1,1,28,27,0.022000," ","int(x^2*(b*x^2+a)*(B*x^2+A),x)","\frac{B b \,x^{7}}{7}+\frac{A a \,x^{3}}{3}+\frac{\left(A b +B a \right) x^{5}}{5}"," ",0,"1/3*a*A*x^3+1/5*(A*b+B*a)*x^5+1/7*b*B*x^7","A"
2,1,28,27,0.001000," ","int(x*(b*x^2+a)*(B*x^2+A),x)","\frac{B b \,x^{6}}{6}+\frac{A a \,x^{2}}{2}+\frac{\left(A b +B a \right) x^{4}}{4}"," ",0,"1/2*a*A*x^2+1/4*(A*b+B*a)*x^4+1/6*b*B*x^6","A"
3,1,25,24,0.002000," ","int((b*x^2+a)*(B*x^2+A),x)","\frac{B b \,x^{5}}{5}+A a x +\frac{\left(A b +B a \right) x^{3}}{3}"," ",0,"a*A*x+1/3*(A*b+B*a)*x^3+1/5*b*B*x^5","A"
4,1,28,25,0.019000," ","int((b*x^2+a)*(B*x^2+A)/x,x)","\frac{B b \,x^{4}}{4}+\frac{A b \,x^{2}}{2}+\frac{B a \,x^{2}}{2}+A a \ln \left(x \right)"," ",0,"1/4*b*B*x^4+1/2*A*x^2*b+1/2*B*x^2*a+a*A*ln(x)","A"
5,1,24,24,0.048000," ","int((b*x^2+a)*(B*x^2+A)/x^2,x)","\frac{B b \,x^{3}}{3}+A b x +B a x -\frac{A a}{x}"," ",0,"1/3*b*B*x^3+A*b*x+B*a*x-a*A/x","A"
6,1,26,25,0.010000," ","int((b*x^2+a)*(B*x^2+A)/x^3,x)","\frac{B b \,x^{2}}{2}+A b \ln \left(x \right)+B a \ln \left(x \right)-\frac{A a}{2 x^{2}}"," ",0,"1/2*b*B*x^2-1/2*a*A/x^2+A*ln(x)*b+B*ln(x)*a","A"
7,1,25,25,0.005000," ","int((b*x^2+a)*(B*x^2+A)/x^4,x)","B b x -\frac{A a}{3 x^{3}}-\frac{A b +B a}{x}"," ",0,"b*B*x-(A*b+B*a)/x-1/3*a*A/x^3","A"
8,1,28,27,0.005000," ","int((b*x^2+a)*(B*x^2+A)/x^5,x)","B b \ln \left(x \right)-\frac{A b}{2 x^{2}}-\frac{B a}{2 x^{2}}-\frac{A a}{4 x^{4}}"," ",0,"-1/4*a*A/x^4-1/2/x^2*A*b-1/2/x^2*B*a+b*B*ln(x)","A"
9,1,28,29,0.011000," ","int((b*x^2+a)*(B*x^2+A)/x^6,x)","-\frac{B b}{x}-\frac{A a}{5 x^{5}}-\frac{A b +B a}{3 x^{3}}"," ",0,"-b*B/x-1/3*(A*b+B*a)/x^3-1/5*a*A/x^5","A"
10,1,28,29,0.006000," ","int((b*x^2+a)*(B*x^2+A)/x^7,x)","-\frac{B b}{2 x^{2}}-\frac{A a}{6 x^{6}}-\frac{A b +B a}{4 x^{4}}"," ",0,"-1/4*(A*b+B*a)/x^4-1/6*a*A/x^6-1/2*b*B/x^2","A"
11,1,52,47,0.001000," ","int(x^2*(b*x^2+a)^2*(B*x^2+A),x)","\frac{B \,b^{2} x^{9}}{9}+\frac{\left(b^{2} A +2 a b B \right) x^{7}}{7}+\frac{A \,a^{2} x^{3}}{3}+\frac{\left(2 a b A +a^{2} B \right) x^{5}}{5}"," ",0,"1/9*b^2*B*x^9+1/7*(A*b^2+2*B*a*b)*x^7+1/5*(2*A*a*b+B*a^2)*x^5+1/3*a^2*A*x^3","A"
12,1,52,38,0.003000," ","int(x*(b*x^2+a)^2*(B*x^2+A),x)","\frac{B \,b^{2} x^{8}}{8}+\frac{\left(b^{2} A +2 a b B \right) x^{6}}{6}+\frac{A \,a^{2} x^{2}}{2}+\frac{\left(2 a b A +a^{2} B \right) x^{4}}{4}"," ",0,"1/8*b^2*B*x^8+1/6*(A*b^2+2*B*a*b)*x^6+1/4*(2*A*a*b+B*a^2)*x^4+1/2*a^2*A*x^2","A"
13,1,49,44,0.005000," ","int((b*x^2+a)^2*(B*x^2+A),x)","\frac{B \,b^{2} x^{7}}{7}+\frac{\left(b^{2} A +2 a b B \right) x^{5}}{5}+A \,a^{2} x +\frac{\left(2 a b A +a^{2} B \right) x^{3}}{3}"," ",0,"1/7*b^2*B*x^7+1/5*(A*b^2+2*B*a*b)*x^5+1/3*(2*A*a*b+B*a^2)*x^3+a^2*A*x","A"
14,1,51,39,0.007000," ","int((b*x^2+a)^2*(B*x^2+A)/x,x)","\frac{B \,b^{2} x^{6}}{6}+\frac{A \,b^{2} x^{4}}{4}+\frac{B a b \,x^{4}}{2}+A a b \,x^{2}+\frac{B \,a^{2} x^{2}}{2}+A \,a^{2} \ln \left(x \right)"," ",0,"1/6*B*b^2*x^6+1/4*A*b^2*x^4+1/2*B*x^4*a*b+a*A*b*x^2+1/2*B*x^2*a^2+a^2*A*ln(x)","A"
15,1,49,44,0.007000," ","int((b*x^2+a)^2*(B*x^2+A)/x^2,x)","\frac{B \,b^{2} x^{5}}{5}+\frac{A \,b^{2} x^{3}}{3}+\frac{2 B a b \,x^{3}}{3}+2 A a b x +B \,a^{2} x -\frac{A \,a^{2}}{x}"," ",0,"1/5*b^2*B*x^5+1/3*A*x^3*b^2+2/3*B*x^3*a*b+2*a*b*A*x+a^2*B*x-a^2*A/x","A"
16,1,50,45,0.013000," ","int((b*x^2+a)^2*(B*x^2+A)/x^3,x)","\frac{B \,b^{2} x^{4}}{4}+\frac{A \,b^{2} x^{2}}{2}+B a b \,x^{2}+2 A a b \ln \left(x \right)+B \,a^{2} \ln \left(x \right)-\frac{A \,a^{2}}{2 x^{2}}"," ",0,"1/4*b^2*B*x^4+1/2*A*x^2*b^2+B*x^2*a*b-1/2*a^2*A/x^2+2*A*ln(x)*a*b+B*ln(x)*a^2","A"
17,1,46,44,0.013000," ","int((b*x^2+a)^2*(B*x^2+A)/x^4,x)","\frac{B \,b^{2} x^{3}}{3}+A \,b^{2} x +2 B a b x -\frac{A \,a^{2}}{3 x^{3}}-\frac{\left(2 A b +B a \right) a}{x}"," ",0,"1/3*b^2*B*x^3+b^2*A*x+2*a*b*B*x-a*(2*A*b+B*a)/x-1/3*a^2*A/x^3","A"
18,1,51,45,0.022000," ","int((b*x^2+a)^2*(B*x^2+A)/x^5,x)","\frac{B \,b^{2} x^{2}}{2}+A \,b^{2} \ln \left(x \right)+2 B a b \ln \left(x \right)-\frac{A a b}{x^{2}}-\frac{B \,a^{2}}{2 x^{2}}-\frac{A \,a^{2}}{4 x^{4}}"," ",0,"1/2*b^2*B*x^2-1/4*a^2*A/x^4-a/x^2*A*b-1/2*a^2/x^2*B+A*ln(x)*b^2+2*B*ln(x)*a*b","A"
19,1,45,44,0.015000," ","int((b*x^2+a)^2*(B*x^2+A)/x^6,x)","B \,b^{2} x -\frac{\left(A b +2 B a \right) b}{x}-\frac{A \,a^{2}}{5 x^{5}}-\frac{\left(2 A b +B a \right) a}{3 x^{3}}"," ",0,"-1/5*a^2*A/x^5-1/3*a*(2*A*b+B*a)/x^3-b*(A*b+2*B*a)/x+b^2*B*x","A"
20,1,52,45,0.008000," ","int((b*x^2+a)^2*(B*x^2+A)/x^7,x)","B \,b^{2} \ln \left(x \right)-\frac{A \,b^{2}}{2 x^{2}}-\frac{B a b}{x^{2}}-\frac{A a b}{2 x^{4}}-\frac{B \,a^{2}}{4 x^{4}}-\frac{A \,a^{2}}{6 x^{6}}"," ",0,"-1/2*a/x^4*A*b-1/4*a^2/x^4*B-1/2*b^2/x^2*A-b/x^2*B*a-1/6*a^2*A/x^6+b^2*B*ln(x)","A"
21,1,48,47,0.005000," ","int((b*x^2+a)^2*(B*x^2+A)/x^8,x)","-\frac{B \,b^{2}}{x}-\frac{\left(A b +2 B a \right) b}{3 x^{3}}-\frac{A \,a^{2}}{7 x^{7}}-\frac{\left(2 A b +B a \right) a}{5 x^{5}}"," ",0,"-1/7*a^2*A/x^7-1/5*a*(2*A*b+B*a)/x^5-1/3*b*(A*b+2*B*a)/x^3-b^2*B/x","A"
22,1,48,44,0.006000," ","int((b*x^2+a)^2*(B*x^2+A)/x^9,x)","-\frac{B \,b^{2}}{2 x^{2}}-\frac{\left(A b +2 B a \right) b}{4 x^{4}}-\frac{A \,a^{2}}{8 x^{8}}-\frac{\left(2 A b +B a \right) a}{6 x^{6}}"," ",0,"-1/8*A*a^2/x^8-1/4*b*(A*b+2*B*a)/x^4-1/2*B*b^2/x^2-1/6*a*(2*A*b+B*a)/x^6","A"
23,1,124,103,0.005000," ","int(x^9*(b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{22}}{22}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{20}}{20}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{18}}{18}+\frac{A \,a^{5} x^{10}}{10}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{16}}{16}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{14}}{14}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{12}}{12}"," ",0,"1/22*b^5*B*x^22+1/20*(A*b^5+5*B*a*b^4)*x^20+1/18*(5*A*a*b^4+10*B*a^2*b^3)*x^18+1/16*(10*A*a^2*b^3+10*B*a^3*b^2)*x^16+1/14*(10*A*a^3*b^2+5*B*a^4*b)*x^14+1/12*(5*A*a^4*b+B*a^5)*x^12+1/10*a^5*A*x^10","A"
24,1,124,103,0.000000," ","int(x^8*(b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{21}}{21}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{19}}{19}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{17}}{17}+\frac{A \,a^{5} x^{9}}{9}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{15}}{15}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{13}}{13}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{11}}{11}"," ",0,"1/21*b^5*B*x^21+1/19*(A*b^5+5*B*a*b^4)*x^19+1/17*(5*A*a*b^4+10*B*a^2*b^3)*x^17+1/15*(10*A*a^2*b^3+10*B*a^3*b^2)*x^15+1/13*(10*A*a^3*b^2+5*B*a^4*b)*x^13+1/11*(5*A*a^4*b+B*a^5)*x^11+1/9*a^5*A*x^9","A"
25,1,124,112,0.000000," ","int(x^7*(b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{20}}{20}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{18}}{18}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{16}}{16}+\frac{A \,a^{5} x^{8}}{8}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{14}}{14}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{12}}{12}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{10}}{10}"," ",0,"1/20*b^5*B*x^20+1/18*(A*b^5+5*B*a*b^4)*x^18+1/16*(5*A*a*b^4+10*B*a^2*b^3)*x^16+1/14*(10*A*a^2*b^3+10*B*a^3*b^2)*x^14+1/12*(10*A*a^3*b^2+5*B*a^4*b)*x^12+1/10*(5*A*a^4*b+B*a^5)*x^10+1/8*a^5*A*x^8","A"
26,1,124,103,0.000000," ","int(x^6*(b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{19}}{19}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{17}}{17}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{15}}{15}+\frac{A \,a^{5} x^{7}}{7}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{13}}{13}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{11}}{11}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{9}}{9}"," ",0,"1/19*b^5*B*x^19+1/17*(A*b^5+5*B*a*b^4)*x^17+1/15*(5*A*a*b^4+10*B*a^2*b^3)*x^15+1/13*(10*A*a^2*b^3+10*B*a^3*b^2)*x^13+1/11*(10*A*a^3*b^2+5*B*a^4*b)*x^11+1/9*(5*A*a^4*b+B*a^5)*x^9+1/7*a^5*A*x^7","A"
27,1,124,87,0.001000," ","int(x^5*(b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{18}}{18}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{16}}{16}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{14}}{14}+\frac{A \,a^{5} x^{6}}{6}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{12}}{12}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{10}}{10}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{8}}{8}"," ",0,"1/18*b^5*B*x^18+1/16*(A*b^5+5*B*a*b^4)*x^16+1/14*(5*A*a*b^4+10*B*a^2*b^3)*x^14+1/12*(10*A*a^2*b^3+10*B*a^3*b^2)*x^12+1/10*(10*A*a^3*b^2+5*B*a^4*b)*x^10+1/8*(5*A*a^4*b+B*a^5)*x^8+1/6*a^5*A*x^6","A"
28,1,124,103,0.002000," ","int(x^4*(b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{17}}{17}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{15}}{15}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{13}}{13}+\frac{A \,a^{5} x^{5}}{5}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{11}}{11}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{9}}{9}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{7}}{7}"," ",0,"1/17*b^5*B*x^17+1/15*(A*b^5+5*B*a*b^4)*x^15+1/13*(5*A*a*b^4+10*B*a^2*b^3)*x^13+1/11*(10*A*a^2*b^3+10*B*a^3*b^2)*x^11+1/9*(10*A*a^3*b^2+5*B*a^4*b)*x^9+1/7*(5*A*a^4*b+B*a^5)*x^7+1/5*a^5*A*x^5","A"
29,1,124,61,0.001000," ","int(x^3*(b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{16}}{16}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{14}}{14}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{12}}{12}+\frac{A \,a^{5} x^{4}}{4}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{10}}{10}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{8}}{8}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{6}}{6}"," ",0,"1/16*b^5*B*x^16+1/14*(A*b^5+5*B*a*b^4)*x^14+1/12*(5*A*a*b^4+10*B*a^2*b^3)*x^12+1/10*(10*A*a^2*b^3+10*B*a^3*b^2)*x^10+1/8*(10*A*a^3*b^2+5*B*a^4*b)*x^8+1/6*(5*A*a^4*b+B*a^5)*x^6+1/4*a^5*A*x^4","B"
30,1,124,103,0.003000," ","int(x^2*(b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{15}}{15}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{13}}{13}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{11}}{11}+\frac{A \,a^{5} x^{3}}{3}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{9}}{9}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{7}}{7}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{5}}{5}"," ",0,"1/15*b^5*B*x^15+1/13*(A*b^5+5*B*a*b^4)*x^13+1/11*(5*A*a*b^4+10*B*a^2*b^3)*x^11+1/9*(10*A*a^2*b^3+10*B*a^3*b^2)*x^9+1/7*(10*A*a^3*b^2+5*B*a^4*b)*x^7+1/5*(5*A*a^4*b+B*a^5)*x^5+1/3*a^5*A*x^3","A"
31,1,124,38,0.002000," ","int(x*(b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{14}}{14}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{12}}{12}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{10}}{10}+\frac{A \,a^{5} x^{2}}{2}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{8}}{8}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{6}}{6}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{4}}{4}"," ",0,"1/14*b^5*B*x^14+1/12*(A*b^5+5*B*a*b^4)*x^12+1/10*(5*A*a*b^4+10*B*a^2*b^3)*x^10+1/8*(10*A*a^2*b^3+10*B*a^3*b^2)*x^8+1/6*(10*A*a^3*b^2+5*B*a^4*b)*x^6+1/4*(5*A*a^4*b+B*a^5)*x^4+1/2*a^5*A*x^2","B"
32,1,121,99,0.001000," ","int((b*x^2+a)^5*(B*x^2+A),x)","\frac{B \,b^{5} x^{13}}{13}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{11}}{11}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{9}}{9}+A \,a^{5} x +\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{7}}{7}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{5}}{5}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{3}}{3}"," ",0,"1/13*b^5*B*x^13+1/11*(A*b^5+5*B*a*b^4)*x^11+1/9*(5*A*a*b^4+10*B*a^2*b^3)*x^9+1/7*(10*A*a^2*b^3+10*B*a^3*b^2)*x^7+1/5*(10*A*a^3*b^2+5*B*a^4*b)*x^5+1/3*(5*A*a^4*b+B*a^5)*x^3+a^5*A*x","A"
33,1,124,76,0.004000," ","int((b*x^2+a)^5*(B*x^2+A)/x,x)","\frac{B \,b^{5} x^{12}}{12}+\frac{A \,b^{5} x^{10}}{10}+\frac{B a \,b^{4} x^{10}}{2}+\frac{5 A a \,b^{4} x^{8}}{8}+\frac{5 B \,a^{2} b^{3} x^{8}}{4}+\frac{5 A \,a^{2} b^{3} x^{6}}{3}+\frac{5 B \,a^{3} b^{2} x^{6}}{3}+\frac{5 A \,a^{3} b^{2} x^{4}}{2}+\frac{5 B \,a^{4} b \,x^{4}}{4}+\frac{5 A \,a^{4} b \,x^{2}}{2}+\frac{B \,a^{5} x^{2}}{2}+A \,a^{5} \ln \left(x \right)"," ",0,"1/12*B*b^5*x^12+1/10*A*b^5*x^10+1/2*B*x^10*a*b^4+5/8*a*A*b^4*x^8+5/4*B*x^8*a^2*b^3+5/3*a^2*A*b^3*x^6+5/3*B*x^6*a^3*b^2+5/2*a^3*A*b^2*x^4+5/4*B*x^4*a^4*b+5/2*a^4*A*b*x^2+1/2*B*x^2*a^5+a^5*A*ln(x)","A"
34,1,121,100,0.004000," ","int((b*x^2+a)^5*(B*x^2+A)/x^2,x)","\frac{B \,b^{5} x^{11}}{11}+\frac{A \,b^{5} x^{9}}{9}+\frac{5 B a \,b^{4} x^{9}}{9}+\frac{5 A a \,b^{4} x^{7}}{7}+\frac{10 B \,a^{2} b^{3} x^{7}}{7}+2 A \,a^{2} b^{3} x^{5}+2 B \,a^{3} b^{2} x^{5}+\frac{10 A \,a^{3} b^{2} x^{3}}{3}+\frac{5 B \,a^{4} b \,x^{3}}{3}+5 A \,a^{4} b x +B \,a^{5} x -\frac{A \,a^{5}}{x}"," ",0,"1/11*b^5*B*x^11+1/9*A*x^9*b^5+5/9*B*x^9*a*b^4+5/7*A*x^7*a*b^4+10/7*B*x^7*a^2*b^3+2*A*x^5*a^2*b^3+2*B*x^5*a^3*b^2+10/3*A*x^3*a^3*b^2+5/3*B*x^3*a^4*b+5*a^4*b*A*x+a^5*B*x-a^5*A/x","A"
35,1,123,101,0.008000," ","int((b*x^2+a)^5*(B*x^2+A)/x^3,x)","\frac{B \,b^{5} x^{10}}{10}+\frac{A \,b^{5} x^{8}}{8}+\frac{5 B a \,b^{4} x^{8}}{8}+\frac{5 A a \,b^{4} x^{6}}{6}+\frac{5 B \,a^{2} b^{3} x^{6}}{3}+\frac{5 A \,a^{2} b^{3} x^{4}}{2}+\frac{5 B \,a^{3} b^{2} x^{4}}{2}+5 A \,a^{3} b^{2} x^{2}+\frac{5 B \,a^{4} b \,x^{2}}{2}+5 A \,a^{4} b \ln \left(x \right)+B \,a^{5} \ln \left(x \right)-\frac{A \,a^{5}}{2 x^{2}}"," ",0,"1/10*b^5*B*x^10+1/8*A*x^8*b^5+5/8*B*x^8*a*b^4+5/6*A*x^6*a*b^4+5/3*B*x^6*a^2*b^3+5/2*A*x^4*a^2*b^3+5/2*B*x^4*a^3*b^2+5*A*x^2*a^3*b^2+5/2*B*x^2*a^4*b-1/2*a^5*A/x^2+5*A*ln(x)*a^4*b+B*ln(x)*a^5","A"
36,1,118,100,0.005000," ","int((b*x^2+a)^5*(B*x^2+A)/x^4,x)","\frac{B \,b^{5} x^{9}}{9}+\frac{A \,b^{5} x^{7}}{7}+\frac{5 B a \,b^{4} x^{7}}{7}+A a \,b^{4} x^{5}+2 B \,a^{2} b^{3} x^{5}+\frac{10 A \,a^{2} b^{3} x^{3}}{3}+\frac{10 B \,a^{3} b^{2} x^{3}}{3}+10 A \,a^{3} b^{2} x +5 B \,a^{4} b x -\frac{A \,a^{5}}{3 x^{3}}-\frac{\left(5 A b +B a \right) a^{4}}{x}"," ",0,"1/9*b^5*B*x^9+1/7*A*x^7*b^5+5/7*B*x^7*a*b^4+A*x^5*a*b^4+2*B*x^5*a^2*b^3+10/3*A*x^3*a^2*b^3+10/3*B*x^3*a^3*b^2+10*a^3*b^2*A*x+5*a^4*b*B*x-a^4*(5*A*b+B*a)/x-1/3*a^5*A/x^3","A"
37,1,124,102,0.009000," ","int((b*x^2+a)^5*(B*x^2+A)/x^5,x)","\frac{B \,b^{5} x^{8}}{8}+\frac{A \,b^{5} x^{6}}{6}+\frac{5 B a \,b^{4} x^{6}}{6}+\frac{5 A a \,b^{4} x^{4}}{4}+\frac{5 B \,a^{2} b^{3} x^{4}}{2}+5 A \,a^{2} b^{3} x^{2}+5 B \,a^{3} b^{2} x^{2}+10 A \,a^{3} b^{2} \ln \left(x \right)+5 B \,a^{4} b \ln \left(x \right)-\frac{5 A \,a^{4} b}{2 x^{2}}-\frac{B \,a^{5}}{2 x^{2}}-\frac{A \,a^{5}}{4 x^{4}}"," ",0,"1/8*b^5*B*x^8+1/6*A*x^6*b^5+5/6*B*x^6*a*b^4+5/4*A*x^4*a*b^4+5/2*B*x^4*a^2*b^3+5*A*x^2*a^2*b^3+5*B*x^2*a^3*b^2-1/4*a^5*A/x^4-5/2*a^4/x^2*A*b-1/2*a^5/x^2*B+10*A*ln(x)*a^3*b^2+5*B*ln(x)*a^4*b","A"
38,1,113,101,0.006000," ","int((b*x^2+a)^5*(B*x^2+A)/x^6,x)","\frac{B \,b^{5} x^{7}}{7}+\frac{A \,b^{5} x^{5}}{5}+B a \,b^{4} x^{5}+\frac{5 A a \,b^{4} x^{3}}{3}+\frac{10 B \,a^{2} b^{3} x^{3}}{3}+10 A \,a^{2} b^{3} x +10 B \,a^{3} b^{2} x -\frac{5 \left(2 A b +B a \right) a^{3} b}{x}-\frac{A \,a^{5}}{5 x^{5}}-\frac{\left(5 A b +B a \right) a^{4}}{3 x^{3}}"," ",0,"1/7*b^5*B*x^7+1/5*A*x^5*b^5+B*x^5*a*b^4+5/3*A*x^3*a*b^4+10/3*B*x^3*a^2*b^3+10*a^2*b^3*A*x+10*a^3*b^2*B*x-1/5*a^5*A/x^5-5*a^3*b*(2*A*b+B*a)/x-1/3*a^4*(5*A*b+B*a)/x^3","A"
39,1,124,102,0.009000," ","int((b*x^2+a)^5*(B*x^2+A)/x^7,x)","\frac{B \,b^{5} x^{6}}{6}+\frac{A \,b^{5} x^{4}}{4}+\frac{5 B a \,b^{4} x^{4}}{4}+\frac{5 A a \,b^{4} x^{2}}{2}+5 B \,a^{2} b^{3} x^{2}+10 A \,a^{2} b^{3} \ln \left(x \right)+10 B \,a^{3} b^{2} \ln \left(x \right)-\frac{5 A \,a^{3} b^{2}}{x^{2}}-\frac{5 B \,a^{4} b}{2 x^{2}}-\frac{5 A \,a^{4} b}{4 x^{4}}-\frac{B \,a^{5}}{4 x^{4}}-\frac{A \,a^{5}}{6 x^{6}}"," ",0,"1/6*b^5*B*x^6+1/4*A*x^4*b^5+5/4*B*x^4*a*b^4+5/2*A*x^2*a*b^4+5*B*x^2*a^2*b^3-5/4*a^4/x^4*A*b-1/4*a^5/x^4*B-1/6*a^5*A/x^6-5*a^3*b^2/x^2*A-5/2*a^4*b/x^2*B+10*A*ln(x)*a^2*b^3+10*B*ln(x)*a^3*b^2","A"
40,1,108,101,0.007000," ","int((b*x^2+a)^5*(B*x^2+A)/x^8,x)","\frac{B \,b^{5} x^{5}}{5}+\frac{A \,b^{5} x^{3}}{3}+\frac{5 B a \,b^{4} x^{3}}{3}+5 A a \,b^{4} x +10 B \,a^{2} b^{3} x -\frac{10 \left(A b +B a \right) a^{2} b^{2}}{x}-\frac{5 \left(2 A b +B a \right) a^{3} b}{3 x^{3}}-\frac{A \,a^{5}}{7 x^{7}}-\frac{\left(5 A b +B a \right) a^{4}}{5 x^{5}}"," ",0,"1/5*b^5*B*x^5+1/3*A*x^3*b^5+5/3*B*x^3*a*b^4+5*a*b^4*A*x+10*a^2*b^3*B*x-1/5*a^4*(5*A*b+B*a)/x^5-10*a^2*b^2*(A*b+B*a)/x-1/7*a^5*A/x^7-5/3*a^3*b*(2*A*b+B*a)/x^3","A"
41,1,124,102,0.008000," ","int((b*x^2+a)^5*(B*x^2+A)/x^9,x)","\frac{B \,b^{5} x^{4}}{4}+\frac{A \,b^{5} x^{2}}{2}+\frac{5 B a \,b^{4} x^{2}}{2}+5 A a \,b^{4} \ln \left(x \right)+10 B \,a^{2} b^{3} \ln \left(x \right)-\frac{5 A \,a^{2} b^{3}}{x^{2}}-\frac{5 B \,a^{3} b^{2}}{x^{2}}-\frac{5 A \,a^{3} b^{2}}{2 x^{4}}-\frac{5 B \,a^{4} b}{4 x^{4}}-\frac{5 A \,a^{4} b}{6 x^{6}}-\frac{B \,a^{5}}{6 x^{6}}-\frac{A \,a^{5}}{8 x^{8}}"," ",0,"1/4*b^5*B*x^4+1/2*A*x^2*b^5+5/2*B*x^2*a*b^4-5/2*a^3*b^2/x^4*A-5/4*a^4*b/x^4*B-5/6*a^4/x^6*A*b-1/6*a^5/x^6*B-1/8*a^5*A/x^8-5*a^2*b^3/x^2*A-5*a^3*b^2/x^2*B+5*A*ln(x)*a*b^4+10*B*ln(x)*a^2*b^3","A"
42,1,102,100,0.007000," ","int((b*x^2+a)^5*(B*x^2+A)/x^10,x)","\frac{B \,b^{5} x^{3}}{3}+A \,b^{5} x +5 B a \,b^{4} x -\frac{5 \left(A b +2 B a \right) a \,b^{3}}{x}-\frac{10 \left(A b +B a \right) a^{2} b^{2}}{3 x^{3}}-\frac{\left(2 A b +B a \right) a^{3} b}{x^{5}}-\frac{A \,a^{5}}{9 x^{9}}-\frac{\left(5 A b +B a \right) a^{4}}{7 x^{7}}"," ",0,"1/3*b^5*B*x^3+b^5*A*x+5*a*b^4*B*x-a^3*b*(2*A*b+B*a)/x^5-5*a*b^3*(A*b+2*B*a)/x-1/7*a^4*(5*A*b+B*a)/x^7-1/9*a^5*A/x^9-10/3*a^2*b^2*(A*b+B*a)/x^3","A"
43,1,123,101,0.010000," ","int((b*x^2+a)^5*(B*x^2+A)/x^11,x)","\frac{B \,b^{5} x^{2}}{2}+A \,b^{5} \ln \left(x \right)+5 B a \,b^{4} \ln \left(x \right)-\frac{5 A a \,b^{4}}{2 x^{2}}-\frac{5 B \,a^{2} b^{3}}{x^{2}}-\frac{5 A \,a^{2} b^{3}}{2 x^{4}}-\frac{5 B \,a^{3} b^{2}}{2 x^{4}}-\frac{5 A \,a^{3} b^{2}}{3 x^{6}}-\frac{5 B \,a^{4} b}{6 x^{6}}-\frac{5 A \,a^{4} b}{8 x^{8}}-\frac{B \,a^{5}}{8 x^{8}}-\frac{A \,a^{5}}{10 x^{10}}"," ",0,"1/2*b^5*B*x^2-5/2*a^2*b^3/x^4*A-5/2*a^3*b^2/x^4*B-1/10*a^5*A/x^10-5/3*a^3*b^2/x^6*A-5/6*a^4*b/x^6*B-5/8*a^4/x^8*A*b-1/8*a^5/x^8*B-5/2*a*b^4/x^2*A-5*a^2*b^3/x^2*B+A*ln(x)*b^5+5*B*ln(x)*a*b^4","A"
44,1,101,100,0.006000," ","int((b*x^2+a)^5*(B*x^2+A)/x^12,x)","B \,b^{5} x -\frac{\left(A b +5 B a \right) b^{4}}{x}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{3 x^{3}}-\frac{2 \left(A b +B a \right) a^{2} b^{2}}{x^{5}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{7 x^{7}}-\frac{A \,a^{5}}{11 x^{11}}-\frac{\left(5 A b +B a \right) a^{4}}{9 x^{9}}"," ",0,"-1/11*a^5*A/x^11-1/9*a^4*(5*A*b+B*a)/x^9-5/7*a^3*b*(2*A*b+B*a)/x^7-2*a^2*b^2*(A*b+B*a)/x^5-5/3*a*b^3*(A*b+2*B*a)/x^3-b^4*(A*b+5*B*a)/x+b^5*B*x","A"
