 a c^2 x^3 \left(10 d^2+e^2 x^2\right)+8 c^3 d^2 x^5\right)+2 b^4 \left(2 a e (d+5 e x)-5 c x \left(d^2+8 d e x-9 e^2 x^2\right)\right)+b^5 \left(3 d^2+10 d e x+15 e^2 x^2\right)\right)}{15 \left(b^2-4 a c\right)^3 (a+x (b+c x))^{5/2}}","-\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(b^2 \left(a B e^2+A c d e+2 B c d^2\right)+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)-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}}",1,"(-2*A*(b^5*(3*d^2 + 10*d*e*x + 15*e^2*x^2) + 2*b^4*(2*a*e*(d + 5*e*x) - 5*c*x*(d^2 + 8*d*e*x - 9*e^2*x^2)) + 32*c^2*(-6*a^3*d*e + 8*c^3*d^2*x^5 + 5*a^2*c*x*(3*d^2 + e^2*x^2) + 2*a*c^2*x^3*(10*d^2 + e^2*x^2)) + 16*b*c*(6*a^3*e^2 + 8*c^3*d*x^4*(5*d - 2*e*x) + 15*a^2*c*(d - e*x)^2 + 10*a*c^2*x^2*(6*d^2 - 4*d*e*x + e^2*x^2)) + 16*b^2*c*(3*a^2*e*(-2*d + 5*e*x) + 15*a*c*x*(d^2 - 4*d*e*x + e^2*x^2) + c^2*x^3*(30*d^2 - 40*d*e*x + 3*e^2*x^2)) + 8*b^3*(a^2*e^2 - 5*a*c*(d^2 + 6*d*e*x - 5*e^2*x^2) + 5*c^2*x^2*(2*d^2 - 12*d*e*x + 3*e^2*x^2))) + 2*B*(64*a^4*c*e^2 + b*x*(128*c^4*d^2*x^4 + 32*b*c^3*d*x^3*(10*d - 3*e*x) - 5*b^4*(d^2 + 6*d*e*x - 3*e^2*x^2) + 8*b^2*c^2*x^2*(30*d^2 - 30*d*e*x + e^2*x^2) + 20*b^3*c*x*(2*d^2 - 9*d*e*x + e^2*x^2)) + 16*a^3*(3*b^2*e^2 + 2*b*c*e*(-6*d + 5*e*x) + 2*c^2*(3*d^2 + 5*e^2*x^2)) - 8*a^2*(40*c^3*d*e*x^3 + b^3*e*(2*d - 15*e*x) - 30*b*c^2*x*(d - e*x)^2 - 6*b^2*c*(d^2 - 10*d*e*x + 5*e^2*x^2)) - 2*a*(64*c^4*d*e*x^5 + b^4*(d^2 + 20*d*e*x - 45*e^2*x^2) - 120*b^2*c^2*x^2*(2*d^2 - 2*d*e*x + e^2*x^2) - 16*b*c^3*x^3*(10*d^2 - 10*d*e*x + 3*e^2*x^2) - 20*b^3*c*x*(3*d^2 - 10*d*e*x + 5*e^2*x^2))))/(15*(b^2 - 4*a*c)^3*(a + x*(b + c*x))^(5/2))","B",1
2492,1,200,225,0.5886016,"\int \frac{(A+B x) (d+e x)}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[((A + B*x)*(d + e*x))/(a + b*x + c*x^2)^(7/2),x]","\frac{2 \left(-3 \left(b^2-4 a c\right)^2 (A c (-2 a e+b (d-e x)+2 c d x)+B (a b e-2 a c (d+e x)+b x (b e-c d)))+\left(b^2-4 a c\right) (b+2 c x) (a+x (b+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)-8 c (b+2 c x) (a+x (b+c x))^2 \left(4 c (a B e+4 A c d)-8 b c (A e+B d)+3 b^2 B e\right)\right)}{15 c \left(b^2-4 a c\right)^3 (a+x (b+c x))^{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*((b^2 - 4*a*c)*(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)*(a + x*(b + c*x)) - 8*c*(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)*(a + x*(b + c*x))^2 - 3*(b^2 - 4*a*c)^2*(A*c*(-2*a*e + 2*c*d*x + b*(d - e*x)) + B*(a*b*e + b*(-(c*d) + b*e)*x - 2*a*c*(d + e*x)))))/(15*c*(b^2 - 4*a*c)^3*(a + x*(b + c*x))^(5/2))","A",1
2493,1,120,133,0.1970584,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[(A + B*x)/(a + b*x + c*x^2)^(7/2),x]","\frac{2 \left(3 \left(b^2-4 a c\right)^2 (B (2 a+b x)-A (b+2 c x))-8 \left(b^2-4 a c\right) (b+2 c x) (a+x (b+c x)) (b B-2 A c)+64 c (b+2 c x) (a+x (b+c x))^2 (b B-2 A c)\right)}{15 \left(b^2-4 a c\right)^3 (a+x (b+c x))^{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*(-8*(b^2 - 4*a*c)*(b*B - 2*A*c)*(b + 2*c*x)*(a + x*(b + c*x)) + 64*c*(b*B - 2*A*c)*(b + 2*c*x)*(a + x*(b + c*x))^2 + 3*(b^2 - 4*a*c)^2*(B*(2*a + b*x) - A*(b + 2*c*x))))/(15*(b^2 - 4*a*c)^3*(a + x*(b + c*x))^(5/2))","A",1
2494,1,1120,974,6.2401579,"\int \frac{A+B x}{(d+e x) \left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[(A + B*x)/((d + e*x)*(a + b*x + c*x^2)^(7/2)),x]","-\frac{2 \left(-\frac{2 \left(4 a c e (2 c d-b e) (b B d-2 A c d+A b e-2 a B e)+\frac{1}{2} \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(4 c e (b d-2 a e) (b B d-2 A c d+A b e-2 a B e)+\frac{1}{2} (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)}{3 \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)^{3/2}}-\frac{2 \left(\frac{15 \left(b^2-4 a c\right)^2 e^5 (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)}{\sqrt{c d^2-b e d+a e^2} \left(4 c d^2-4 b e d+4 a e^2\right)}-\frac{2 \left(-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)+\frac{1}{4} \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(\frac{1}{4} (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)-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)\right) x\right)}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \sqrt{c x^2+b x+a}}\right)}{3 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)}\right) \left(c x^2+b x+a\right)^{7/2}}{5 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (a+x (b+c x))^{7/2}}-\frac{2 \left(-a B (2 c d-b e)+A \left(-e b^2+c d b+2 a c e\right)+c (A (2 c d-b e)-B (b d-2 a e)) x\right) \left(c x^2+b x+a\right)}{5 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (a+x (b+c x))^{7/2}}","-\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*e)) + A*(2*c*d - b*e))*x)*(a + b*x + c*x^2))/(5*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + x*(b + c*x))^(7/2)) - (2*(a + b*x + c*x^2)^(7/2)*((-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)*(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*(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)*(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)*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*((-2*(-(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))))/4 + c*(-(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))))/4)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) + (15*(b^2 - 4*a*c)^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])])/(Sqrt[c*d^2 - b*d*e + a*e^2]*(4*c*d^2 - 4*b*d*e + 4*a*e^2))))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2))))/(5*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + x*(b + c*x))^(7/2))","A",1
2495,1,72,137,0.051354,"\int \frac{(5-x) (3+2 x)^4}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^4)/Sqrt[2 + 5*x + 3*x^2],x]","\frac{140255 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(3456 x^4-2160 x^3-93912 x^2-268750 x-281829\right)}{19440}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-281829 - 268750*x - 93912*x^2 - 2160*x^3 + 3456*x^4) + 140255*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/19440","A",1
2496,1,67,112,0.0333388,"\int \frac{(5-x) (3+2 x)^3}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^3)/Sqrt[2 + 5*x + 3*x^2],x]","\frac{19405 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(432 x^3-1128 x^2-11690 x-21759\right)}{3888}","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-21759 - 11690*x - 1128*x^2 + 432*x^3) + 19405*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/3888","A",1
2497,1,62,87,0.0261648,"\int \frac{(5-x) (3+2 x)^2}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^2)/Sqrt[2 + 5*x + 3*x^2],x]","\frac{1}{324} \left(1147 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2} \left(24 x^2-122 x-645\right)\right)","-\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,"(-6*Sqrt[2 + 5*x + 3*x^2]*(-645 - 122*x + 24*x^2) + 1147*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/324","A",1
2498,1,57,62,0.019546,"\int \frac{(5-x) (3+2 x)}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x))/Sqrt[2 + 5*x + 3*x^2],x]","\frac{1}{12} \left(31 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-2 (2 x-19) \sqrt{3 x^2+5 x+2}\right)","\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,"(-2*(-19 + 2*x)*Sqrt[2 + 5*x + 3*x^2] + 31*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/12","A",1
2499,1,52,57,0.0093414,"\int \frac{5-x}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/Sqrt[2 + 5*x + 3*x^2],x]","\frac{1}{18} \left(35 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)-6 \sqrt{3 x^2+5 x+2}\right)","\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,"(-6*Sqrt[2 + 5*x + 3*x^2] + 35*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/18","A",1
2500,1,72,77,0.0178119,"\int \frac{5-x}{(3+2 x) \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{1}{30} \left(-39 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-5 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)\right)","\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,"(-39*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])] - 5*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/30","A",1
2501,1,64,64,0.022307,"\int \frac{5-x}{(3+2 x)^2 \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2]),x]","-\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{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",1
2502,1,69,89,0.0336656,"\int \frac{5-x}{(3+2 x)^3 \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^3*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{1}{500} \left(-\frac{10 \sqrt{3 x^2+5 x+2} (292 x+503)}{(2 x+3)^2}-389 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)","-\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,"((-10*(503 + 292*x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2 - 389*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/500","A",1
2503,1,74,114,0.0421797,"\int \frac{5-x}{(3+2 x)^4 \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^4*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{-\frac{10 \sqrt{3 x^2+5 x+2} \left(1728 x^2+5674 x+4753\right)}{(2 x+3)^3}-993 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1500}","-\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,"((-10*Sqrt[2 + 5*x + 3*x^2]*(4753 + 5674*x + 1728*x^2))/(3 + 2*x)^3 - 993*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/1500","A",1
2504,1,79,139,0.0504501,"\int \frac{5-x}{(3+2 x)^5 \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^5*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{-17313 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-\frac{10 \sqrt{3 x^2+5 x+2} \left(65376 x^3+314692 x^2+509668 x+279039\right)}{(2 x+3)^4}}{30000}","-\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,"((-10*Sqrt[2 + 5*x + 3*x^2]*(279039 + 509668*x + 314692*x^2 + 65376*x^3))/(3 + 2*x)^4 - 17313*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/30000","A",1
2505,1,84,164,0.0623825,"\int \frac{5-x}{(3+2 x)^6 \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^6*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{-385143 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-\frac{10 \sqrt{3 x^2+5 x+2} \left(3051072 x^4+19313432 x^3+46092332 x^2+49233702 x+19918587\right)}{(2 x+3)^5}}{750000}","-\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,"((-10*Sqrt[2 + 5*x + 3*x^2]*(19918587 + 49233702*x + 46092332*x^2 + 19313432*x^3 + 3051072*x^4))/(3 + 2*x)^5 - 385143*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/750000","A",1
2506,1,81,117,0.039712,"\int \frac{(5-x) (3+2 x)^4}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{6 \left(72 x^4-102 x^3-3331 x^2+6920 x+9591\right)-6265 \sqrt{9 x^2+15 x+6} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)}{243 \sqrt{3 x^2+5 x+2}}","-\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,"-1/243*(6*(9591 + 6920*x - 3331*x^2 - 102*x^3 + 72*x^4) - 6265*Sqrt[6 + 15*x + 9*x^2]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/Sqrt[2 + 5*x + 3*x^2]","A",1
2507,1,76,92,0.0342282,"\int \frac{(5-x) (3+2 x)^3}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{6 \left(6 x^3-31 x^2+806 x+789\right)-247 \sqrt{9 x^2+15 x+6} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)}{27 \sqrt{3 x^2+5 x+2}}","-\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,"-1/27*(6*(789 + 806*x - 31*x^2 + 6*x^3) - 247*Sqrt[6 + 15*x + 9*x^2]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/Sqrt[2 + 5*x + 3*x^2]","A",1
2508,1,68,83,0.0287772,"\int \frac{(5-x) (3+2 x)^2}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{4 x^2-6 \sqrt{9 x^2+15 x+6} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+398 x+358}{3 \sqrt{3 x^2+5 x+2}}","-\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,"-1/3*(358 + 398*x + 4*x^2 - 6*Sqrt[6 + 15*x + 9*x^2]*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/Sqrt[2 + 5*x + 3*x^2]","A",1
2509,1,53,62,0.0913467,"\int \frac{(5-x) (3+2 x)}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2}{9} \left(\frac{417 x+363}{\sqrt{3 x^2+5 x+2}}+\sqrt{3} \log \left(2 \sqrt{9 x^2+15 x+6}+6 x+5\right)\right)","-\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*((363 + 417*x)/Sqrt[2 + 5*x + 3*x^2] + Sqrt[3]*Log[5 + 6*x + 2*Sqrt[6 + 15*x + 9*x^2]]))/9","A",1
2510,1,21,21,0.0405291,"\int \frac{5-x}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(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
2511,1,62,62,0.0258405,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{2 (141 x+111)}{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{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,"(-2*(111 + 141*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",1
2512,1,90,94,0.0313814,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{2 \left(6420 x^2+151 \sqrt{5} (2 x+3) \sqrt{3 x^2+5 x+2} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)+14225 x+7055\right)}{125 (2 x+3) \sqrt{3 x^2+5 x+2}}","-\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,"(-2*(7055 + 14225*x + 6420*x^2 + 151*Sqrt[5]*(3 + 2*x)*Sqrt[2 + 5*x + 3*x^2]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/(125*(3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2513,1,79,119,0.04582,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{483 \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25 \sqrt{5}}-\frac{2 \left(2592 x^3+9453 x^2+10988 x+3977\right)}{25 (2 x+3)^2 \sqrt{3 x^2+5 x+2}}","-\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,"(-2*(3977 + 10988*x + 9453*x^2 + 2592*x^3))/(25*(3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2]) - (483*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(25*Sqrt[5])","A",1
2514,1,84,144,0.0562121,"\int \frac{5-x}{(3+2 x)^4 \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^4*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{-9867 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-\frac{10 \left(83376 x^4+424938 x^3+792065 x^2+634312 x+181559\right)}{(2 x+3)^3 \sqrt{3 x^2+5 x+2}}}{1875}","-\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,"((-10*(181559 + 634312*x + 792065*x^2 + 424938*x^3 + 83376*x^4))/((3 + 2*x)^3*Sqrt[2 + 5*x + 3*x^2]) - 9867*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/1875","A",1
2515,1,89,169,0.0647108,"\int \frac{5-x}{(3+2 x)^5 \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^5*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{-246117 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)-\frac{10 \left(3665952 x^5+24066204 x^4+62190544 x^3+78737669 x^2+48537379 x+11545002\right)}{(2 x+3)^4 \sqrt{3 x^2+5 x+2}}}{37500}","-\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,"((-10*(11545002 + 48537379*x + 78737669*x^2 + 62190544*x^3 + 24066204*x^4 + 3665952*x^5))/((3 + 2*x)^4*Sqrt[2 + 5*x + 3*x^2]) - 246117*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/37500","A",1
2516,1,83,115,0.0725974,"\int \frac{(5-x) (3+2 x)^4}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 \left(-216 x^4+176160 x^3+438540 x^2+76 \sqrt{3} \left(3 x^2+5 x+2\right)^{3/2} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\right)+354459 x+92457\right)}{81 \left(3 x^2+5 x+2\right)^{3/2}}","-\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*(92457 + 354459*x + 438540*x^2 + 176160*x^3 - 216*x^4 + 76*Sqrt[3]*(2 + 5*x + 3*x^2)^(3/2)*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])]))/(81*(2 + 5*x + 3*x^2)^(3/2))","A",1