45,1,124,79,0.008000," ","int((b*x^2+a)^5*(B*x^2+A)/x^13,x)","B \,b^{5} \ln \left(x \right)-\frac{A \,b^{5}}{2 x^{2}}-\frac{5 B a \,b^{4}}{2 x^{2}}-\frac{5 A a \,b^{4}}{4 x^{4}}-\frac{5 B \,a^{2} b^{3}}{2 x^{4}}-\frac{5 A \,a^{2} b^{3}}{3 x^{6}}-\frac{5 B \,a^{3} b^{2}}{3 x^{6}}-\frac{5 A \,a^{3} b^{2}}{4 x^{8}}-\frac{5 B \,a^{4} b}{8 x^{8}}-\frac{A \,a^{4} b}{2 x^{10}}-\frac{B \,a^{5}}{10 x^{10}}-\frac{A \,a^{5}}{12 x^{12}}"," ",0,"-5/4*a*b^4/x^4*A-5/2*a^2*b^3*B/x^4-1/2*a^4/x^10*A*b-1/10*a^5*B/x^10-5/3*a^2*b^3/x^6*A-5/3*a^3*b^2*B/x^6-5/4*a^3*b^2/x^8*A-5/8*a^4*b*B/x^8-1/2*b^5/x^2*A-5/2*a*b^4*B/x^2-1/12*A*a^5/x^12+b^5*B*ln(x)","A"
46,1,104,103,0.007000," ","int((b*x^2+a)^5*(B*x^2+A)/x^14,x)","-\frac{B \,b^{5}}{x}-\frac{\left(A b +5 B a \right) b^{4}}{3 x^{3}}-\frac{\left(A b +2 B a \right) a \,b^{3}}{x^{5}}-\frac{10 \left(A b +B a \right) a^{2} b^{2}}{7 x^{7}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{9 x^{9}}-\frac{A \,a^{5}}{13 x^{13}}-\frac{\left(5 A b +B a \right) a^{4}}{11 x^{11}}"," ",0,"-1/13*a^5*A/x^13-1/11*a^4*(5*A*b+B*a)/x^11-5/9*a^3*b*(2*A*b+B*a)/x^9-10/7*a^2*b^2*(A*b+B*a)/x^7-a*b^3*(A*b+2*B*a)/x^5-1/3*b^4*(A*b+5*B*a)/x^3-b^5*B/x","A"
47,1,104,44,0.007000," ","int((b*x^2+a)^5*(B*x^2+A)/x^15,x)","-\frac{B \,b^{5}}{2 x^{2}}-\frac{\left(A b +5 B a \right) b^{4}}{4 x^{4}}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{6 x^{6}}-\frac{5 \left(A b +B a \right) a^{2} b^{2}}{4 x^{8}}-\frac{\left(2 A b +B a \right) a^{3} b}{2 x^{10}}-\frac{A \,a^{5}}{14 x^{14}}-\frac{\left(5 A b +B a \right) a^{4}}{12 x^{12}}"," ",0,"-1/2*a^3*b*(2*A*b+B*a)/x^10-5/6*a*b^3*(A*b+2*B*a)/x^6-5/4*a^2*b^2*(A*b+B*a)/x^8-1/2*B*b^5/x^2-1/14*A*a^5/x^14-1/4*b^4*(A*b+5*B*a)/x^4-1/12*a^4*(5*A*b+B*a)/x^12","B"
48,1,104,103,0.007000," ","int((b*x^2+a)^5*(B*x^2+A)/x^16,x)","-\frac{B \,b^{5}}{3 x^{3}}-\frac{\left(A b +5 B a \right) b^{4}}{5 x^{5}}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{7 x^{7}}-\frac{10 \left(A b +B a \right) a^{2} b^{2}}{9 x^{9}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{11 x^{11}}-\frac{A \,a^{5}}{15 x^{15}}-\frac{\left(5 A b +B a \right) a^{4}}{13 x^{13}}"," ",0,"-1/15*a^5*A/x^15-1/13*a^4*(5*A*b+B*a)/x^13-5/11*a^3*b*(2*A*b+B*a)/x^11-10/9*a^2*b^2*(A*b+B*a)/x^9-5/7*a*b^3*(A*b+2*B*a)/x^7-1/5*b^4*(A*b+5*B*a)/x^5-1/3*b^5*B/x^3","A"
49,1,104,70,0.007000," ","int((b*x^2+a)^5*(B*x^2+A)/x^17,x)","-\frac{B \,b^{5}}{4 x^{4}}-\frac{\left(A b +5 B a \right) b^{4}}{6 x^{6}}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{8 x^{8}}-\frac{\left(A b +B a \right) a^{2} b^{2}}{x^{10}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{12 x^{12}}-\frac{A \,a^{5}}{16 x^{16}}-\frac{\left(5 A b +B a \right) a^{4}}{14 x^{14}}"," ",0,"-1/16*A*a^5/x^16-a^2*b^2*(A*b+B*a)/x^10-1/6*b^4*(A*b+5*B*a)/x^6-5/8*a*b^3*(A*b+2*B*a)/x^8-1/4*B*b^5/x^4-1/14*a^4*(5*A*b+B*a)/x^14-5/12*a^3*b*(2*A*b+B*a)/x^12","A"
50,1,104,103,0.006000," ","int((b*x^2+a)^5*(B*x^2+A)/x^18,x)","-\frac{B \,b^{5}}{5 x^{5}}-\frac{\left(A b +5 B a \right) b^{4}}{7 x^{7}}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{9 x^{9}}-\frac{10 \left(A b +B a \right) a^{2} b^{2}}{11 x^{11}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{13 x^{13}}-\frac{A \,a^{5}}{17 x^{17}}-\frac{\left(5 A b +B a \right) a^{4}}{15 x^{15}}"," ",0,"-1/17*a^5*A/x^17-1/15*a^4*(5*A*b+B*a)/x^15-5/13*a^3*b*(2*A*b+B*a)/x^13-10/11*a^2*b^2*(A*b+B*a)/x^11-5/9*a*b^3*(A*b+2*B*a)/x^9-1/7*b^4*(A*b+5*B*a)/x^7-1/5*b^5*B/x^5","A"
51,1,104,103,0.007000," ","int((b*x^2+a)^5*(B*x^2+A)/x^19,x)","-\frac{B \,b^{5}}{6 x^{6}}-\frac{\left(A b +5 B a \right) b^{4}}{8 x^{8}}-\frac{\left(A b +2 B a \right) a \,b^{3}}{2 x^{10}}-\frac{5 \left(A b +B a \right) a^{2} b^{2}}{6 x^{12}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{14 x^{14}}-\frac{A \,a^{5}}{18 x^{18}}-\frac{\left(5 A b +B a \right) a^{4}}{16 x^{16}}"," ",0,"-1/18*a^5*A/x^18-1/16*a^4*(5*A*b+B*a)/x^16-5/14*a^3*b*(2*A*b+B*a)/x^14-5/6*a^2*b^2*(A*b+B*a)/x^12-1/2*a*b^3*(A*b+2*B*a)/x^10-1/8*b^4*(A*b+5*B*a)/x^8-1/6*b^5*B/x^6","A"
52,1,104,103,0.007000," ","int((b*x^2+a)^5*(B*x^2+A)/x^20,x)","-\frac{B \,b^{5}}{7 x^{7}}-\frac{\left(A b +5 B a \right) b^{4}}{9 x^{9}}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{11 x^{11}}-\frac{10 \left(A b +B a \right) a^{2} b^{2}}{13 x^{13}}-\frac{\left(2 A b +B a \right) a^{3} b}{3 x^{15}}-\frac{A \,a^{5}}{19 x^{19}}-\frac{\left(5 A b +B a \right) a^{4}}{17 x^{17}}"," ",0,"-1/19*a^5*A/x^19-1/17*a^4*(5*A*b+B*a)/x^17-1/3*a^3*b*(2*A*b+B*a)/x^15-10/13*a^2*b^2*(A*b+B*a)/x^13-5/11*a*b^3*(A*b+2*B*a)/x^11-1/9*b^4*(A*b+5*B*a)/x^9-1/7*b^5*B/x^7","A"
53,1,104,103,0.007000," ","int((b*x^2+a)^5*(B*x^2+A)/x^21,x)","-\frac{B \,b^{5}}{8 x^{8}}-\frac{\left(A b +5 B a \right) b^{4}}{10 x^{10}}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{12 x^{12}}-\frac{5 \left(A b +B a \right) a^{2} b^{2}}{7 x^{14}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{16 x^{16}}-\frac{A \,a^{5}}{20 x^{20}}-\frac{\left(5 A b +B a \right) a^{4}}{18 x^{18}}"," ",0,"-1/20*a^5*A/x^20-1/18*a^4*(5*A*b+B*a)/x^18-5/16*a^3*b*(2*A*b+B*a)/x^16-5/7*a^2*b^2*(A*b+B*a)/x^14-5/12*a*b^3*(A*b+2*B*a)/x^12-1/10*b^4*(A*b+5*B*a)/x^10-1/8*b^5*B/x^8","A"
54,1,104,103,0.006000," ","int((b*x^2+a)^5*(B*x^2+A)/x^22,x)","-\frac{B \,b^{5}}{9 x^{9}}-\frac{\left(A b +5 B a \right) b^{4}}{11 x^{11}}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{13 x^{13}}-\frac{2 \left(A b +B a \right) a^{2} b^{2}}{3 x^{15}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{17 x^{17}}-\frac{A \,a^{5}}{21 x^{21}}-\frac{\left(5 A b +B a \right) a^{4}}{19 x^{19}}"," ",0,"-1/21*a^5*A/x^21-1/19*a^4*(5*A*b+B*a)/x^19-5/17*a^3*b*(2*A*b+B*a)/x^17-2/3*a^2*b^2*(A*b+B*a)/x^15-5/13*a*b^3*(A*b+2*B*a)/x^13-1/11*b^4*(A*b+5*B*a)/x^11-1/9*b^5*B/x^9","A"
55,1,104,103,0.006000," ","int((b*x^2+a)^5*(B*x^2+A)/x^23,x)","-\frac{B \,b^{5}}{10 x^{10}}-\frac{\left(A b +5 B a \right) b^{4}}{12 x^{12}}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{14 x^{14}}-\frac{5 \left(A b +B a \right) a^{2} b^{2}}{8 x^{16}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{18 x^{18}}-\frac{A \,a^{5}}{22 x^{22}}-\frac{\left(5 A b +B a \right) a^{4}}{20 x^{20}}"," ",0,"-1/22*a^5*A/x^22-1/20*a^4*(5*A*b+B*a)/x^20-5/18*a^3*b*(2*A*b+B*a)/x^18-5/8*a^2*b^2*(A*b+B*a)/x^16-5/14*a*b^3*(A*b+2*B*a)/x^14-1/12*b^4*(A*b+5*B*a)/x^12-1/10*b^5*B/x^10","A"
56,1,116,84,0.010000," ","int(x^6*(B*x^2+A)/(b*x^2+a),x)","\frac{B \,x^{7}}{7 b}+\frac{A \,x^{5}}{5 b}-\frac{B a \,x^{5}}{5 b^{2}}-\frac{A a \,x^{3}}{3 b^{2}}+\frac{B \,a^{2} x^{3}}{3 b^{3}}-\frac{A \,a^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{B \,a^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{4}}+\frac{A \,a^{2} x}{b^{3}}-\frac{B \,a^{3} x}{b^{4}}"," ",0,"1/7*B*x^7/b+1/5/b*A*x^5-1/5/b^2*B*x^5*a-1/3/b^2*A*x^3*a+1/3/b^3*B*x^3*a^2+1/b^3*A*a^2*x-1/b^4*B*a^3*x-a^3/b^3/(a*b)^(1/2)*arctan(b*x/(a*b)^(1/2))*A+a^4/b^4/(a*b)^(1/2)*arctan(b*x/(a*b)^(1/2))*B","A"
57,1,86,67,0.005000," ","int(x^5*(B*x^2+A)/(b*x^2+a),x)","\frac{B \,x^{6}}{6 b}+\frac{A \,x^{4}}{4 b}-\frac{B a \,x^{4}}{4 b^{2}}-\frac{A a \,x^{2}}{2 b^{2}}+\frac{B \,a^{2} x^{2}}{2 b^{3}}+\frac{A \,a^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{3}}-\frac{B \,a^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}"," ",0,"1/6*B*x^6/b+1/4/b*A*x^4-1/4/b^2*B*x^4*a-1/2/b^2*A*x^2*a+1/2/b^3*B*x^2*a^2+1/2*a^2/b^3*ln(b*x^2+a)*A-1/2*a^3/b^4*ln(b*x^2+a)*B","A"
58,1,92,65,0.004000," ","int(x^4*(B*x^2+A)/(b*x^2+a),x)","\frac{B \,x^{5}}{5 b}+\frac{A \,x^{3}}{3 b}-\frac{B a \,x^{3}}{3 b^{2}}+\frac{A \,a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{B \,a^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}-\frac{A a x}{b^{2}}+\frac{B \,a^{2} x}{b^{3}}"," ",0,"1/5*B*x^5/b+1/3/b*A*x^3-1/3/b^2*B*x^3*a-1/b^2*a*A*x+1/b^3*a^2*B*x+a^2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-a^3/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
59,1,62,48,0.003000," ","int(x^3*(B*x^2+A)/(b*x^2+a),x)","\frac{B \,x^{4}}{4 b}+\frac{A \,x^{2}}{2 b}-\frac{B a \,x^{2}}{2 b^{2}}-\frac{A a \ln \left(b \,x^{2}+a \right)}{2 b^{2}}+\frac{B \,a^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{3}}"," ",0,"1/4*B*x^4/b+1/2/b*A*x^2-1/2/b^2*B*x^2*a-1/2*a/b^2*ln(b*x^2+a)*A+1/2*a^2/b^3*ln(b*x^2+a)*B","A"
60,1,68,48,0.004000," ","int(x^2*(B*x^2+A)/(b*x^2+a),x)","\frac{B \,x^{3}}{3 b}-\frac{A a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{B \,a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}+\frac{A x}{b}-\frac{B a x}{b^{2}}"," ",0,"1/3*B*x^3/b+1/b*A*x-1/b^2*B*a*x-a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+a^2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
61,1,40,31,0.005000," ","int(x*(B*x^2+A)/(b*x^2+a),x)","\frac{B \,x^{2}}{2 b}+\frac{A \ln \left(b \,x^{2}+a \right)}{2 b}-\frac{B a \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/2*B*x^2/b+1/2/b*ln(b*x^2+a)*A-1/2/b^2*ln(b*x^2+a)*B*a","A"
62,1,45,31,0.004000," ","int((B*x^2+A)/(b*x^2+a),x)","\frac{A \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}-\frac{B a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{B x}{b}"," ",0,"B*x/b+1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-1/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B*a","A"
63,1,37,32,0.006000," ","int((B*x^2+A)/x/(b*x^2+a),x)","\frac{A \ln \left(x \right)}{a}-\frac{A \ln \left(b \,x^{2}+a \right)}{2 a}+\frac{B \ln \left(b \,x^{2}+a \right)}{2 b}"," ",0,"-1/2/a*ln(b*x^2+a)*A+1/2/b*ln(b*x^2+a)*B+A*ln(x)/a","A"
64,1,48,35,0.015000," ","int((B*x^2+A)/x^2/(b*x^2+a),x)","-\frac{A b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}+\frac{B \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}-\frac{A}{a x}"," ",0,"-1/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A*b+1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-A/a/x","A"
65,1,56,46,0.010000," ","int((B*x^2+A)/x^3/(b*x^2+a),x)","-\frac{A b \ln \left(x \right)}{a^{2}}+\frac{A b \ln \left(b \,x^{2}+a \right)}{2 a^{2}}+\frac{B \ln \left(x \right)}{a}-\frac{B \ln \left(b \,x^{2}+a \right)}{2 a}-\frac{A}{2 a \,x^{2}}"," ",0,"1/2/a^2*ln(b*x^2+a)*A*b-1/2/a*ln(b*x^2+a)*B-1/2*A/a/x^2-1/a^2*ln(x)*A*b+1/a*ln(x)*B","A"
66,1,72,49,0.009000," ","int((B*x^2+A)/x^4/(b*x^2+a),x)","\frac{A \,b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{2}}-\frac{B b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}+\frac{A b}{a^{2} x}-\frac{B}{a x}-\frac{A}{3 a \,x^{3}}"," ",0,"b^2/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-b/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-1/3*A/a/x^3+1/a^2/x*A*b-1/a/x*B","A"
67,1,81,63,0.010000," ","int((B*x^2+A)/x^5/(b*x^2+a),x)","\frac{A \,b^{2} \ln \left(x \right)}{a^{3}}-\frac{A \,b^{2} \ln \left(b \,x^{2}+a \right)}{2 a^{3}}-\frac{B b \ln \left(x \right)}{a^{2}}+\frac{B b \ln \left(b \,x^{2}+a \right)}{2 a^{2}}+\frac{A b}{2 a^{2} x^{2}}-\frac{B}{2 a \,x^{2}}-\frac{A}{4 a \,x^{4}}"," ",0,"-1/2*b^2/a^3*ln(b*x^2+a)*A+1/2*b/a^2*ln(b*x^2+a)*B-1/4*A/a/x^4+1/2/a^2/x^2*A*b-1/2/a/x^2*B+1/a^3*b^2*ln(x)*A-1/a^2*b*ln(x)*B","A"
68,1,96,68,0.008000," ","int((B*x^2+A)/x^6/(b*x^2+a),x)","-\frac{A \,b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{3}}+\frac{B \,b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{2}}-\frac{A \,b^{2}}{a^{3} x}+\frac{B b}{a^{2} x}+\frac{A b}{3 a^{2} x^{3}}-\frac{B}{3 a \,x^{3}}-\frac{A}{5 a \,x^{5}}"," ",0,"-b^3/a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+b^2/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-1/5*A/a/x^5+1/3/a^2/x^3*A*b-1/3/a/x^3*B-1/a^3*b^2/x*A+1/a^2*b/x*B","A"
69,1,107,85,0.010000," ","int((B*x^2+A)/x^7/(b*x^2+a),x)","-\frac{A \,b^{3} \ln \left(x \right)}{a^{4}}+\frac{A \,b^{3} \ln \left(b \,x^{2}+a \right)}{2 a^{4}}+\frac{B \,b^{2} \ln \left(x \right)}{a^{3}}-\frac{B \,b^{2} \ln \left(b \,x^{2}+a \right)}{2 a^{3}}-\frac{A \,b^{2}}{2 a^{3} x^{2}}+\frac{B b}{2 a^{2} x^{2}}+\frac{A b}{4 a^{2} x^{4}}-\frac{B}{4 a \,x^{4}}-\frac{A}{6 a \,x^{6}}"," ",0,"1/2*b^3/a^4*ln(b*x^2+a)*A-1/2*b^2/a^3*ln(b*x^2+a)*B-1/6*A/a/x^6+1/4/a^2/x^4*A*b-1/4/a/x^4*B-1/2/a^3*b^2/x^2*A+1/2/a^2*b/x^2*B-1/a^4*b^3*ln(x)*A+1/a^3*b^2*ln(x)*B","A"
70,1,120,85,0.010000," ","int((B*x^2+A)/x^8/(b*x^2+a),x)","\frac{A \,b^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{4}}-\frac{B \,b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{3}}+\frac{A \,b^{3}}{a^{4} x}-\frac{B \,b^{2}}{a^{3} x}-\frac{A \,b^{2}}{3 a^{3} x^{3}}+\frac{B b}{3 a^{2} x^{3}}+\frac{A b}{5 a^{2} x^{5}}-\frac{B}{5 a \,x^{5}}-\frac{A}{7 a \,x^{7}}"," ",0,"b^4/a^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-b^3/a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-1/7*A/a/x^7+1/5/a^2/x^5*A*b-1/5/a/x^5*B-1/3/a^3*b^2/x^3*A+1/3/a^2*b/x^3*B+1/a^4*b^3/x*A-1/a^3*b^2/x*B","A"
71,1,146,114,0.024000," ","int(x^9*(B*x^2+A)/(b*x^2+a)^2,x)","\frac{B \,x^{8}}{8 b^{2}}+\frac{A \,x^{6}}{6 b^{2}}-\frac{B a \,x^{6}}{3 b^{3}}-\frac{A a \,x^{4}}{2 b^{3}}+\frac{3 B \,a^{2} x^{4}}{4 b^{4}}+\frac{3 A \,a^{2} x^{2}}{2 b^{4}}-\frac{2 B \,a^{3} x^{2}}{b^{5}}-\frac{A \,a^{4}}{2 \left(b \,x^{2}+a \right) b^{5}}-\frac{2 A \,a^{3} \ln \left(b \,x^{2}+a \right)}{b^{5}}+\frac{B \,a^{5}}{2 \left(b \,x^{2}+a \right) b^{6}}+\frac{5 B \,a^{4} \ln \left(b \,x^{2}+a \right)}{2 b^{6}}"," ",0,"1/8*B*x^8/b^2+1/6/b^2*x^6*A-1/3/b^3*x^6*B*a-1/2/b^3*x^4*A*a+3/4/b^4*x^4*B*a^2+3/2/b^4*x^2*A*a^2-2/b^5*x^2*B*a^3-1/2*a^4/b^5/(b*x^2+a)*A+1/2*a^5/b^6/(b*x^2+a)*B-2*a^3/b^5*ln(b*x^2+a)*A+5/2*a^4/b^6*ln(b*x^2+a)*B","A"
72,1,155,113,0.021000," ","int(x^8*(B*x^2+A)/(b*x^2+a)^2,x)","\frac{B \,x^{7}}{7 b^{2}}+\frac{A \,x^{5}}{5 b^{2}}-\frac{2 B a \,x^{5}}{5 b^{3}}-\frac{2 A a \,x^{3}}{3 b^{3}}+\frac{B \,a^{2} x^{3}}{b^{4}}+\frac{A \,a^{3} x}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{7 A \,a^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{4}}-\frac{B \,a^{4} x}{2 \left(b \,x^{2}+a \right) b^{5}}+\frac{9 B \,a^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{5}}+\frac{3 A \,a^{2} x}{b^{4}}-\frac{4 B \,a^{3} x}{b^{5}}"," ",0,"1/7*B*x^7/b^2+1/5/b^2*A*x^5-2/5/b^3*B*x^5*a-2/3/b^3*A*x^3*a+1/b^4*B*x^3*a^2+3/b^4*A*a^2*x-4/b^5*B*a^3*x+1/2*a^3/b^4*x/(b*x^2+a)*A-1/2*a^4/b^5*x/(b*x^2+a)*B-7/2*a^3/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+9/2*a^4/b^5/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
73,1,122,94,0.015000," ","int(x^7*(B*x^2+A)/(b*x^2+a)^2,x)","\frac{B \,x^{6}}{6 b^{2}}+\frac{A \,x^{4}}{4 b^{2}}-\frac{B a \,x^{4}}{2 b^{3}}-\frac{A a \,x^{2}}{b^{3}}+\frac{3 B \,a^{2} x^{2}}{2 b^{4}}+\frac{A \,a^{3}}{2 \left(b \,x^{2}+a \right) b^{4}}+\frac{3 A \,a^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}-\frac{B \,a^{4}}{2 \left(b \,x^{2}+a \right) b^{5}}-\frac{2 B \,a^{3} \ln \left(b \,x^{2}+a \right)}{b^{5}}"," ",0,"1/6*B*x^6/b^2+1/4/b^2*A*x^4-1/2/b^3*B*x^4*a-1/b^3*A*x^2*a+3/2/b^4*B*x^2*a^2+1/2*a^3/b^4/(b*x^2+a)*A-1/2*a^4/b^5/(b*x^2+a)*B+3/2*a^2/b^4*ln(b*x^2+a)*A-2*a^3/b^5*ln(b*x^2+a)*B","A"
74,1,132,94,0.010000," ","int(x^6*(B*x^2+A)/(b*x^2+a)^2,x)","\frac{B \,x^{5}}{5 b^{2}}+\frac{A \,x^{3}}{3 b^{2}}-\frac{2 B a \,x^{3}}{3 b^{3}}-\frac{A \,a^{2} x}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{5 A \,a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}+\frac{B \,a^{3} x}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{7 B \,a^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{4}}-\frac{2 A a x}{b^{3}}+\frac{3 B \,a^{2} x}{b^{4}}"," ",0,"1/5*B*x^5/b^2+1/3/b^2*A*x^3-2/3/b^3*B*x^3*a-2/b^3*a*A*x+3/b^4*a^2*B*x-1/2*a^2/b^3*x/(b*x^2+a)*A+1/2*a^3/b^4*x/(b*x^2+a)*B+5/2*a^2/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-7/2*a^3/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
75,1,98,74,0.016000," ","int(x^5*(B*x^2+A)/(b*x^2+a)^2,x)","\frac{B \,x^{4}}{4 b^{2}}+\frac{A \,x^{2}}{2 b^{2}}-\frac{B a \,x^{2}}{b^{3}}-\frac{A \,a^{2}}{2 \left(b \,x^{2}+a \right) b^{3}}-\frac{A a \ln \left(b \,x^{2}+a \right)}{b^{3}}+\frac{B \,a^{3}}{2 \left(b \,x^{2}+a \right) b^{4}}+\frac{3 B \,a^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}"," ",0,"1/4*B*x^4/b^2+1/2/b^2*A*x^2-1/b^3*B*x^2*a-1/2*a^2/b^3/(b*x^2+a)*A+1/2*a^3/b^4/(b*x^2+a)*B-a/b^3*ln(b*x^2+a)*A+3/2*a^2/b^4*ln(b*x^2+a)*B","A"
76,1,105,73,0.010000," ","int(x^4*(B*x^2+A)/(b*x^2+a)^2,x)","\frac{B \,x^{3}}{3 b^{2}}+\frac{A a x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 A a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}-\frac{B \,a^{2} x}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{5 B \,a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}+\frac{A x}{b^{2}}-\frac{2 B a x}{b^{3}}"," ",0,"1/3*B*x^3/b^2+1/b^2*A*x-2/b^3*B*a*x+1/2*a/b^2*x/(b*x^2+a)*A-1/2*a^2/b^3*x/(b*x^2+a)*B-3/2*a/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+5/2*a^2/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
77,1,74,54,0.010000," ","int(x^3*(B*x^2+A)/(b*x^2+a)^2,x)","\frac{B \,x^{2}}{2 b^{2}}+\frac{A a}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{A \ln \left(b \,x^{2}+a \right)}{2 b^{2}}-\frac{B \,a^{2}}{2 \left(b \,x^{2}+a \right) b^{3}}-\frac{B a \ln \left(b \,x^{2}+a \right)}{b^{3}}"," ",0,"1/2*B*x^2/b^2+1/2/b^2*a/(b*x^2+a)*A-1/2/b^3*a^2/(b*x^2+a)*B+1/2/b^2*ln(b*x^2+a)*A-1/b^3*ln(b*x^2+a)*B*a","A"
78,1,82,55,0.011000," ","int(x^2*(B*x^2+A)/(b*x^2+a)^2,x)","-\frac{A x}{2 \left(b \,x^{2}+a \right) b}+\frac{A \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}+\frac{B a x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 B a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}+\frac{B x}{b^{2}}"," ",0,"B*x/b^2-1/2/b*x/(b*x^2+a)*A+1/2/b^2*x/(b*x^2+a)*B*a+1/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-3/2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B*a","A"
79,1,47,37,0.012000," ","int(x*(B*x^2+A)/(b*x^2+a)^2,x)","-\frac{A}{2 \left(b \,x^{2}+a \right) b}+\frac{B a}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{B \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"-1/2/b/(b*x^2+a)*A+1/2/b^2/(b*x^2+a)*B*a+1/2*B*ln(b*x^2+a)/b^2","A"
80,1,68,51,0.009000," ","int((B*x^2+A)/(b*x^2+a)^2,x)","\frac{A \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}+\frac{B \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}+\frac{\left(A b -B a \right) x}{2 \left(b \,x^{2}+a \right) a b}"," ",0,"1/2*(A*b-B*a)*x/a/b/(b*x^2+a)+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+1/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
81,1,53,47,0.015000," ","int((B*x^2+A)/x/(b*x^2+a)^2,x)","\frac{A}{2 \left(b \,x^{2}+a \right) a}+\frac{A \ln \left(x \right)}{a^{2}}-\frac{A \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{B}{2 \left(b \,x^{2}+a \right) b}"," ",0,"1/2/a/(b*x^2+a)*A-1/2/b/(b*x^2+a)*B-1/2*A*ln(b*x^2+a)/a^2+A*ln(x)/a^2","A"
82,1,85,59,0.013000," ","int((B*x^2+A)/x^2/(b*x^2+a)^2,x)","-\frac{A b x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 A b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}+\frac{B x}{2 \left(b \,x^{2}+a \right) a}+\frac{B \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{A}{a^{2} x}"," ",0,"-1/2/a^2*x/(b*x^2+a)*A*b+1/2/a*x/(b*x^2+a)*B-3/2/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A*b+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-A/a^2/x","A"
83,1,86,70,0.019000," ","int((B*x^2+A)/x^3/(b*x^2+a)^2,x)","-\frac{A b}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{2 A b \ln \left(x \right)}{a^{3}}+\frac{A b \ln \left(b \,x^{2}+a \right)}{a^{3}}+\frac{B}{2 \left(b \,x^{2}+a \right) a}+\frac{B \ln \left(x \right)}{a^{2}}-\frac{B \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{A}{2 a^{2} x^{2}}"," ",0,"-1/2/a^2*b/(b*x^2+a)*A+1/2/a/(b*x^2+a)*B+1/a^3*b*ln(b*x^2+a)*A-1/2/a^2*ln(b*x^2+a)*B-1/2*A/a^2/x^2-2/a^3*ln(x)*A*b+1/a^2*ln(x)*B","A"
84,1,110,76,0.021000," ","int((B*x^2+A)/x^4/(b*x^2+a)^2,x)","\frac{A \,b^{2} x}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{5 A \,b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{3}}-\frac{B b x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 B b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}+\frac{2 A b}{a^{3} x}-\frac{B}{a^{2} x}-\frac{A}{3 a^{2} x^{3}}"," ",0,"1/2/a^3*b^2*x/(b*x^2+a)*A-1/2/a^2*b*x/(b*x^2+a)*B+5/2/a^3*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-3/2/a^2*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-1/3*A/a^2/x^3+2/a^3/x*A*b-1/a^2/x*B","A"
85,1,114,89,0.020000," ","int((B*x^2+A)/x^5/(b*x^2+a)^2,x)","\frac{A \,b^{2}}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{3 A \,b^{2} \ln \left(x \right)}{a^{4}}-\frac{3 A \,b^{2} \ln \left(b \,x^{2}+a \right)}{2 a^{4}}-\frac{B b}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{2 B b \ln \left(x \right)}{a^{3}}+\frac{B b \ln \left(b \,x^{2}+a \right)}{a^{3}}+\frac{A b}{a^{3} x^{2}}-\frac{B}{2 a^{2} x^{2}}-\frac{A}{4 a^{2} x^{4}}"," ",0,"1/2/a^3*b^2/(b*x^2+a)*A-1/2/a^2*b/(b*x^2+a)*B-3/2/a^4*b^2*ln(b*x^2+a)*A+1/a^3*b*ln(b*x^2+a)*B-1/4*A/a^2/x^4+1/a^3/x^2*A*b-1/2/a^2/x^2*B+3*b^2/a^4*ln(x)*A-2*b/a^3*ln(x)*B","A"
86,1,136,97,0.016000," ","int((B*x^2+A)/x^6/(b*x^2+a)^2,x)","-\frac{A \,b^{3} x}{2 \left(b \,x^{2}+a \right) a^{4}}-\frac{7 A \,b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{4}}+\frac{B \,b^{2} x}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{5 B \,b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{3}}-\frac{3 A \,b^{2}}{a^{4} x}+\frac{2 B b}{a^{3} x}+\frac{2 A b}{3 a^{3} x^{3}}-\frac{B}{3 a^{2} x^{3}}-\frac{A}{5 a^{2} x^{5}}"," ",0,"-1/2/a^4*b^3*x/(b*x^2+a)*A+1/2/a^3*b^2*x/(b*x^2+a)*B-7/2/a^4*b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+5/2/a^3*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-1/5*A/a^2/x^5+2/3/a^3/x^3*A*b-1/3/a^2/x^3*B-3*b^2/a^4/x*A+2*b/a^3/x*B","A"
87,1,143,114,0.020000," ","int((B*x^2+A)/x^7/(b*x^2+a)^2,x)","-\frac{A \,b^{3}}{2 \left(b \,x^{2}+a \right) a^{4}}-\frac{4 A \,b^{3} \ln \left(x \right)}{a^{5}}+\frac{2 A \,b^{3} \ln \left(b \,x^{2}+a \right)}{a^{5}}+\frac{B \,b^{2}}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{3 B \,b^{2} \ln \left(x \right)}{a^{4}}-\frac{3 B \,b^{2} \ln \left(b \,x^{2}+a \right)}{2 a^{4}}-\frac{3 A \,b^{2}}{2 a^{4} x^{2}}+\frac{B b}{a^{3} x^{2}}+\frac{A b}{2 a^{3} x^{4}}-\frac{B}{4 a^{2} x^{4}}-\frac{A}{6 a^{2} x^{6}}"," ",0,"-1/2/a^4*b^3/(b*x^2+a)*A+1/2/a^3*b^2/(b*x^2+a)*B+2/a^5*b^3*ln(b*x^2+a)*A-3/2/a^4*b^2*ln(b*x^2+a)*B-1/6*A/a^2/x^6+1/2/a^3/x^4*A*b-1/4/a^2/x^4*B-3/2*b^2/a^4/x^2*A+b/a^3/x^2*B-4*b^3/a^5*ln(x)*A+3*b^2/a^4*ln(x)*B","A"
88,1,182,138,0.023000," ","int(x^11*(B*x^2+A)/(b*x^2+a)^3,x)","\frac{B \,x^{8}}{8 b^{3}}+\frac{A \,x^{6}}{6 b^{3}}-\frac{B a \,x^{6}}{2 b^{4}}-\frac{3 A a \,x^{4}}{4 b^{4}}+\frac{3 B \,a^{2} x^{4}}{2 b^{5}}+\frac{A \,a^{5}}{4 \left(b \,x^{2}+a \right)^{2} b^{6}}+\frac{3 A \,a^{2} x^{2}}{b^{5}}-\frac{B \,a^{6}}{4 \left(b \,x^{2}+a \right)^{2} b^{7}}-\frac{5 B \,a^{3} x^{2}}{b^{6}}-\frac{5 A \,a^{4}}{2 \left(b \,x^{2}+a \right) b^{6}}-\frac{5 A \,a^{3} \ln \left(b \,x^{2}+a \right)}{b^{6}}+\frac{3 B \,a^{5}}{\left(b \,x^{2}+a \right) b^{7}}+\frac{15 B \,a^{4} \ln \left(b \,x^{2}+a \right)}{2 b^{7}}"," ",0,"1/8*B*x^8/b^3+1/6/b^3*x^6*A-1/2/b^4*x^6*B*a-3/4/b^4*x^4*a*A+3/2/b^5*x^4*a^2*B+3/b^5*A*x^2*a^2-5/b^6*B*x^2*a^3-5/2*a^4/b^6/(b*x^2+a)*A+3*a^5/b^7/(b*x^2+a)*B+1/4*a^5/b^6/(b*x^2+a)^2*A-1/4*a^6/b^7/(b*x^2+a)^2*B-5*a^3/b^6*ln(b*x^2+a)*A+15/2*a^4/b^7*ln(b*x^2+a)*B","A"
89,1,158,118,0.017000," ","int(x^9*(B*x^2+A)/(b*x^2+a)^3,x)","\frac{B \,x^{6}}{6 b^{3}}+\frac{A \,x^{4}}{4 b^{3}}-\frac{3 B a \,x^{4}}{4 b^{4}}-\frac{A \,a^{4}}{4 \left(b \,x^{2}+a \right)^{2} b^{5}}-\frac{3 A a \,x^{2}}{2 b^{4}}+\frac{B \,a^{5}}{4 \left(b \,x^{2}+a \right)^{2} b^{6}}+\frac{3 B \,a^{2} x^{2}}{b^{5}}+\frac{2 A \,a^{3}}{\left(b \,x^{2}+a \right) b^{5}}+\frac{3 A \,a^{2} \ln \left(b \,x^{2}+a \right)}{b^{5}}-\frac{5 B \,a^{4}}{2 \left(b \,x^{2}+a \right) b^{6}}-\frac{5 B \,a^{3} \ln \left(b \,x^{2}+a \right)}{b^{6}}"," ",0,"1/6*B*x^6/b^3+1/4/b^3*A*x^4-3/4/b^4*B*x^4*a-3/2/b^4*A*x^2*a+3/b^5*B*x^2*a^2+2*a^3/b^5/(b*x^2+a)*A-5/2*a^4/b^6/(b*x^2+a)*B-1/4*a^4/b^5/(b*x^2+a)^2*A+1/4*a^5/b^6/(b*x^2+a)^2*B+3*a^2/b^5*ln(b*x^2+a)*A-5*a^3/b^6*ln(b*x^2+a)*B","A"
90,1,134,99,0.015000," ","int(x^7*(B*x^2+A)/(b*x^2+a)^3,x)","\frac{B \,x^{4}}{4 b^{3}}+\frac{A \,a^{3}}{4 \left(b \,x^{2}+a \right)^{2} b^{4}}+\frac{A \,x^{2}}{2 b^{3}}-\frac{B \,a^{4}}{4 \left(b \,x^{2}+a \right)^{2} b^{5}}-\frac{3 B a \,x^{2}}{2 b^{4}}-\frac{3 A \,a^{2}}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{3 A a \ln \left(b \,x^{2}+a \right)}{2 b^{4}}+\frac{2 B \,a^{3}}{\left(b \,x^{2}+a \right) b^{5}}+\frac{3 B \,a^{2} \ln \left(b \,x^{2}+a \right)}{b^{5}}"," ",0,"1/4*B*x^4/b^3-3/2/b^4*B*x^2*a+1/2/b^3*A*x^2-3/2*a^2/b^4/(b*x^2+a)*A+2*a^3/b^5/(b*x^2+a)*B+1/4*a^3/b^4/(b*x^2+a)^2*A-1/4*a^4/b^5/(b*x^2+a)^2*B-3/2*a/b^4*ln(b*x^2+a)*A+3*a^2/b^5*ln(b*x^2+a)*B","A"
91,1,109,80,0.013000," ","int(x^5*(B*x^2+A)/(b*x^2+a)^3,x)","-\frac{A \,a^{2}}{4 \left(b \,x^{2}+a \right)^{2} b^{3}}+\frac{B \,a^{3}}{4 \left(b \,x^{2}+a \right)^{2} b^{4}}+\frac{B \,x^{2}}{2 b^{3}}+\frac{A a}{\left(b \,x^{2}+a \right) b^{3}}+\frac{A \ln \left(b \,x^{2}+a \right)}{2 b^{3}}-\frac{3 B \,a^{2}}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{3 B a \ln \left(b \,x^{2}+a \right)}{2 b^{4}}"," ",0,"1/2*B*x^2/b^3+1/b^3*a/(b*x^2+a)*A-3/2/b^4*a^2/(b*x^2+a)*B-1/4/b^3*a^2/(b*x^2+a)^2*A+1/4/b^4*a^3/(b*x^2+a)^2*B+1/2/b^3*ln(b*x^2+a)*A-3/2/b^4*ln(b*x^2+a)*B*a","A"
92,1,80,61,0.011000," ","int(x^3*(B*x^2+A)/(b*x^2+a)^3,x)","\frac{A a}{4 \left(b \,x^{2}+a \right)^{2} b^{2}}-\frac{B \,a^{2}}{4 \left(b \,x^{2}+a \right)^{2} b^{3}}-\frac{A}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{B a}{\left(b \,x^{2}+a \right) b^{3}}+\frac{B \ln \left(b \,x^{2}+a \right)}{2 b^{3}}"," ",0,"-1/2/b^2/(b*x^2+a)*A+1/b^3/(b*x^2+a)*B*a+1/4*a/b^2/(b*x^2+a)^2*A-1/4*a^2/b^3/(b*x^2+a)^2*B+1/2*B*ln(b*x^2+a)/b^3","A"
93,1,39,30,0.009000," ","int(x*(B*x^2+A)/(b*x^2+a)^3,x)","-\frac{B}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{A b -B a}{4 \left(b \,x^{2}+a \right)^{2} b^{2}}"," ",0,"-1/2*B/b^2/(b*x^2+a)-1/4*(A*b-B*a)/b^2/(b*x^2+a)^2","A"
94,1,68,62,0.014000," ","int((B*x^2+A)/x/(b*x^2+a)^3,x)","\frac{A}{4 \left(b \,x^{2}+a \right)^{2} a}-\frac{B}{4 \left(b \,x^{2}+a \right)^{2} b}+\frac{A}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{A \ln \left(x \right)}{a^{3}}-\frac{A \ln \left(b \,x^{2}+a \right)}{2 a^{3}}"," ",0,"1/2*A/a^2/(b*x^2+a)+1/4/a/(b*x^2+a)^2*A-1/4/b/(b*x^2+a)^2*B-1/2*A*ln(b*x^2+a)/a^3+A*ln(x)/a^3","A"
95,1,118,92,0.017000," ","int((B*x^2+A)/x^3/(b*x^2+a)^3,x)","-\frac{A b}{4 \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{B}{4 \left(b \,x^{2}+a \right)^{2} a}-\frac{A b}{\left(b \,x^{2}+a \right) a^{3}}-\frac{3 A b \ln \left(x \right)}{a^{4}}+\frac{3 A b \ln \left(b \,x^{2}+a \right)}{2 a^{4}}+\frac{B}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{B \ln \left(x \right)}{a^{3}}-\frac{B \ln \left(b \,x^{2}+a \right)}{2 a^{3}}-\frac{A}{2 a^{3} x^{2}}"," ",0,"-1/a^3*b/(b*x^2+a)*A+1/2/a^2/(b*x^2+a)*B-1/4/a^2*b/(b*x^2+a)^2*A+1/4/a/(b*x^2+a)^2*B+3/2/a^4*b*ln(b*x^2+a)*A-1/2/a^3*ln(b*x^2+a)*B-1/2*A/a^3/x^2-3/a^4*ln(x)*A*b+1/a^3*ln(x)*B","A"
96,1,150,114,0.018000," ","int((B*x^2+A)/x^5/(b*x^2+a)^3,x)","\frac{A \,b^{2}}{4 \left(b \,x^{2}+a \right)^{2} a^{3}}-\frac{B b}{4 \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{3 A \,b^{2}}{2 \left(b \,x^{2}+a \right) a^{4}}+\frac{6 A \,b^{2} \ln \left(x \right)}{a^{5}}-\frac{3 A \,b^{2} \ln \left(b \,x^{2}+a \right)}{a^{5}}-\frac{B b}{\left(b \,x^{2}+a \right) a^{3}}-\frac{3 B b \ln \left(x \right)}{a^{4}}+\frac{3 B b \ln \left(b \,x^{2}+a \right)}{2 a^{4}}+\frac{3 A b}{2 a^{4} x^{2}}-\frac{B}{2 a^{3} x^{2}}-\frac{A}{4 a^{3} x^{4}}"," ",0,"3/2/a^4*b^2/(b*x^2+a)*A-1/a^3*b/(b*x^2+a)*B+1/4/a^3*b^2/(b*x^2+a)^2*A-1/4/a^2*b/(b*x^2+a)^2*B-3/a^5*b^2*ln(b*x^2+a)*A+3/2/a^4*b*ln(b*x^2+a)*B-1/4*A/a^3/x^4+3/2/a^4/x^2*A*b-1/2/a^3/x^2*B+6*b^2/a^5*ln(x)*A-3*b/a^4*ln(x)*B","A"
97,1,180,139,0.020000," ","int((B*x^2+A)/x^7/(b*x^2+a)^3,x)","-\frac{A \,b^{3}}{4 \left(b \,x^{2}+a \right)^{2} a^{4}}+\frac{B \,b^{2}}{4 \left(b \,x^{2}+a \right)^{2} a^{3}}-\frac{2 A \,b^{3}}{\left(b \,x^{2}+a \right) a^{5}}-\frac{10 A \,b^{3} \ln \left(x \right)}{a^{6}}+\frac{5 A \,b^{3} \ln \left(b \,x^{2}+a \right)}{a^{6}}+\frac{3 B \,b^{2}}{2 \left(b \,x^{2}+a \right) a^{4}}+\frac{6 B \,b^{2} \ln \left(x \right)}{a^{5}}-\frac{3 B \,b^{2} \ln \left(b \,x^{2}+a \right)}{a^{5}}-\frac{3 A \,b^{2}}{a^{5} x^{2}}+\frac{3 B b}{2 a^{4} x^{2}}+\frac{3 A b}{4 a^{4} x^{4}}-\frac{B}{4 a^{3} x^{4}}-\frac{A}{6 a^{3} x^{6}}"," ",0,"-2/a^5*b^3/(b*x^2+a)*A+3/2/a^4*b^2/(b*x^2+a)*B-1/4/a^4*b^3/(b*x^2+a)^2*A+1/4/a^3*b^2/(b*x^2+a)^2*B+5/a^6*b^3*ln(b*x^2+a)*A-3/a^5*b^2*ln(b*x^2+a)*B-1/6*A/a^3/x^6+3/4/a^4/x^4*A*b-1/4/a^3/x^4*B-3*b^2/a^5/x^2*A+3/2*b/a^4/x^2*B-10*b^3/a^6*ln(x)*A+6*b^2/a^5*ln(x)*B","A"
98,1,198,140,0.015000," ","int(x^10*(B*x^2+A)/(b*x^2+a)^3,x)","\frac{B \,x^{7}}{7 b^{3}}+\frac{17 A \,a^{3} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{4}}+\frac{A \,x^{5}}{5 b^{3}}-\frac{21 B \,a^{4} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{5}}-\frac{3 B a \,x^{5}}{5 b^{4}}+\frac{15 A \,a^{4} x}{8 \left(b \,x^{2}+a \right)^{2} b^{5}}-\frac{A a \,x^{3}}{b^{4}}-\frac{19 B \,a^{5} x}{8 \left(b \,x^{2}+a \right)^{2} b^{6}}+\frac{2 B \,a^{2} x^{3}}{b^{5}}-\frac{63 A \,a^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{5}}+\frac{99 B \,a^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{6}}+\frac{6 A \,a^{2} x}{b^{5}}-\frac{10 B \,a^{3} x}{b^{6}}"," ",0,"1/7*B*x^7/b^3+1/5/b^3*A*x^5-3/5/b^4*B*x^5*a-1/b^4*A*x^3*a+2/b^5*B*x^3*a^2+6/b^5*A*a^2*x-10/b^6*B*a^3*x+17/8*a^3/b^4/(b*x^2+a)^2*A*x^3-21/8*a^4/b^5/(b*x^2+a)^2*B*x^3+15/8*a^4/b^5/(b*x^2+a)^2*A*x-19/8*a^5/b^6/(b*x^2+a)^2*B*x-63/8*a^3/b^5/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+99/8*a^4/b^6/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
99,1,174,120,0.039000," ","int(x^8*(B*x^2+A)/(b*x^2+a)^3,x)","-\frac{13 A \,a^{2} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{3}}+\frac{17 B \,a^{3} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{4}}+\frac{B \,x^{5}}{5 b^{3}}-\frac{11 A \,a^{3} x}{8 \left(b \,x^{2}+a \right)^{2} b^{4}}+\frac{A \,x^{3}}{3 b^{3}}+\frac{15 B \,a^{4} x}{8 \left(b \,x^{2}+a \right)^{2} b^{5}}-\frac{B a \,x^{3}}{b^{4}}+\frac{35 A \,a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{4}}-\frac{63 B \,a^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{5}}-\frac{3 A a x}{b^{4}}+\frac{6 B \,a^{2} x}{b^{5}}"," ",0,"1/5*B*x^5/b^3+1/3/b^3*A*x^3-1/b^4*B*x^3*a-3/b^4*a*A*x+6/b^5*a^2*B*x-13/8*a^2/b^3/(b*x^2+a)^2*A*x^3+17/8*a^3/b^4/(b*x^2+a)^2*B*x^3-11/8*a^3/b^4/(b*x^2+a)^2*A*x+15/8*a^4/b^5/(b*x^2+a)^2*B*x+35/8*a^2/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-63/8*a^3/b^5/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
100,1,147,100,0.012000," ","int(x^6*(B*x^2+A)/(b*x^2+a)^3,x)","\frac{9 A a \,x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{2}}-\frac{13 B \,a^{2} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{3}}+\frac{7 A \,a^{2} x}{8 \left(b \,x^{2}+a \right)^{2} b^{3}}-\frac{11 B \,a^{3} x}{8 \left(b \,x^{2}+a \right)^{2} b^{4}}+\frac{B \,x^{3}}{3 b^{3}}-\frac{15 A a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{3}}+\frac{35 B \,a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{4}}+\frac{A x}{b^{3}}-\frac{3 B a x}{b^{4}}"," ",0,"1/3*B*x^3/b^3+1/b^3*A*x-3/b^4*B*a*x+9/8*a/b^2/(b*x^2+a)^2*A*x^3-13/8*a^2/b^3/(b*x^2+a)^2*B*x^3+7/8*a^2/b^3/(b*x^2+a)^2*A*x-11/8*a^3/b^4/(b*x^2+a)^2*B*x-15/8*a/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+35/8*a^2/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
101,1,122,80,0.013000," ","int(x^4*(B*x^2+A)/(b*x^2+a)^3,x)","-\frac{5 A \,x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b}+\frac{9 B a \,x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{2}}-\frac{3 A a x}{8 \left(b \,x^{2}+a \right)^{2} b^{2}}+\frac{7 B \,a^{2} x}{8 \left(b \,x^{2}+a \right)^{2} b^{3}}+\frac{3 A \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{2}}-\frac{15 B a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{3}}+\frac{B x}{b^{3}}"," ",0,"B*x/b^3-5/8/b/(b*x^2+a)^2*A*x^3+9/8/b^2/(b*x^2+a)^2*B*x^3*a-3/8/b^2/(b*x^2+a)^2*a*A*x+7/8/b^3/(b*x^2+a)^2*a^2*B*x+3/8/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-15/8/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B*a","A"
102,1,89,75,0.010000," ","int(x^2*(B*x^2+A)/(b*x^2+a)^3,x)","\frac{A \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a b}+\frac{3 B \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{2}}+\frac{\frac{\left(A b -5 B a \right) x^{3}}{8 a b}-\frac{\left(A b +3 B a \right) x}{8 b^{2}}}{\left(b \,x^{2}+a \right)^{2}}"," ",0,"(1/8*(A*b-5*B*a)/a/b*x^3-1/8*(A*b+3*B*a)/b^2*x)/(b*x^2+a)^2+1/8/b/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+3/8/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
103,1,90,78,0.008000," ","int((B*x^2+A)/(b*x^2+a)^3,x)","\frac{3 A \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{2}}+\frac{B \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a b}+\frac{\frac{\left(3 A b +B a \right) x^{3}}{8 a^{2}}+\frac{\left(5 A b -B a \right) x}{8 a b}}{\left(b \,x^{2}+a \right)^{2}}"," ",0,"(1/8*(3*A*b+B*a)/a^2*x^3+1/8*(5*A*b-B*a)/a/b*x)/(b*x^2+a)^2+3/8/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+1/8/a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B","A"
104,1,125,83,0.013000," ","int((B*x^2+A)/x^2/(b*x^2+a)^3,x)","-\frac{7 A \,b^{2} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a^{3}}+\frac{3 B b \,x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a^{2}}-\frac{9 A b x}{8 \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{5 B x}{8 \left(b \,x^{2}+a \right)^{2} a}-\frac{15 A b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{3}}+\frac{3 B \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{2}}-\frac{A}{a^{3} x}"," ",0,"-7/8/a^3/(b*x^2+a)^2*A*x^3*b^2+3/8/a^2/(b*x^2+a)^2*B*x^3*b-9/8/a^2/(b*x^2+a)^2*b*A*x+5/8/a/(b*x^2+a)^2*B*x-15/8/a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A*b+3/8/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-A/a^3/x","A"
105,1,152,101,0.017000," ","int((B*x^2+A)/x^4/(b*x^2+a)^3,x)","\frac{11 A \,b^{3} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a^{4}}-\frac{7 B \,b^{2} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a^{3}}+\frac{13 A \,b^{2} x}{8 \left(b \,x^{2}+a \right)^{2} a^{3}}-\frac{9 B b x}{8 \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{35 A \,b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{4}}-\frac{15 B b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{3}}+\frac{3 A b}{a^{4} x}-\frac{B}{a^{3} x}-\frac{A}{3 a^{3} x^{3}}"," ",0,"11/8/a^4*b^3/(b*x^2+a)^2*A*x^3-7/8/a^3*b^2/(b*x^2+a)^2*B*x^3+13/8/a^3*b^2/(b*x^2+a)^2*A*x-9/8/a^2*b/(b*x^2+a)^2*B*x+35/8/a^4*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A-15/8/a^3*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-1/3*A/a^3/x^3+3/a^4/x*A*b-1/a^3/x*B","A"
106,1,177,124,0.027000," ","int((B*x^2+A)/x^6/(b*x^2+a)^3,x)","-\frac{15 A \,b^{4} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a^{5}}+\frac{11 B \,b^{3} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a^{4}}-\frac{17 A \,b^{3} x}{8 \left(b \,x^{2}+a \right)^{2} a^{4}}+\frac{13 B \,b^{2} x}{8 \left(b \,x^{2}+a \right)^{2} a^{3}}-\frac{63 A \,b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{5}}+\frac{35 B \,b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{4}}-\frac{6 A \,b^{2}}{a^{5} x}+\frac{3 B b}{a^{4} x}+\frac{A b}{a^{4} x^{3}}-\frac{B}{3 a^{3} x^{3}}-\frac{A}{5 a^{3} x^{5}}"," ",0,"-15/8/a^5*b^4/(b*x^2+a)^2*A*x^3+11/8/a^4*b^3/(b*x^2+a)^2*B*x^3-17/8/a^4*b^3/(b*x^2+a)^2*A*x+13/8/a^3*b^2/(b*x^2+a)^2*B*x-63/8/a^5*b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*A+35/8/a^4*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*B-1/5*A/a^3/x^5+1/a^4/x^3*A*b-1/3/a^3/x^3*B-6*b^2/a^5/x*A+3*b/a^4/x*B","A"
107,1,14,12,0.003000," ","int((b*x^2+a)/(x^2+1),x)","a \arctan \left(x \right)+b x -b \arctan \left(x \right)"," ",0,"b*x+arctan(x)*a-arctan(x)*b","A"
108,1,34,11,0.005000," ","int((b*x^2+a)/(-x^2+1),x)","-\frac{a \ln \left(x -1\right)}{2}+\frac{a \ln \left(x +1\right)}{2}-b x -\frac{b \ln \left(x -1\right)}{2}+\frac{b \ln \left(x +1\right)}{2}"," ",0,"-b*x-1/2*ln(x-1)*a-1/2*ln(x-1)*b+1/2*ln(x+1)*a+1/2*ln(x+1)*b","B"
109,1,16,11,0.005000," ","int((x^2+1)/(x^2-1)^2,x)","-\frac{1}{2 \left(x +1\right)}-\frac{1}{2 \left(x -1\right)}"," ",0,"-1/2/(x+1)-1/2/(x-1)","A"
110,1,10,9,0.007000," ","int((-x^2+1)/(x^2+1)^2,x)","\frac{x}{x^{2}+1}"," ",0,"x/(x^2+1)","A"
111,1,16,15,0.007000," ","int((2*x^2+3)/(x^2+1)^2,x)","\frac{x}{2 x^{2}+2}+\frac{5 \arctan \left(x \right)}{2}"," ",0,"1/2/(x^2+1)*x+5/2*arctan(x)","A"
112,1,16,15,0.005000," ","int((x^2-2)/(x^2+1)^2,x)","-\frac{3 x}{2 \left(x^{2}+1\right)}-\frac{\arctan \left(x \right)}{2}"," ",0,"-3/2/(x^2+1)*x-1/2*arctan(x)","A"