2517,1,67,92,0.0588266,"\int \frac{(5-x) (3+2 x)^3}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 \left(16448 x^3+41074 x^2+33443 x+8835\right)}{9 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{8 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{9 x^2+15 x+6}}\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*(8835 + 33443*x + 41074*x^2 + 16448*x^3))/(9*(2 + 5*x + 3*x^2)^(3/2)) - (8*ArcTanh[(5 + 6*x)/(2*Sqrt[6 + 15*x + 9*x^2])])/(9*Sqrt[3])","A",1
2518,1,33,54,0.0318452,"\int \frac{(5-x) (3+2 x)^2}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 \left(4372 x^3+10932 x^2+8925 x+2371\right)}{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*(2371 + 8925*x + 10932*x^2 + 4372*x^3))/(3*(2 + 5*x + 3*x^2)^(3/2))","A",1
2519,1,31,47,0.0578057,"\int \frac{(5-x) (3+2 x)}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 \left(1124 x^3+2810 x^2+2295 x+611\right)}{\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*(611 + 2295*x + 2810*x^2 + 1124*x^3))/(2 + 5*x + 3*x^2)^(3/2)","A",1
2520,1,31,47,0.0428584,"\int \frac{5-x}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 \left(840 x^3+2100 x^2+1715 x+457\right)}{\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*(457 + 1715*x + 2100*x^2 + 840*x^3))/(2 + 5*x + 3*x^2)^(3/2)","A",1
2521,1,72,85,0.0540082,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{2}{125} \left(\frac{5 \left(15048 x^3+37698 x^2+30827 x+8227\right)}{\left(3 x^2+5 x+2\right)^{3/2}}-52 \sqrt{5} \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)","-\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*((5*(8227 + 30827*x + 37698*x^2 + 15048*x^3))/(2 + 5*x + 3*x^2)^(3/2) - 52*Sqrt[5]*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])]))/125","A",1
2522,1,113,124,0.0574609,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{10 \left(19872 x^4+80100 x^3+116826 x^2+73215 x+16667\right)-408 \sqrt{5} \sqrt{3 x^2+5 x+2} \left(6 x^3+19 x^2+19 x+6\right) \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{125 (2 x+3) \left(3 x^2+5 x+2\right)^{3/2}}","-\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,"(10*(16667 + 73215*x + 116826*x^2 + 80100*x^3 + 19872*x^4) - 408*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2]*(6 + 19*x + 19*x^2 + 6*x^3)*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(125*(3 + 2*x)*(2 + 5*x + 3*x^2)^(3/2))","A",1
2523,1,143,147,0.0783783,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{2 \left(142500 \left(3 x^2+5 x+2\right)^2+50 (6336 x+5721) \left(3 x^2+5 x+2\right)+18 (2 x+3) \left(3 x^2+5 x+2\right)^{3/2} \left(4920 \sqrt{3 x^2+5 x+2}-407 \sqrt{5} (2 x+3) \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)-375 (47 x+37)\right)}{1875 (2 x+3)^2 \left(3 x^2+5 x+2\right)^{3/2}}","-\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*(-375*(37 + 47*x) + 50*(5721 + 6336*x)*(2 + 5*x + 3*x^2) + 142500*(2 + 5*x + 3*x^2)^2 + 18*(3 + 2*x)*(2 + 5*x + 3*x^2)^(3/2)*(4920*Sqrt[2 + 5*x + 3*x^2] - 407*Sqrt[5]*(3 + 2*x)*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])))/(1875*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(3/2))","A",1
2524,1,150,174,0.1126502,"\int \frac{5-x}{(3+2 x)^4 \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^4*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{2 \left(594400 \left(3 x^2+5 x+2\right)^2+2250 (638 x+603) \left(3 x^2+5 x+2\right)+2 (2 x+3) \left(3 x^2+5 x+2\right)^{3/2} \left(10 (7272 x+27283) \sqrt{3 x^2+5 x+2}-34581 \sqrt{5} (2 x+3)^2 \tanh ^{-1}\left(\frac{-8 x-7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)\right)-1875 (47 x+37)\right)}{9375 (2 x+3)^3 \left(3 x^2+5 x+2\right)^{3/2}}","-\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*(-1875*(37 + 47*x) + 2250*(603 + 638*x)*(2 + 5*x + 3*x^2) + 594400*(2 + 5*x + 3*x^2)^2 + 2*(3 + 2*x)*(2 + 5*x + 3*x^2)^(3/2)*(10*(27283 + 7272*x)*Sqrt[2 + 5*x + 3*x^2] - 34581*Sqrt[5]*(3 + 2*x)^2*ArcTanh[(-7 - 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])))/(9375*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(3/2))","A",1
2525,1,35,35,0.0066763,"\int \frac{-1+x}{(1+x) \sqrt{1+x+x^2}} \, dx","Integrate[(-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",1
2526,1,28,53,0.0138276,"\int (5-x) (3+2 x)^{7/2} \left(2+5 x+3 x^2\right) \, dx","Integrate[(5 - x)*(3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2),x]","-\frac{(2 x+3)^{9/2} \left(1287 x^3-5841 x^2-10269 x-3727\right)}{6435}","-\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,"-1/6435*((3 + 2*x)^(9/2)*(-3727 - 10269*x - 5841*x^2 + 1287*x^3))","A",1
2527,1,28,53,0.0123795,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right) \, dx","Integrate[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2),x]","-\frac{(2 x+3)^{7/2} \left(2079 x^3-9891 x^2-16429 x-5829\right)}{9009}","-\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,"-1/9009*((3 + 2*x)^(7/2)*(-5829 - 16429*x - 9891*x^2 + 2079*x^3))","A",1
2528,1,28,53,0.0119339,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right) \, dx","Integrate[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2),x]","-\frac{1}{693} (2 x+3)^{5/2} \left(189 x^3-959 x^2-1455 x-513\right)","-\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,"-1/693*((3 + 2*x)^(5/2)*(-513 - 1455*x - 959*x^2 + 189*x^3))","A",1
2529,1,28,53,0.0102001,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right) \, dx","Integrate[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2),x]","-\frac{1}{105} (2 x+3)^{3/2} \left(35 x^3-195 x^2-249 x-101\right)","-\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,"-1/105*((3 + 2*x)^(3/2)*(-101 - 249*x - 195*x^2 + 35*x^3))","A",1
2530,1,28,53,0.0117807,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)}{\sqrt{3+2 x}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2))/Sqrt[3 + 2*x],x]","-\frac{1}{105} \sqrt{2 x+3} \left(45 x^3-291 x^2-223 x-381\right)","-\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,"-1/105*(Sqrt[3 + 2*x]*(-381 - 223*x - 291*x^2 + 45*x^3))","A",1
2531,1,28,53,0.0117558,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)}{(3+2 x)^{3/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2))/(3 + 2*x)^(3/2),x]","-\frac{9 x^3-77 x^2+117 x+501}{15 \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,"-1/15*(501 + 117*x - 77*x^2 + 9*x^3)/Sqrt[3 + 2*x]","A",1
2532,1,28,53,0.0116289,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)}{(3+2 x)^{5/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2))/(3 + 2*x)^(5/2),x]","-\frac{3 x^3-57 x^2-273 x-263}{3 (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,"-1/3*(-263 - 273*x - 57*x^2 + 3*x^3)/(3 + 2*x)^(3/2)","A",1
2533,1,28,53,0.0117959,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)}{(3+2 x)^{7/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2))/(3 + 2*x)^(7/2),x]","-\frac{9 x^3+111 x^2+245 x+153}{3 (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,"-1/3*(153 + 245*x + 111*x^2 + 9*x^3)/(3 + 2*x)^(5/2)","A",1
2534,1,38,79,0.0168087,"\int (5-x) (3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^2 \, dx","Integrate[(5 - x)*(3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^2,x]","-\frac{(2 x+3)^{9/2} \left(984555 x^5-2702700 x^4-13495911 x^3-17037702 x^2-8846388 x-1670104\right)}{2078505}","-\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,"-1/2078505*((3 + 2*x)^(9/2)*(-1670104 - 8846388*x - 17037702*x^2 - 13495911*x^3 - 2702700*x^4 + 984555*x^5))","A",1
2535,1,38,79,0.0158239,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^2 \, dx","Integrate[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^2,x]","-\frac{(2 x+3)^{7/2} \left(27027 x^5-78078 x^4-371679 x^3-461664 x^2-236768 x-44388\right)}{51051}","-\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,"-1/51051*((3 + 2*x)^(7/2)*(-44388 - 236768*x - 461664*x^2 - 371679*x^3 - 78078*x^4 + 27027*x^5))","A",1
2536,1,38,79,0.015027,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^2 \, dx","Integrate[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^2,x]","-\frac{(2 x+3)^{5/2} \left(9009 x^5-27720 x^4-124005 x^3-151270 x^2-76260 x-14304\right)}{15015}","-\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,"-1/15015*((3 + 2*x)^(5/2)*(-14304 - 76260*x - 151270*x^2 - 124005*x^3 - 27720*x^4 + 9009*x^5))","A",1
2537,1,38,79,0.014192,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right)^2 \, dx","Integrate[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^2,x]","-\frac{1}{117} (2 x+3)^{3/2} \left(81 x^5-270 x^4-1109 x^3-1332 x^2-648 x-132\right)","-\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,"-1/117*((3 + 2*x)^(3/2)*(-132 - 648*x - 1332*x^2 - 1109*x^3 - 270*x^4 + 81*x^5))","A",1
2538,1,38,79,0.0161551,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^2}{\sqrt{3+2 x}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^2)/Sqrt[3 + 2*x],x]","-\frac{\sqrt{2 x+3} \left(945 x^5-3500 x^4-12645 x^3-15354 x^2-6252 x-4344\right)}{1155}","-\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,"-1/1155*(Sqrt[3 + 2*x]*(-4344 - 6252*x - 15354*x^2 - 12645*x^3 - 3500*x^4 + 945*x^5))","A",1
2539,1,38,79,0.0153966,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^2}{(3+2 x)^{3/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^2)/(3 + 2*x)^(3/2),x]","-\frac{35 x^5-150 x^4-431 x^3-632 x^2+432 x+1996}{35 \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,"-1/35*(1996 + 432*x - 632*x^2 - 431*x^3 - 150*x^4 + 35*x^5)/Sqrt[3 + 2*x]","A",1
2540,1,38,79,0.0154411,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^2}{(3+2 x)^{5/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^2)/(3 + 2*x)^(5/2),x]","-\frac{27 x^5-144 x^4-215 x^3-1530 x^2-7164 x-7024}{21 (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,"-1/21*(-7024 - 7164*x - 1530*x^2 - 215*x^3 - 144*x^4 + 27*x^5)/(3 + 2*x)^(3/2)","A",1
2541,1,38,79,0.0154726,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^2}{(3+2 x)^{7/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^2)/(3 + 2*x)^(7/2),x]","-\frac{9 x^5-70 x^4+275 x^3+3300 x^2+6760 x+4076}{5 (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,"-1/5*(4076 + 6760*x + 3300*x^2 + 275*x^3 - 70*x^4 + 9*x^5)/(3 + 2*x)^(5/2)","A",1
2542,1,48,105,0.0208665,"\int (5-x) (3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^3 \, dx","Integrate[(5 - x)*(3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^3,x]","-\frac{(2 x+3)^{9/2} \left(56119635 x^7-56119635 x^6-943203690 x^5-2232945000 x^4-2481091899 x^3-1481619843 x^2-460865502 x-58847566\right)}{47805615}","-\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,"-1/47805615*((3 + 2*x)^(9/2)*(-58847566 - 460865502*x - 1481619843*x^2 - 2481091899*x^3 - 2232945000*x^4 - 943203690*x^5 - 56119635*x^6 + 56119635*x^7))","A",1
2543,1,48,105,0.0193116,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^3 \, dx","Integrate[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^3,x]","-\frac{(2 x+3)^{7/2} \left(20007 x^7-22113 x^6-339066 x^5-791700 x^4-871983 x^3-517293 x^2-160006 x-20346\right)}{15561}","-\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,"-1/15561*((3 + 2*x)^(7/2)*(-20346 - 160006*x - 517293*x^2 - 871983*x^3 - 791700*x^4 - 339066*x^5 - 22113*x^6 + 20007*x^7))","A",1
2544,1,48,105,0.018813,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^3 \, dx","Integrate[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^3,x]","-\frac{(2 x+3)^{5/2} \left(6891885 x^7-8513505 x^6-117819702 x^5-270695040 x^4-295054725 x^3-173763625 x^2-53367570 x-6778218\right)}{4849845}","-\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,"-1/4849845*((3 + 2*x)^(5/2)*(-6778218 - 53367570*x - 173763625*x^2 - 295054725*x^3 - 270695040*x^4 - 117819702*x^5 - 8513505*x^6 + 6891885*x^7))","A",1
2545,1,48,105,0.0172958,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right)^3 \, dx","Integrate[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^3,x]","-\frac{(2 x+3)^{3/2} \left(1216215 x^7-1702701 x^6-20968794 x^5-47286540 x^4-50880095 x^3-29756385 x^2-9013014 x-1197186\right)}{765765}","-\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,"-1/765765*((3 + 2*x)^(3/2)*(-1197186 - 9013014*x - 29756385*x^2 - 50880095*x^3 - 47286540*x^4 - 20968794*x^5 - 1702701*x^6 + 1216215*x^7))","A",1
2546,1,48,105,0.0202528,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^3}{\sqrt{3+2 x}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^3)/Sqrt[3 + 2*x],x]","-\frac{\sqrt{2 x+3} \left(81081 x^7-130977 x^6-1407294 x^5-3109960 x^4-3285105 x^3-1924641 x^2-535098 x-196506\right)}{45045}","-\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,"-1/45045*(Sqrt[3 + 2*x]*(-196506 - 535098*x - 1924641*x^2 - 3285105*x^3 - 3109960*x^4 - 1407294*x^5 - 130977*x^6 + 81081*x^7))","A",1
2547,1,48,105,0.0184774,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^3}{(3+2 x)^{3/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(3/2),x]","-\frac{10395 x^7-19845 x^6-180530 x^5-392500 x^4-398339 x^3-256433 x^2+77138 x+431614}{5005 \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,"-1/5005*(431614 + 77138*x - 256433*x^2 - 398339*x^3 - 392500*x^4 - 180530*x^5 - 19845*x^6 + 10395*x^7)/Sqrt[3 + 2*x]","A",1
2548,1,48,105,0.0187417,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^3}{(3+2 x)^{5/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(5/2),x]","-\frac{567 x^7-1323 x^6-9666 x^5-21360 x^4-17663 x^3-42003 x^2-184566 x-181486}{231 (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,"-1/231*(-181486 - 184566*x - 42003*x^2 - 17663*x^3 - 21360*x^4 - 9666*x^5 - 1323*x^6 + 567*x^7)/(3 + 2*x)^(3/2)","A",1
2549,1,48,105,0.0191499,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^3}{(3+2 x)^{7/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(7/2),x]","-\frac{45 x^7-135 x^6-702 x^5-1940 x^4+3195 x^3+41805 x^2+85070 x+51162}{15 (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,"-1/15*(51162 + 85070*x + 41805*x^2 + 3195*x^3 - 1940*x^4 - 702*x^5 - 135*x^6 + 45*x^7)/(3 + 2*x)^(5/2)","A",1
2550,1,70,94,0.0679968,"\int \frac{(5-x) (3+2 x)^{7/2}}{2+5 x+3 x^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2),x]","-\frac{8 \sqrt{2 x+3} \left(270 x^3-738 x^2-8639 x-24728\right)}{2835}+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,"(-8*Sqrt[3 + 2*x]*(-24728 - 8639*x - 738*x^2 + 270*x^3))/2835 + 12*ArcTanh[Sqrt[3 + 2*x]] - (4250*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/81","A",1
2551,1,64,81,0.0668713,"\int \frac{(5-x) (3+2 x)^{5/2}}{2+5 x+3 x^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2),x]","12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{2}{405} \left(3 \sqrt{2 x+3} \left(36 x^2-202 x-1699\right)+2125 \sqrt{15} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)\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,"12*ArcTanh[Sqrt[3 + 2*x]] - (2*(3*Sqrt[3 + 2*x]*(-1699 - 202*x + 36*x^2) + 2125*Sqrt[15]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]]))/405","A",1
2552,1,56,68,0.0293806,"\int \frac{(5-x) (3+2 x)^{3/2}}{2+5 x+3 x^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2),x]","-\frac{2}{27} \left(6 \sqrt{2 x+3} (x-14)-162 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+85 \sqrt{15} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)\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,"(-2*(6*(-14 + x)*Sqrt[3 + 2*x] - 162*ArcTanh[Sqrt[3 + 2*x]] + 85*Sqrt[15]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]]))/27","A",1
2553,1,55,55,0.0150575,"\int \frac{(5-x) \sqrt{3+2 x}}{2+5 x+3 x^2} \, dx","Integrate[((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",1
2554,1,38,38,0.0130549,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)} \, dx","Integrate[(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",1
2555,1,55,55,0.0371972,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)} \, dx","Integrate[(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",1
2556,1,65,68,0.0836563,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)} \, dx","Integrate[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)),x]","12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{2 \left(2970 x+153 \sqrt{15} (2 x+3)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)+4780\right)}{375 (2 x+3)^{3/2}}","-\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,"12*ArcTanh[Sqrt[3 + 2*x]] - (2*(4780 + 2970*x + 153*Sqrt[15]*(3 + 2*x)^(3/2)*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]]))/(375*(3 + 2*x)^(3/2))","A",1
2557,1,63,81,0.094461,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)} \, dx","Integrate[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)),x]","\frac{2}{625} \left(-\frac{5 \left(2388 x^2+7494 x+5933\right)}{(2 x+3)^{5/2}}+3750 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-153 \sqrt{15} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)\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,"(2*((-5*(5933 + 7494*x + 2388*x^2))/(3 + 2*x)^(5/2) + 3750*ArcTanh[Sqrt[3 + 2*x]] - 153*Sqrt[15]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]]))/625","A",1
2558,1,81,98,0.0884455,"\int \frac{(5-x) (3+2 x)^{7/2}}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2)^2,x]","\frac{1}{81} \left(2800 \sqrt{15} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)-\frac{3 \sqrt{2 x+3} \left(48 x^3-400 x^2+1843 x+2129\right)}{3 x^2+5 x+2}\right)-154 \tanh ^{-1}\left(\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,"-154*ArcTanh[Sqrt[3 + 2*x]] + ((-3*Sqrt[3 + 2*x]*(2129 + 1843*x - 400*x^2 + 48*x^3))/(2 + 5*x + 3*x^2) + 2800*Sqrt[15]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/81","A",1
2559,1,92,81,0.0483174,"\int \frac{(5-x) (3+2 x)^{5/2}}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2)^2,x]","-\frac{\sqrt{2 x+3} \left(8 x^2+209 x+183\right)+390 \left(3 x^2+5 x+2\right) \tanh ^{-1}\left(\sqrt{2 x+3}\right)-100 \sqrt{15} \left(3 x^2+5 x+2\right) \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)}{9 x^2+15 x+6}","-\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,"-((Sqrt[3 + 2*x]*(183 + 209*x + 8*x^2) + 390*(2 + 5*x + 3*x^2)*ArcTanh[Sqrt[3 + 2*x]] - 100*Sqrt[15]*(2 + 5*x + 3*x^2)*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/(6 + 15*x + 9*x^2))","A",1
2560,1,70,72,0.0537363,"\int \frac{(5-x) (3+2 x)^{3/2}}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2)^2,x]","\frac{1}{9} \left(-\frac{3 \sqrt{2 x+3} (139 x+121)}{3 x^2+5 x+2}-954 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+248 \sqrt{15} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)\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,"((-3*Sqrt[3 + 2*x]*(121 + 139*x))/(2 + 5*x + 3*x^2) - 954*ArcTanh[Sqrt[3 + 2*x]] + 248*Sqrt[15]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/9","A",1
2561,1,66,66,0.0563331,"\int \frac{(5-x) \sqrt{3+2 x}}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[((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",1
2562,1,72,72,0.059018,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(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",1
2563,1,85,85,0.0779652,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(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",1
2564,1,94,98,0.1111905,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^2),x]","\frac{1}{75} \left(-\frac{45 (47 x+37)}{(2 x+3)^{3/2} \left(3 x^2+5 x+2\right)}-\frac{2058}{\sqrt{2 x+3}}-\frac{1310}{(2 x+3)^{3/2}}-750 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+2808 \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)\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,"(-1310/(3 + 2*x)^(3/2) - 2058/Sqrt[3 + 2*x] - (45*(37 + 47*x))/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)) - 750*ArcTanh[Sqrt[3 + 2*x]] + 2808*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/75","A",1
2565,1,86,111,0.1979021,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^2),x]","\frac{47628 \sqrt{15} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)-\frac{5 \left(886536 x^4+4348428 x^3+7782530 x^2+5977997 x+1646109\right)}{(2 x+3)^{5/2} \left(3 x^2+5 x+2\right)}}{9375}+14 \tanh ^{-1}\left(\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,"14*ArcTanh[Sqrt[3 + 2*x]] + ((-5*(1646109 + 5977997*x + 7782530*x^2 + 4348428*x^3 + 886536*x^4))/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)) + 47628*Sqrt[15]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/9375","A",1
2566,1,86,115,0.1182649,"\int \frac{(5-x) (3+2 x)^{9/2}}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((5 - x)*(3 + 2*x)^(9/2))/(2 + 5*x + 3*x^2)^3,x]","\frac{1}{54} \left(-\frac{3 \sqrt{2 x+3} \left(192 x^4-45083 x^3-112467 x^2-90465 x-23327\right)}{\left(3 x^2+5 x+2\right)^2}-27350 \sqrt{15} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)\right)+1962 \tanh ^{-1}\left(\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,"1962*ArcTanh[Sqrt[3 + 2*x]] + ((-3*Sqrt[3 + 2*x]*(-23327 - 90465*x - 112467*x^2 - 45083*x^3 + 192*x^4))/(2 + 5*x + 3*x^2)^2 - 27350*Sqrt[15]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/54","A",1
2567,1,80,100,0.082122,"\int \frac{(5-x) (3+2 x)^{7/2}}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2)^3,x]","\frac{\sqrt{2 x+3} \left(12443 x^3+30979 x^2+25073 x+6555\right)}{6 \left(3 x^2+5 x+2\right)^2}+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,"(Sqrt[3 + 2*x]*(6555 + 25073*x + 30979*x^2 + 12443*x^3))/(6*(2 + 5*x + 3*x^2)^2) + 1582*ArcTanh[Sqrt[3 + 2*x]] - 1225*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]]","A",1
2568,1,82,102,0.0814365,"\int \frac{(5-x) (3+2 x)^{5/2}}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2)^3,x]","\frac{\sqrt{2 x+3} \left(9825 x^3+24497 x^2+19891 x+5237\right)}{6 \left(3 x^2+5 x+2\right)^2}+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,"(Sqrt[3 + 2*x]*(5237 + 19891*x + 24497*x^2 + 9825*x^3))/(6*(2 + 5*x + 3*x^2)^2) + 1250*ArcTanh[Sqrt[3 + 2*x]] - (2905*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/3","A",1
2569,1,80,100,0.0767705,"\int \frac{(5-x) (3+2 x)^{3/2}}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2)^3,x]","\frac{\sqrt{2 x+3} \left(2529 x^3+6305 x^2+5123 x+1353\right)}{2 \left(3 x^2+5 x+2\right)^2}+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]*(1353 + 5123*x + 6305*x^2 + 2529*x^3))/(2*(2 + 5*x + 3*x^2)^2) + 966*ArcTanh[Sqrt[3 + 2*x]] - 1247*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]]","A",1
2570,1,81,102,0.1490079,"\int \frac{(5-x) \sqrt{3+2 x}}{\left(2+5 x+3 x^2\right)^3} \, dx","Integrate[((5 - x)*Sqrt[3 + 2*x])/(2 + 5*x + 3*x^2)^3,x]","\frac{1}{50} \left(\frac{5 \sqrt{2 x+3} \left(9567 x^3+23847 x^2+19373 x+5123\right)}{\left(3 x^2+5 x+2\right)^2}-9426 \sqrt{15} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)\right)+730 \tanh ^{-1}\left(\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,"730*ArcTanh[Sqrt[3 + 2*x]] + ((5*Sqrt[3 + 2*x]*(5123 + 19373*x + 23847*x^2 + 9567*x^3))/(2 + 5*x + 3*x^2)^2 - 9426*Sqrt[15]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/50","A",1
2571,1,81,102,0.0971229,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)^3} \, dx","Integrate[(5 - x)/(Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^3),x]","\frac{1}{50} \left(\frac{\sqrt{2 x+3} \left(35217 x^3+87897 x^2+71443 x+18913\right)}{\left(3 x^2+5 x+2\right)^2}+27100 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-34926 \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)\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,"((Sqrt[3 + 2*x]*(18913 + 71443*x + 87897*x^2 + 35217*x^3))/(2 + 5*x + 3*x^2)^2 + 27100*ArcTanh[Sqrt[3 + 2*x]] - 34926*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/50","A",1
2572,1,86,115,0.1408821,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^3} \, dx","Integrate[(5 - x)/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^3),x]","\frac{1}{50} \left(\frac{48006 x^4+193455 x^3+281403 x^2+175465 x+39661}{\sqrt{2 x+3} \left(3 x^2+5 x+2\right)^2}+20100 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-25434 \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)\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,"((39661 + 175465*x + 281403*x^2 + 193455*x^3 + 48006*x^4)/(Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^2) + 20100*ArcTanh[Sqrt[3 + 2*x]] - 25434*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/50","A",1
2573,1,91,128,0.2863992,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^3} \, dx","Integrate[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^3),x]","\frac{\frac{5 \left(740124 x^5+4247856 x^4+9453447 x^3+10168583 x^2+5278129 x+1057511\right)}{(2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^2}-273618 \sqrt{15} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)}{3750}+310 \tanh ^{-1}\left(\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,"310*ArcTanh[Sqrt[3 + 2*x]] + ((5*(1057511 + 5278129*x + 10168583*x^2 + 9453447*x^3 + 4247856*x^4 + 740124*x^5))/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^2) - 273618*Sqrt[15]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/3750","A",1
2574,1,121,141,0.1758463,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^3} \, dx","Integrate[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^3),x]","\frac{-\frac{28125 (47 x+37)}{\left(3 x^2+5 x+2\right)^2}+\frac{1875 (9957 x+8852)}{3 x^2+5 x+2}+2 (2 x+3) \left(21 (2 x+3) \left(593750 \sqrt{2 x+3} \tanh ^{-1}\left(\sqrt{2 x+3}\right)-115263 \sqrt{30 x+45} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)-17435\right)+2567425\right)+8459850}{93750 (2 x+3)^{5/2}}","-\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,"(8459850 - (28125*(37 + 47*x))/(2 + 5*x + 3*x^2)^2 + (1875*(8852 + 9957*x))/(2 + 5*x + 3*x^2) + 2*(3 + 2*x)*(2567425 + 21*(3 + 2*x)*(-17435 + 593750*Sqrt[3 + 2*x]*ArcTanh[Sqrt[3 + 2*x]] - 115263*Sqrt[45 + 30*x]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])))/(93750*(3 + 2*x)^(5/2))","A",1
2575,1,141,105,0.2730963,"\int \frac{5+\sqrt{35}+10 x}{\sqrt{1+2 x} \left(2+3 x+5 x^2\right)} \, dx","Integrate[(5 + Sqrt[35] + 10*x)/(Sqrt[1 + 2*x]*(2 + 3*x + 5*x^2)),x]","\frac{2}{217} \left(\sqrt{2-i \sqrt{31}} \left(31 \sqrt{7}-7 i \sqrt{155}-2 i \sqrt{217}\right) \tanh ^{-1}\left(\frac{\sqrt{10 x+5}}{\sqrt{2-i \sqrt{31}}}\right)+\sqrt{2+i \sqrt{31}} \left(31 \sqrt{7}+7 i \sqrt{155}+2 i \sqrt{217}\right) \tanh ^{-1}\left(\frac{\sqrt{10 x+5}}{\sqrt{2+i \sqrt{31}}}\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[2 - I*Sqrt[31]]*(31*Sqrt[7] - (7*I)*Sqrt[155] - (2*I)*Sqrt[217])*ArcTanh[Sqrt[5 + 10*x]/Sqrt[2 - I*Sqrt[31]]] + Sqrt[2 + I*Sqrt[31]]*(31*Sqrt[7] + (7*I)*Sqrt[155] + (2*I)*Sqrt[217])*ArcTanh[Sqrt[5 + 10*x]/Sqrt[2 + I*Sqrt[31]]]))/217","C",1
2576,1,208,224,0.3695608,"\int (5-x) (3+2 x)^{5/2} \sqrt{2+5 x+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2 \left(734832 x^7+789264 x^6-18348768 x^5-80563032 x^4-147414969 x^3-137602437 x^2-64194200 x-11846900\right) \sqrt{2 x+3}-127082 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+227969 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{336798 (2 x+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,"-1/336798*(2*Sqrt[3 + 2*x]*(-11846900 - 64194200*x - 137602437*x^2 - 147414969*x^3 - 80563032*x^4 - 18348768*x^5 + 789264*x^6 + 734832*x^7) + 227969*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 127082*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2577,1,203,197,0.3240377,"\int (5-x) (3+2 x)^{3/2} \sqrt{2+5 x+3 x^2} \, dx","Integrate[(5 - x)*(3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2 \left(68040 x^6-59940 x^5-1799874 x^4-5185953 x^3-6208230 x^2-3389617 x-695446\right) \sqrt{2 x+3}-15784 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+33103 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{51030 (2 x+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,"-1/51030*(2*Sqrt[3 + 2*x]*(-695446 - 3389617*x - 6208230*x^2 - 5185953*x^3 - 1799874*x^4 - 59940*x^5 + 68040*x^6) + 33103*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 15784*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2578,1,198,170,0.2958507,"\int (5-x) \sqrt{3+2 x} \sqrt{2+5 x+3 x^2} \, dx","Integrate[(5 - x)*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2 \left(4860 x^5-15552 x^4-121239 x^3-200865 x^2-128926 x-28888\right) \sqrt{2 x+3}-1762 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+4879 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{5670 (2 x+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,"-1/5670*(2*Sqrt[3 + 2*x]*(-28888 - 128926*x - 200865*x^2 - 121239*x^3 - 15552*x^4 + 4860*x^5) + 4879*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 1762*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2579,1,193,143,0.3091499,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{\sqrt{3+2 x}} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/Sqrt[3 + 2*x],x]","-\frac{2 \left(162 x^4-1071 x^3-2220 x^2-1049 x-62\right) \sqrt{2 x+3}-188 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+761 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{270 (2 x+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,"-1/270*(2*Sqrt[3 + 2*x]*(-62 - 1049*x - 2220*x^2 - 1071*x^3 + 162*x^4) + 761*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 188*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2580,1,185,141,0.3356599,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^{3/2}} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^(3/2),x]","\frac{10 \left(-9 x^3+159 x^2+284 x+116\right)-122 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+605 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{90 \sqrt{2 x+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,"(10*(116 + 284*x + 159*x^2 - 9*x^3) + 605*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 122*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/(90*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])","A",1