113,1,15,14,0.006000," ","int((x^2+3)/(x^2+1)^2,x)","\frac{x}{x^{2}+1}+2 \arctan \left(x \right)"," ",0,"1/(x^2+1)*x+2*arctan(x)","A"
114,1,15,12,0.006000," ","int((b*x^2+a)/(b*x^2-a)^2,x)","-\frac{x}{b \,x^{2}-a}"," ",0,"-x/(b*x^2-a)","A"
115,1,15,12,0.006000," ","int((b*x^2+a)/(-b*x^2+a)^2,x)","-\frac{x}{b \,x^{2}-a}"," ",0,"-1/(b*x^2-a)*x","A"
116,1,37,31,0.004000," ","int((B*x^2+A)/(-b*x^2+a),x)","-\frac{B x}{b}-\frac{\left(-A b -B a \right) \arctanh \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}"," ",0,"-B/b*x-(-A*b-B*a)/b/(a*b)^(1/2)*arctanh(1/(a*b)^(1/2)*b*x)","A"
117,1,25,27,0.008000," ","int((x^2+1)/(x^2+16)^3,x)","\frac{19 \arctan \left(\frac{x}{4}\right)}{8192}+\frac{\frac{19}{2048} x^{3}-\frac{11}{128} x}{\left(x^{2}+16\right)^{2}}"," ",0,"(19/2048*x^3-11/128*x)/(x^2+16)^2+19/8192*arctan(1/4*x)","A"
118,1,30,12,0.012000," ","int((2*x^2+1)/x^5/(x^2+1)^3,x)","\frac{1}{2 x^{2}}-\frac{1}{4 x^{4}}-\frac{1}{2 \left(x^{2}+1\right)}-\frac{1}{4 \left(x^{2}+1\right)^{2}}"," ",0,"-1/2/(x^2+1)-1/4/(x^2+1)^2-1/4/x^4+1/2/x^2","B"
119,1,2,1,0.000000," ","int((-x^2+1)^2/(x^2-1)^2,x)","x"," ",0,"x","A"
120,1,7,6,0.002000," ","int(x^3*(b*c*x^2+a*c)/(b*x^2+a),x)","\frac{c \,x^{4}}{4}"," ",0,"1/4*c*x^4","A"
121,1,7,6,0.001000," ","int(x^2*(b*c*x^2+a*c)/(b*x^2+a),x)","\frac{c \,x^{3}}{3}"," ",0,"1/3*c*x^3","A"
122,1,7,6,0.000000," ","int(x*(b*c*x^2+a*c)/(b*x^2+a),x)","\frac{c \,x^{2}}{2}"," ",0,"1/2*c*x^2","A"
123,1,4,3,0.001000," ","int((b*c*x^2+a*c)/(b*x^2+a),x)","c x"," ",0,"c*x","A"
124,1,5,4,0.001000," ","int((b*c*x^2+a*c)/x/(b*x^2+a),x)","c \ln \left(x \right)"," ",0,"c*ln(x)","A"
125,1,7,6,0.001000," ","int((b*c*x^2+a*c)/x^2/(b*x^2+a),x)","-\frac{c}{x}"," ",0,"-c/x","A"
126,1,7,6,0.001000," ","int((b*c*x^2+a*c)/x^3/(b*x^2+a),x)","-\frac{c}{2 x^{2}}"," ",0,"-1/2*c/x^2","A"
127,1,26,25,0.002000," ","int(x^3*(b*c*x^2+a*c)/(b*x^2+a)^2,x)","\frac{c \,x^{2}}{2 b}-\frac{a c \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/2*c*x^2/b-1/2*a*c*ln(b*x^2+a)/b^2","A"
128,1,29,25,0.003000," ","int(x^2*(b*c*x^2+a*c)/(b*x^2+a)^2,x)","-\frac{a c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{c x}{b}"," ",0,"c*x/b-c*a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
129,1,15,14,0.002000," ","int(x*(b*c*x^2+a*c)/(b*x^2+a)^2,x)","\frac{c \ln \left(b \,x^{2}+a \right)}{2 b}"," ",0,"1/2*c*ln(b*x^2+a)/b","A"
130,1,17,17,0.003000," ","int((b*c*x^2+a*c)/(b*x^2+a)^2,x)","\frac{c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"c/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
131,1,23,22,0.004000," ","int((b*c*x^2+a*c)/x/(b*x^2+a)^2,x)","\frac{c \ln \left(x \right)}{a}-\frac{c \ln \left(b \,x^{2}+a \right)}{2 a}"," ",0,"c*ln(x)/a-1/2*c*ln(b*x^2+a)/a","A"
132,1,32,28,0.004000," ","int((b*c*x^2+a*c)/x^2/(b*x^2+a)^2,x)","-\frac{b c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}-\frac{c}{a x}"," ",0,"-c*b/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-c/a/x","A"
133,1,35,34,0.008000," ","int((b*c*x^2+a*c)/x^3/(b*x^2+a)^2,x)","-\frac{b c \ln \left(x \right)}{a^{2}}+\frac{b c \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{c}{2 a \,x^{2}}"," ",0,"-1/2*c/a/x^2-b*c*ln(x)/a^2+1/2*b*c*ln(b*x^2+a)/a^2","A"
134,1,32,31,0.009000," ","int(x^3*(b*c*x^2+a*c)/(b*x^2+a)^3,x)","\frac{a c}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{c \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/2*a*c/b^2/(b*x^2+a)+1/2*c*ln(b*x^2+a)/b^2","A"
135,1,38,35,0.007000," ","int(x^2*(b*c*x^2+a*c)/(b*x^2+a)^3,x)","-\frac{c x}{2 \left(b \,x^{2}+a \right) b}+\frac{c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}"," ",0,"-1/2*c*x/b/(b*x^2+a)+1/2*c/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
136,1,16,15,0.001000," ","int(x*(b*c*x^2+a*c)/(b*x^2+a)^3,x)","-\frac{c}{2 \left(b \,x^{2}+a \right) b}"," ",0,"-1/2*c/b/(b*x^2+a)","A"
137,1,38,35,0.004000," ","int((b*c*x^2+a*c)/(b*x^2+a)^3,x)","\frac{c x}{2 \left(b \,x^{2}+a \right) a}+\frac{c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}"," ",0,"1/2*c*x/a/(b*x^2+a)+1/2*c/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
138,1,38,37,0.012000," ","int((b*c*x^2+a*c)/x/(b*x^2+a)^3,x)","\frac{c}{2 \left(b \,x^{2}+a \right) a}+\frac{c \ln \left(x \right)}{a^{2}}-\frac{c \ln \left(b \,x^{2}+a \right)}{2 a^{2}}"," ",0,"1/2*c/a/(b*x^2+a)+c*ln(x)/a^2-1/2*c*ln(b*x^2+a)/a^2","A"
139,1,49,46,0.010000," ","int((b*c*x^2+a*c)/x^2/(b*x^2+a)^3,x)","-\frac{b c x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}-\frac{c}{a^{2} x}"," ",0,"-1/2*c/a^2*b*x/(b*x^2+a)-3/2*c/a^2*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-c/a^2/x","A"
140,1,50,49,0.015000," ","int((b*c*x^2+a*c)/x^3/(b*x^2+a)^3,x)","-\frac{b c}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{2 b c \ln \left(x \right)}{a^{3}}+\frac{b c \ln \left(b \,x^{2}+a \right)}{a^{3}}-\frac{c}{2 a^{2} x^{2}}"," ",0,"-1/2*c/a^2/x^2-1/2*b*c/a^2/(b*x^2+a)-2*b*c*ln(x)/a^3+b*c*ln(b*x^2+a)/a^3","A"
141,1,52,47,0.001000," ","int(x^4*(b*x^2+a)^2*(d*x^2+c),x)","\frac{b^{2} d \,x^{11}}{11}+\frac{\left(2 a b d +b^{2} c \right) x^{9}}{9}+\frac{a^{2} c \,x^{5}}{5}+\frac{\left(a^{2} d +2 a b c \right) x^{7}}{7}"," ",0,"1/11*b^2*d*x^11+1/9*(2*a*b*d+b^2*c)*x^9+1/7*(a^2*d+2*a*b*c)*x^7+1/5*a^2*c*x^5","A"
142,1,52,47,0.001000," ","int(x^3*(b*x^2+a)^2*(d*x^2+c),x)","\frac{b^{2} d \,x^{10}}{10}+\frac{\left(2 a b d +b^{2} c \right) x^{8}}{8}+\frac{a^{2} c \,x^{4}}{4}+\frac{\left(a^{2} d +2 a b c \right) x^{6}}{6}"," ",0,"1/10*b^2*d*x^10+1/8*(2*a*b*d+b^2*c)*x^8+1/6*(a^2*d+2*a*b*c)*x^6+1/4*a^2*c*x^4","A"
143,1,52,47,0.002000," ","int(x^2*(b*x^2+a)^2*(d*x^2+c),x)","\frac{b^{2} d \,x^{9}}{9}+\frac{\left(2 a b d +b^{2} c \right) x^{7}}{7}+\frac{a^{2} c \,x^{3}}{3}+\frac{\left(a^{2} d +2 a b c \right) x^{5}}{5}"," ",0,"1/9*b^2*d*x^9+1/7*(2*a*b*d+b^2*c)*x^7+1/5*(a^2*d+2*a*b*c)*x^5+1/3*a^2*c*x^3","A"
144,1,52,38,0.002000," ","int(x*(b*x^2+a)^2*(d*x^2+c),x)","\frac{b^{2} d \,x^{8}}{8}+\frac{\left(2 a b d +b^{2} c \right) x^{6}}{6}+\frac{a^{2} c \,x^{2}}{2}+\frac{\left(a^{2} d +2 a b c \right) x^{4}}{4}"," ",0,"1/8*b^2*d*x^8+1/6*(2*a*b*d+b^2*c)*x^6+1/4*(a^2*d+2*a*b*c)*x^4+1/2*a^2*c*x^2","A"
145,1,49,44,0.000000," ","int((b*x^2+a)^2*(d*x^2+c),x)","\frac{b^{2} d \,x^{7}}{7}+\frac{\left(2 a b d +b^{2} c \right) x^{5}}{5}+a^{2} c x +\frac{\left(a^{2} d +2 a b c \right) x^{3}}{3}"," ",0,"1/7*b^2*d*x^7+1/5*(2*a*b*d+b^2*c)*x^5+1/3*(a^2*d+2*a*b*c)*x^3+a^2*c*x","A"
146,1,51,39,0.002000," ","int((b*x^2+a)^2*(d*x^2+c)/x,x)","\frac{b^{2} d \,x^{6}}{6}+\frac{a b d \,x^{4}}{2}+\frac{b^{2} c \,x^{4}}{4}+\frac{a^{2} d \,x^{2}}{2}+a b c \,x^{2}+a^{2} c \ln \left(x \right)"," ",0,"1/6*b^2*d*x^6+1/2*x^4*a*b*d+1/4*b^2*c*x^4+1/2*x^2*a^2*d+a*b*c*x^2+a^2*c*ln(x)","A"
147,1,49,44,0.005000," ","int((b*x^2+a)^2*(d*x^2+c)/x^2,x)","\frac{b^{2} d \,x^{5}}{5}+\frac{2 a b d \,x^{3}}{3}+\frac{b^{2} c \,x^{3}}{3}+a^{2} d x +2 a b c x -\frac{a^{2} c}{x}"," ",0,"1/5*b^2*d*x^5+2/3*x^3*a*b*d+1/3*x^3*b^2*c+a^2*d*x+2*a*b*c*x-a^2*c/x","A"
148,1,50,45,0.006000," ","int((b*x^2+a)^2*(d*x^2+c)/x^3,x)","\frac{b^{2} d \,x^{4}}{4}+a b d \,x^{2}+\frac{b^{2} c \,x^{2}}{2}+a^{2} d \ln \left(x \right)+2 a b c \ln \left(x \right)-\frac{a^{2} c}{2 x^{2}}"," ",0,"1/4*b^2*d*x^4+x^2*a*b*d+1/2*b^2*c*x^2-1/2*a^2*c/x^2+ln(x)*a^2*d+2*ln(x)*a*b*c","A"
149,1,46,44,0.004000," ","int((b*x^2+a)^2*(d*x^2+c)/x^4,x)","\frac{b^{2} d \,x^{3}}{3}+2 a b d x +b^{2} c x -\frac{a^{2} c}{3 x^{3}}-\frac{\left(a d +2 b c \right) a}{x}"," ",0,"1/3*b^2*d*x^3+2*a*b*d*x+b^2*c*x-a*(a*d+2*b*c)/x-1/3*a^2*c/x^3","A"
150,1,90,77,0.000000," ","int(x^4*(b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{b^{2} d^{2} x^{13}}{13}+\frac{\left(2 a b \,d^{2}+2 b^{2} c d \right) x^{11}}{11}+\frac{a^{2} c^{2} x^{5}}{5}+\frac{\left(a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right) x^{9}}{9}+\frac{\left(2 a^{2} c d +2 a b \,c^{2}\right) x^{7}}{7}"," ",0,"1/13*b^2*d^2*x^13+1/11*(2*a*b*d^2+2*b^2*c*d)*x^11+1/9*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^9+1/7*(2*a^2*c*d+2*a*b*c^2)*x^7+1/5*a^2*c^2*x^5","A"
151,1,90,77,0.001000," ","int(x^3*(b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{b^{2} d^{2} x^{12}}{12}+\frac{\left(2 a b \,d^{2}+2 b^{2} c d \right) x^{10}}{10}+\frac{a^{2} c^{2} x^{4}}{4}+\frac{\left(a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right) x^{8}}{8}+\frac{\left(2 a^{2} c d +2 a b \,c^{2}\right) x^{6}}{6}"," ",0,"1/12*b^2*d^2*x^12+1/10*(2*a*b*d^2+2*b^2*c*d)*x^10+1/8*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^8+1/6*(2*a^2*c*d+2*a*b*c^2)*x^6+1/4*a^2*c^2*x^4","A"
152,1,90,77,0.001000," ","int(x^2*(b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{b^{2} d^{2} x^{11}}{11}+\frac{\left(2 a b \,d^{2}+2 b^{2} c d \right) x^{9}}{9}+\frac{a^{2} c^{2} x^{3}}{3}+\frac{\left(a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right) x^{7}}{7}+\frac{\left(2 a^{2} c d +2 a b \,c^{2}\right) x^{5}}{5}"," ",0,"1/11*b^2*d^2*x^11+1/9*(2*a*b*d^2+2*b^2*c*d)*x^9+1/7*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^7+1/5*(2*a^2*c*d+2*a*b*c^2)*x^5+1/3*a^2*c^2*x^3","A"
153,1,90,65,0.000000," ","int(x*(b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{b^{2} d^{2} x^{10}}{10}+\frac{\left(2 a b \,d^{2}+2 b^{2} c d \right) x^{8}}{8}+\frac{a^{2} c^{2} x^{2}}{2}+\frac{\left(a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right) x^{6}}{6}+\frac{\left(2 a^{2} c d +2 a b \,c^{2}\right) x^{4}}{4}"," ",0,"1/10*b^2*d^2*x^10+1/8*(2*a*b*d^2+2*b^2*c*d)*x^8+1/6*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^6+1/4*(2*a^2*c*d+2*a*b*c^2)*x^4+1/2*a^2*c^2*x^2","A"
154,1,87,74,0.001000," ","int((b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{b^{2} d^{2} x^{9}}{9}+\frac{\left(2 a b \,d^{2}+2 b^{2} c d \right) x^{7}}{7}+a^{2} c^{2} x +\frac{\left(a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right) x^{5}}{5}+\frac{\left(2 a^{2} c d +2 a b \,c^{2}\right) x^{3}}{3}"," ",0,"1/9*b^2*d^2*x^9+1/7*(2*a*b*d^2+2*b^2*c*d)*x^7+1/5*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^5+1/3*(2*a^2*c*d+2*a*b*c^2)*x^3+a^2*c^2*x","A"
155,1,90,74,0.003000," ","int((b*x^2+a)^2*(d*x^2+c)^2/x,x)","\frac{b^{2} d^{2} x^{8}}{8}+\frac{a b \,d^{2} x^{6}}{3}+\frac{b^{2} c d \,x^{6}}{3}+\frac{a^{2} d^{2} x^{4}}{4}+a b c d \,x^{4}+\frac{b^{2} c^{2} x^{4}}{4}+a^{2} c d \,x^{2}+a b \,c^{2} x^{2}+a^{2} c^{2} \ln \left(x \right)"," ",0,"1/8*b^2*d^2*x^8+1/3*x^6*a*b*d^2+1/3*x^6*b^2*c*d+1/4*x^4*a^2*d^2+x^4*a*b*c*d+1/4*x^4*b^2*c^2+x^2*a^2*c*d+x^2*a*b*c^2+a^2*c^2*ln(x)","A"
156,1,91,75,0.005000," ","int((b*x^2+a)^2*(d*x^2+c)^2/x^2,x)","\frac{b^{2} d^{2} x^{7}}{7}+\frac{2 a b \,d^{2} x^{5}}{5}+\frac{2 b^{2} c d \,x^{5}}{5}+\frac{a^{2} d^{2} x^{3}}{3}+\frac{4 a b c d \,x^{3}}{3}+\frac{b^{2} c^{2} x^{3}}{3}+2 a^{2} c d x +2 a b \,c^{2} x -\frac{a^{2} c^{2}}{x}"," ",0,"1/7*b^2*d^2*x^7+2/5*x^5*a*b*d^2+2/5*x^5*b^2*c*d+1/3*x^3*a^2*d^2+4/3*x^3*a*b*c*d+1/3*x^3*b^2*c^2+2*a^2*c*d*x+2*a*b*c^2*x-a^2*c^2/x","A"
157,1,93,76,0.007000," ","int((b*x^2+a)^2*(d*x^2+c)^2/x^3,x)","\frac{b^{2} d^{2} x^{6}}{6}+\frac{a b \,d^{2} x^{4}}{2}+\frac{b^{2} c d \,x^{4}}{2}+\frac{a^{2} d^{2} x^{2}}{2}+2 a b c d \,x^{2}+\frac{b^{2} c^{2} x^{2}}{2}+2 a^{2} c d \ln \left(x \right)+2 a b \,c^{2} \ln \left(x \right)-\frac{a^{2} c^{2}}{2 x^{2}}"," ",0,"1/6*b^2*d^2*x^6+1/2*x^4*a*b*d^2+1/2*x^4*b^2*c*d+1/2*x^2*a^2*d^2+2*x^2*a*b*c*d+1/2*x^2*b^2*c^2-1/2*a^2*c^2/x^2+2*ln(x)*a^2*c*d+2*ln(x)*a*b*c^2","A"
158,1,81,74,0.007000," ","int((b*x^2+a)^2*(d*x^2+c)^2/x^4,x)","\frac{b^{2} d^{2} x^{5}}{5}+\frac{2 a b \,d^{2} x^{3}}{3}+\frac{2 b^{2} c d \,x^{3}}{3}+a^{2} d^{2} x +4 a b c d x +b^{2} c^{2} x -\frac{a^{2} c^{2}}{3 x^{3}}-\frac{2 \left(a d +b c \right) a c}{x}"," ",0,"1/5*b^2*d^2*x^5+2/3*x^3*a*b*d^2+2/3*x^3*b^2*c*d+a^2*d^2*x+4*a*b*c*d*x+b^2*c^2*x-2*a*c*(a*d+b*c)/x-1/3*a^2*c^2/x^3","A"
159,1,128,115,0.001000," ","int(x^4*(b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{b^{2} d^{3} x^{15}}{15}+\frac{\left(2 a b \,d^{3}+3 b^{2} c \,d^{2}\right) x^{13}}{13}+\frac{\left(a^{2} d^{3}+6 a b c \,d^{2}+3 b^{2} c^{2} d \right) x^{11}}{11}+\frac{a^{2} c^{3} x^{5}}{5}+\frac{\left(3 a^{2} c \,d^{2}+6 a b \,c^{2} d +b^{2} c^{3}\right) x^{9}}{9}+\frac{\left(3 a^{2} c^{2} d +2 a b \,c^{3}\right) x^{7}}{7}"," ",0,"1/15*b^2*d^3*x^15+1/13*(2*a*b*d^3+3*b^2*c*d^2)*x^13+1/11*(a^2*d^3+6*a*b*c*d^2+3*b^2*c^2*d)*x^11+1/9*(3*a^2*c*d^2+6*a*b*c^2*d+b^2*c^3)*x^9+1/7*(3*a^2*c^2*d+2*a*b*c^3)*x^7+1/5*a^2*c^3*x^5","A"
160,1,128,98,0.000000," ","int(x^3*(b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{b^{2} d^{3} x^{14}}{14}+\frac{\left(2 a b \,d^{3}+3 b^{2} c \,d^{2}\right) x^{12}}{12}+\frac{\left(a^{2} d^{3}+6 a b c \,d^{2}+3 b^{2} c^{2} d \right) x^{10}}{10}+\frac{a^{2} c^{3} x^{4}}{4}+\frac{\left(3 a^{2} c \,d^{2}+6 a b \,c^{2} d +b^{2} c^{3}\right) x^{8}}{8}+\frac{\left(3 a^{2} c^{2} d +2 a b \,c^{3}\right) x^{6}}{6}"," ",0,"1/14*b^2*d^3*x^14+1/12*(2*a*b*d^3+3*b^2*c*d^2)*x^12+1/10*(a^2*d^3+6*a*b*c*d^2+3*b^2*c^2*d)*x^10+1/8*(3*a^2*c*d^2+6*a*b*c^2*d+b^2*c^3)*x^8+1/6*(3*a^2*c^2*d+2*a*b*c^3)*x^6+1/4*a^2*c^3*x^4","A"
161,1,128,115,0.001000," ","int(x^2*(b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{b^{2} d^{3} x^{13}}{13}+\frac{\left(2 a b \,d^{3}+3 b^{2} c \,d^{2}\right) x^{11}}{11}+\frac{\left(a^{2} d^{3}+6 a b c \,d^{2}+3 b^{2} c^{2} d \right) x^{9}}{9}+\frac{a^{2} c^{3} x^{3}}{3}+\frac{\left(3 a^{2} c \,d^{2}+6 a b \,c^{2} d +b^{2} c^{3}\right) x^{7}}{7}+\frac{\left(3 a^{2} c^{2} d +2 a b \,c^{3}\right) x^{5}}{5}"," ",0,"1/13*b^2*d^3*x^13+1/11*(2*a*b*d^3+3*b^2*c*d^2)*x^11+1/9*(a^2*d^3+6*a*b*c*d^2+3*b^2*c^2*d)*x^9+1/7*(3*a^2*c*d^2+6*a*b*c^2*d+b^2*c^3)*x^7+1/5*(3*a^2*c^2*d+2*a*b*c^3)*x^5+1/3*a^2*c^3*x^3","A"
162,1,128,65,0.001000," ","int(x*(b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{b^{2} d^{3} x^{12}}{12}+\frac{\left(2 a b \,d^{3}+3 b^{2} c \,d^{2}\right) x^{10}}{10}+\frac{\left(a^{2} d^{3}+6 a b c \,d^{2}+3 b^{2} c^{2} d \right) x^{8}}{8}+\frac{a^{2} c^{3} x^{2}}{2}+\frac{\left(3 a^{2} c \,d^{2}+6 a b \,c^{2} d +b^{2} c^{3}\right) x^{6}}{6}+\frac{\left(3 a^{2} c^{2} d +2 a b \,c^{3}\right) x^{4}}{4}"," ",0,"1/12*b^2*d^3*x^12+1/10*(2*a*b*d^3+3*b^2*c*d^2)*x^10+1/8*(a^2*d^3+6*a*b*c*d^2+3*b^2*c^2*d)*x^8+1/6*(3*a^2*c*d^2+6*a*b*c^2*d+b^2*c^3)*x^6+1/4*(3*a^2*c^2*d+2*a*b*c^3)*x^4+1/2*a^2*c^3*x^2","A"
163,1,125,112,0.001000," ","int((b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{b^{2} d^{3} x^{11}}{11}+\frac{\left(2 a b \,d^{3}+3 b^{2} c \,d^{2}\right) x^{9}}{9}+\frac{\left(a^{2} d^{3}+6 a b c \,d^{2}+3 b^{2} c^{2} d \right) x^{7}}{7}+a^{2} c^{3} x +\frac{\left(3 a^{2} c \,d^{2}+6 a b \,c^{2} d +b^{2} c^{3}\right) x^{5}}{5}+\frac{\left(3 a^{2} c^{2} d +2 a b \,c^{3}\right) x^{3}}{3}"," ",0,"1/11*b^2*d^3*x^11+1/9*(2*a*b*d^3+3*b^2*c*d^2)*x^9+1/7*(a^2*d^3+6*a*b*c*d^2+3*b^2*c^2*d)*x^7+1/5*(3*a^2*c*d^2+6*a*b*c^2*d+b^2*c^3)*x^5+1/3*(3*a^2*c^2*d+2*a*b*c^3)*x^3+a^2*c^3*x","A"
164,1,132,113,0.005000," ","int((b*x^2+a)^2*(d*x^2+c)^3/x,x)","\frac{b^{2} d^{3} x^{10}}{10}+\frac{a b \,d^{3} x^{8}}{4}+\frac{3 b^{2} c \,d^{2} x^{8}}{8}+\frac{a^{2} d^{3} x^{6}}{6}+a b c \,d^{2} x^{6}+\frac{b^{2} c^{2} d \,x^{6}}{2}+\frac{3 a^{2} c \,d^{2} x^{4}}{4}+\frac{3 a b \,c^{2} d \,x^{4}}{2}+\frac{b^{2} c^{3} x^{4}}{4}+\frac{3 a^{2} c^{2} d \,x^{2}}{2}+a b \,c^{3} x^{2}+a^{2} c^{3} \ln \left(x \right)"," ",0,"1/10*b^2*d^3*x^10+1/4*x^8*a*b*d^3+3/8*x^8*b^2*c*d^2+1/6*x^6*a^2*d^3+x^6*a*b*c*d^2+1/2*x^6*b^2*c^2*d+3/4*x^4*a^2*c*d^2+3/2*x^4*a*b*c^2*d+1/4*x^4*b^2*c^3+3/2*x^2*a^2*c^2*d+x^2*a*b*c^3+a^2*c^3*ln(x)","A"
165,1,131,112,0.005000," ","int((b*x^2+a)^2*(d*x^2+c)^3/x^2,x)","\frac{b^{2} d^{3} x^{9}}{9}+\frac{2 a b \,d^{3} x^{7}}{7}+\frac{3 b^{2} c \,d^{2} x^{7}}{7}+\frac{a^{2} d^{3} x^{5}}{5}+\frac{6 a b c \,d^{2} x^{5}}{5}+\frac{3 b^{2} c^{2} d \,x^{5}}{5}+a^{2} c \,d^{2} x^{3}+2 a b \,c^{2} d \,x^{3}+\frac{b^{2} c^{3} x^{3}}{3}+3 a^{2} c^{2} d x +2 a b \,c^{3} x -\frac{a^{2} c^{3}}{x}"," ",0,"1/9*b^2*d^3*x^9+2/7*x^7*a*b*d^3+3/7*x^7*b^2*c*d^2+1/5*x^5*a^2*d^3+6/5*x^5*a*b*c*d^2+3/5*x^5*b^2*c^2*d+x^3*a^2*c*d^2+2*x^3*a*b*c^2*d+1/3*x^3*b^2*c^3+3*a^2*c^2*d*x+2*a*b*c^3*x-a^2*c^3/x","A"
166,1,134,113,0.006000," ","int((b*x^2+a)^2*(d*x^2+c)^3/x^3,x)","\frac{b^{2} d^{3} x^{8}}{8}+\frac{a b \,d^{3} x^{6}}{3}+\frac{b^{2} c \,d^{2} x^{6}}{2}+\frac{a^{2} d^{3} x^{4}}{4}+\frac{3 a b c \,d^{2} x^{4}}{2}+\frac{3 b^{2} c^{2} d \,x^{4}}{4}+\frac{3 a^{2} c \,d^{2} x^{2}}{2}+3 a b \,c^{2} d \,x^{2}+\frac{b^{2} c^{3} x^{2}}{2}+3 a^{2} c^{2} d \ln \left(x \right)+2 a b \,c^{3} \ln \left(x \right)-\frac{a^{2} c^{3}}{2 x^{2}}"," ",0,"1/8*b^2*d^3*x^8+1/3*x^6*a*b*d^3+1/2*x^6*b^2*c*d^2+1/4*x^4*a^2*d^3+3/2*x^4*a*b*c*d^2+3/4*x^4*b^2*c^2*d+3/2*x^2*a^2*c*d^2+3*x^2*a*b*c^2*d+1/2*x^2*b^2*c^3-1/2*a^2*c^3/x^2+3*ln(x)*a^2*c^2*d+2*ln(x)*a*b*c^3","A"
167,1,124,112,0.006000," ","int((b*x^2+a)^2*(d*x^2+c)^3/x^4,x)","\frac{b^{2} d^{3} x^{7}}{7}+\frac{2 a b \,d^{3} x^{5}}{5}+\frac{3 b^{2} c \,d^{2} x^{5}}{5}+\frac{a^{2} d^{3} x^{3}}{3}+2 a b c \,d^{2} x^{3}+b^{2} c^{2} d \,x^{3}+3 a^{2} c \,d^{2} x +6 a b \,c^{2} d x +b^{2} c^{3} x -\frac{a^{2} c^{3}}{3 x^{3}}-\frac{\left(3 a d +2 b c \right) a \,c^{2}}{x}"," ",0,"1/7*b^2*d^3*x^7+2/5*x^5*a*b*d^3+3/5*x^5*b^2*c*d^2+1/3*x^3*a^2*d^3+2*x^3*a*b*c*d^2+x^3*b^2*c^2*d+3*a^2*c*d^2*x+6*a*b*c^2*d*x+b^2*c^3*x-a*c^2*(3*a*d+2*b*c)/x-1/3*a^2*c^3/x^3","A"
168,1,176,90,0.007000," ","int(x^4*(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} x^{7}}{7 d}+\frac{2 a b \,x^{5}}{5 d}-\frac{b^{2} c \,x^{5}}{5 d^{2}}+\frac{a^{2} x^{3}}{3 d}-\frac{2 a b c \,x^{3}}{3 d^{2}}+\frac{b^{2} c^{2} x^{3}}{3 d^{3}}+\frac{a^{2} c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{2}}-\frac{2 a b \,c^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{3}}+\frac{b^{2} c^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{4}}-\frac{a^{2} c x}{d^{2}}+\frac{2 a b \,c^{2} x}{d^{3}}-\frac{b^{2} c^{3} x}{d^{4}}"," ",0,"1/7*b^2*x^7/d+2/5/d*x^5*a*b-1/5/d^2*x^5*b^2*c+1/3/d*x^3*a^2-2/3/d^2*x^3*a*b*c+1/3/d^3*x^3*b^2*c^2-1/d^2*a^2*c*x+2/d^3*a*b*c^2*x-1/d^4*b^2*c^3*x+c^2/d^2/(c*d)^(1/2)*arctan(d*x/(c*d)^(1/2))*a^2-2*c^3/d^3/(c*d)^(1/2)*arctan(d*x/(c*d)^(1/2))*a*b+c^4/d^4/(c*d)^(1/2)*arctan(d*x/(c*d)^(1/2))*b^2","A"
169,1,124,71,0.004000," ","int(x^3*(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} x^{6}}{6 d}+\frac{a b \,x^{4}}{2 d}-\frac{b^{2} c \,x^{4}}{4 d^{2}}+\frac{a^{2} x^{2}}{2 d}-\frac{a b c \,x^{2}}{d^{2}}+\frac{b^{2} c^{2} x^{2}}{2 d^{3}}-\frac{a^{2} c \ln \left(d \,x^{2}+c \right)}{2 d^{2}}+\frac{a b \,c^{2} \ln \left(d \,x^{2}+c \right)}{d^{3}}-\frac{b^{2} c^{3} \ln \left(d \,x^{2}+c \right)}{2 d^{4}}"," ",0,"1/6*b^2*x^6/d+1/2/d*x^4*a*b-1/4/d^2*x^4*b^2*c+1/2/d*x^2*a^2-1/d^2*x^2*a*b*c+1/2/d^3*x^2*b^2*c^2-1/2*c/d^2*ln(d*x^2+c)*a^2+c^2/d^3*ln(d*x^2+c)*a*b-1/2*c^3/d^4*ln(d*x^2+c)*b^2","A"