2581,1,182,143,0.2975979,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^{5/2}} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^(5/2),x]","-\frac{90 x^3+480 x^2+610 x-16 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{5/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+67 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{5/2} \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+220}{30 (2 x+3)^{3/2} \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,"-1/30*(220 + 610*x + 480*x^2 + 90*x^3 + 67*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 16*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2582,1,182,170,0.2948586,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^{7/2}} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^(7/2),x]","\frac{1290 x^3+3110 x^2+2460 x+22 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{7/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-49 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{7/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+640}{250 (2 x+3)^{5/2} \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,"(640 + 2460*x + 3110*x^2 + 1290*x^3 - 49*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 22*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/(250*(3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2583,1,217,197,0.3829083,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^{9/2}} \, dx","Integrate[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^(9/2),x]","-\frac{6 (2 x+3)^3 \left(742 \left(3 x^2+5 x+2\right)-188 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+371 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)-4 \left(3 x^2+5 x+2\right) \left(8904 x^3+43728 x^2+74557 x+39436\right)}{17500 (2 x+3)^{7/2} \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,"-1/17500*(-4*(2 + 5*x + 3*x^2)*(39436 + 74557*x + 43728*x^2 + 8904*x^3) + 6*(3 + 2*x)^3*(742*(2 + 5*x + 3*x^2) + 371*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 188*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/((3 + 2*x)^(7/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2584,1,218,256,0.3486722,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 \left(630485856 x^9+1907623872 x^8-11776907520 x^7-82311172272 x^6-217661096106 x^5-319887585072 x^4-283276026729 x^3-150475882830 x^2-44206631441 x-5523159638\right) \sqrt{2 x+3}+1590604 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+1454957 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{131351220 (2 x+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,"-1/131351220*(2*Sqrt[3 + 2*x]*(-5523159638 - 44206631441*x - 150475882830*x^2 - 283276026729*x^3 - 319887585072*x^4 - 217661096106*x^5 - 82311172272*x^6 - 11776907520*x^7 + 1907623872*x^8 + 630485856*x^9) + 1454957*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 1590604*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2585,1,213,229,0.3322454,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 \left(40415760 x^8+52050600 x^7-895236300 x^6-4079217510 x^5-7944858702 x^4-8470029969 x^3-5141306625 x^2-1668494576 x-224705588\right) \sqrt{2 x+3}-71222 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+1068599 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{14594580 (2 x+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,"-1/14594580*(2*Sqrt[3 + 2*x]*(-224705588 - 1668494576*x - 5141306625*x^2 - 8470029969*x^3 - 7944858702*x^4 - 4079217510*x^5 - 895236300*x^6 + 52050600*x^7 + 40415760*x^8) + 1068599*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 71222*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2586,1,208,202,0.3317582,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Integrate[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 \left(87480 x^7-48600 x^6-2001510 x^5-6002964 x^4-8112483 x^3-5740860 x^2-2059597 x-293686\right) \sqrt{2 x+3}-2824 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+15283 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{53460 (2 x+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,"-1/53460*(2*Sqrt[3 + 2*x]*(-293686 - 2059597*x - 5740860*x^2 - 8112483*x^3 - 6002964*x^4 - 2001510*x^5 - 48600*x^6 + 87480*x^7) + 15283*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 2824*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2587,1,203,175,0.3231465,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{\sqrt{3+2 x}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/Sqrt[3 + 2*x],x]","-\frac{2 \left(34020 x^6-88290 x^5-687798 x^4-1306791 x^3-1043385 x^2-312914 x-10832\right) \sqrt{2 x+3}-16358 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+77861 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{34020 (2 x+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,"-1/34020*(2*Sqrt[3 + 2*x]*(-10832 - 312914*x - 1043385*x^2 - 1306791*x^3 - 687798*x^4 - 88290*x^5 + 34020*x^6) + 77861*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 16358*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2588,1,192,173,0.3342968,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{3/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(3/2),x]","\frac{-1620 x^5+8208 x^4+18846 x^3+53340 x^2+73094 x-3596 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{3/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+16877 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{3/2} \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+28772}{1260 \sqrt{2 x+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,"(28772 + 73094*x + 53340*x^2 + 18846*x^3 + 8208*x^4 - 1620*x^5 + 16877*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 3596*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/(1260*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])","A",1
2589,1,195,175,0.3137302,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{5/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(5/2),x]","-\frac{2 \left(54 x^5-396 x^4+777 x^3+6107 x^2+7444 x-117 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{5/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+2564\right)+1101 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{5/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{60 (2 x+3)^{3/2} \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,"-1/60*(1101*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 2*(2564 + 7444*x + 6107*x^2 + 777*x^3 - 396*x^4 + 54*x^5 - 117*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/((3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2590,1,192,175,0.342125,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{7/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(7/2),x]","\frac{-900 x^5+16800 x^4+100610 x^3+190440 x^2+147790 x-592 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{7/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+2779 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{7/2} \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+40260}{300 (2 x+3)^{5/2} \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,"(40260 + 147790*x + 190440*x^2 + 100610*x^3 + 16800*x^4 - 900*x^5 + 2779*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 592*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/(300*(3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2591,1,192,175,0.3298675,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{9/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(9/2),x]","-\frac{31500 x^5+323760 x^4+1009230 x^3+1386750 x^2+878020 x-1066 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{9/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+5047 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{9/2} \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+208240}{3500 (2 x+3)^{7/2} \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,"-1/3500*(208240 + 878020*x + 1386750*x^2 + 1009230*x^3 + 323760*x^4 + 31500*x^5 + 5047*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(9/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 1066*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(9/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)^(7/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2592,1,192,202,0.4352356,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{11/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(11/2),x]","\frac{204180 x^5+822160 x^4+1297210 x^3+998860 x^2+373610 x-44 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{11/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+23 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{11/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+53980}{22500 (2 x+3)^{9/2} \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,"(53980 + 373610*x + 998860*x^2 + 1297210*x^3 + 822160*x^4 + 204180*x^5 + 23*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(11/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 44*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(11/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/(22500*(3 + 2*x)^(9/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2593,1,227,229,0.4699015,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{13/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(13/2),x]","-\frac{2 (2 x+3)^5 \left(82054 \left(3 x^2+5 x+2\right)+3394 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+41027 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)-4 \left(3 x^2+5 x+2\right) \left(1312864 x^5+11031040 x^4+41848650 x^3+65139670 x^2+42879355 x+9919671\right)}{17325000 (2 x+3)^{11/2} \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,"-1/17325000*(-4*(2 + 5*x + 3*x^2)*(9919671 + 42879355*x + 65139670*x^2 + 41848650*x^3 + 11031040*x^4 + 1312864*x^5) + 2*(3 + 2*x)^5*(82054*(2 + 5*x + 3*x^2) + 41027*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 3394*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/((3 + 2*x)^(11/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2594,1,228,288,0.3765817,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{-30234850 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+115524325 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+2 \left(64309557312 x^{11}+311460012864 x^{10}-694795413312 x^9-9445976815968 x^8-34294970344572 x^7-69684837178068 x^6-90580760151282 x^5-78460508136978 x^4-45255052994607 x^3-16735272462363 x^2-3595384785664 x-341519551612\right) \sqrt{2 x+3}}{5656859208 (2 x+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,"-1/5656859208*(2*Sqrt[3 + 2*x]*(-341519551612 - 3595384785664*x - 16735272462363*x^2 - 45255052994607*x^3 - 78460508136978*x^4 - 90580760151282*x^5 - 69684837178068*x^6 - 34294970344572*x^7 - 9445976815968*x^8 - 694795413312*x^9 + 311460012864*x^10 + 64309557312*x^11) + 115524325*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 30234850*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2595,1,223,261,0.3655623,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 \left(28371863520 x^{10}+90474720336 x^9-474654810168 x^8-3544442250300 x^7-9891695193912 x^6-15763726088406 x^5-15827034250764 x^4-10225439632143 x^3-4138096653600 x^2-956384897657 x-96409103246\right) \sqrt{2 x+3}-54474128 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+240489851 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{4465941480 (2 x+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,"-1/4465941480*(2*Sqrt[3 + 2*x]*(-96409103246 - 956384897657*x - 4138096653600*x^2 - 10225439632143*x^3 - 15827034250764*x^4 - 15763726088406*x^5 - 9891695193912*x^6 - 3544442250300*x^7 - 474654810168*x^8 + 90474720336*x^9 + 28371863520*x^10) + 240489851*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 54474128*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2596,1,218,234,0.362653,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right)^{5/2} \, dx","Integrate[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 \left(315242928 x^9+468822816 x^8-6333945660 x^7-30512259036 x^6-63978029658 x^5-76896556902 x^4-56607962679 x^3-25296672765 x^2-6298405666 x-666434848\right) \sqrt{2 x+3}-4132174 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+19196233 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{87567480 (2 x+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,"-1/87567480*(2*Sqrt[3 + 2*x]*(-666434848 - 6298405666*x - 25296672765*x^2 - 56607962679*x^3 - 76896556902*x^4 - 63978029658*x^5 - 30512259036*x^6 - 6333945660*x^7 + 468822816*x^8 + 315242928*x^9) + 19196233*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 4132174*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2597,1,213,207,0.3310836,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{\sqrt{3+2 x}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/Sqrt[3 + 2*x],x]","-\frac{2 \left(4041576 x^8-1163484 x^7-83553120 x^6-268524558 x^5-406647648 x^4-349849791 x^3-170798082 x^2-39284147 x-1864706\right) \sqrt{2 x+3}-971132 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+4561319 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{1945944 (2 x+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,"-1/1945944*(2*Sqrt[3 + 2*x]*(-1864706 - 39284147*x - 170798082*x^2 - 349849791*x^3 - 406647648*x^4 - 268524558*x^5 - 83553120*x^6 - 1163484*x^7 + 4041576*x^8) + 4561319*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 971132*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2598,1,205,205,0.400503,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{3/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(3/2),x]","\frac{2 \left(-183708 x^7+401436 x^6+3305934 x^5+7163046 x^4+6935769 x^3+6834513 x^2+6998740 x-336013 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{3/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+2657740\right)+3159317 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{149688 \sqrt{2 x+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,"(3159317*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 2*(2657740 + 6998740*x + 6834513*x^2 + 6935769*x^3 + 7163046*x^4 + 3305934*x^5 + 401436*x^6 - 183708*x^7 - 336013*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/(149688*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])","A",1
2599,1,202,205,0.3147453,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{5/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(5/2),x]","-\frac{13608 x^7-38232 x^6-234684 x^5-561564 x^4+120594 x^3+2607724 x^2+3207982 x-49640 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{5/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+233345 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{5/2} \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+1099572}{4536 (2 x+3)^{3/2} \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,"-1/4536*(1099572 + 3207982*x + 2607724*x^2 + 120594*x^3 - 561564*x^4 - 234684*x^5 - 38232*x^6 + 13608*x^7 + 233345*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 49640*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2600,1,202,207,0.4300089,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{7/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(7/2),x]","\frac{-3240 x^7+12744 x^6+41220 x^5+335988 x^4+1717690 x^3+3262382 x^2+2556580 x-10422 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{7/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+48993 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{7/2} \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+701136}{840 (2 x+3)^{5/2} \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,"(701136 + 2556580*x + 3262382*x^2 + 1717690*x^3 + 335988*x^4 + 41220*x^5 + 12744*x^6 - 3240*x^7 + 48993*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 10422*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/(840*(3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2601,1,202,207,0.3907435,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{9/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(9/2),x]","-\frac{4536 x^7-29736 x^6+158172 x^5+2140148 x^4+6437058 x^3+8516152 x^2+5250234 x-6092 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{9/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+28637 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{9/2} \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+1223436}{840 (2 x+3)^{7/2} \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,"-1/840*(1223436 + 5250234*x + 8516152*x^2 + 6437058*x^3 + 2140148*x^4 + 158172*x^5 - 29736*x^6 + 4536*x^7 + 28637*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(9/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 6092*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(9/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)^(7/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2602,1,227,207,0.4360745,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{11/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(11/2),x]","-\frac{8 \left(3 x^2+5 x+2\right) \left(18900 x^5+1579088 x^4+8510198 x^3+17853828 x^2+16893773 x+6047963\right)-4 (2 x+3)^4 \left(247786 \left(3 x^2+5 x+2\right)-26354 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+123893 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)}{50400 (2 x+3)^{9/2} \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,"-1/50400*(8*(2 + 5*x + 3*x^2)*(6047963 + 16893773*x + 17853828*x^2 + 8510198*x^3 + 1579088*x^4 + 18900*x^5) - 4*(3 + 2*x)^4*(247786*(2 + 5*x + 3*x^2) + 123893*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 26354*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/((3 + 2*x)^(9/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2603,1,227,207,0.4538355,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{13/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(13/2),x]","-\frac{4 (2 x+3)^5 \left(1509998 \left(3 x^2+5 x+2\right)-160672 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+754999 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)-8 \left(3 x^2+5 x+2\right) \left(21041468 x^5+140915480 x^4+387989550 x^3+544712540 x^2+387631385 x+111387702\right)}{2772000 (2 x+3)^{11/2} \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,"-1/2772000*(-8*(2 + 5*x + 3*x^2)*(111387702 + 387631385*x + 544712540*x^2 + 387989550*x^3 + 140915480*x^4 + 21041468*x^5) + 4*(3 + 2*x)^5*(1509998*(2 + 5*x + 3*x^2) + 754999*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 160672*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/((3 + 2*x)^(11/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2604,1,232,234,0.5098825,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{15/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(15/2),x]","-\frac{8 \left(3 x^2+5 x+2\right) \left(2277184 x^6+6409516 x^5+12953760 x^4+33648370 x^3+54318160 x^2+41339721 x+11865789\right)-4 (2 x+3)^6 \left(71162 \left(3 x^2+5 x+2\right)-7318 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+35581 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)}{13860000 (2 x+3)^{13/2} \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,"-1/13860000*(8*(2 + 5*x + 3*x^2)*(11865789 + 41339721*x + 54318160*x^2 + 33648370*x^3 + 12953760*x^4 + 6409516*x^5 + 2277184*x^6) - 4*(3 + 2*x)^6*(71162*(2 + 5*x + 3*x^2) + 35581*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 7318*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/((3 + 2*x)^(13/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2605,1,237,261,0.5283654,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{17/2}} \, dx","Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(17/2),x]","-\frac{2 (2 x+3)^7 \left(9400244 \left(3 x^2+5 x+2\right)-1131016 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+4700122 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)-8 \left(3 x^2+5 x+2\right) \left(300807808 x^7+3348834304 x^6+17742950508 x^5+46830142120 x^4+67557035830 x^3+55283449932 x^2+24502214271 x+4641518352\right)}{4504500000 (2 x+3)^{15/2} \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,"-1/4504500000*(-8*(2 + 5*x + 3*x^2)*(4641518352 + 24502214271*x + 55283449932*x^2 + 67557035830*x^3 + 46830142120*x^4 + 17742950508*x^5 + 3348834304*x^6 + 300807808*x^7) + 2*(3 + 2*x)^7*(9400244*(2 + 5*x + 3*x^2) + 4700122*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 1131016*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/((3 + 2*x)^(15/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2606,1,198,192,0.315513,"\int \frac{(5-x) (3+2 x)^{5/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^(5/2))/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{8 \left(162 x^5-216 x^4-5526 x^3-18501 x^2-20111 x-6758\right) \sqrt{2 x+3}+4540 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-6055 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{567 (2 x+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,"-1/567*(8*Sqrt[3 + 2*x]*(-6758 - 20111*x - 18501*x^2 - 5526*x^3 - 216*x^4 + 162*x^5) - 6055*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 4540*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2607,1,193,165,0.2866542,"\int \frac{(5-x) (3+2 x)^{3/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^(3/2))/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2 \left(324 x^4-1422 x^3-14955 x^2-21143 x-7934\right) \sqrt{2 x+3}+2254 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-2743 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{405 (2 x+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,"-1/405*(2*Sqrt[3 + 2*x]*(-7934 - 21143*x - 14955*x^2 - 1422*x^3 + 324*x^4) - 2743*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 2254*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2608,1,188,138,0.3062095,"\int \frac{(5-x) \sqrt{3+2 x}}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[((5 - x)*Sqrt[3 + 2*x])/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{4 \left(9 x^3-123 x^2-224 x-92\right) \sqrt{2 x+3}+104 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-101 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{27 (2 x+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,"-1/27*(4*Sqrt[3 + 2*x]*(-92 - 224*x - 123*x^2 + 9*x^3) - 101*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 104*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2609,1,177,107,0.3976628,"\int \frac{5-x}{\sqrt{3+2 x} \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/(Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{30 x^2+50 x+34 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{3/2} \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+5 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{3/2} \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+20}{15 \sqrt{2 x+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,"-1/15*(20 + 50*x + 30*x^2 + 5*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 34*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/(Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])","A",1
2610,1,104,136,0.1710999,"\int \frac{5-x}{(3+2 x)^{3/2} \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{(x+1) \sqrt{\frac{3 x+2}{2 x+3}} \left(13 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-12 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)}{\sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \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,"((1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*(13*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 12*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/(Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*Sqrt[2 + 5*x + 3*x^2])","A",1
2611,1,183,165,0.3084459,"\int \frac{5-x}{(3+2 x)^{5/2} \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{193 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)^{5/2} \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-2 \left(65 \left(3 x^2+5 x+2\right)+77 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{5/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)}{75 (2 x+3)^{3/2} \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,"(193*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 2*(65*(2 + 5*x + 3*x^2) + 77*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/(75*(3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2612,1,182,192,0.2919749,"\int \frac{5-x}{(3+2 x)^{7/2} \sqrt{2+5 x+3 x^2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^(7/2)*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{23460 x^3+80140 x^2+84040 x+3328 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{7/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-4501 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{7/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+27360}{1875 (2 x+3)^{5/2} \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,"-1/1875*(27360 + 84040*x + 80140*x^2 + 23460*x^3 - 4501*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 3328*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2613,1,192,197,0.3333794,"\int \frac{(5-x) (3+2 x)^{7/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 \left(\left(432 x^4-936 x^3-30120 x^2+13231 x+39553\right) \sqrt{2 x+3}+8036 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-17087 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)}{405 (2 x+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*(Sqrt[3 + 2*x]*(39553 + 13231*x - 30120*x^2 - 936*x^3 + 432*x^4) - 17087*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 8036*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/(405*(3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2614,1,187,170,0.3231162,"\int \frac{(5-x) (3+2 x)^{5/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 \left(\left(72 x^3-696 x^2+6521 x+6803\right) \sqrt{2 x+3}+670 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-1915 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)}{81 (2 x+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*(Sqrt[3 + 2*x]*(6803 + 6521*x - 696*x^2 + 72*x^3) - 1915*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 670*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/(81*(3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2615,1,183,143,0.3280846,"\int \frac{(5-x) (3+2 x)^{3/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 \left(12 x^2+607 x+541\right) \sqrt{2 x+3}+64 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-274 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{9 (2 x+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,"-1/9*(2*Sqrt[3 + 2*x]*(541 + 607*x + 12*x^2) - 274*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 64*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2616,1,178,137,0.3168249,"\int \frac{(5-x) \sqrt{3+2 x}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[((5 - x)*Sqrt[3 + 2*x])/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{10 (139 x+121) \sqrt{2 x+3}+68 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-350 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{15 (2 x+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,"-1/15*(10*Sqrt[3 + 2*x]*(121 + 139*x) - 350*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 68*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2617,1,178,141,0.3106696,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/(Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{-10 (35 x+29) \sqrt{2 x+3}-24 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+94 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{5 (2 x+3) \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,"(-10*Sqrt[3 + 2*x]*(29 + 35*x) + 94*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 24*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^2*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/(5*(3 + 2*x)*Sqrt[2 + 5*x + 3*x^2])","A",1
2618,1,172,170,0.3150598,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{2 \left(705 x+86 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-227 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+555\right)}{25 \sqrt{2 x+3} \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,"(-2*(555 + 705*x - 227*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 86*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/(25*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])","A",1
2619,1,177,197,0.3378708,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{2 \left(-18870 x^2-42025 x-1832 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{5/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+3719 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{5/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-20905\right)}{375 (2 x+3)^{3/2} \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,"(2*(-20905 - 42025*x - 18870*x^2 + 3719*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 1832*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(5/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/(375*(3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2620,1,182,224,0.3746686,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{2 \left(922020 x^3+3383680 x^2+3957355 x+60586 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{7/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-106687 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{7/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+1439445\right)}{9375 (2 x+3)^{5/2} \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,"(-2*(1439445 + 3957355*x + 3383680*x^2 + 922020*x^3 - 106687*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 60586*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(7/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/(9375*(3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2])","A",1
2621,1,220,202,0.4815102,"\int \frac{(5-x) (3+2 x)^{9/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^(9/2))/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 \left(2 \left(3 x^2+5 x+2\right) \left(55258 \left(3 x^2+5 x+2\right)-5312 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+27629 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)+3 (2 x+3) \left(144 x^4-166566 x^3-411640 x^2-330053 x-85285\right)\right)}{243 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}}","-\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*(3 + 2*x)*(-85285 - 330053*x - 411640*x^2 - 166566*x^3 + 144*x^4) + 2*(2 + 5*x + 3*x^2)*(55258*(2 + 5*x + 3*x^2) + 27629*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 5312*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])))/(243*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2))","A",1