170,1,135,71,0.005000," ","int(x^2*(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} x^{5}}{5 d}+\frac{2 a b \,x^{3}}{3 d}-\frac{b^{2} c \,x^{3}}{3 d^{2}}-\frac{a^{2} c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d}+\frac{2 a b \,c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{2}}-\frac{b^{2} c^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{3}}+\frac{a^{2} x}{d}-\frac{2 a b c x}{d^{2}}+\frac{b^{2} c^{2} x}{d^{3}}"," ",0,"1/5*b^2*x^5/d+2/3/d*x^3*a*b-1/3/d^2*x^3*b^2*c+1/d*a^2*x-2/d^2*a*b*c*x+1/d^3*b^2*c^2*x-c/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+2*c^2/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-c^3/d^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","A"
171,1,85,55,0.003000," ","int(x*(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} x^{4}}{4 d}+\frac{a b \,x^{2}}{d}-\frac{b^{2} c \,x^{2}}{2 d^{2}}+\frac{a^{2} \ln \left(d \,x^{2}+c \right)}{2 d}-\frac{a b c \ln \left(d \,x^{2}+c \right)}{d^{2}}+\frac{b^{2} c^{2} \ln \left(d \,x^{2}+c \right)}{2 d^{3}}"," ",0,"1/4*b^2/d*x^4+b/d*a*x^2-1/2*b^2/d^2*c*x^2+1/2/d*ln(d*x^2+c)*a^2-1/d^2*ln(d*x^2+c)*a*b*c+1/2/d^3*ln(d*x^2+c)*b^2*c^2","A"
172,1,95,53,0.004000," ","int((b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} x^{3}}{3 d}+\frac{a^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}}-\frac{2 a b c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d}+\frac{b^{2} c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{2}}+\frac{2 a b x}{d}-\frac{b^{2} c x}{d^{2}}"," ",0,"1/3*b^2*x^3/d+2*b/d*a*x-b^2/d^2*c*x+1/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-2/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*c+1/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2*c^2","A"
173,1,69,47,0.005000," ","int((b*x^2+a)^2/x/(d*x^2+c),x)","\frac{b^{2} x^{2}}{2 d}+\frac{a^{2} \ln \left(x \right)}{c}-\frac{a^{2} \ln \left(d \,x^{2}+c \right)}{2 c}+\frac{a b \ln \left(d \,x^{2}+c \right)}{d}-\frac{b^{2} c \ln \left(d \,x^{2}+c \right)}{2 d^{2}}"," ",0,"1/2*b^2*x^2/d-1/2/c*ln(d*x^2+c)*a^2+1/d*ln(d*x^2+c)*a*b-1/2*c/d^2*ln(d*x^2+c)*b^2+a^2*ln(x)/c","A"
174,1,85,47,0.007000," ","int((b*x^2+a)^2/x^2/(d*x^2+c),x)","-\frac{a^{2} d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, c}+\frac{2 a b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}}-\frac{b^{2} c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d}+\frac{b^{2} x}{d}-\frac{a^{2}}{c x}"," ",0,"b^2*x/d-1/c*d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-c/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-a^2/c/x","A"
175,1,81,54,0.007000," ","int((b*x^2+a)^2/x^3/(d*x^2+c),x)","-\frac{a^{2} d \ln \left(x \right)}{c^{2}}+\frac{a^{2} d \ln \left(d \,x^{2}+c \right)}{2 c^{2}}+\frac{2 a b \ln \left(x \right)}{c}-\frac{a b \ln \left(d \,x^{2}+c \right)}{c}+\frac{b^{2} \ln \left(d \,x^{2}+c \right)}{2 d}-\frac{a^{2}}{2 c \,x^{2}}"," ",0,"1/2/c^2*d*ln(d*x^2+c)*a^2-1/c*ln(d*x^2+c)*a*b+1/2/d*ln(d*x^2+c)*b^2-1/2*a^2/c/x^2-a^2/c^2*ln(x)*d+2*a/c*ln(x)*b","A"
176,1,98,56,0.008000," ","int((b*x^2+a)^2/x^4/(d*x^2+c),x)","\frac{a^{2} d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, c^{2}}-\frac{2 a b d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, c}+\frac{b^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}}+\frac{a^{2} d}{c^{2} x}-\frac{2 a b}{c x}-\frac{a^{2}}{3 c \,x^{3}}"," ",0,"1/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2*d^2-2/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*d+1/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-1/3*a^2/c/x^3+a^2/c^2/x*d-2*a/c/x*b","A"
177,1,116,69,0.008000," ","int((b*x^2+a)^2/x^5/(d*x^2+c),x)","\frac{a^{2} d^{2} \ln \left(x \right)}{c^{3}}-\frac{a^{2} d^{2} \ln \left(d \,x^{2}+c \right)}{2 c^{3}}-\frac{2 a b d \ln \left(x \right)}{c^{2}}+\frac{a b d \ln \left(d \,x^{2}+c \right)}{c^{2}}+\frac{b^{2} \ln \left(x \right)}{c}-\frac{b^{2} \ln \left(d \,x^{2}+c \right)}{2 c}+\frac{a^{2} d}{2 c^{2} x^{2}}-\frac{a b}{c \,x^{2}}-\frac{a^{2}}{4 c \,x^{4}}"," ",0,"-1/2/c^3*ln(d*x^2+c)*a^2*d^2+1/c^2*ln(d*x^2+c)*a*b*d-1/2/c*ln(d*x^2+c)*b^2-1/4*a^2/c/x^4+1/c^3*ln(x)*a^2*d^2-2/c^2*ln(x)*a*b*d+1/c*ln(x)*b^2+1/2*a^2/c^2/x^2*d-a/c/x^2*b","A"
178,1,143,75,0.006000," ","int((b*x^2+a)^2/x^6/(d*x^2+c),x)","-\frac{a^{2} d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, c^{3}}+\frac{2 a b \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, c^{2}}-\frac{b^{2} d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, c}-\frac{a^{2} d^{2}}{c^{3} x}+\frac{2 a b d}{c^{2} x}-\frac{b^{2}}{c x}+\frac{a^{2} d}{3 c^{2} x^{3}}-\frac{2 a b}{3 c \,x^{3}}-\frac{a^{2}}{5 c \,x^{5}}"," ",0,"-d^3/c^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+2*d^2/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-d/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-1/5*a^2/c/x^5-1/c^3/x*a^2*d^2+2/c^2/x*a*b*d-1/c/x*b^2+1/3*a^2/c^2/x^3*d-2/3*a/c/x^3*b","A"
179,1,160,90,0.009000," ","int((b*x^2+a)^2/x^7/(d*x^2+c),x)","-\frac{a^{2} d^{3} \ln \left(x \right)}{c^{4}}+\frac{a^{2} d^{3} \ln \left(d \,x^{2}+c \right)}{2 c^{4}}+\frac{2 a b \,d^{2} \ln \left(x \right)}{c^{3}}-\frac{a b \,d^{2} \ln \left(d \,x^{2}+c \right)}{c^{3}}-\frac{b^{2} d \ln \left(x \right)}{c^{2}}+\frac{b^{2} d \ln \left(d \,x^{2}+c \right)}{2 c^{2}}-\frac{a^{2} d^{2}}{2 c^{3} x^{2}}+\frac{a b d}{c^{2} x^{2}}-\frac{b^{2}}{2 c \,x^{2}}+\frac{a^{2} d}{4 c^{2} x^{4}}-\frac{a b}{2 c \,x^{4}}-\frac{a^{2}}{6 c \,x^{6}}"," ",0,"1/2*d^3/c^4*ln(d*x^2+c)*a^2-d^2/c^3*ln(d*x^2+c)*a*b+1/2*d/c^2*ln(d*x^2+c)*b^2-1/6*a^2/c/x^6-1/2/c^3/x^2*a^2*d^2+1/c^2/x^2*a*b*d-1/2/c/x^2*b^2+1/4*a^2/c^2/x^4*d-1/2*a/c/x^4*b-1/c^4*d^3*ln(x)*a^2+2/c^3*d^2*ln(x)*a*b-1/c^2*d*ln(x)*b^2","A"
180,1,196,127,0.013000," ","int(x^4*(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{b^{2} x^{5}}{5 d^{2}}+\frac{2 a b \,x^{3}}{3 d^{2}}-\frac{2 b^{2} c \,x^{3}}{3 d^{3}}+\frac{a^{2} c x}{2 \left(d \,x^{2}+c \right) d^{2}}-\frac{3 a^{2} c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d^{2}}-\frac{a b \,c^{2} x}{\left(d \,x^{2}+c \right) d^{3}}+\frac{5 a b \,c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{3}}+\frac{b^{2} c^{3} x}{2 \left(d \,x^{2}+c \right) d^{4}}-\frac{7 b^{2} c^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d^{4}}+\frac{a^{2} x}{d^{2}}-\frac{4 a b c x}{d^{3}}+\frac{3 b^{2} c^{2} x}{d^{4}}"," ",0,"1/5*b^2*x^5/d^2+2/3/d^2*x^3*a*b-2/3/d^3*x^3*b^2*c+1/d^2*a^2*x-4/d^3*a*b*c*x+3/d^4*b^2*c^2*x+1/2*c/d^2*x/(d*x^2+c)*a^2-c^2/d^3*x/(d*x^2+c)*a*b+1/2*c^3/d^4*x/(d*x^2+c)*b^2-3/2*c/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+5*c^2/d^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-7/2*c^3/d^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","A"
181,1,142,84,0.011000," ","int(x^3*(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{b^{2} x^{4}}{4 d^{2}}+\frac{a b \,x^{2}}{d^{2}}-\frac{b^{2} c \,x^{2}}{d^{3}}+\frac{a^{2} c}{2 \left(d \,x^{2}+c \right) d^{2}}+\frac{a^{2} \ln \left(d \,x^{2}+c \right)}{2 d^{2}}-\frac{a b \,c^{2}}{\left(d \,x^{2}+c \right) d^{3}}-\frac{2 a b c \ln \left(d \,x^{2}+c \right)}{d^{3}}+\frac{b^{2} c^{3}}{2 \left(d \,x^{2}+c \right) d^{4}}+\frac{3 b^{2} c^{2} \ln \left(d \,x^{2}+c \right)}{2 d^{4}}"," ",0,"1/4*b^2*x^4/d^2+b/d^2*a*x^2-b^2/d^3*c*x^2+1/2/d^2*ln(d*x^2+c)*a^2-2/d^3*ln(d*x^2+c)*a*b*c+3/2/d^4*ln(d*x^2+c)*b^2*c^2+1/2/d^2*c/(d*x^2+c)*a^2-1/d^3*c^2/(d*x^2+c)*a*b+1/2/d^4*c^3/(d*x^2+c)*b^2","A"
182,1,156,102,0.010000," ","int(x^2*(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{b^{2} x^{3}}{3 d^{2}}-\frac{a^{2} x}{2 \left(d \,x^{2}+c \right) d}+\frac{a^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d}+\frac{a b c x}{\left(d \,x^{2}+c \right) d^{2}}-\frac{3 a b c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{2}}-\frac{b^{2} c^{2} x}{2 \left(d \,x^{2}+c \right) d^{3}}+\frac{5 b^{2} c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d^{3}}+\frac{2 a b x}{d^{2}}-\frac{2 b^{2} c x}{d^{3}}"," ",0,"1/3*b^2*x^3/d^2+2*b/d^2*a*x-2*b^2/d^3*c*x-1/2/d*x/(d*x^2+c)*a^2+1/d^2*x/(d*x^2+c)*a*b*c-1/2/d^3*x/(d*x^2+c)*b^2*c^2+1/2/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-3/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*c+5/2/d^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2*c^2","A"
183,1,97,58,0.010000," ","int(x*(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{b^{2} x^{2}}{2 d^{2}}-\frac{a^{2}}{2 \left(d \,x^{2}+c \right) d}+\frac{a b c}{\left(d \,x^{2}+c \right) d^{2}}+\frac{a b \ln \left(d \,x^{2}+c \right)}{d^{2}}-\frac{b^{2} c^{2}}{2 \left(d \,x^{2}+c \right) d^{3}}-\frac{b^{2} c \ln \left(d \,x^{2}+c \right)}{d^{3}}"," ",0,"1/2*b^2*x^2/d^2+1/d^2*b*ln(d*x^2+c)*a-1/d^3*b^2*ln(d*x^2+c)*c-1/2/d/(d*x^2+c)*a^2+1/d^2/(d*x^2+c)*a*b*c-1/2/d^3/(d*x^2+c)*b^2*c^2","A"
184,1,129,70,0.010000," ","int((b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a^{2} x}{2 \left(d \,x^{2}+c \right) c}+\frac{a^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, c}-\frac{a b x}{\left(d \,x^{2}+c \right) d}+\frac{a b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d}+\frac{b^{2} c x}{2 \left(d \,x^{2}+c \right) d^{2}}-\frac{3 b^{2} c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d^{2}}+\frac{b^{2} x}{d^{2}}"," ",0,"b^2*x/d^2+1/2/c*x/(d*x^2+c)*a^2-1/d*x/(d*x^2+c)*a*b+1/2/d^2*c*x/(d*x^2+c)*b^2+1/2/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+1/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-3/2/d^2*c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","A"
185,1,94,63,0.014000," ","int((b*x^2+a)^2/x/(d*x^2+c)^2,x)","\frac{a^{2}}{2 \left(d \,x^{2}+c \right) c}+\frac{a^{2} \ln \left(x \right)}{c^{2}}-\frac{a^{2} \ln \left(d \,x^{2}+c \right)}{2 c^{2}}-\frac{a b}{\left(d \,x^{2}+c \right) d}+\frac{b^{2} c}{2 \left(d \,x^{2}+c \right) d^{2}}+\frac{b^{2} \ln \left(d \,x^{2}+c \right)}{2 d^{2}}"," ",0,"-1/2/c^2*ln(d*x^2+c)*a^2+1/2/d^2*ln(d*x^2+c)*b^2+1/2/c/(d*x^2+c)*a^2-1/d/(d*x^2+c)*a*b+1/2*c/d^2/(d*x^2+c)*b^2+a^2*ln(x)/c^2","A"
186,1,131,94,0.028000," ","int((b*x^2+a)^2/x^2/(d*x^2+c)^2,x)","-\frac{a^{2} d x}{2 \left(d \,x^{2}+c \right) c^{2}}-\frac{3 a^{2} d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, c^{2}}+\frac{a b x}{\left(d \,x^{2}+c \right) c}+\frac{a b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, c}-\frac{b^{2} x}{2 \left(d \,x^{2}+c \right) d}+\frac{b^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d}-\frac{a^{2}}{c^{2} x}"," ",0,"-1/2/c^2*d*x/(d*x^2+c)*a^2+1/c*x/(d*x^2+c)*a*b-1/2/d*x/(d*x^2+c)*b^2-3/2/c^2*d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+1/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+1/2/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-a^2/c^2/x","A"
187,1,114,77,0.017000," ","int((b*x^2+a)^2/x^3/(d*x^2+c)^2,x)","-\frac{a^{2} d}{2 \left(d \,x^{2}+c \right) c^{2}}-\frac{2 a^{2} d \ln \left(x \right)}{c^{3}}+\frac{a^{2} d \ln \left(d \,x^{2}+c \right)}{c^{3}}+\frac{a b}{\left(d \,x^{2}+c \right) c}+\frac{2 a b \ln \left(x \right)}{c^{2}}-\frac{a b \ln \left(d \,x^{2}+c \right)}{c^{2}}-\frac{b^{2}}{2 \left(d \,x^{2}+c \right) d}-\frac{a^{2}}{2 c^{2} x^{2}}"," ",0,"1/c^3*a^2*ln(d*x^2+c)*d-1/c^2*a*ln(d*x^2+c)*b-1/2/c^2/(d*x^2+c)*a^2*d+1/c/(d*x^2+c)*a*b-1/2/d/(d*x^2+c)*b^2-1/2*a^2/c^2/x^2-2*a^2/c^3*ln(x)*d+2*a/c^2*ln(x)*b","A"
188,1,161,110,0.016000," ","int((b*x^2+a)^2/x^4/(d*x^2+c)^2,x)","\frac{a^{2} d^{2} x}{2 \left(d \,x^{2}+c \right) c^{3}}+\frac{5 a^{2} d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, c^{3}}-\frac{a b d x}{\left(d \,x^{2}+c \right) c^{2}}-\frac{3 a b d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, c^{2}}+\frac{b^{2} x}{2 \left(d \,x^{2}+c \right) c}+\frac{b^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, c}+\frac{2 a^{2} d}{c^{3} x}-\frac{2 a b}{c^{2} x}-\frac{a^{2}}{3 c^{2} x^{3}}"," ",0,"1/2/c^3*x/(d*x^2+c)*a^2*d^2-1/c^2*x/(d*x^2+c)*a*b*d+1/2/c*x/(d*x^2+c)*b^2+5/2/c^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2*d^2-3/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*d+1/2/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-1/3*a^2/c^2/x^3+2*a^2/c^3/x*d-2*a/c^2/x*b","A"
189,1,223,145,0.015000," ","int(x^4*(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{5 a^{2} x^{3}}{8 \left(d \,x^{2}+c \right)^{2} d}+\frac{9 a b c \,x^{3}}{4 \left(d \,x^{2}+c \right)^{2} d^{2}}-\frac{13 b^{2} c^{2} x^{3}}{8 \left(d \,x^{2}+c \right)^{2} d^{3}}-\frac{3 a^{2} c x}{8 \left(d \,x^{2}+c \right)^{2} d^{2}}+\frac{7 a b \,c^{2} x}{4 \left(d \,x^{2}+c \right)^{2} d^{3}}-\frac{11 b^{2} c^{3} x}{8 \left(d \,x^{2}+c \right)^{2} d^{4}}+\frac{b^{2} x^{3}}{3 d^{3}}+\frac{3 a^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, d^{2}}-\frac{15 a b c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \sqrt{c d}\, d^{3}}+\frac{35 b^{2} c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, d^{4}}+\frac{2 a b x}{d^{3}}-\frac{3 b^{2} c x}{d^{4}}"," ",0,"1/3*b^2*x^3/d^3+2*b/d^3*a*x-3*b^2/d^4*c*x-5/8/d/(d*x^2+c)^2*x^3*a^2+9/4/d^2/(d*x^2+c)^2*x^3*a*b*c-13/8/d^3/(d*x^2+c)^2*x^3*b^2*c^2-3/8/d^2/(d*x^2+c)^2*a^2*c*x+7/4/d^3/(d*x^2+c)^2*a*b*c^2*x-11/8/d^4/(d*x^2+c)^2*b^2*c^3*x+3/8/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-15/4/d^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*c+35/8/d^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2*c^2","A"
190,1,155,91,0.015000," ","int(x^3*(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{a^{2} c}{4 \left(d \,x^{2}+c \right)^{2} d^{2}}-\frac{a b \,c^{2}}{2 \left(d \,x^{2}+c \right)^{2} d^{3}}+\frac{b^{2} c^{3}}{4 \left(d \,x^{2}+c \right)^{2} d^{4}}+\frac{b^{2} x^{2}}{2 d^{3}}-\frac{a^{2}}{2 \left(d \,x^{2}+c \right) d^{2}}+\frac{2 a b c}{\left(d \,x^{2}+c \right) d^{3}}+\frac{a b \ln \left(d \,x^{2}+c \right)}{d^{3}}-\frac{3 b^{2} c^{2}}{2 \left(d \,x^{2}+c \right) d^{4}}-\frac{3 b^{2} c \ln \left(d \,x^{2}+c \right)}{2 d^{4}}"," ",0,"1/2*b^2*x^2/d^3+1/4/d^2*c/(d*x^2+c)^2*a^2-1/2/d^3*c^2/(d*x^2+c)^2*a*b+1/4/d^4*c^3/(d*x^2+c)^2*b^2+1/d^3*b*ln(d*x^2+c)*a-3/2/d^4*b^2*ln(d*x^2+c)*c-1/2/d^2/(d*x^2+c)*a^2+2/d^3/(d*x^2+c)*a*b*c-3/2/d^4/(d*x^2+c)*b^2*c^2","A"
191,1,196,113,0.013000," ","int(x^2*(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{a^{2} x^{3}}{8 \left(d \,x^{2}+c \right)^{2} c}-\frac{5 a b \,x^{3}}{4 \left(d \,x^{2}+c \right)^{2} d}+\frac{9 b^{2} c \,x^{3}}{8 \left(d \,x^{2}+c \right)^{2} d^{2}}-\frac{a^{2} x}{8 \left(d \,x^{2}+c \right)^{2} d}-\frac{3 a b c x}{4 \left(d \,x^{2}+c \right)^{2} d^{2}}+\frac{7 b^{2} c^{2} x}{8 \left(d \,x^{2}+c \right)^{2} d^{3}}+\frac{a^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c d}+\frac{3 a b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \sqrt{c d}\, d^{2}}-\frac{15 b^{2} c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, d^{3}}+\frac{b^{2} x}{d^{3}}"," ",0,"b^2*x/d^3+1/8/(d*x^2+c)^2/c*x^3*a^2-5/4/d/(d*x^2+c)^2*x^3*a*b+9/8/d^2/(d*x^2+c)^2*x^3*b^2*c-1/8/d/(d*x^2+c)^2*a^2*x-3/4/d^2/(d*x^2+c)^2*a*b*c*x+7/8/d^3/(d*x^2+c)^2*b^2*c^2*x+1/8/d/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+3/4/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-15/8/d^3*c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","A"
192,1,105,63,0.011000," ","int(x*(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{a^{2}}{4 \left(d \,x^{2}+c \right)^{2} d}+\frac{a b c}{2 \left(d \,x^{2}+c \right)^{2} d^{2}}-\frac{b^{2} c^{2}}{4 \left(d \,x^{2}+c \right)^{2} d^{3}}-\frac{a b}{\left(d \,x^{2}+c \right) d^{2}}+\frac{b^{2} c}{\left(d \,x^{2}+c \right) d^{3}}+\frac{b^{2} \ln \left(d \,x^{2}+c \right)}{2 d^{3}}"," ",0,"-1/4/d/(d*x^2+c)^2*a^2+1/2/d^2/(d*x^2+c)^2*a*b*c-1/4/d^3/(d*x^2+c)^2*b^2*c^2+1/2*b^2*ln(d*x^2+c)/d^3-b/d^2/(d*x^2+c)*a+b^2/d^3/(d*x^2+c)*c","A"
193,1,147,102,0.011000," ","int((b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{3 a^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c^{2}}+\frac{a b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \sqrt{c d}\, c d}+\frac{3 b^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, d^{2}}+\frac{\frac{\left(3 a^{2} d^{2}+2 a b c d -5 b^{2} c^{2}\right) x^{3}}{8 c^{2} d}+\frac{\left(5 a^{2} d^{2}-2 a b c d -3 b^{2} c^{2}\right) x}{8 c \,d^{2}}}{\left(d \,x^{2}+c \right)^{2}}"," ",0,"(1/8*(3*a^2*d^2+2*a*b*c*d-5*b^2*c^2)/c^2/d*x^3+1/8*(5*a^2*d^2-2*a*b*c*d-3*b^2*c^2)/d^2/c*x)/(d*x^2+c)^2+3/8/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+1/4/c/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+3/8/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","A"
194,1,112,80,0.015000," ","int((b*x^2+a)^2/x/(d*x^2+c)^3,x)","\frac{a^{2}}{4 \left(d \,x^{2}+c \right)^{2} c}-\frac{a b}{2 \left(d \,x^{2}+c \right)^{2} d}+\frac{b^{2} c}{4 \left(d \,x^{2}+c \right)^{2} d^{2}}+\frac{a^{2}}{2 \left(d \,x^{2}+c \right) c^{2}}+\frac{a^{2} \ln \left(x \right)}{c^{3}}-\frac{a^{2} \ln \left(d \,x^{2}+c \right)}{2 c^{3}}-\frac{b^{2}}{2 \left(d \,x^{2}+c \right) d^{2}}"," ",0,"1/4/c/(d*x^2+c)^2*a^2-1/2/d/(d*x^2+c)^2*a*b+1/4*c/d^2/(d*x^2+c)^2*b^2-1/2*a^2*ln(d*x^2+c)/c^3+1/2/c^2/(d*x^2+c)*a^2-1/2/d^2/(d*x^2+c)*b^2+a^2*ln(x)/c^3","A"
195,1,199,138,0.015000," ","int((b*x^2+a)^2/x^2/(d*x^2+c)^3,x)","-\frac{7 a^{2} d^{2} x^{3}}{8 \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{3 a b d \,x^{3}}{4 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{b^{2} x^{3}}{8 \left(d \,x^{2}+c \right)^{2} c}-\frac{9 a^{2} d x}{8 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{5 a b x}{4 \left(d \,x^{2}+c \right)^{2} c}-\frac{b^{2} x}{8 \left(d \,x^{2}+c \right)^{2} d}-\frac{15 a^{2} d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c^{3}}+\frac{3 a b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \sqrt{c d}\, c^{2}}+\frac{b^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c d}-\frac{a^{2}}{c^{3} x}"," ",0,"-7/8/c^3/(d*x^2+c)^2*x^3*a^2*d^2+3/4/c^2/(d*x^2+c)^2*x^3*a*b*d+1/8/c/(d*x^2+c)^2*x^3*b^2-9/8/c^2/(d*x^2+c)^2*a^2*d*x+5/4/c/(d*x^2+c)^2*a*b*x-1/8/(d*x^2+c)^2/d*x*b^2-15/8/c^3*d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+3/4/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+1/8/c/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-a^2/c^3/x","A"
196,1,149,100,0.019000," ","int((b*x^2+a)^2/x^3/(d*x^2+c)^3,x)","-\frac{a^{2} d}{4 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{a b}{2 \left(d \,x^{2}+c \right)^{2} c}-\frac{b^{2}}{4 \left(d \,x^{2}+c \right)^{2} d}-\frac{a^{2} d}{\left(d \,x^{2}+c \right) c^{3}}-\frac{3 a^{2} d \ln \left(x \right)}{c^{4}}+\frac{3 a^{2} d \ln \left(d \,x^{2}+c \right)}{2 c^{4}}+\frac{a b}{\left(d \,x^{2}+c \right) c^{2}}+\frac{2 a b \ln \left(x \right)}{c^{3}}-\frac{a b \ln \left(d \,x^{2}+c \right)}{c^{3}}-\frac{a^{2}}{2 c^{3} x^{2}}"," ",0,"-1/4/c^2*d/(d*x^2+c)^2*a^2+1/2/c/(d*x^2+c)^2*a*b-1/4/d/(d*x^2+c)^2*b^2+3/2/c^4*ln(d*x^2+c)*a^2*d-1/c^3*ln(d*x^2+c)*a*b-1/c^3/(d*x^2+c)*a^2*d+1/c^2/(d*x^2+c)*a*b-1/2*a^2/c^3/x^2-3*a^2/c^4*ln(x)*d+2*a/c^3*ln(x)*b","A"
197,1,227,143,0.014000," ","int((b*x^2+a)^2/x^4/(d*x^2+c)^3,x)","\frac{11 a^{2} d^{3} x^{3}}{8 \left(d \,x^{2}+c \right)^{2} c^{4}}-\frac{7 a b \,d^{2} x^{3}}{4 \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{3 b^{2} d \,x^{3}}{8 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{13 a^{2} d^{2} x}{8 \left(d \,x^{2}+c \right)^{2} c^{3}}-\frac{9 a b d x}{4 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{5 b^{2} x}{8 \left(d \,x^{2}+c \right)^{2} c}+\frac{35 a^{2} d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c^{4}}-\frac{15 a b d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \sqrt{c d}\, c^{3}}+\frac{3 b^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c^{2}}+\frac{3 a^{2} d}{c^{4} x}-\frac{2 a b}{c^{3} x}-\frac{a^{2}}{3 c^{3} x^{3}}"," ",0,"11/8/c^4/(d*x^2+c)^2*x^3*a^2*d^3-7/4/c^3/(d*x^2+c)^2*x^3*a*b*d^2+3/8/c^2/(d*x^2+c)^2*x^3*b^2*d+13/8/c^3/(d*x^2+c)^2*a^2*d^2*x-9/4/c^2/(d*x^2+c)^2*a*b*d*x+5/8/c/(d*x^2+c)^2*b^2*x+35/8/c^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2*d^2-15/4/c^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*d+3/8/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-1/3*a^2/c^3/x^3+3*a^2/c^4/x*d-2*a/c^3/x*b","A"
198,1,86,67,0.003000," ","int(x^5*(d*x^2+c)/(b*x^2+a),x)","\frac{d \,x^{6}}{6 b}-\frac{a d \,x^{4}}{4 b^{2}}+\frac{c \,x^{4}}{4 b}+\frac{a^{2} d \,x^{2}}{2 b^{3}}-\frac{a c \,x^{2}}{2 b^{2}}-\frac{a^{3} d \ln \left(b \,x^{2}+a \right)}{2 b^{4}}+\frac{a^{2} c \ln \left(b \,x^{2}+a \right)}{2 b^{3}}"," ",0,"1/6*d*x^6/b-1/4/b^2*x^4*a*d+1/4/b*x^4*c+1/2/b^3*x^2*a^2*d-1/2/b^2*x^2*a*c-1/2*a^3/b^4*ln(b*x^2+a)*d+1/2*a^2/b^3*ln(b*x^2+a)*c","A"
199,1,92,65,0.004000," ","int(x^4*(d*x^2+c)/(b*x^2+a),x)","\frac{d \,x^{5}}{5 b}-\frac{a d \,x^{3}}{3 b^{2}}+\frac{c \,x^{3}}{3 b}-\frac{a^{3} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{a^{2} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}+\frac{a^{2} d x}{b^{3}}-\frac{a c x}{b^{2}}"," ",0,"1/5*d*x^5/b-1/3/b^2*x^3*a*d+1/3/b*x^3*c+1/b^3*a^2*d*x-1/b^2*a*c*x-a^3/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+a^2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c","A"
200,1,62,48,0.003000," ","int(x^3*(d*x^2+c)/(b*x^2+a),x)","\frac{d \,x^{4}}{4 b}-\frac{a d \,x^{2}}{2 b^{2}}+\frac{c \,x^{2}}{2 b}+\frac{a^{2} d \ln \left(b \,x^{2}+a \right)}{2 b^{3}}-\frac{a c \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/4*d*x^4/b-1/2/b^2*a*d*x^2+1/2/b*c*x^2+1/2*a^2/b^3*ln(b*x^2+a)*d-1/2*a/b^2*c*ln(b*x^2+a)","A"
201,1,68,48,0.010000," ","int(x^2*(d*x^2+c)/(b*x^2+a),x)","\frac{d \,x^{3}}{3 b}+\frac{a^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{a c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}-\frac{a d x}{b^{2}}+\frac{c x}{b}"," ",0,"1/3*d*x^3/b-1/b^2*a*d*x+1/b*c*x+a^2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-1/(a*b)^(1/2)*a/b*c*arctan(1/(a*b)^(1/2)*b*x)","A"
202,1,40,31,0.004000," ","int(x*(d*x^2+c)/(b*x^2+a),x)","\frac{d \,x^{2}}{2 b}-\frac{a d \ln \left(b \,x^{2}+a \right)}{2 b^{2}}+\frac{c \ln \left(b \,x^{2}+a \right)}{2 b}"," ",0,"1/2*d*x^2/b-1/2/b^2*ln(b*x^2+a)*a*d+1/2/b*c*ln(b*x^2+a)","A"
203,1,45,31,0.003000," ","int((d*x^2+c)/(b*x^2+a),x)","-\frac{a d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}+\frac{d x}{b}"," ",0,"d*x/b-1/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*d+1/(a*b)^(1/2)*c*arctan(1/(a*b)^(1/2)*b*x)","A"
204,1,37,32,0.004000," ","int((d*x^2+c)/x/(b*x^2+a),x)","\frac{c \ln \left(x \right)}{a}-\frac{c \ln \left(b \,x^{2}+a \right)}{2 a}+\frac{d \ln \left(b \,x^{2}+a \right)}{2 b}"," ",0,"1/2/b*ln(b*x^2+a)*d-1/2/a*c*ln(b*x^2+a)+1/a*c*ln(x)","A"
205,1,48,35,0.006000," ","int((d*x^2+c)/x^2/(b*x^2+a),x)","-\frac{b c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}+\frac{d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}-\frac{c}{a x}"," ",0,"1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-1/(a*b)^(1/2)/a*b*c*arctan(1/(a*b)^(1/2)*b*x)-1/a*c/x","A"
206,1,56,46,0.007000," ","int((d*x^2+c)/x^3/(b*x^2+a),x)","\frac{d \ln \left(x \right)}{a}-\frac{d \ln \left(b \,x^{2}+a \right)}{2 a}-\frac{b c \ln \left(x \right)}{a^{2}}+\frac{b c \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{c}{2 a \,x^{2}}"," ",0,"-1/2/a*ln(b*x^2+a)*d+1/2/a^2*b*c*ln(b*x^2+a)-1/2/a*c/x^2+1/a*ln(x)*d-1/a^2*b*c*ln(x)","A"
207,1,72,49,0.009000," ","int((d*x^2+c)/x^4/(b*x^2+a),x)","-\frac{b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}+\frac{b^{2} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{2}}-\frac{d}{a x}+\frac{b c}{a^{2} x}-\frac{c}{3 a \,x^{3}}"," ",0,"-b/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+b^2/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c-1/3*c/a/x^3-1/a/x*d+1/a^2/x*b*c","A"
208,1,165,93,0.005000," ","int(x^5*(d*x^2+c)^2/(b*x^2+a),x)","\frac{d^{2} x^{8}}{8 b}-\frac{a \,d^{2} x^{6}}{6 b^{2}}+\frac{c d \,x^{6}}{3 b}+\frac{a^{2} d^{2} x^{4}}{4 b^{3}}-\frac{a c d \,x^{4}}{2 b^{2}}+\frac{c^{2} x^{4}}{4 b}-\frac{a^{3} d^{2} x^{2}}{2 b^{4}}+\frac{a^{2} c d \,x^{2}}{b^{3}}-\frac{a \,c^{2} x^{2}}{2 b^{2}}+\frac{a^{4} d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{5}}-\frac{a^{3} c d \ln \left(b \,x^{2}+a \right)}{b^{4}}+\frac{a^{2} c^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{3}}"," ",0,"1/8*d^2*x^8/b-1/6/b^2*x^6*a*d^2+1/3/b*x^6*c*d+1/4/b^3*x^4*a^2*d^2-1/2/b^2*x^4*a*c*d+1/4/b*x^4*c^2-1/2/b^4*x^2*a^3*d^2+1/b^3*x^2*a^2*c*d-1/2/b^2*x^2*a*c^2+1/2*a^4/b^5*ln(b*x^2+a)*d^2-a^3/b^4*ln(b*x^2+a)*c*d+1/2*a^2/b^3*ln(b*x^2+a)*c^2","A"
209,1,176,91,0.005000," ","int(x^4*(d*x^2+c)^2/(b*x^2+a),x)","\frac{d^{2} x^{7}}{7 b}-\frac{a \,d^{2} x^{5}}{5 b^{2}}+\frac{2 c d \,x^{5}}{5 b}+\frac{a^{2} d^{2} x^{3}}{3 b^{3}}-\frac{2 a c d \,x^{3}}{3 b^{2}}+\frac{c^{2} x^{3}}{3 b}+\frac{a^{4} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{4}}-\frac{2 a^{3} c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{a^{2} c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{a^{3} d^{2} x}{b^{4}}+\frac{2 a^{2} c d x}{b^{3}}-\frac{a \,c^{2} x}{b^{2}}"," ",0,"1/7*d^2*x^7/b-1/5/b^2*x^5*a*d^2+2/5/b*x^5*c*d+1/3/b^3*x^3*a^2*d^2-2/3/b^2*x^3*a*c*d+1/3/b*x^3*c^2-1/b^4*a^3*d^2*x+2/b^3*a^2*c*d*x-1/b^2*a*c^2*x+a^4/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2-2*a^3/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d+a^2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
210,1,124,72,0.003000," ","int(x^3*(d*x^2+c)^2/(b*x^2+a),x)","\frac{d^{2} x^{6}}{6 b}-\frac{a \,d^{2} x^{4}}{4 b^{2}}+\frac{c d \,x^{4}}{2 b}+\frac{a^{2} d^{2} x^{2}}{2 b^{3}}-\frac{a c d \,x^{2}}{b^{2}}+\frac{c^{2} x^{2}}{2 b}-\frac{a^{3} d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}+\frac{a^{2} c d \ln \left(b \,x^{2}+a \right)}{b^{3}}-\frac{a \,c^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/6*d^2*x^6/b-1/4/b^2*x^4*a*d^2+1/2/b*x^4*c*d+1/2/b^3*x^2*a^2*d^2-1/b^2*x^2*a*c*d+1/2/b*x^2*c^2-1/2*a^3/b^4*ln(b*x^2+a)*d^2+a^2/b^3*ln(b*x^2+a)*c*d-1/2*a/b^2*ln(b*x^2+a)*c^2","A"
211,1,135,72,0.004000," ","int(x^2*(d*x^2+c)^2/(b*x^2+a),x)","\frac{d^{2} x^{5}}{5 b}-\frac{a \,d^{2} x^{3}}{3 b^{2}}+\frac{2 c d \,x^{3}}{3 b}-\frac{a^{3} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{2 a^{2} c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{a \,c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{a^{2} d^{2} x}{b^{3}}-\frac{2 a c d x}{b^{2}}+\frac{c^{2} x}{b}"," ",0,"1/5*d^2*x^5/b-1/3/b^2*x^3*a*d^2+2/3/b*x^3*c*d+1/b^3*a^2*d^2*x-2/b^2*a*c*d*x+1/b*c^2*x-a^3/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2+2*a^2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d-a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
212,1,85,55,0.004000," ","int(x*(d*x^2+c)^2/(b*x^2+a),x)","\frac{d^{2} x^{4}}{4 b}-\frac{a \,d^{2} x^{2}}{2 b^{2}}+\frac{c d \,x^{2}}{b}+\frac{a^{2} d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{3}}-\frac{a c d \ln \left(b \,x^{2}+a \right)}{b^{2}}+\frac{c^{2} \ln \left(b \,x^{2}+a \right)}{2 b}"," ",0,"1/4*d^2/b*x^4-1/2*d^2/b^2*a*x^2+d/b*c*x^2+1/2/b^3*ln(b*x^2+a)*a^2*d^2-1/b^2*ln(b*x^2+a)*a*c*d+1/2/b*ln(b*x^2+a)*c^2","A"
213,1,95,53,0.004000," ","int((d*x^2+c)^2/(b*x^2+a),x)","\frac{d^{2} x^{3}}{3 b}+\frac{a^{2} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{2 a c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}-\frac{a \,d^{2} x}{b^{2}}+\frac{2 c d x}{b}"," ",0,"1/3*d^2*x^3/b-d^2/b^2*a*x+2*d/b*c*x+1/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^2*d^2-2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*c*d+1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
214,1,69,47,0.005000," ","int((d*x^2+c)^2/x/(b*x^2+a),x)","\frac{d^{2} x^{2}}{2 b}-\frac{a \,d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}+\frac{c^{2} \ln \left(x \right)}{a}-\frac{c^{2} \ln \left(b \,x^{2}+a \right)}{2 a}+\frac{c d \ln \left(b \,x^{2}+a \right)}{b}"," ",0,"1/2*d^2*x^2/b-1/2*a/b^2*ln(b*x^2+a)*d^2+1/b*ln(b*x^2+a)*c*d-1/2/a*ln(b*x^2+a)*c^2+c^2*ln(x)/a","A"
215,1,85,47,0.007000," ","int((d*x^2+c)^2/x^2/(b*x^2+a),x)","-\frac{a \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}-\frac{b \,c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}+\frac{2 c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}+\frac{d^{2} x}{b}-\frac{c^{2}}{a x}"," ",0,"d^2*x/b-a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2+2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d-1/a*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2-c^2/a/x","A"
216,1,81,54,0.007000," ","int((d*x^2+c)^2/x^3/(b*x^2+a),x)","\frac{2 c d \ln \left(x \right)}{a}-\frac{c d \ln \left(b \,x^{2}+a \right)}{a}-\frac{b \,c^{2} \ln \left(x \right)}{a^{2}}+\frac{b \,c^{2} \ln \left(b \,x^{2}+a \right)}{2 a^{2}}+\frac{d^{2} \ln \left(b \,x^{2}+a \right)}{2 b}-\frac{c^{2}}{2 a \,x^{2}}"," ",0,"1/2/b*ln(b*x^2+a)*d^2-1/a*ln(b*x^2+a)*c*d+1/2/a^2*b*ln(b*x^2+a)*c^2-1/2*c^2/a/x^2+2*c/a*ln(x)*d-c^2/a^2*ln(x)*b","A"
217,1,98,54,0.007000," ","int((d*x^2+c)^2/x^4/(b*x^2+a),x)","-\frac{2 b c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}+\frac{b^{2} c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{2}}+\frac{d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}-\frac{2 c d}{a x}+\frac{b \,c^{2}}{a^{2} x}-\frac{c^{2}}{3 a \,x^{3}}"," ",0,"1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2-2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*b*c*d+1/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*b^2*c^2-1/3*c^2/a/x^3-2*c/a/x*d+c^2/a^2/x*b","A"
218,1,263,126,0.007000," ","int(x^5*(d*x^2+c)^3/(b*x^2+a),x)","\frac{d^{3} x^{10}}{10 b}-\frac{a \,d^{3} x^{8}}{8 b^{2}}+\frac{3 c \,d^{2} x^{8}}{8 b}+\frac{a^{2} d^{3} x^{6}}{6 b^{3}}-\frac{a c \,d^{2} x^{6}}{2 b^{2}}+\frac{c^{2} d \,x^{6}}{2 b}-\frac{a^{3} d^{3} x^{4}}{4 b^{4}}+\frac{3 a^{2} c \,d^{2} x^{4}}{4 b^{3}}-\frac{3 a \,c^{2} d \,x^{4}}{4 b^{2}}+\frac{c^{3} x^{4}}{4 b}+\frac{a^{4} d^{3} x^{2}}{2 b^{5}}-\frac{3 a^{3} c \,d^{2} x^{2}}{2 b^{4}}+\frac{3 a^{2} c^{2} d \,x^{2}}{2 b^{3}}-\frac{a \,c^{3} x^{2}}{2 b^{2}}-\frac{a^{5} d^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{6}}+\frac{3 a^{4} c \,d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{5}}-\frac{3 a^{3} c^{2} d \ln \left(b \,x^{2}+a \right)}{2 b^{4}}+\frac{a^{2} c^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{3}}"," ",0,"1/10*d^3*x^10/b-1/8/b^2*x^8*a*d^3+3/8/b*x^8*c*d^2+1/6/b^3*x^6*a^2*d^3-1/2/b^2*x^6*a*c*d^2+1/2/b*x^6*c^2*d-1/4/b^4*x^4*a^3*d^3+3/4/b^3*x^4*a^2*c*d^2-3/4/b^2*x^4*a*c^2*d+1/4/b*x^4*c^3+1/2/b^5*x^2*a^4*d^3-3/2/b^4*x^2*a^3*c*d^2+3/2/b^3*x^2*a^2*c^2*d-1/2/b^2*x^2*a*c^3-1/2*a^5/b^6*ln(b*x^2+a)*d^3+3/2*a^4/b^5*ln(b*x^2+a)*c*d^2-3/2*a^3/b^4*ln(b*x^2+a)*c^2*d+1/2*a^2/b^3*ln(b*x^2+a)*c^3","B"
219,1,276,124,0.006000," ","int(x^4*(d*x^2+c)^3/(b*x^2+a),x)","\frac{d^{3} x^{9}}{9 b}-\frac{a \,d^{3} x^{7}}{7 b^{2}}+\frac{3 c \,d^{2} x^{7}}{7 b}+\frac{a^{2} d^{3} x^{5}}{5 b^{3}}-\frac{3 a c \,d^{2} x^{5}}{5 b^{2}}+\frac{3 c^{2} d \,x^{5}}{5 b}-\frac{a^{3} d^{3} x^{3}}{3 b^{4}}+\frac{a^{2} c \,d^{2} x^{3}}{b^{3}}-\frac{a \,c^{2} d \,x^{3}}{b^{2}}+\frac{c^{3} x^{3}}{3 b}-\frac{a^{5} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{5}}+\frac{3 a^{4} c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{4}}-\frac{3 a^{3} c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{a^{2} c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}+\frac{a^{4} d^{3} x}{b^{5}}-\frac{3 a^{3} c \,d^{2} x}{b^{4}}+\frac{3 a^{2} c^{2} d x}{b^{3}}-\frac{a \,c^{3} x}{b^{2}}"," ",0,"1/9*d^3*x^9/b-1/7/b^2*x^7*a*d^3+3/7/b*x^7*c*d^2+1/5/b^3*x^5*a^2*d^3-3/5/b^2*x^5*a*c*d^2+3/5/b*x^5*c^2*d-1/3/b^4*x^3*a^3*d^3+1/b^3*x^3*a^2*c*d^2-1/b^2*x^3*a*c^2*d+1/3/b*x^3*c^3+1/b^5*a^4*d^3*x-3/b^4*a^3*c*d^2*x+3/b^3*a^2*c^2*d*x-1/b^2*a*c^3*x-a^5/b^5/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3+3*a^4/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2-3*a^3/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d+a^2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3","B"
220,1,205,105,0.005000," ","int(x^3*(d*x^2+c)^3/(b*x^2+a),x)","\frac{d^{3} x^{8}}{8 b}-\frac{a \,d^{3} x^{6}}{6 b^{2}}+\frac{c \,d^{2} x^{6}}{2 b}+\frac{a^{2} d^{3} x^{4}}{4 b^{3}}-\frac{3 a c \,d^{2} x^{4}}{4 b^{2}}+\frac{3 c^{2} d \,x^{4}}{4 b}-\frac{a^{3} d^{3} x^{2}}{2 b^{4}}+\frac{3 a^{2} c \,d^{2} x^{2}}{2 b^{3}}-\frac{3 a \,c^{2} d \,x^{2}}{2 b^{2}}+\frac{c^{3} x^{2}}{2 b}+\frac{a^{4} d^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{5}}-\frac{3 a^{3} c \,d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}+\frac{3 a^{2} c^{2} d \ln \left(b \,x^{2}+a \right)}{2 b^{3}}-\frac{a \,c^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/8*d^3*x^8/b-1/6/b^2*x^6*a*d^3+1/2/b*x^6*c*d^2+1/4/b^3*x^4*a^2*d^3-3/4/b^2*x^4*a*c*d^2+3/4/b*x^4*c^2*d-1/2/b^4*x^2*a^3*d^3+3/2/b^3*x^2*a^2*c*d^2-3/2/b^2*x^2*a*c^2*d+1/2/b*x^2*c^3+1/2*a^4/b^5*ln(b*x^2+a)*d^3-3/2*a^3/b^4*ln(b*x^2+a)*c*d^2+3/2*a^2/b^3*ln(b*x^2+a)*c^2*d-1/2*a/b^2*ln(b*x^2+a)*c^3","A"
221,1,218,105,0.005000," ","int(x^2*(d*x^2+c)^3/(b*x^2+a),x)","\frac{d^{3} x^{7}}{7 b}-\frac{a \,d^{3} x^{5}}{5 b^{2}}+\frac{3 c \,d^{2} x^{5}}{5 b}+\frac{a^{2} d^{3} x^{3}}{3 b^{3}}-\frac{a c \,d^{2} x^{3}}{b^{2}}+\frac{c^{2} d \,x^{3}}{b}+\frac{a^{4} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{4}}-\frac{3 a^{3} c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{3 a^{2} c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{a \,c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}-\frac{a^{3} d^{3} x}{b^{4}}+\frac{3 a^{2} c \,d^{2} x}{b^{3}}-\frac{3 a \,c^{2} d x}{b^{2}}+\frac{c^{3} x}{b}"," ",0,"1/7*d^3*x^7/b-1/5/b^2*x^5*a*d^3+3/5/b*x^5*c*d^2+1/3/b^3*x^3*a^2*d^3-1/b^2*x^3*a*c*d^2+1/b*x^3*c^2*d-1/b^4*a^3*d^3*x+3/b^3*a^2*c*d^2*x-3/b^2*a*c^2*d*x+1/b*c^3*x+a^4/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3-3*a^3/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2+3*a^2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d-a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3","B"
222,1,149,79,0.003000," ","int(x*(d*x^2+c)^3/(b*x^2+a),x)","\frac{d^{3} x^{6}}{6 b}-\frac{a \,d^{3} x^{4}}{4 b^{2}}+\frac{3 c \,d^{2} x^{4}}{4 b}+\frac{a^{2} d^{3} x^{2}}{2 b^{3}}-\frac{3 a c \,d^{2} x^{2}}{2 b^{2}}+\frac{3 c^{2} d \,x^{2}}{2 b}-\frac{a^{3} d^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}+\frac{3 a^{2} c \,d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{3}}-\frac{3 a \,c^{2} d \ln \left(b \,x^{2}+a \right)}{2 b^{2}}+\frac{c^{3} \ln \left(b \,x^{2}+a \right)}{2 b}"," ",0,"1/6*d^3/b*x^6-1/4*d^3/b^2*x^4*a+3/4*d^2/b*x^4*c+1/2*d^3/b^3*x^2*a^2-3/2*d^2/b^2*x^2*a*c+3/2*d/b*x^2*c^2-1/2/b^4*ln(b*x^2+a)*a^3*d^3+3/2/b^3*ln(b*x^2+a)*a^2*c*d^2-3/2/b^2*ln(b*x^2+a)*a*c^2*d+1/2/b*ln(b*x^2+a)*c^3","A"
223,1,161,86,0.005000," ","int((d*x^2+c)^3/(b*x^2+a),x)","\frac{d^{3} x^{5}}{5 b}-\frac{a \,d^{3} x^{3}}{3 b^{2}}+\frac{c \,d^{2} x^{3}}{b}-\frac{a^{3} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{3 a^{2} c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{3 a \,c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}+\frac{a^{2} d^{3} x}{b^{3}}-\frac{3 a c \,d^{2} x}{b^{2}}+\frac{3 c^{2} d x}{b}"," ",0,"1/5*d^3*x^5/b-1/3*d^3/b^2*x^3*a+d^2/b*x^3*c+d^3/b^3*a^2*x-3*d^2/b^2*a*c*x+3*d/b*c^2*x-1/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^3*d^3+3/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^2*c*d^2-3/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*c^2*d+1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3","A"
224,1,116,67,0.008000," ","int((d*x^2+c)^3/x/(b*x^2+a),x)","\frac{d^{3} x^{4}}{4 b}-\frac{a \,d^{3} x^{2}}{2 b^{2}}+\frac{3 c \,d^{2} x^{2}}{2 b}+\frac{a^{2} d^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{3}}-\frac{3 a c \,d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}+\frac{c^{3} \ln \left(x \right)}{a}-\frac{c^{3} \ln \left(b \,x^{2}+a \right)}{2 a}+\frac{3 c^{2} d \ln \left(b \,x^{2}+a \right)}{2 b}"," ",0,"1/4*d^3*x^4/b-1/2*d^3/b^2*a*x^2+3/2*d^2/b*c*x^2+1/2*a^2/b^3*ln(b*x^2+a)*d^3-3/2*a/b^2*ln(b*x^2+a)*c*d^2+3/2/b*ln(b*x^2+a)*c^2*d-1/2/a*ln(b*x^2+a)*c^3+c^3*ln(x)/a","A"
225,1,135,67,0.007000," ","int((d*x^2+c)^3/x^2/(b*x^2+a),x)","\frac{d^{3} x^{3}}{3 b}+\frac{a^{2} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{3 a c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}-\frac{b \,c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}+\frac{3 c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}-\frac{a \,d^{3} x}{b^{2}}+\frac{3 c \,d^{2} x}{b}-\frac{c^{3}}{a x}"," ",0,"1/3*d^3*x^3/b-d^3/b^2*a*x+3*d^2/b*c*x+a^2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3-3*a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2+3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d-1/a*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3-c^3/a/x","A"