2622,1,196,175,0.3543555,"\int \frac{(5-x) (3+2 x)^{7/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{\frac{63784 \left(3 x^2+5 x+2\right)}{\sqrt{2 x+3}}-\frac{6 \sqrt{2 x+3} \left(47766 x^3+118690 x^2+96107 x+25237\right)}{3 x^2+5 x+2}-\frac{6776 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}+\frac{31892 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}}{81 \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,"-1/81*((63784*(2 + 5*x + 3*x^2))/Sqrt[3 + 2*x] - (6*Sqrt[3 + 2*x]*(25237 + 96107*x + 118690*x^2 + 47766*x^3))/(2 + 5*x + 3*x^2) + (31892*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)] - (6776*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)])/Sqrt[2 + 5*x + 3*x^2]","A",1
2623,1,196,175,0.3437988,"\int \frac{(5-x) (3+2 x)^{5/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{\frac{17240 \left(3 x^2+5 x+2\right)}{\sqrt{2 x+3}}-\frac{6 \sqrt{2 x+3} \left(12930 x^3+32192 x^2+26161 x+6917\right)}{3 x^2+5 x+2}-\frac{1840 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}+\frac{8620 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}}{27 \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,"-1/27*((17240*(2 + 5*x + 3*x^2))/Sqrt[3 + 2*x] - (6*Sqrt[3 + 2*x]*(6917 + 26161*x + 32192*x^2 + 12930*x^3))/(2 + 5*x + 3*x^2) + (8620*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)] - (1840*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)])/Sqrt[2 + 5*x + 3*x^2]","A",1
2624,1,196,175,0.346687,"\int \frac{(5-x) (3+2 x)^{3/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{\frac{22520 \left(3 x^2+5 x+2\right)}{\sqrt{2 x+3}}-\frac{30 \sqrt{2 x+3} \left(3378 x^3+8410 x^2+6839 x+1813\right)}{3 x^2+5 x+2}-\frac{2392 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}+\frac{11260 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}}{45 \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,"-1/45*((22520*(2 + 5*x + 3*x^2))/Sqrt[3 + 2*x] - (30*Sqrt[3 + 2*x]*(1813 + 6839*x + 8410*x^2 + 3378*x^3))/(2 + 5*x + 3*x^2) + (11260*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)] - (2392*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)])/Sqrt[2 + 5*x + 3*x^2]","A",1
2625,1,196,173,0.3431364,"\int \frac{(5-x) \sqrt{3+2 x}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[((5 - x)*Sqrt[3 + 2*x])/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{\frac{5704 \left(3 x^2+5 x+2\right)}{\sqrt{2 x+3}}-\frac{6 \sqrt{2 x+3} \left(4278 x^3+10648 x^2+8657 x+2297\right)}{3 x^2+5 x+2}-\frac{608 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}+\frac{2852 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}}{15 \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,"-1/15*((5704*(2 + 5*x + 3*x^2))/Sqrt[3 + 2*x] - (6*Sqrt[3 + 2*x]*(2297 + 8657*x + 10648*x^2 + 4278*x^3))/(2 + 5*x + 3*x^2) + (2852*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)] - (608*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)])/Sqrt[2 + 5*x + 3*x^2]","A",1
2626,1,196,175,0.3337748,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/(Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{-\frac{6952 \left(3 x^2+5 x+2\right)}{\sqrt{2 x+3}}+\frac{2 \sqrt{2 x+3} \left(15642 x^3+38982 x^2+31713 x+8423\right)}{3 x^2+5 x+2}+\frac{728 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}-\frac{3476 (x+1) \sqrt{\frac{3 x+2}{2 x+3}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)}{\sqrt{\frac{x+1}{10 x+15}}}}{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,"((-6952*(2 + 5*x + 3*x^2))/Sqrt[3 + 2*x] + (2*Sqrt[3 + 2*x]*(8423 + 31713*x + 38982*x^2 + 15642*x^3))/(2 + 5*x + 3*x^2) - (3476*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)] + (728*(1 + x)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])/Sqrt[(1 + x)/(15 + 10*x)])/(25*Sqrt[2 + 5*x + 3*x^2])","A",1
2627,1,215,202,0.3829203,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{2 \left(5 \left(14454 x^3+36414 x^2+29941 x+8031\right)+1048 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{2 x+3} \sqrt{\frac{3 x+2}{2 x+3}} \left(6 x^3+19 x^2+19 x+6\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)-5866 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{2 x+3} \sqrt{\frac{3 x+2}{2 x+3}} \left(6 x^3+19 x^2+19 x+6\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)}{125 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}}","-\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*(5*(8031 + 29941*x + 36414*x^2 + 14454*x^3) - 5866*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*Sqrt[3 + 2*x]*Sqrt[(2 + 3*x)/(3 + 2*x)]*(6 + 19*x + 19*x^2 + 6*x^3)*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 1048*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*Sqrt[3 + 2*x]*Sqrt[(2 + 3*x)/(3 + 2*x)]*(6 + 19*x + 19*x^2 + 6*x^3)*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5]))/(125*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2))","A",1
2628,1,222,229,0.5247998,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{2 \left(1717128 x^5+9687072 x^4+21265294 x^3+22647906 x^2-2 (2 x+3) \left(3 x^2+5 x+2\right) \left(47698 \left(3 x^2+5 x+2\right)-722 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+23849 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)+11683203 x+2334397\right)}{1875 (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{3/2}}","-\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*(2334397 + 11683203*x + 22647906*x^2 + 21265294*x^3 + 9687072*x^4 + 1717128*x^5 - 2*(3 + 2*x)*(2 + 5*x + 3*x^2)*(47698*(2 + 5*x + 3*x^2) + 23849*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] - 722*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])))/(1875*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(3/2))","A",1
2629,1,229,256,0.5089299,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Integrate[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{2 \left(3871728 x^6+36155064 x^5+129381052 x^4+231620622 x^3+220795962 x^2-2 (2 x+3)^2 \left(3 x^2+5 x+2\right) \left(53774 \left(3 x^2+5 x+2\right)+70064 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)+26887 \sqrt{5} \sqrt{\frac{x+1}{2 x+3}} \sqrt{\frac{3 x+2}{2 x+3}} (2 x+3)^{3/2} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}}}{\sqrt{2 x+3}}\right)|\frac{3}{5}\right)\right)+106756189 x+20514383\right)}{15625 (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)^{3/2}}","-\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*(20514383 + 106756189*x + 220795962*x^2 + 231620622*x^3 + 129381052*x^4 + 36155064*x^5 + 3871728*x^6 - 2*(3 + 2*x)^2*(2 + 5*x + 3*x^2)*(53774*(2 + 5*x + 3*x^2) + 26887*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticE[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5] + 70064*Sqrt[5]*Sqrt[(1 + x)/(3 + 2*x)]*(3 + 2*x)^(3/2)*Sqrt[(2 + 3*x)/(3 + 2*x)]*EllipticF[ArcSin[Sqrt[5/3]/Sqrt[3 + 2*x]], 3/5])))/(15625*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(3/2))","A",1
2630,1,978,545,10.582916,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{c x^2+b x+a} \left(\left(10 A c e (2 c d-b e)+B \left(3 c^2 d^2+8 b^2 e^2-c e (13 b d+9 a e)\right)\right) \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)-\frac{i \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+1} \left(\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(10 A c e (2 c d-b e)+B \left(3 c^2 d^2+8 b^2 e^2-c e (13 b d+9 a e)\right)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(8 b^3 B e^3-b^2 \left(21 c d B+8 \sqrt{\left(b^2-4 a c\right) e^2} B+10 A c e\right) e^2+b c \left(10 A e \left(3 c d+\sqrt{\left(b^2-4 a c\right) e^2}\right)+B \left(15 c d^2+13 \sqrt{\left(b^2-4 a c\right) e^2} d-17 a e^2\right)\right) e+c \left(-3 B c \sqrt{\left(b^2-4 a c\right) e^2} d^2+3 a B e^2 \left(8 c d+3 \sqrt{\left(b^2-4 a c\right) e^2}\right)-10 A c e \left(3 c d^2+2 \sqrt{\left(b^2-4 a c\right) e^2} d-a e^2\right)\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{2 \sqrt{2} \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{d+e x}}\right) (d+e x)^{3/2}}{15 c^3 e^2 \sqrt{a+x (b+c x)} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^2}}}+\frac{\left(\frac{2 (6 B c d-4 b B e+5 A c e)}{15 c^2}+\frac{2 B e x}{5 c}\right) \left(c x^2+b x+a\right) \sqrt{d+e x}}{\sqrt{a+x (b+c 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}",1,"(Sqrt[d + e*x]*((2*(6*B*c*d - 4*b*B*e + 5*A*c*e))/(15*c^2) + (2*B*e*x)/(5*c))*(a + b*x + c*x^2))/Sqrt[a + x*(b + c*x)] + (2*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2]*((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)))*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)) - ((I/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(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)))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (8*b^3*B*e^3 - b^2*e^2*(21*B*c*d + 10*A*c*e + 8*B*Sqrt[(b^2 - 4*a*c)*e^2]) + c*(-3*B*c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] + 3*a*B*e^2*(8*c*d + 3*Sqrt[(b^2 - 4*a*c)*e^2]) - 10*A*c*e*(3*c*d^2 - a*e^2 + 2*d*Sqrt[(b^2 - 4*a*c)*e^2])) + b*c*e*(10*A*e*(3*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + B*(15*c*d^2 - 17*a*e^2 + 13*d*Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[d + e*x])))/(15*c^3*e^2*Sqrt[a + x*(b + c*x)]*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
2631,1,653,452,7.124664,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{a+b x+c x^2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{d+e x} \left(B c (a+x (b+c x))+\frac{(d+e x) \left(\frac{e^2 (a+x (b+c x)) (3 A c e-2 b B e+B c d)}{(d+e x)^2}+\frac{i \sqrt{1-\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}+1} \left(\left(-b e \left(2 B \sqrt{e^2 \left(b^2-4 a c\right)}+3 A c e+3 B c d\right)+c \left(3 A e \left(\sqrt{e^2 \left(b^2-4 a c\right)}+2 c d\right)+B d \sqrt{e^2 \left(b^2-4 a c\right)}-2 a B e^2\right)+2 b^2 B e^2\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right) (-3 A c e+2 b B e-B c d) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{2 \sqrt{2} \sqrt{d+e x} \sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}\right)}{e^2}\right)}{3 c^2 \sqrt{a+x (b+c 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}",1,"(2*Sqrt[d + e*x]*(B*c*(a + x*(b + c*x)) + ((d + e*x)*((e^2*(B*c*d - 2*b*B*e + 3*A*c*e)*(a + x*(b + c*x)))/(d + e*x)^2 + ((I/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((-(B*c*d) + 2*b*B*e - 3*A*c*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (2*b^2*B*e^2 - b*e*(3*B*c*d + 3*A*c*e + 2*B*Sqrt[(b^2 - 4*a*c)*e^2]) + c*(-2*a*B*e^2 + B*d*Sqrt[(b^2 - 4*a*c)*e^2] + 3*A*e*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[d + e*x])))/e^2))/(3*c^2*Sqrt[a + x*(b + c*x)])","C",1
2632,1,814,393,5.2029356,"\int \frac{A+B x}{\sqrt{d+e x} \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2]),x]","-\frac{(d+e x)^{3/2} \left(-\frac{4 B \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} (a+x (b+c x)) e^2}{(d+e x)^2}+\frac{i \sqrt{2} B \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+b (d-e x) e+\sqrt{\left(b^2-4 a c\right) e^2} (d+e x)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+b (e x-d) e+\sqrt{\left(b^2-4 a c\right) e^2} (d+e x)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}-\frac{i \sqrt{2} \left(-b e B+\sqrt{\left(b^2-4 a c\right) e^2} B+2 A c e\right) \sqrt{\frac{-2 a e^2+2 c d x e+b (d-e x) e+\sqrt{\left(b^2-4 a c\right) e^2} (d+e x)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+b (e x-d) e+\sqrt{\left(b^2-4 a c\right) e^2} (d+e x)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{2 c e^2 \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{a+x (b+c 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}}",1,"-1/2*((d + e*x)^(3/2)*((-4*B*e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x)))/(d + e*x)^2 + (I*Sqrt[2]*B*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + 2*c*d*e*x + b*e*(d - e*x) + Sqrt[(b^2 - 4*a*c)*e^2]*(d + e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 - 2*c*d*e*x + b*e*(-d + e*x) + Sqrt[(b^2 - 4*a*c)*e^2]*(d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] - (I*Sqrt[2]*(-(b*B*e) + 2*A*c*e + B*Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + 2*c*d*e*x + b*e*(d - e*x) + Sqrt[(b^2 - 4*a*c)*e^2]*(d + e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 - 2*c*d*e*x + b*e*(-d + e*x) + Sqrt[(b^2 - 4*a*c)*e^2]*(d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/(c*e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[a + x*(b + c*x)])","C",1
2633,1,550,460,4.5025507,"\int \frac{A+B x}{(d+e x)^{3/2} \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2]),x]","-\frac{i (d+e x) \sqrt{1-\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right)}} \sqrt{\frac{2 \left(e (a e-b d)+c d^2\right)}{(d+e x) \left(\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d\right)}+1} \left(\left(-A e \left(\sqrt{e^2 \left(b^2-4 a c\right)}+2 c d\right)+B d \sqrt{e^2 \left(b^2-4 a c\right)}-2 a B e^2+b e (A e+B d)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+(A e-B d) \left(\sqrt{e^2 \left(b^2-4 a c\right)}-b e+2 c d\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{\sqrt{2} e^2 \sqrt{a+x (b+c x)} \left(e (a e-b d)+c d^2\right) \sqrt{\frac{e (a e-b d)+c d^2}{\sqrt{e^2 \left(b^2-4 a c\right)}+b e-2 c d}}}","-\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,"((-I)*(d + e*x)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((-(B*d) + A*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (-2*a*B*e^2 + B*d*Sqrt[(b^2 - 4*a*c)*e^2] + b*e*(B*d + A*e) - A*e*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2]))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*e^2*(c*d^2 + e*(-(b*d) + a*e))*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[a + x*(b + c*x)])","C",1
2634,1,992,591,9.6809879,"\int \frac{A+B x}{(d+e x)^{5/2} \sqrt{a+b x+c x^2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(5/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{c x^2+b x+a} \left(\frac{i \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+1} \left(\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(B c d^2+B e (b d-3 a e)+2 A e (b e-2 c d)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)-\left(B c \sqrt{\left(b^2-4 a c\right) e^2} d^2-8 a B c e^2 d-b^2 e^2 (B d+2 A e)+2 A c e \left(-3 c d^2-2 \sqrt{\left(b^2-4 a c\right) e^2} d+a e^2\right)+b e \left(2 A e \left(3 c d+\sqrt{\left(b^2-4 a c\right) e^2}\right)+B \left(3 c d^2+\sqrt{\left(b^2-4 a c\right) e^2} d+3 a e^2\right)\right)-3 a B e^2 \sqrt{\left(b^2-4 a c\right) e^2}\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{2 \sqrt{2} \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{d+e x}}-\left(B c d^2+B e (b d-3 a e)+2 A e (b e-2 c d)\right) \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)\right) (d+e x)^{3/2}}{3 e^2 \left(c d^2-b e d+a e^2\right)^2 \sqrt{a+x (b+c x)} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^2}}}+\frac{\left(c x^2+b x+a\right) \left(-\frac{2 (A e-B d)}{3 \left(c d^2-b e d+a e^2\right) (d+e x)^2}-\frac{2 \left(-B c d^2-b B e d+4 A c e d-2 A b e^2+3 a B e^2\right)}{3 \left(c d^2-b e d+a e^2\right)^2 (d+e x)}\right) \sqrt{d+e x}}{\sqrt{a+x (b+c 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(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,"(Sqrt[d + e*x]*(a + b*x + c*x^2)*((-2*(-(B*d) + A*e))/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (2*(-(B*c*d^2) - b*B*d*e + 4*A*c*d*e - 2*A*b*e^2 + 3*a*B*e^2))/(3*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x))))/Sqrt[a + x*(b + c*x)] + (2*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2]*(-((B*c*d^2 + B*e*(b*d - 3*a*e) + 2*A*e*(-2*c*d + b*e))*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x))) + ((I/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(B*c*d^2 + B*e*(b*d - 3*a*e) + 2*A*e*(-2*c*d + b*e))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] - (-8*a*B*c*d*e^2 + B*c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] - 3*a*B*e^2*Sqrt[(b^2 - 4*a*c)*e^2] - b^2*e^2*(B*d + 2*A*e) + 2*A*c*e*(-3*c*d^2 + a*e^2 - 2*d*Sqrt[(b^2 - 4*a*c)*e^2]) + b*e*(2*A*e*(3*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + B*(3*c*d^2 + 3*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[d + e*x])))/(3*e^2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[a + x*(b + c*x)]*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
2635,1,1287,678,12.4277711,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^(3/2),x]","\frac{\sqrt{d+e x} \left(\frac{2 B e^2}{3 c^2}+\frac{2 \left(-B e^2 x b^3-a B e^2 b^2+A c e^2 x b^2+2 B c d e x b^2+A c^2 d^2 b+a A c e^2 b+2 a B c d e b-B c^2 d^2 x b+3 a B c e^2 x b-2 A c^2 d e x b-2 a B c^2 d^2+2 a^2 B c e^2-4 a A c^2 d e+2 A c^3 d^2 x-2 a A c^2 e^2 x-4 a B c^2 d e x\right)}{c^2 \left(4 a c-b^2\right) \left(c x^2+b x+a\right)}\right) \left(c x^2+b x+a\right)^2}{(a+x (b+c x))^{3/2}}+\frac{2 (d+e x)^{3/2} \left(\left(8 B e^2 b^3-c e (13 B d+6 A e) b^2+c \left(3 B c d^2+6 A c e d-29 a B e^2\right) b+2 c^2 \left(-3 A c d^2+20 a B e d+9 a A e^2\right)\right) \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)-\frac{i \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+1} \left(\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(8 B e^2 b^3-c e (13 B d+6 A e) b^2+c \left(3 B c d^2+6 A c e d-29 a B e^2\right) b+2 c^2 \left(-3 A c d^2+20 a B e d+9 a A e^2\right)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(8 B e^3 b^4-e^2 \left(21 c d B+8 \sqrt{\left(b^2-4 a c\right) e^2} B+6 A c e\right) b^3+c e \left(6 A e \left(2 c d+\sqrt{\left(b^2-4 a c\right) e^2}\right)+B \left(15 c d^2+13 \sqrt{\left(b^2-4 a c\right) e^2} d-37 a e^2\right)\right) b^2+c \left(a e^2 \left(84 c d B+29 \sqrt{\left(b^2-4 a c\right) e^2} B+24 A c e\right)-3 c d \sqrt{\left(b^2-4 a c\right) e^2} (B d+2 A e)\right) b+2 c^2 \left(10 a^2 B e^3-a \left(10 B d \left(3 c d+2 \sqrt{\left(b^2-4 a c\right) e^2}\right)+3 A e \left(8 c d+3 \sqrt{\left(b^2-4 a c\right) e^2}\right)\right) e+3 A c d^2 \sqrt{\left(b^2-4 a c\right) e^2}\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{2 \sqrt{2} \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{d+e x}}\right) \left(c x^2+b x+a\right)^{3/2}}{3 c^3 \left(4 a c-b^2\right) e (a+x (b+c x))^{3/2} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^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{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{\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)}}}",1,"(Sqrt[d + e*x]*(a + b*x + c*x^2)^2*((2*B*e^2)/(3*c^2) + (2*(A*b*c^2*d^2 - 2*a*B*c^2*d^2 + 2*a*b*B*c*d*e - 4*a*A*c^2*d*e - a*b^2*B*e^2 + a*A*b*c*e^2 + 2*a^2*B*c*e^2 - b*B*c^2*d^2*x + 2*A*c^3*d^2*x + 2*b^2*B*c*d*e*x - 2*A*b*c^2*d*e*x - 4*a*B*c^2*d*e*x - b^3*B*e^2*x + A*b^2*c*e^2*x + 3*a*b*B*c*e^2*x - 2*a*A*c^2*e^2*x))/(c^2*(-b^2 + 4*a*c)*(a + b*x + c*x^2))))/(a + x*(b + c*x))^(3/2) + (2*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)*((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))*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)) - ((I/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^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))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (8*b^4*B*e^3 - b^3*e^2*(21*B*c*d + 6*A*c*e + 8*B*Sqrt[(b^2 - 4*a*c)*e^2]) + b*c*(-3*c*d*Sqrt[(b^2 - 4*a*c)*e^2]*(B*d + 2*A*e) + a*e^2*(84*B*c*d + 24*A*c*e + 29*B*Sqrt[(b^2 - 4*a*c)*e^2])) + b^2*c*e*(6*A*e*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + B*(15*c*d^2 - 37*a*e^2 + 13*d*Sqrt[(b^2 - 4*a*c)*e^2])) + 2*c^2*(10*a^2*B*e^3 + 3*A*c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] - a*e*(10*B*d*(3*c*d + 2*Sqrt[(b^2 - 4*a*c)*e^2]) + 3*A*e*(8*c*d + 3*Sqrt[(b^2 - 4*a*c)*e^2]))))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[d + e*x])))/(3*c^3*(-b^2 + 4*a*c)*e*(a + x*(b + c*x))^(3/2)*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
2636,1,932,530,9.7043781,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{d+e x} \left(B e x b^2+A c d b+a B e b-B c d x b-A c e x b-2 a B c d-2 a A c e+2 A c^2 d x-2 a B c e x\right) \left(c x^2+b x+a\right)}{c \left(4 a c-b^2\right) (a+x (b+c x))^{3/2}}-\frac{2 (d+e x)^{3/2} \left(c x^2+b x+a\right)^{3/2} \left(-\left(\left(-2 B e b^2+B c d b+A c e b-2 A c^2 d+6 a B c e\right) \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)\right)-\frac{i \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+1} \left(\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(2 B e b^2-c (B d+A e) b+2 c (A c d-3 a B e)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(2 B e^2 b^3-e \left(3 c d B+2 \sqrt{\left(b^2-4 a c\right) e^2} B+A c e\right) b^2+c \left(\sqrt{\left(b^2-4 a c\right) e^2} (B d+A e)-8 a B e^2\right) b+2 c \left(a e \left(6 c d B+3 \sqrt{\left(b^2-4 a c\right) e^2} B+2 A c e\right)-A c d \sqrt{\left(b^2-4 a c\right) e^2}\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{2 \sqrt{2} \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{d+e x}}\right)}{c^2 \left(4 a c-b^2\right) e (a+x (b+c x))^{3/2} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^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]*(A*b*c*d - 2*a*B*c*d + a*b*B*e - 2*a*A*c*e - b*B*c*d*x + 2*A*c^2*d*x + b^2*B*e*x - A*b*c*e*x - 2*a*B*c*e*x)*(a + b*x + c*x^2))/(c*(-b^2 + 4*a*c)*(a + x*(b + c*x))^(3/2)) - (2*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)*(-((b*B*c*d - 2*A*c^2*d - 2*b^2*B*e + A*b*c*e + 6*a*B*c*e)*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x))) - ((I/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(2*b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - 3*a*B*e))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (2*b^3*B*e^2 - b^2*e*(3*B*c*d + A*c*e + 2*B*Sqrt[(b^2 - 4*a*c)*e^2]) + b*c*(-8*a*B*e^2 + Sqrt[(b^2 - 4*a*c)*e^2]*(B*d + A*e)) + 2*c*(-(A*c*d*Sqrt[(b^2 - 4*a*c)*e^2]) + a*e*(6*B*c*d + 2*A*c*e + 3*B*Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[d + e*x])))/(c^2*(-b^2 + 4*a*c)*e*(a + x*(b + c*x))^(3/2)*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
2637,1,962,460,9.0450393,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^(3/2),x]","\frac{\sqrt{d+e x} \left(\frac{4 (B (2 a+b x)-A (b+2 c x))}{b^2-4 a c}+\frac{(d+e x) \left(\frac{4 (b B-2 A c) \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} (a+x (b+c x)) e^2}{(d+e x)^2}-\frac{i \sqrt{2} (b B-2 A c) \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}-\frac{i \sqrt{2} \left(B e b^2-B \sqrt{\left(b^2-4 a c\right) e^2} b-4 a B c e+2 A c \sqrt{\left(b^2-4 a c\right) e^2}\right) \sqrt{\frac{-2 a e^2+2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (d-e x) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 a e^2-2 c d x e+\sqrt{\left(b^2-4 a c\right) e^2} x e+b (e x-d) e+d \sqrt{\left(b^2-4 a c\right) e^2}}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)}{\sqrt{d+e x}}\right)}{c \left(4 a c-b^2\right) e \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}\right)}{2 \sqrt{a+x (b+c 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)}}}",1,"(Sqrt[d + e*x]*((4*(B*(2*a + b*x) - A*(b + 2*c*x)))/(b^2 - 4*a*c) + ((d + e*x)*((4*(b*B - 2*A*c)*e^2*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*(a + x*(b + c*x)))/(d + e*x)^2 - (I*Sqrt[2]*(b*B - 2*A*c)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x] - (I*Sqrt[2]*(b^2*B*e - 4*a*B*c*e - b*B*Sqrt[(b^2 - 4*a*c)*e^2] + 2*A*c*Sqrt[(b^2 - 4*a*c)*e^2])*Sqrt[(-2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] + 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(d - e*x))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[(2*a*e^2 + d*Sqrt[(b^2 - 4*a*c)*e^2] - 2*c*d*e*x + e*Sqrt[(b^2 - 4*a*c)*e^2]*x + b*e*(-d + e*x))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))])/Sqrt[d + e*x]))/(c*(-b^2 + 4*a*c)*e*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])))/(2*Sqrt[a + x*(b + c*x)])","C",1
2638,1,893,528,9.0042094,"\int \frac{A+B x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \sqrt{d+e x} \left(-A e b^2+A c d b+a B e b-B c d x b-A c e x b-2 a B c d+2 a A c e+2 A c^2 d x+2 a B c e x\right) \left(c x^2+b x+a\right)}{\left(4 a c-b^2\right) \left(c d^2-b e d+a e^2\right) (a+x (b+c x))^{3/2}}-\frac{2 (d+e x)^{3/2} \left(c x^2+b x+a\right)^{3/2} \left(\frac{i \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+1} \left((b B d-2 A c d+A b e-2 a B e) \left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)-\left(e (B d-A e) b^2+\sqrt{\left(b^2-4 a c\right) e^2} (B d+A e) b-2 a e \left(2 c d B+\sqrt{\left(b^2-4 a c\right) e^2} B-2 A c e\right)-2 A c d \sqrt{\left(b^2-4 a c\right) e^2}\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{2 \sqrt{2} \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{d+e x}}-(b B d-2 A c d+A b e-2 a B e) \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)\right)}{\left(4 a c-b^2\right) e \left(c d^2-b e d+a e^2\right) (a+x (b+c x))^{3/2} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^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*c*d - 2*a*B*c*d - A*b^2*e + a*b*B*e + 2*a*A*c*e - b*B*c*d*x + 2*A*c^2*d*x - A*b*c*e*x + 2*a*B*c*e*x)*(a + b*x + c*x^2))/((-b^2 + 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + x*(b + c*x))^(3/2)) - (2*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)*(-((b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x))) + ((I/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] - (-2*A*c*d*Sqrt[(b^2 - 4*a*c)*e^2] + b^2*e*(B*d - A*e) + b*Sqrt[(b^2 - 4*a*c)*e^2]*(B*d + A*e) - 2*a*e*(2*B*c*d - 2*A*c*e + B*Sqrt[(b^2 - 4*a*c)*e^2]))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[d + e*x])))/((-b^2 + 4*a*c)*e*(c*d^2 - b*d*e + a*e^2)*(a + x*(b + c*x))^(3/2)*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
2639,1,1267,705,11.646936,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(A + B*x)/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)),x]","\frac{\sqrt{d+e x} \left(c x^2+b x+a\right)^2 \left(\frac{2 \left(A e^2 b^3-a B e^2 b^2-2 A c d e b^2+A c e^2 x b^2+A c^2 d^2 b-3 a A c e^2 b+2 a B c d e b-B c^2 d^2 x b-a B c e^2 x b-2 A c^2 d e x b-2 a B c^2 d^2+2 a^2 B c e^2+4 a A c^2 d e+2 A c^3 d^2 x-2 a A c^2 e^2 x+4 a B c^2 d e x\right)}{\left(4 a c-b^2\right) \left(c d^2-b e d+a e^2\right)^2 \left(c x^2+b x+a\right)}-\frac{2 e^2 (A e-B d)}{\left(c d^2-b e d+a e^2\right)^2 (d+e x)}\right)}{(a+x (b+c x))^{3/2}}-\frac{2 (d+e x)^{3/2} \left(c x^2+b x+a\right)^{3/2} \left(-\left(\left(e (B d-2 A e) b^2+\left(B c d^2+2 A c e d+a B e^2\right) b-2 c \left(A c d^2+4 a B e d-3 a A e^2\right)\right) \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)\right)-\frac{i \sqrt{1-\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}} \sqrt{\frac{2 \left(c d^2+e (a e-b d)\right)}{\left(-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) (d+e x)}+1} \left(\left(2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}\right) \left(e (2 A e-B d) b^2-\left(B c d^2+2 A c e d+a B e^2\right) b+2 c \left(A c d^2+4 a B e d-3 a A e^2\right)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)+\left(e^2 (2 A e-B d) b^3-e \left(2 A e \left(2 c d+\sqrt{\left(b^2-4 a c\right) e^2}\right)+B \left(-3 c d^2-\sqrt{\left(b^2-4 a c\right) e^2} d+a e^2\right)\right) b^2+\left(a \left(4 c d B+\sqrt{\left(b^2-4 a c\right) e^2} B-8 A c e\right) e^2+c d \sqrt{\left(b^2-4 a c\right) e^2} (B d+2 A e)\right) b-2 c \left(-2 a^2 B e^3+a \left(6 B c d^2-8 A c e d+4 B \sqrt{\left(b^2-4 a c\right) e^2} d-3 A e \sqrt{\left(b^2-4 a c\right) e^2}\right) e+A c d^2 \sqrt{\left(b^2-4 a c\right) e^2}\right)\right) F\left(i \sinh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{c d^2-b e d+a e^2}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}}}{\sqrt{d+e x}}\right)|-\frac{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}{2 c d-b e+\sqrt{\left(b^2-4 a c\right) e^2}}\right)\right)}{2 \sqrt{2} \sqrt{\frac{c d^2+e (a e-b d)}{-2 c d+b e+\sqrt{\left(b^2-4 a c\right) e^2}}} \sqrt{d+e x}}\right)}{\left(4 a c-b^2\right) e \left(c d^2-b e d+a e^2\right)^2 (a+x (b+c x))^{3/2} \sqrt{\frac{(d+e x)^2 \left(c \left(\frac{d}{d+e x}-1\right)^2+\frac{e \left(-\frac{d b}{d+e x}+b+\frac{a e}{d+e x}\right)}{d+e x}\right)}{e^2}}}","\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,"(Sqrt[d + e*x]*(a + b*x + c*x^2)^2*((-2*e^2*(-(B*d) + A*e))/((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + (2*(A*b*c^2*d^2 - 2*a*B*c^2*d^2 - 2*A*b^2*c*d*e + 2*a*b*B*c*d*e + 4*a*A*c^2*d*e + A*b^3*e^2 - a*b^2*B*e^2 - 3*a*A*b*c*e^2 + 2*a^2*B*c*e^2 - b*B*c^2*d^2*x + 2*A*c^3*d^2*x - 2*A*b*c^2*d*e*x + 4*a*B*c^2*d*e*x + A*b^2*c*e^2*x - a*b*B*c*e^2*x - 2*a*A*c^2*e^2*x))/((-b^2 + 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2))))/(a + x*(b + c*x))^(3/2) - (2*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)*(-((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))*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x))) - ((I/2)*Sqrt[1 - (2*(c*d^2 + e*(-(b*d) + a*e)))/((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*Sqrt[1 + (2*(c*d^2 + e*(-(b*d) + a*e)))/((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])*(d + e*x))]*((2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^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))*EllipticE[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))] + (b^3*e^2*(-(B*d) + 2*A*e) + b*(c*d*Sqrt[(b^2 - 4*a*c)*e^2]*(B*d + 2*A*e) + a*e^2*(4*B*c*d - 8*A*c*e + B*Sqrt[(b^2 - 4*a*c)*e^2])) - b^2*e*(2*A*e*(2*c*d + Sqrt[(b^2 - 4*a*c)*e^2]) + B*(-3*c*d^2 + a*e^2 - d*Sqrt[(b^2 - 4*a*c)*e^2])) - 2*c*(-2*a^2*B*e^3 + A*c*d^2*Sqrt[(b^2 - 4*a*c)*e^2] + a*e*(6*B*c*d^2 - 8*A*c*d*e + 4*B*d*Sqrt[(b^2 - 4*a*c)*e^2] - 3*A*e*Sqrt[(b^2 - 4*a*c)*e^2])))*EllipticF[I*ArcSinh[(Sqrt[2]*Sqrt[(c*d^2 - b*d*e + a*e^2)/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])])/Sqrt[d + e*x]], -((-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])/(2*c*d - b*e + Sqrt[(b^2 - 4*a*c)*e^2]))]))/(Sqrt[2]*Sqrt[(c*d^2 + e*(-(b*d) + a*e))/(-2*c*d + b*e + Sqrt[(b^2 - 4*a*c)*e^2])]*Sqrt[d + e*x])))/((-b^2 + 4*a*c)*e*(c*d^2 - b*d*e + a*e^2)^2*(a + x*(b + c*x))^(3/2)*Sqrt[((d + e*x)^2*(c*(-1 + d/(d + e*x))^2 + (e*(b - (b*d)/(d + e*x) + (a*e)/(d + e*x)))/(d + e*x)))/e^2])","C",1