226,1,114,67,0.009000," ","int((d*x^2+c)^3/x^3/(b*x^2+a),x)","\frac{d^{3} x^{2}}{2 b}-\frac{a \,d^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}+\frac{3 c^{2} d \ln \left(x \right)}{a}-\frac{3 c^{2} d \ln \left(b \,x^{2}+a \right)}{2 a}-\frac{b \,c^{3} \ln \left(x \right)}{a^{2}}+\frac{b \,c^{3} \ln \left(b \,x^{2}+a \right)}{2 a^{2}}+\frac{3 c \,d^{2} \ln \left(b \,x^{2}+a \right)}{2 b}-\frac{c^{3}}{2 a \,x^{2}}"," ",0,"1/2*d^3*x^2/b-1/2*a/b^2*ln(b*x^2+a)*d^3+3/2/b*ln(b*x^2+a)*c*d^2-3/2/a*ln(b*x^2+a)*c^2*d+1/2/a^2*b*ln(b*x^2+a)*c^3-1/2*c^3/a/x^2+3*c^2/a*ln(x)*d-c^3/a^2*ln(x)*b","A"
227,1,135,64,0.010000," ","int((d*x^2+c)^3/x^4/(b*x^2+a),x)","-\frac{a \,d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}-\frac{3 b \,c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}+\frac{b^{2} c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{2}}+\frac{3 c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}+\frac{d^{3} x}{b}-\frac{3 c^{2} d}{a x}+\frac{b \,c^{3}}{a^{2} x}-\frac{c^{3}}{3 a \,x^{3}}"," ",0,"d^3*x/b-a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3+3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2-3/a*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d+1/a^2*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3-1/3*c^3/a/x^3-3*c^2/a/x*d+c^3/a^2/x*b","B"
228,1,65,64,0.009000," ","int(x^5/(b*x^2+a)/(d*x^2+c),x)","-\frac{a^{2} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right) b^{2}}+\frac{c^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right) d^{2}}+\frac{x^{2}}{2 b d}"," ",0,"1/2*x^2/b/d-1/2*a^2/b^2/(a*d-b*c)*ln(b*x^2+a)+1/2*c^2/d^2/(a*d-b*c)*ln(d*x^2+c)","A"
229,1,73,62,0.009000," ","int(x^4/(b*x^2+a)/(d*x^2+c),x)","-\frac{a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right) \sqrt{a b}\, b}+\frac{c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right) \sqrt{c d}\, d}+\frac{x}{b d}"," ",0,"x/b/d-1/b*a^2/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)+1/d*c^2/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)","A"
230,1,50,49,0.009000," ","int(x^3/(b*x^2+a)/(d*x^2+c),x)","\frac{a \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right) b}-\frac{c \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right) d}"," ",0,"1/2*a/(a*d-b*c)/b*ln(b*x^2+a)-1/2*c/(a*d-b*c)/d*ln(d*x^2+c)","A"
231,1,55,54,0.009000," ","int(x^2/(b*x^2+a)/(d*x^2+c),x)","\frac{a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right) \sqrt{a b}}-\frac{c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right) \sqrt{c d}}"," ",0,"a/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-c/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)","A"
232,1,42,41,0.007000," ","int(x/(b*x^2+a)/(d*x^2+c),x)","-\frac{\ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)}+\frac{\ln \left(d \,x^{2}+c \right)}{2 a d -2 b c}"," ",0,"-1/2/(a*d-b*c)*ln(b*x^2+a)+1/2/(a*d-b*c)*ln(d*x^2+c)","A"
233,1,55,54,0.009000," ","int(1/(b*x^2+a)/(d*x^2+c),x)","-\frac{b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right) \sqrt{a b}}+\frac{d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right) \sqrt{c d}}"," ",0,"-b/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)+d/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)","A"
234,1,59,58,0.010000," ","int(1/x/(b*x^2+a)/(d*x^2+c),x)","\frac{b \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right) a}-\frac{d \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right) c}+\frac{\ln \left(x \right)}{a c}"," ",0,"1/2*b/a/(a*d-b*c)*ln(b*x^2+a)-1/2*d/c/(a*d-b*c)*ln(d*x^2+c)+ln(x)/a/c","A"
235,1,76,65,0.010000," ","int(1/x^2/(b*x^2+a)/(d*x^2+c),x)","\frac{b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right) \sqrt{a b}\, a}-\frac{d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right) \sqrt{c d}\, c}-\frac{1}{a c x}"," ",0,"1/a*b^2/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-1/c*d^2/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)-1/a/c/x","A"
236,1,87,81,0.014000," ","int(1/x^3/(b*x^2+a)/(d*x^2+c),x)","-\frac{b^{2} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right) a^{2}}+\frac{d^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right) c^{2}}-\frac{d \ln \left(x \right)}{a \,c^{2}}-\frac{b \ln \left(x \right)}{a^{2} c}-\frac{1}{2 a c \,x^{2}}"," ",0,"-1/2*b^2/a^2/(a*d-b*c)*ln(b*x^2+a)+1/2*d^2/c^2/(a*d-b*c)*ln(d*x^2+c)-1/2/a/c/x^2-1/a/c^2*ln(x)*d-1/a^2/c*ln(x)*b","A"
237,1,98,82,0.013000," ","int(1/x^4/(b*x^2+a)/(d*x^2+c),x)","-\frac{b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right) \sqrt{a b}\, a^{2}}+\frac{d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right) \sqrt{c d}\, c^{2}}+\frac{d}{a \,c^{2} x}+\frac{b}{a^{2} c x}-\frac{1}{3 a c \,x^{3}}"," ",0,"-1/a^2*b^3/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)+1/c^2*d^3/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)-1/3/a/c/x^3+1/a/c^2/x*d+1/a^2/c/x*b","A"
238,1,124,111,0.016000," ","int(1/x^5/(b*x^2+a)/(d*x^2+c),x)","\frac{b^{3} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right) a^{3}}-\frac{d^{3} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right) c^{3}}+\frac{d^{2} \ln \left(x \right)}{a \,c^{3}}+\frac{b d \ln \left(x \right)}{a^{2} c^{2}}+\frac{b^{2} \ln \left(x \right)}{a^{3} c}+\frac{d}{2 a \,c^{2} x^{2}}+\frac{b}{2 a^{2} c \,x^{2}}-\frac{1}{4 a c \,x^{4}}"," ",0,"1/2*b^3/a^3/(a*d-b*c)*ln(b*x^2+a)-1/2*d^3/c^3/(a*d-b*c)*ln(d*x^2+c)-1/4/a/c/x^4+1/2/a/c^2/x^2*d+1/2/a^2/c/x^2*b+1/a/c^3*ln(x)*d^2+1/a^2/c^2*ln(x)*b*d+1/a^3/c*ln(x)*b^2","A"
239,1,141,116,0.014000," ","int(1/x^6/(b*x^2+a)/(d*x^2+c),x)","\frac{b^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right) \sqrt{a b}\, a^{3}}-\frac{d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right) \sqrt{c d}\, c^{3}}-\frac{d^{2}}{a \,c^{3} x}-\frac{b d}{a^{2} c^{2} x}-\frac{b^{2}}{a^{3} c x}+\frac{d}{3 a \,c^{2} x^{3}}+\frac{b}{3 a^{2} c \,x^{3}}-\frac{1}{5 a c \,x^{5}}"," ",0,"1/a^3*b^4/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-1/c^3*d^4/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)-1/5/a/c/x^5+1/3/a/c^2/x^3*d+1/3/a^2/c/x^3*b-1/a/c^3/x*d^2-1/a^2/c^2/x*b*d-1/a^3/c/x*b^2","A"
240,1,184,148,0.017000," ","int(1/x^7/(b*x^2+a)/(d*x^2+c),x)","-\frac{b^{4} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right) a^{4}}+\frac{d^{4} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right) c^{4}}-\frac{d^{3} \ln \left(x \right)}{a \,c^{4}}-\frac{b \,d^{2} \ln \left(x \right)}{a^{2} c^{3}}-\frac{b^{2} d \ln \left(x \right)}{a^{3} c^{2}}-\frac{b^{3} \ln \left(x \right)}{a^{4} c}-\frac{d^{2}}{2 a \,c^{3} x^{2}}-\frac{b d}{2 a^{2} c^{2} x^{2}}-\frac{b^{2}}{2 a^{3} c \,x^{2}}+\frac{d}{4 a \,c^{2} x^{4}}+\frac{b}{4 a^{2} c \,x^{4}}-\frac{1}{6 a c \,x^{6}}"," ",0,"-1/2*b^4/a^4/(a*d-b*c)*ln(b*x^2+a)+1/2*d^4/c^4/(a*d-b*c)*ln(d*x^2+c)-1/6/a/c/x^6+1/4/a/c^2/x^4*d+1/4/a^2/c/x^4*b-1/2/a/c^3/x^2*d^2-1/2/a^2/c^2/x^2*b*d-1/2/a^3/c/x^2*b^2-1/a/c^4*ln(x)*d^3-1/a^2/c^3*ln(x)*b*d^2-1/a^3/c^2*ln(x)*b^2*d-1/a^4/c*ln(x)*b^3","A"
241,1,136,87,0.013000," ","int(x^5/(b*x^2+a)^2/(d*x^2+c),x)","\frac{a^{3} d}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) b^{2}}-\frac{a^{2} c}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) b}+\frac{a^{2} d \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2} b^{2}}-\frac{a c \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{2} b}+\frac{c^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2} d}"," ",0,"1/2*a^3/(a*d-b*c)^2/b^2/(b*x^2+a)*d-1/2*a^2/(a*d-b*c)^2/b/(b*x^2+a)*c+1/2*a^2/(a*d-b*c)^2/b^2*ln(b*x^2+a)*d-a/(a*d-b*c)^2/b*ln(b*x^2+a)*c+1/2*c^2/(a*d-b*c)^2/d*ln(d*x^2+c)","A"
242,1,144,88,0.013000," ","int(x^4/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{2} \sqrt{a b}}+\frac{a c x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}-\frac{3 a c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}}-\frac{b \,c^{2} x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) d}+\frac{b \,c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}\, d}"," ",0,"a^2/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)+1/2*c/(a*d-b*c)^2*x/(d*x^2+c)*a-1/2*c^2/(a*d-b*c)^2/d*x/(d*x^2+c)*b-3/2*c/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a+1/2*c^2/(a*d-b*c)^2/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b","A"
243,1,95,68,0.012000," ","int(x^3/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a c}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}-\frac{a \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2}}+\frac{a \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2}}-\frac{b \,c^{2}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) d}"," ",0,"-1/2*a/(a*d-b*c)^2*ln(b*x^2+a)+1/2/(a*d-b*c)^2*a*ln(d*x^2+c)+1/2/(a*d-b*c)^2*c/(d*x^2+c)*a-1/2/(a*d-b*c)^2*c^2/d/(d*x^2+c)*b","A"
244,1,134,84,0.012000," ","int(x^2/(b*x^2+a)/(d*x^2+c)^2,x)","-\frac{a b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{2} \sqrt{a b}}-\frac{a d x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{a d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}}+\frac{b c x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{b c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}}"," ",0,"-b/(a*d-b*c)^2*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-1/2/(a*d-b*c)^2*x/(d*x^2+c)*a*d+1/2/(a*d-b*c)^2*x/(d*x^2+c)*b*c+1/2/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*d+1/2/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b*c","A"
245,1,90,64,0.013000," ","int(x/(b*x^2+a)/(d*x^2+c)^2,x)","-\frac{a d}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{b c}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{b \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2}}-\frac{b \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2}}"," ",0,"1/2*b/(a*d-b*c)^2*ln(b*x^2+a)-1/2/(a*d-b*c)^2*b*ln(d*x^2+c)-1/2*d/(a*d-b*c)^2/(d*x^2+c)*a+1/2/(a*d-b*c)^2/(d*x^2+c)*b*c","A"
246,1,144,89,0.010000," ","int(1/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a \,d^{2} x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c}+\frac{a \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}\, c}+\frac{b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{2} \sqrt{a b}}-\frac{b d x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}-\frac{3 b d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}}"," ",0,"b^2/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)+1/2*d^2/(a*d-b*c)^2/c*x/(d*x^2+c)*a-1/2*d/(a*d-b*c)^2*x/(d*x^2+c)*b+1/2*d^2/(a*d-b*c)^2/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a-3/2*d/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b","A"
247,1,139,94,0.017000," ","int(1/x/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a \,d^{2}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c}-\frac{a \,d^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2} c^{2}}-\frac{b^{2} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2} a}+\frac{b d \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{2} c}-\frac{b d}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{\ln \left(x \right)}{a \,c^{2}}"," ",0,"-1/2*b^2/a/(a*d-b*c)^2*ln(b*x^2+a)-1/2*d^2/c^2/(a*d-b*c)^2*ln(d*x^2+c)*a+d/c/(a*d-b*c)^2*ln(d*x^2+c)*b+1/2*d^2/c/(a*d-b*c)^2/(d*x^2+c)*a-1/2*d/(a*d-b*c)^2/(d*x^2+c)*b+ln(x)/a/c^2","A"
248,1,169,122,0.016000," ","int(1/x^2/(b*x^2+a)/(d*x^2+c)^2,x)","-\frac{a \,d^{3} x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c^{2}}-\frac{3 a \,d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}\, c^{2}}-\frac{b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{2} \sqrt{a b}\, a}+\frac{b \,d^{2} x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c}+\frac{5 b \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}\, c}-\frac{1}{a \,c^{2} x}"," ",0,"-1/a*b^3/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-1/2*d^3/c^2/(a*d-b*c)^2*x/(d*x^2+c)*a+1/2*d^2/c/(a*d-b*c)^2*x/(d*x^2+c)*b-3/2*d^3/c^2/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a+5/2*d^2/c/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b-1/a/c^2/x","A"
249,1,170,118,0.020000," ","int(1/x^3/(b*x^2+a)/(d*x^2+c)^2,x)","-\frac{a \,d^{3}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c^{2}}+\frac{a \,d^{3} \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{2} c^{3}}+\frac{b^{3} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2} a^{2}}+\frac{b \,d^{2}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c}-\frac{3 b \,d^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2} c^{2}}-\frac{2 d \ln \left(x \right)}{a \,c^{3}}-\frac{b \ln \left(x \right)}{a^{2} c^{2}}-\frac{1}{2 a \,c^{2} x^{2}}"," ",0,"1/2*b^3/a^2/(a*d-b*c)^2*ln(b*x^2+a)+d^3/c^3/(a*d-b*c)^2*ln(d*x^2+c)*a-3/2*d^2/c^2/(a*d-b*c)^2*ln(d*x^2+c)*b-1/2*d^3/c^2/(a*d-b*c)^2/(d*x^2+c)*a+1/2*d^2/c/(a*d-b*c)^2/(d*x^2+c)*b-1/2/a/c^2/x^2-2/a/c^3*ln(x)*d-1/a^2/c^2*ln(x)*b","A"
250,1,191,165,0.017000," ","int(1/x^4/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a \,d^{4} x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c^{3}}+\frac{5 a \,d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}\, c^{3}}+\frac{b^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{2} \sqrt{a b}\, a^{2}}-\frac{b \,d^{3} x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c^{2}}-\frac{7 b \,d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}\, c^{2}}+\frac{2 d}{a \,c^{3} x}+\frac{b}{a^{2} c^{2} x}-\frac{1}{3 a \,c^{2} x^{3}}"," ",0,"1/a^2*b^4/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)+1/2*d^4/c^3/(a*d-b*c)^2*x/(d*x^2+c)*a-1/2*d^3/c^2/(a*d-b*c)^2*x/(d*x^2+c)*b+5/2*d^4/c^3/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a-7/2*d^3/c^2/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b-1/3/a/c^2/x^3+2/a/c^3/x*d+1/a^2/c^2/x*b","A"
251,1,218,108,0.013000," ","int(x^5/(b*x^2+a)^3/(d*x^2+c),x)","\frac{a^{4} d^{2}}{4 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)^{2} b^{2}}-\frac{a^{3} c d}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)^{2} b}+\frac{a^{2} c^{2}}{4 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)^{2}}-\frac{a^{3} d^{2}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) b^{2}}+\frac{3 a^{2} c d}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) b}-\frac{a \,c^{2}}{\left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{c^{2} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{3}}+\frac{c^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3}}"," ",0,"-1/2/(a*d-b*c)^3*a^3/b^2/(b*x^2+a)*d^2+3/2/(a*d-b*c)^3*a^2/b/(b*x^2+a)*c*d-1/(a*d-b*c)^3*a/(b*x^2+a)*c^2+1/4/(a*d-b*c)^3*a^4/b^2/(b*x^2+a)^2*d^2-1/2/(a*d-b*c)^3*a^3/b/(b*x^2+a)^2*c*d+1/4/(a*d-b*c)^3*a^2/(b*x^2+a)^2*c^2-1/2/(a*d-b*c)^3*c^2*ln(b*x^2+a)+1/2*c^2/(a*d-b*c)^3*ln(d*x^2+c)","B"
252,1,299,135,0.014000," ","int(x^4/(b*x^2+a)/(d*x^2+c)^3,x)","-\frac{5 a^{2} d^{2} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{3 a b c d \,x^{3}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{b^{2} c^{2} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{3 a^{2} c d x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{a b \,c^{2} x}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{b^{2} c^{3} x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} d}-\frac{a^{2} b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{3} \sqrt{a b}}+\frac{3 a^{2} d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}}+\frac{3 a b c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{c d}}-\frac{b^{2} c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}\, d}"," ",0,"-a^2*b/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-5/8/(a*d-b*c)^3/(d*x^2+c)^2*x^3*a^2*d^2+3/4/(a*d-b*c)^3/(d*x^2+c)^2*x^3*a*b*c*d-1/8/(a*d-b*c)^3/(d*x^2+c)^2*x^3*b^2*c^2-3/8/(a*d-b*c)^3/(d*x^2+c)^2*a^2*c*d*x+1/4/(a*d-b*c)^3/(d*x^2+c)^2*a*b*c^2*x+1/8/(a*d-b*c)^3/(d*x^2+c)^2*c^3/d*x*b^2+3/8/(a*d-b*c)^3*d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+3/4/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*c-1/8/(a*d-b*c)^3/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2*c^2","B"
253,1,177,92,0.013000," ","int(x^3/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{a^{2} c d}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{a b \,c^{2}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{b^{2} c^{3}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} d}-\frac{a^{2} d}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{a b c}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{a b \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{3}}-\frac{a b \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3}}"," ",0,"1/2*a*b/(a*d-b*c)^3*ln(b*x^2+a)+1/4/(a*d-b*c)^3*c*d/(d*x^2+c)^2*a^2-1/2/(a*d-b*c)^3*c^2/(d*x^2+c)^2*a*b+1/4/(a*d-b*c)^3*c^3/d/(d*x^2+c)^2*b^2-1/2/(a*d-b*c)^3*a*b*ln(d*x^2+c)-1/2/(a*d-b*c)^3*a^2/(d*x^2+c)*d+1/2/(a*d-b*c)^3*a/(d*x^2+c)*b*c","A"
254,1,298,133,0.011000," ","int(x^2/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{a^{2} d^{3} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}+\frac{a b \,d^{2} x^{3}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{3 b^{2} c d \,x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{a^{2} d^{2} x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{3 a b c d x}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{5 b^{2} c^{2} x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{a^{2} d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}\, c}+\frac{a \,b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{3} \sqrt{a b}}-\frac{3 a b d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{c d}}-\frac{3 b^{2} c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}}"," ",0,"a*b^2/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)+1/8/(a*d-b*c)^3/(d*x^2+c)^2*d^3/c*x^3*a^2+1/4/(a*d-b*c)^3/(d*x^2+c)^2*x^3*a*b*d^2-3/8/(a*d-b*c)^3/(d*x^2+c)^2*x^3*b^2*c*d+3/4/(a*d-b*c)^3/(d*x^2+c)^2*a*b*c*d*x-5/8/(a*d-b*c)^3/(d*x^2+c)^2*b^2*c^2*x-1/8/(a*d-b*c)^3/(d*x^2+c)^2*a^2*d^2*x+1/8/(a*d-b*c)^3/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2*d^2-3/4/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*d-3/8/(a*d-b*c)^3*c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","B"
255,1,176,90,0.013000," ","int(x/(b*x^2+a)/(d*x^2+c)^3,x)","-\frac{a^{2} d^{2}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{a b c d}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{b^{2} c^{2}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{a b d}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{b^{2} c}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{b^{2} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{3}}+\frac{b^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3}}"," ",0,"-1/2*b^2/(a*d-b*c)^3*ln(b*x^2+a)-1/4*d^2/(a*d-b*c)^3/(d*x^2+c)^2*a^2+1/2*d/(a*d-b*c)^3/(d*x^2+c)^2*a*b*c-1/4/(a*d-b*c)^3/(d*x^2+c)^2*b^2*c^2+1/2/(a*d-b*c)^3*ln(d*x^2+c)*b^2+1/2*d/(a*d-b*c)^3*b/(d*x^2+c)*a-1/2/(a*d-b*c)^3*b^2/(d*x^2+c)*c","A"