2640,1,4291,594,6.6985088,"\int (A+B x) (d+e x)^m \left(a+b x+c x^2\right)^3 \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a + b*x + c*x^2)^3,x]","\text{Result too large to show}","-\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 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{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{(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,"((d + e*x)^(1 + m)*(-(B*(7*c*d - 3*b*e)) + A*c*e*(8 + m) + B*c*e*(7 + m)*x)*(a + b*x + c*x^2)^3)/(c*e^2*(7 + m)*(8 + m)) - (3*(((d + e*x)^(1 + m)*(c*e*(6 + m)*(-(b*B*d*(7*c*d - 3*b*e)) + A*c*e*(b*d - 2*a*e)*(8 + m) - a*B*e*(2*c*d*m - b*e*(1 + m))) - (5*c*d - 2*b*e)*(A*c*e*(2*c*d - b*e)*(8 + m) - B*(14*c^2*d^2 - b^2*e^2*(4 + m) - c*e*(b*d*(6 - m) - 2*a*e*(7 + m)))) + c*e*(5 + m)*(A*c*e*(2*c*d - b*e)*(8 + m) - B*(14*c^2*d^2 - b^2*e^2*(4 + m) - c*e*(b*d*(6 - m) - 2*a*e*(7 + m))))*x)*(a + b*x + c*x^2)^2)/(c*e^2*(5 + m)*(6 + m)) - (2*(((d + e*x)^(1 + m)*(c*e*(4 + m)*(c*e*(b*d - 2*a*e)*(6 + m)*(-(b*B*d*(7*c*d - 3*b*e)) + A*c*e*(b*d - 2*a*e)*(8 + m) - a*B*e*(2*c*d*m - b*e*(1 + m))) + (b*d*(-5*c*d + 2*b*e) + a*e*(b*e - 2*c*d*m + b*e*m))*(A*c*e*(2*c*d - b*e)*(8 + m) - B*(14*c^2*d^2 - b^2*e^2*(4 + m) - c*e*(b*d*(6 - m) - 2*a*e*(7 + m))))) - (3*c*d - b*e)*(c*e*(2*c*d - b*e)*(6 + m)*(-(b*B*d*(7*c*d - 3*b*e)) + A*c*e*(b*d - 2*a*e)*(8 + m) - a*B*e*(2*c*d*m - b*e*(1 + m))) + (-10*c^2*d^2 + b^2*e^2*(3 + m) - c*e*(b*d*(-4 + m) + 2*a*e*(5 + m)))*(A*c*e*(2*c*d - b*e)*(8 + m) - B*(14*c^2*d^2 - b^2*e^2*(4 + m) - c*e*(b*d*(6 - m) - 2*a*e*(7 + m))))) + c*e*(3 + m)*(c*e*(2*c*d - b*e)*(6 + m)*(-(b*B*d*(7*c*d - 3*b*e)) + A*c*e*(b*d - 2*a*e)*(8 + m) - a*B*e*(2*c*d*m - b*e*(1 + m))) + (-10*c^2*d^2 + b^2*e^2*(3 + m) - c*e*(b*d*(-4 + m) + 2*a*e*(5 + m)))*(A*c*e*(2*c*d - b*e)*(8 + m) - B*(14*c^2*d^2 - b^2*e^2*(4 + m) - c*e*(b*d*(6 - m) - 2*a*e*(7 + m)))))*x)*(a + b*x + c*x^2))/(c*e^2*(3 + m)*(4 + m)) - (((840*B*c^6*d^7 - 2460*b*B*c^5*d^6*e - 960*A*c^6*d^6*e + 2340*b^2*B*c^4*d^5*e^2 + 2880*A*b*c^5*d^5*e^2 + 2520*a*B*c^5*d^5*e^2 - 684*b^3*B*c^3*d^4*e^3 - 2832*A*b^2*c^4*d^4*e^3 - 4764*a*b*B*c^4*d^4*e^3 - 3072*a*A*c^5*d^4*e^3 - 12*b^4*B*c^2*d^3*e^4 + 864*A*b^3*c^3*d^3*e^4 + 1968*a*b^2*B*c^3*d^3*e^4 + 6144*a*A*b*c^4*d^3*e^4 + 2520*a^2*B*c^4*d^3*e^4 - 12*b^5*B*c*d^2*e^5 + 24*A*b^4*c^2*d^2*e^5 + 132*a*b^3*B*c^2*d^2*e^5 - 2784*a*A*b^2*c^3*d^2*e^5 - 1956*a^2*b*B*c^3*d^2*e^5 - 3648*a^2*A*c^4*d^2*e^5 - 12*b^6*B*d*e^6 + 24*A*b^5*c*d*e^6 + 144*a*b^4*B*c*d*e^6 - 288*a*A*b^3*c^2*d*e^6 - 564*a^2*b^2*B*c^2*d*e^6 + 3648*a^2*A*b*c^3*d*e^6 + 840*a^3*B*c^3*d*e^6 + 12*a*b^5*B*e^7 - 24*a*A*b^4*c*e^7 - 120*a^2*b^3*B*c*e^7 + 240*a^2*A*b^2*c^2*e^7 + 348*a^3*b*B*c^2*e^7 - 1536*a^3*A*c^3*e^7 + 60*b*B*c^5*d^6*e*m - 120*A*c^6*d^6*e*m - 160*b^2*B*c^4*d^5*e^2*m + 360*A*b*c^5*d^5*e^2*m - 80*a*B*c^5*d^5*e^2*m + 111*b^3*B*c^3*d^4*e^3*m - 322*A*b^2*c^4*d^4*e^3*m + 456*a*b*B*c^4*d^4*e^3*m - 512*a*A*c^5*d^4*e^3*m + 15*b^4*B*c^2*d^3*e^4*m + 44*A*b^3*c^3*d^3*e^4*m - 608*a*b^2*B*c^3*d^3*e^4*m + 1024*a*A*b*c^4*d^3*e^4*m - 208*a^2*B*c^4*d^3*e^4*m - 7*b^5*B*c*d^2*e^5*m + 3*A*b^4*c^2*d^2*e^5*m + 22*a*b^3*B*c^2*d^2*e^5*m - 156*a*A*b^2*c^3*d^2*e^5*m + 924*a^2*b*B*c^3*d^2*e^5*m - 1224*a^2*A*c^4*d^2*e^5*m - 19*b^6*B*d*e^6*m + 35*A*b^5*c*d*e^6*m + 207*a*b^4*B*c*d*e^6*m - 356*a*A*b^3*c^2*d*e^6*m - 672*a^2*b^2*B*c^2*d*e^6*m + 1224*a^2*A*b*c^3*d*e^6*m - 128*a^3*B*c^3*d*e^6*m + 19*a*b^5*B*e^7*m - 35*a*A*b^4*c*e^7*m - 181*a^2*b^3*B*c*e^7*m + 318*a^2*A*b^2*c^2*e^7*m + 480*a^3*b*B*c^2*e^7*m - 832*a^3*A*c^3*e^7*m + 20*b^2*B*c^4*d^5*e^2*m^2 - 80*a*B*c^5*d^5*e^2*m^2 - 44*b^3*B*c^3*d^4*e^3*m^2 - 12*A*b^2*c^4*d^4*e^3*m^2 + 176*a*b*B*c^4*d^4*e^3*m^2 + 48*a*A*c^5*d^4*e^3*m^2 + 24*b^4*B*c^2*d^3*e^4*m^2 + 24*A*b^3*c^3*d^3*e^4*m^2 - 40*a*b^2*B*c^3*d^3*e^4*m^2 - 96*a*A*b*c^4*d^3*e^4*m^2 - 224*a^2*B*c^4*d^3*e^4*m^2 + 8*b^5*B*c*d^2*e^5*m^2 - 24*A*b^4*c^2*d^2*e^5*m^2 - 128*a*b^3*B*c^2*d^2*e^5*m^2 + 120*a*A*b^2*c^3*d^2*e^5*m^2 + 384*a^2*b*B*c^3*d^2*e^5*m^2 - 96*a^2*A*c^4*d^2*e^5*m^2 - 8*b^6*B*d*e^6*m^2 + 12*A*b^5*c*d*e^6*m^2 + 68*a*b^4*B*c*d*e^6*m^2 - 72*a*A*b^3*c^2*d*e^6*m^2 - 108*a^2*b^2*B*c^2*d*e^6*m^2 + 96*a^2*A*b*c^3*d*e^6*m^2 - 144*a^3*B*c^3*d*e^6*m^2 + 8*a*b^5*B*e^7*m^2 - 12*a*A*b^4*c*e^7*m^2 - 68*a^2*b^3*B*c*e^7*m^2 + 84*a^2*A*b^2*c^2*e^7*m^2 + 144*a^3*b*B*c^2*e^7*m^2 - 144*a^3*A*c^3*e^7*m^2 + b^3*B*c^3*d^4*e^3*m^3 - 2*A*b^2*c^4*d^4*e^3*m^3 - 4*a*b*B*c^4*d^4*e^3*m^3 + 8*a*A*c^5*d^4*e^3*m^3 - 3*b^4*B*c^2*d^3*e^4*m^3 + 4*A*b^3*c^3*d^3*e^4*m^3 + 16*a*b^2*B*c^3*d^3*e^4*m^3 - 16*a*A*b*c^4*d^3*e^4*m^3 - 16*a^2*B*c^4*d^3*e^4*m^3 + 3*b^5*B*c*d^2*e^5*m^3 - 3*A*b^4*c^2*d^2*e^5*m^3 - 18*a*b^3*B*c^2*d^2*e^5*m^3 + 12*a*A*b^2*c^3*d^2*e^5*m^3 + 24*a^2*b*B*c^3*d^2*e^5*m^3 - b^6*B*d*e^6*m^3 + A*b^5*c*d*e^6*m^3 + 5*a*b^4*B*c*d*e^6*m^3 - 4*a*A*b^3*c^2*d*e^6*m^3 - 16*a^3*B*c^3*d*e^6*m^3 + a*b^5*B*e^7*m^3 - a*A*b^4*c*e^7*m^3 - 7*a^2*b^3*B*c*e^7*m^3 + 6*a^2*A*b^2*c^2*e^7*m^3 + 12*a^3*b*B*c^2*e^7*m^3 - 8*a^3*A*c^3*e^7*m^3)*(d + e*x)^(1 + m))/(e^2*(1 + m)) + ((-840*B*c^6*d^6 + 2040*b*B*c^5*d^5*e + 960*A*c^6*d^5*e - 1320*b^2*B*c^4*d^4*e^2 - 2400*A*b*c^5*d^4*e^2 - 2520*a*B*c^5*d^4*e^2 + 24*b^3*B*c^3*d^3*e^3 + 1632*A*b^2*c^4*d^3*e^3 + 3504*a*b*B*c^4*d^3*e^3 + 3072*a*A*c^5*d^3*e^3 + 24*b^4*B*c^2*d^2*e^4 - 48*A*b^3*c^3*d^2*e^4 - 216*a*b^2*B*c^3*d^2*e^4 - 4608*a*A*b*c^4*d^2*e^4 - 2520*a^2*B*c^4*d^2*e^4 + 24*b^5*B*c*d*e^5 - 48*A*b^4*c^2*d*e^5 - 240*a*b^3*B*c^2*d*e^5 + 480*a*A*b^2*c^3*d*e^5 + 696*a^2*b*B*c^3*d*e^5 + 3648*a^2*A*c^4*d*e^5 + 24*b^6*B*e^6 - 48*A*b^5*c*e^6 - 264*a*b^4*B*c*e^6 + 528*a*A*b^3*c^2*e^6 + 912*a^2*b^2*B*c^2*e^6 - 1824*a^2*A*b*c^3*e^6 - 840*a^3*B*c^3*e^6 - 60*b*B*c^5*d^5*e*m + 120*A*c^6*d^5*e*m + 200*b^2*B*c^4*d^4*e^2*m - 300*A*b*c^5*d^4*e^2*m - 200*a*B*c^5*d^4*e^2*m - 146*b^3*B*c^3*d^3*e^3*m + 92*A*b^2*c^4*d^3*e^3*m - 16*a*b*B*c^4*d^3*e^3*m + 832*a*A*c^5*d^3*e^3*m - 42*b^4*B*c^2*d^2*e^4*m + 162*A*b^3*c^3*d^2*e^4*m + 612*a*b^2*B*c^3*d^2*e^4*m - 1248*a*A*b*c^4*d^2*e^4*m - 576*a^2*B*c^4*d^2*e^4*m + 2*b^5*B*c*d*e^5*m + 18*A*b^4*c^2*d*e^5*m + 46*a*b^3*B*c^2*d*e^5*m - 468*a*A*b^2*c^3*d*e^5*m - 516*a^2*b*B*c^3*d*e^5*m + 2184*a^2*A*c^4*d*e^5*m + 26*b^6*B*e^6*m - 46*A*b^5*c*e^6*m - 268*a*b^4*B*c*e^6*m + 442*a*A*b^3*c^2*e^6*m + 828*a^2*b^2*B*c^2*e^6*m - 1092*a^2*A*b*c^3*e^6*m - 568*a^3*B*c^3*e^6*m - 20*b^2*B*c^4*d^4*e^2*m^2 + 80*a*B*c^5*d^4*e^2*m^2 + 39*b^3*B*c^3*d^3*e^3*m^2 + 2*A*b^2*c^4*d^3*e^3*m^2 - 156*a*b*B*c^4*d^3*e^3*m^2 - 8*a*A*c^5*d^3*e^3*m^2 - 21*b^4*B*c^2*d^2*e^4*m^2 - 3*A*b^3*c^3*d^2*e^4*m^2 + 54*a*b^2*B*c^3*d^2*e^4*m^2 + 12*a*A*b*c^4*d^2*e^4*m^2 + 120*a^2*B*c^4*d^2*e^4*m^2 - 11*b^5*B*c*d*e^5*m^2 + 27*A*b^4*c^2*d*e^5*m^2 + 125*a*b^3*B*c^2*d*e^5*m^2 - 210*a*A*b^2*c^3*d*e^5*m^2 - 324*a^2*b*B*c^3*d*e^5*m^2 + 408*a^2*A*c^4*d*e^5*m^2 + 9*b^6*B*e^6*m^2 - 13*A*b^5*c*e^6*m^2 - 84*a*b^4*B*c*e^6*m^2 + 103*a*A*b^3*c^2*e^6*m^2 + 222*a^2*b^2*B*c^2*e^6*m^2 - 204*a^2*A*b*c^3*e^6*m^2 - 120*a^3*B*c^3*e^6*m^2 - b^3*B*c^3*d^3*e^3*m^3 + 2*A*b^2*c^4*d^3*e^3*m^3 + 4*a*b*B*c^4*d^3*e^3*m^3 - 8*a*A*c^5*d^3*e^3*m^3 + 3*b^4*B*c^2*d^2*e^4*m^3 - 3*A*b^3*c^3*d^2*e^4*m^3 - 18*a*b^2*B*c^3*d^2*e^4*m^3 + 12*a*A*b*c^4*d^2*e^4*m^3 + 24*a^2*B*c^4*d^2*e^4*m^3 - 3*b^5*B*c*d*e^5*m^3 + 3*A*b^4*c^2*d*e^5*m^3 + 21*a*b^3*B*c^2*d*e^5*m^3 - 18*a*A*b^2*c^3*d*e^5*m^3 - 36*a^2*b*B*c^3*d*e^5*m^3 + 24*a^2*A*c^4*d*e^5*m^3 + b^6*B*e^6*m^3 - A*b^5*c*e^6*m^3 - 8*a*b^4*B*c*e^6*m^3 + 7*a*A*b^3*c^2*e^6*m^3 + 18*a^2*b^2*B*c^2*e^6*m^3 - 12*a^2*A*b*c^3*e^6*m^3 - 8*a^3*B*c^3*e^6*m^3)*(d + e*x)^(2 + m))/(e^2*(2 + m)))/(c*e^2*(3 + m)*(4 + m))))/(c*e^2*(5 + m)*(6 + m))))/(c*e^2*(7 + m)*(8 + m))","B",1
2641,1,633,333,1.4541007,"\int (A+B x) (d+e x)^m \left(a+b x+c x^2\right)^2 \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(\frac{2 \left(\frac{(d+e x) \left(B \left(c^2 e^2 \left(4 a^2 e^2 \left(m^2+8 m+15\right)+2 a b d e \left(4 m^2+11 m-18\right)+b^2 d^2 \left(m^2-13 m+6\right)\right)-b^2 c e^3 (m+2) (a e (5 m+21)+b d (2 m-3))+2 c^3 d^2 e \left(3 b d (m-14)-2 a e \left(m^2-4 m-30\right)\right)+b^4 e^4 \left(m^2+5 m+6\right)+60 c^4 d^4\right)-A c e (m+6) (2 c d-b e) \left(2 c e (a e (2 m+7)-3 b d)-b^2 e^2 (m+2)+6 c^2 d^2\right)\right)}{e^2 (m+2)}-(a+x (b+c x)) \left(c e (m+3) x \left(B \left(-c e (2 a e (m+5)+b d (m-4))+b^2 e^2 (m+3)-10 c^2 d^2\right)+A c e (m+6) (2 c d-b e)\right)-(3 c d-b e) \left(B \left(-c e (2 a e (m+5)+b d (m-4))+b^2 e^2 (m+3)-10 c^2 d^2\right)+A c e (m+6) (2 c d-b e)\right)+c e (m+4) \left(A c e (m+6) (b d-2 a e)+a b B e^2 (m+1)-2 a B c d e m+b B d (2 b e-5 c d)\right)\right)+\frac{\left(e (a e-b d)+c d^2\right) \left(A c e (m+6) \left(4 c e (a e (m+4)-3 b d)-b^2 e^2 (m+1)+12 c^2 d^2\right)+B \left(2 c^2 d e \left(2 a e \left(m^2+m-15\right)-3 b d (m-9)\right)-b c e^2 (m+1) (2 a e (2 m+9)+b d (m-6))+b^3 e^3 \left(m^2+4 m+3\right)-60 c^3 d^3\right)\right)}{e^2 (m+1)}\right)}{c e^2 (m+3) (m+4)}+(a+x (b+c x))^2 (A c e (m+6)+B (2 b e-5 c d)+B c e (m+5) x)\right)}{c e^2 (m+5) (m+6)}","-\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{(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{(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,"((d + e*x)^(1 + m)*((B*(-5*c*d + 2*b*e) + A*c*e*(6 + m) + B*c*e*(5 + m)*x)*(a + x*(b + c*x))^2 + (2*(((c*d^2 + e*(-(b*d) + a*e))*(A*c*e*(6 + m)*(12*c^2*d^2 - b^2*e^2*(1 + m) + 4*c*e*(-3*b*d + a*e*(4 + m))) + B*(-60*c^3*d^3 + b^3*e^3*(3 + 4*m + m^2) - b*c*e^2*(1 + m)*(b*d*(-6 + m) + 2*a*e*(9 + 2*m)) + 2*c^2*d*e*(-3*b*d*(-9 + m) + 2*a*e*(-15 + m + m^2)))))/(e^2*(1 + m)) + ((-(A*c*e*(2*c*d - b*e)*(6 + m)*(6*c^2*d^2 - b^2*e^2*(2 + m) + 2*c*e*(-3*b*d + a*e*(7 + 2*m)))) + B*(60*c^4*d^4 + b^4*e^4*(6 + 5*m + m^2) - b^2*c*e^3*(2 + m)*(b*d*(-3 + 2*m) + a*e*(21 + 5*m)) + 2*c^3*d^2*e*(3*b*d*(-14 + m) - 2*a*e*(-30 - 4*m + m^2)) + c^2*e^2*(b^2*d^2*(6 - 13*m + m^2) + 4*a^2*e^2*(15 + 8*m + m^2) + 2*a*b*d*e*(-18 + 11*m + 4*m^2))))*(d + e*x))/(e^2*(2 + m)) - (c*e*(4 + m)*(b*B*d*(-5*c*d + 2*b*e) - 2*a*B*c*d*e*m + a*b*B*e^2*(1 + m) + A*c*e*(b*d - 2*a*e)*(6 + m)) - (3*c*d - b*e)*(A*c*e*(2*c*d - b*e)*(6 + m) + B*(-10*c^2*d^2 + b^2*e^2*(3 + m) - c*e*(b*d*(-4 + m) + 2*a*e*(5 + m)))) + c*e*(3 + m)*(A*c*e*(2*c*d - b*e)*(6 + m) + B*(-10*c^2*d^2 + b^2*e^2*(3 + m) - c*e*(b*d*(-4 + m) + 2*a*e*(5 + m))))*x)*(a + x*(b + c*x))))/(c*e^2*(3 + m)*(4 + m))))/(c*e^2*(5 + m)*(6 + m))","A",1
2642,1,181,153,0.3393125,"\int (A+B x) (d+e x)^m \left(a+b x+c x^2\right) \, dx","Integrate[(A + B*x)*(d + e*x)^m*(a + b*x + c*x^2),x]","\frac{(d+e x)^{m+1} \left(\frac{(d+e x) \left(B \left(c e (2 a e (m+3)+b d (m-2))-b^2 e^2 (m+2)+6 c^2 d^2\right)-A c e (m+4) (2 c d-b e)\right)}{e^2 (m+2)}-\frac{\left(e (a e-b d)+c d^2\right) (-2 A c e (m+4)+b B e (m+1)+6 B c d)}{e^2 (m+1)}+(a+x (b+c x)) (A c e (m+4)+B (b e-3 c d)+B c e (m+3) x)\right)}{c e^2 (m+3) (m+4)}","-\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{(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+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 + e*x)^(1 + m)*(-(((c*d^2 + e*(-(b*d) + a*e))*(6*B*c*d + b*B*e*(1 + m) - 2*A*c*e*(4 + m)))/(e^2*(1 + m))) + ((-(A*c*e*(2*c*d - b*e)*(4 + m)) + B*(6*c^2*d^2 - b^2*e^2*(2 + m) + c*e*(b*d*(-2 + m) + 2*a*e*(3 + m))))*(d + e*x))/(e^2*(2 + m)) + (B*(-3*c*d + b*e) + A*c*e*(4 + m) + B*c*e*(3 + m)*x)*(a + x*(b + c*x))))/(c*e^2*(3 + m)*(4 + m))","A",1
2643,1,197,212,0.4017782,"\int \frac{(A+B x) (d+e x)^m}{a+b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^m)/(a + b*x + c*x^2),x]","\frac{(d+e x)^{m+1} \left(-\frac{\left(\frac{2 A c-b B}{\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(\sqrt{b^2-4 a c}-b\right) e}\right)}{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}-\frac{\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)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)}{m+1}","-\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,"((d + e*x)^(1 + m)*(-(((B + (-(b*B) + 2*A*c)/Sqrt[b^2 - 4*a*c])*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)) - ((B + (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*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",1
2644,1,452,538,5.6734543,"\int \frac{(A+B x) (d+e x)^m}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^m)/(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(\frac{c \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 (m-1)+a B d e m+A c d^2\right)+b^2 e (A e m-B d (m-2))}{\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(\sqrt{b^2-4 a c}-b\right) e}\right)}{(m+1) \left(e \left(\sqrt{b^2-4 a c}-b\right)+2 c d\right)}+\frac{c \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 (m-1)+a B d e m+A c d^2\right)+b^2 e (B d (m-2)-A e 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(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}+\frac{-2 A c (a e+c d x)+a B (2 c (d-e x)-b e)+A b^2 e+A b c (e x-d)+b B c d x}{a+x (b+c x)}\right)}{\left(b^2-4 a c\right) \left(e (a e-b d)+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*e + b*B*c*d*x - 2*A*c*(a*e + c*d*x) + A*b*c*(-d + e*x) + a*B*(-(b*e) + 2*c*(d - e*x)))/(a + x*(b + c*x)) + (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])*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)) + (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])*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^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e)))","A",1
2645,1,197,212,0.3396576,"\int \frac{(A+B x) (d+e x)^{1+m}}{a+b x+c x^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(1 + m))/(a + b*x + c*x^2),x]","\frac{(d+e x)^{m+2} \left(-\frac{\left(\frac{2 A c-b B}{\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(\sqrt{b^2-4 a c}-b\right) e}\right)}{e \left(\sqrt{b^2-4 a c}-b\right)+2 c d}-\frac{\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)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)}{m+2}","-\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,"((d + e*x)^(2 + m)*(-(((B + (-(b*B) + 2*A*c)/Sqrt[b^2 - 4*a*c])*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)) - ((B + (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*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",1
2646,1,311,349,0.6245223,"\int (A+B x) (d+e x)^{-3-2 p} \left(a+b x+c x^2\right)^p \, dx","Integrate[(A + B*x)*(d + e*x)^(-3 - 2*p)*(a + b*x + c*x^2)^p,x]","\frac{(d+e x)^{-2 (p+1)} (a+x (b+c x))^p \left(\frac{(d+e x) \left(\sqrt{b^2-4 a c}+b+2 c x\right) (-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(e \left(\sqrt{b^2-4 a c}-b\right)+2 c d\right)}{\left(\sqrt{b^2-4 a c}-b-2 c x\right) \left(e \left(\sqrt{b^2-4 a c}+b\right)-2 c d\right)}\right)^{-p-1} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(\left(b+\sqrt{b^2-4 a c}\right) e-2 c d\right) \left(-b-2 c x+\sqrt{b^2-4 a c}\right)}\right)}{(2 p+1) \left(e \left(\sqrt{b^2-4 a c}+b\right)-2 c d\right)}+\frac{(a+x (b+c x)) (B d-A e)}{p+1}\right)}{2 \left(e (a e-b d)+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,"((a + x*(b + c*x))^p*(((B*d - A*e)*(a + x*(b + c*x)))/(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)*(((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)))^(-1 - p)*(d + e*x)*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*c*d + (b + Sqrt[b^2 - 4*a*c])*e)*(1 + 2*p))))/(2*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)^(2*(1 + p)))","A",1