256,1,310,138,0.013000," ","int(1/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{3 a^{2} d^{4} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{5 a b \,d^{3} x^{3}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}+\frac{7 b^{2} d^{2} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{5 a^{2} d^{3} x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{7 a b \,d^{2} x}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{9 b^{2} c d x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{3 a^{2} d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{2}}-\frac{5 a b \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{c d}\, c}-\frac{b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{3} \sqrt{a b}}+\frac{15 b^{2} d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}}"," ",0,"-b^3/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)+3/8*d^4/(a*d-b*c)^3/(d*x^2+c)^2/c^2*x^3*a^2-5/4*d^3/(a*d-b*c)^3/(d*x^2+c)^2/c*x^3*a*b+7/8*d^2/(a*d-b*c)^3/(d*x^2+c)^2*b^2*x^3+5/8*d^3/(a*d-b*c)^3/(d*x^2+c)^2/c*x*a^2-7/4*d^2/(a*d-b*c)^3/(d*x^2+c)^2*a*b*x+9/8*d/(a*d-b*c)^3/(d*x^2+c)^2*b^2*c*x+3/8*d^3/(a*d-b*c)^3/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-5/4*d^2/(a*d-b*c)^3/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+15/8*d/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","B"
257,1,286,141,0.023000," ","int(1/x/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{a^{2} d^{3}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{a b \,d^{2}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{b^{2} c d}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{a^{2} d^{3}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{2}}-\frac{a^{2} d^{3} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3} c^{3}}-\frac{3 a b \,d^{2}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}+\frac{3 a b \,d^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3} c^{2}}+\frac{b^{3} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{3} a}-\frac{3 b^{2} d \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3} c}+\frac{b^{2} d}{\left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{\ln \left(x \right)}{a \,c^{3}}"," ",0,"1/2*b^3/a/(a*d-b*c)^3*ln(b*x^2+a)+1/4*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*a^2-1/2*d^2/(a*d-b*c)^3/(d*x^2+c)^2*a*b+1/4*d*c/(a*d-b*c)^3/(d*x^2+c)^2*b^2-1/2*d^3/c^3/(a*d-b*c)^3*ln(d*x^2+c)*a^2+3/2*d^2/c^2/(a*d-b*c)^3*ln(d*x^2+c)*a*b-3/2*d/c/(a*d-b*c)^3*ln(d*x^2+c)*b^2+1/2*d^3/c^2/(a*d-b*c)^3/(d*x^2+c)*a^2-3/2*d^2/c/(a*d-b*c)^3/(d*x^2+c)*a*b+d/(a*d-b*c)^3/(d*x^2+c)*b^2+ln(x)/a/c^3","B"
258,1,335,187,0.017000," ","int(1/x^2/(b*x^2+a)/(d*x^2+c)^3,x)","-\frac{7 a^{2} d^{5} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{9 a b \,d^{4} x^{3}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{11 b^{2} d^{3} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{9 a^{2} d^{4} x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{11 a b \,d^{3} x}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{13 b^{2} d^{2} x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{15 a^{2} d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{3}}+\frac{21 a b \,d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{2}}+\frac{b^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{3} \sqrt{a b}\, a}-\frac{35 b^{2} d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}\, c}-\frac{1}{a \,c^{3} x}"," ",0,"1/a*b^4/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-7/8*d^5/c^3/(a*d-b*c)^3/(d*x^2+c)^2*x^3*a^2+9/4*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^3*a*b-11/8*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*x^3*b^2-9/8*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*a^2*x+11/4*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*a*b*x-13/8*d^2/(a*d-b*c)^3/(d*x^2+c)^2*b^2*x-15/8*d^4/c^3/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+21/4*d^3/c^2/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-35/8*d^2/c/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-1/a/c^3/x","A"
259,1,322,168,0.021000," ","int(1/x^3/(b*x^2+a)/(d*x^2+c)^3,x)","-\frac{a^{2} d^{4}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{a b \,d^{3}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{b^{2} d^{2}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{a^{2} d^{4}}{\left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{3}}+\frac{3 a^{2} d^{4} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3} c^{4}}+\frac{5 a b \,d^{3}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{2}}-\frac{4 a b \,d^{3} \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{3} c^{3}}-\frac{b^{4} \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{3} a^{2}}-\frac{3 b^{2} d^{2}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}+\frac{3 b^{2} d^{2} \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{3} c^{2}}-\frac{3 d \ln \left(x \right)}{a \,c^{4}}-\frac{b \ln \left(x \right)}{a^{2} c^{3}}-\frac{1}{2 a \,c^{3} x^{2}}"," ",0,"-1/2*b^4/a^2/(a*d-b*c)^3*ln(b*x^2+a)-1/4*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*a^2+1/2*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*a*b-1/4*d^2/(a*d-b*c)^3/(d*x^2+c)^2*b^2+3/2*d^4/c^4/(a*d-b*c)^3*ln(d*x^2+c)*a^2-4*d^3/c^3/(a*d-b*c)^3*ln(d*x^2+c)*a*b+3*d^2/c^2/(a*d-b*c)^3*ln(d*x^2+c)*b^2-d^4/c^3/(a*d-b*c)^3/(d*x^2+c)*a^2+5/2*d^3/c^2/(a*d-b*c)^3/(d*x^2+c)*a*b-3/2*d^2/c/(a*d-b*c)^3/(d*x^2+c)*b^2-1/2/a/c^3/x^2-3/a/c^4*ln(x)*d-1/a^2/c^3*ln(x)*b","A"
260,1,362,244,0.020000," ","int(1/x^4/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{11 a^{2} d^{6} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{4}}-\frac{13 a b \,d^{5} x^{3}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{15 b^{2} d^{4} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{13 a^{2} d^{5} x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{3}}-\frac{15 a b \,d^{4} x}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{17 b^{2} d^{3} x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}+\frac{35 a^{2} d^{5} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{4}}-\frac{45 a b \,d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{3}}-\frac{b^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{3} \sqrt{a b}\, a^{2}}+\frac{63 b^{2} d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{2}}+\frac{3 d}{a \,c^{4} x}+\frac{b}{a^{2} c^{3} x}-\frac{1}{3 a \,c^{3} x^{3}}"," ",0,"-1/a^2*b^5/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)+11/8*d^6/c^4/(a*d-b*c)^3/(d*x^2+c)^2*x^3*a^2-13/4*d^5/c^3/(a*d-b*c)^3/(d*x^2+c)^2*x^3*a*b+15/8*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^3*b^2+13/8*d^5/c^3/(a*d-b*c)^3/(d*x^2+c)^2*a^2*x-15/4*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*a*b*x+17/8*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*b^2*x+35/8*d^5/c^4/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-45/4*d^4/c^3/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+63/8*d^3/c^2/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-1/3/a/c^3/x^3+3/a/c^4/x*d+1/a^2/c^3/x*b","A"
261,1,18,17,0.007000," ","int(x/(x^2+1)/(x^2+4),x)","\frac{\ln \left(x^{2}+1\right)}{6}-\frac{\ln \left(x^{2}+4\right)}{6}"," ",0,"1/6*ln(x^2+1)-1/6*ln(x^2+4)","A"
262,1,105,73,0.011000," ","int(x^4*(d*x^2+c)/(b*x^2+a)^2,x)","\frac{d \,x^{3}}{3 b^{2}}-\frac{a^{2} d x}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{5 a^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}+\frac{a c x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}-\frac{2 a d x}{b^{3}}+\frac{c x}{b^{2}}"," ",0,"1/3*d*x^3/b^2-2/b^3*a*d*x+1/b^2*c*x-1/2*a^2/b^3*x/(b*x^2+a)*d+1/2*a/b^2*x/(b*x^2+a)*c+5/2*a^2/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-3/2*a/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c","A"
263,1,74,54,0.011000," ","int(x^3*(d*x^2+c)/(b*x^2+a)^2,x)","\frac{d \,x^{2}}{2 b^{2}}-\frac{a^{2} d}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{a c}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{a d \ln \left(b \,x^{2}+a \right)}{b^{3}}+\frac{c \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/2*d*x^2/b^2-1/2/b^3*a^2/(b*x^2+a)*d+1/2/(b*x^2+a)*a/b^2*c-1/b^3*ln(b*x^2+a)*a*d+1/2/b^2*c*ln(b*x^2+a)","A"
264,1,82,55,0.010000," ","int(x^2*(d*x^2+c)/(b*x^2+a)^2,x)","\frac{a d x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}-\frac{c x}{2 \left(b \,x^{2}+a \right) b}+\frac{c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}+\frac{d x}{b^{2}}"," ",0,"d*x/b^2+1/2/b^2*x/(b*x^2+a)*a*d-1/2/(b*x^2+a)/b*c*x-3/2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*d+1/2/(a*b)^(1/2)/b*c*arctan(1/(a*b)^(1/2)*b*x)","A"
265,1,47,37,0.010000," ","int(x*(d*x^2+c)/(b*x^2+a)^2,x)","\frac{a d}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{c}{2 \left(b \,x^{2}+a \right) b}+\frac{d \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/2/b^2/(b*x^2+a)*a*d-1/2/(b*x^2+a)/b*c+1/2*d*ln(b*x^2+a)/b^2","A"
266,1,68,51,0.009000," ","int((d*x^2+c)/(b*x^2+a)^2,x)","\frac{c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}+\frac{d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}-\frac{\left(a d -b c \right) x}{2 \left(b \,x^{2}+a \right) a b}"," ",0,"-1/2*(a*d-b*c)/a/b*x/(b*x^2+a)+1/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+1/2/(a*b)^(1/2)/a*c*arctan(1/(a*b)^(1/2)*b*x)","A"
267,1,53,47,0.012000," ","int((d*x^2+c)/x/(b*x^2+a)^2,x)","\frac{c}{2 \left(b \,x^{2}+a \right) a}+\frac{c \ln \left(x \right)}{a^{2}}-\frac{c \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{d}{2 \left(b \,x^{2}+a \right) b}"," ",0,"-1/2/b/(b*x^2+a)*d+1/2/(b*x^2+a)/a*c-1/2/a^2*c*ln(b*x^2+a)+1/a^2*c*ln(x)","A"
268,1,85,59,0.010000," ","int((d*x^2+c)/x^2/(b*x^2+a)^2,x)","\frac{d x}{2 \left(b \,x^{2}+a \right) a}+\frac{d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{b c x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}-\frac{c}{a^{2} x}"," ",0,"1/2/a*x/(b*x^2+a)*d-1/2/(b*x^2+a)/a^2*b*c*x+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-3/2/(a*b)^(1/2)/a^2*b*c*arctan(1/(a*b)^(1/2)*b*x)-1/a^2*c/x","A"
269,1,86,70,0.015000," ","int((d*x^2+c)/x^3/(b*x^2+a)^2,x)","\frac{d}{2 \left(b \,x^{2}+a \right) a}-\frac{b c}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{d \ln \left(x \right)}{a^{2}}-\frac{d \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{2 b c \ln \left(x \right)}{a^{3}}+\frac{b c \ln \left(b \,x^{2}+a \right)}{a^{3}}-\frac{c}{2 a^{2} x^{2}}"," ",0,"1/2/a/(b*x^2+a)*d-1/2/(b*x^2+a)/a^2*b*c-1/2/a^2*ln(b*x^2+a)*d+1/a^3*b*c*ln(b*x^2+a)-1/2/a^2*c/x^2+1/a^2*ln(x)*d-2/a^3*b*c*ln(x)","A"
270,1,110,76,0.013000," ","int((d*x^2+c)/x^4/(b*x^2+a)^2,x)","-\frac{b d x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}+\frac{b^{2} c x}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{5 b^{2} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{3}}-\frac{d}{a^{2} x}+\frac{2 b c}{a^{3} x}-\frac{c}{3 a^{2} x^{3}}"," ",0,"-1/2/a^2*b*x/(b*x^2+a)*d+1/2/a^3*b^2*x/(b*x^2+a)*c-3/2/a^2*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+5/2/a^3*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c-1/3*c/a^2/x^3-1/a^2/x*d+2/a^3/x*b*c","A"
271,1,196,127,0.013000," ","int(x^4*(d*x^2+c)^2/(b*x^2+a)^2,x)","\frac{d^{2} x^{5}}{5 b^{2}}-\frac{2 a \,d^{2} x^{3}}{3 b^{3}}+\frac{2 c d \,x^{3}}{3 b^{2}}+\frac{a^{3} d^{2} x}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{7 a^{3} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{4}}-\frac{a^{2} c d x}{\left(b \,x^{2}+a \right) b^{3}}+\frac{5 a^{2} c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{a \,c^{2} x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a \,c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}+\frac{3 a^{2} d^{2} x}{b^{4}}-\frac{4 a c d x}{b^{3}}+\frac{c^{2} x}{b^{2}}"," ",0,"1/5*d^2*x^5/b^2-2/3/b^3*x^3*a*d^2+2/3/b^2*x^3*c*d+3/b^4*a^2*d^2*x-4/b^3*a*c*d*x+1/b^2*c^2*x+1/2*a^3/b^4*x/(b*x^2+a)*d^2-a^2/b^3*x/(b*x^2+a)*c*d+1/2*a/b^2*x/(b*x^2+a)*c^2-7/2*a^3/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2+5*a^2/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d-3/2*a/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
272,1,142,82,0.012000," ","int(x^3*(d*x^2+c)^2/(b*x^2+a)^2,x)","\frac{d^{2} x^{4}}{4 b^{2}}-\frac{a \,d^{2} x^{2}}{b^{3}}+\frac{c d \,x^{2}}{b^{2}}+\frac{a^{3} d^{2}}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{a^{2} c d}{\left(b \,x^{2}+a \right) b^{3}}+\frac{3 a^{2} d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}+\frac{a \,c^{2}}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{2 a c d \ln \left(b \,x^{2}+a \right)}{b^{3}}+\frac{c^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/4*d^2*x^4/b^2-d^2/b^3*a*x^2+d/b^2*c*x^2+1/2/b^4*a^3/(b*x^2+a)*d^2-1/b^3*a^2/(b*x^2+a)*d*c+1/2/b^2*a/(b*x^2+a)*c^2+3/2/b^4*ln(b*x^2+a)*a^2*d^2-2/b^3*ln(b*x^2+a)*a*d*c+1/2/b^2*ln(b*x^2+a)*c^2","A"
273,1,156,100,0.011000," ","int(x^2*(d*x^2+c)^2/(b*x^2+a)^2,x)","\frac{d^{2} x^{3}}{3 b^{2}}-\frac{a^{2} d^{2} x}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{5 a^{2} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}+\frac{a c d x}{\left(b \,x^{2}+a \right) b^{2}}-\frac{3 a c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{c^{2} x}{2 \left(b \,x^{2}+a \right) b}+\frac{c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}-\frac{2 a \,d^{2} x}{b^{3}}+\frac{2 c d x}{b^{2}}"," ",0,"1/3*d^2*x^3/b^2-2*d^2/b^3*a*x+2*d/b^2*c*x-1/2/b^3*x/(b*x^2+a)*a^2*d^2+1/b^2*x/(b*x^2+a)*a*c*d-1/2/b*x/(b*x^2+a)*c^2+5/2/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^2*d^2-3/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*c*d+1/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
274,1,97,57,0.013000," ","int(x*(d*x^2+c)^2/(b*x^2+a)^2,x)","\frac{d^{2} x^{2}}{2 b^{2}}-\frac{a^{2} d^{2}}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{a c d}{\left(b \,x^{2}+a \right) b^{2}}-\frac{a \,d^{2} \ln \left(b \,x^{2}+a \right)}{b^{3}}-\frac{c^{2}}{2 \left(b \,x^{2}+a \right) b}+\frac{c d \ln \left(b \,x^{2}+a \right)}{b^{2}}"," ",0,"1/2*d^2*x^2/b^2-1/2/b^3/(b*x^2+a)*a^2*d^2+1/b^2/(b*x^2+a)*a*d*c-1/2/b/(b*x^2+a)*c^2-1/b^3*ln(b*x^2+a)*d^2*a+1/b^2*ln(b*x^2+a)*d*c","A"
275,1,129,70,0.010000," ","int((d*x^2+c)^2/(b*x^2+a)^2,x)","\frac{a \,d^{2} x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}+\frac{c^{2} x}{2 \left(b \,x^{2}+a \right) a}+\frac{c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{c d x}{\left(b \,x^{2}+a \right) b}+\frac{c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{d^{2} x}{b^{2}}"," ",0,"d^2*x/b^2+1/2/b^2*x*a/(b*x^2+a)*d^2-1/b*x/(b*x^2+a)*c*d+1/2*x/a/(b*x^2+a)*c^2-3/2/b^2*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2+1/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
276,1,94,63,0.011000," ","int((d*x^2+c)^2/x/(b*x^2+a)^2,x)","\frac{a \,d^{2}}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{c^{2}}{2 \left(b \,x^{2}+a \right) a}+\frac{c^{2} \ln \left(x \right)}{a^{2}}-\frac{c^{2} \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{c d}{\left(b \,x^{2}+a \right) b}+\frac{d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/2*a/b^2/(b*x^2+a)*d^2-1/b/(b*x^2+a)*d*c+1/2/a/(b*x^2+a)*c^2+1/2/b^2*ln(b*x^2+a)*d^2-1/2/a^2*ln(b*x^2+a)*c^2+c^2*ln(x)/a^2","A"
277,1,131,91,0.013000," ","int((d*x^2+c)^2/x^2/(b*x^2+a)^2,x)","\frac{c d x}{\left(b \,x^{2}+a \right) a}+\frac{c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}-\frac{b \,c^{2} x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b \,c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}-\frac{d^{2} x}{2 \left(b \,x^{2}+a \right) b}+\frac{d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}-\frac{c^{2}}{a^{2} x}"," ",0,"-1/2/b*x/(b*x^2+a)*d^2+1/a*x/(b*x^2+a)*c*d-1/2/a^2*b*x/(b*x^2+a)*c^2+1/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2+1/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d-3/2/a^2*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2-c^2/a^2/x","A"
278,1,114,76,0.014000," ","int((d*x^2+c)^2/x^3/(b*x^2+a)^2,x)","\frac{c d}{\left(b \,x^{2}+a \right) a}-\frac{b \,c^{2}}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{2 c d \ln \left(x \right)}{a^{2}}-\frac{c d \ln \left(b \,x^{2}+a \right)}{a^{2}}-\frac{2 b \,c^{2} \ln \left(x \right)}{a^{3}}+\frac{b \,c^{2} \ln \left(b \,x^{2}+a \right)}{a^{3}}-\frac{d^{2}}{2 \left(b \,x^{2}+a \right) b}-\frac{c^{2}}{2 a^{2} x^{2}}"," ",0,"-1/2/b/(b*x^2+a)*d^2+1/a/(b*x^2+a)*d*c-1/2/a^2/(b*x^2+a)*c^2*b-1/a^2*c*ln(b*x^2+a)*d+1/a^3*c^2*ln(b*x^2+a)*b-1/2*c^2/a^2/x^2+2*c/a^2*ln(x)*d-2*c^2/a^3*ln(x)*b","A"
279,1,161,111,0.013000," ","int((d*x^2+c)^2/x^4/(b*x^2+a)^2,x)","\frac{d^{2} x}{2 \left(b \,x^{2}+a \right) a}+\frac{d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{b c d x}{\left(b \,x^{2}+a \right) a^{2}}-\frac{3 b c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{2}}+\frac{b^{2} c^{2} x}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{5 b^{2} c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{3}}-\frac{2 c d}{a^{2} x}+\frac{2 b \,c^{2}}{a^{3} x}-\frac{c^{2}}{3 a^{2} x^{3}}"," ",0,"1/2/a*x/(b*x^2+a)*d^2-1/a^2*x/(b*x^2+a)*b*c*d+1/2/a^3*x/(b*x^2+a)*b^2*c^2+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2-3/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*b*c*d+5/2/a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*b^2*c^2-1/3*c^2/a^2/x^3-2*c/a^2/x*d+2*c^2/a^3/x*b","A"
280,1,302,149,0.011000," ","int(x^4*(d*x^2+c)^3/(b*x^2+a)^2,x)","\frac{d^{3} x^{7}}{7 b^{2}}-\frac{2 a \,d^{3} x^{5}}{5 b^{3}}+\frac{3 c \,d^{2} x^{5}}{5 b^{2}}+\frac{a^{2} d^{3} x^{3}}{b^{4}}-\frac{2 a c \,d^{2} x^{3}}{b^{3}}+\frac{c^{2} d \,x^{3}}{b^{2}}-\frac{a^{4} d^{3} x}{2 \left(b \,x^{2}+a \right) b^{5}}+\frac{9 a^{4} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{5}}+\frac{3 a^{3} c \,d^{2} x}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{21 a^{3} c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{4}}-\frac{3 a^{2} c^{2} d x}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{15 a^{2} c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}+\frac{a \,c^{3} x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a \,c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}-\frac{4 a^{3} d^{3} x}{b^{5}}+\frac{9 a^{2} c \,d^{2} x}{b^{4}}-\frac{6 a \,c^{2} d x}{b^{3}}+\frac{c^{3} x}{b^{2}}"," ",0,"1/7*d^3*x^7/b^2-2/5/b^3*x^5*a*d^3+3/5/b^2*x^5*c*d^2+1/b^4*x^3*a^2*d^3-2/b^3*x^3*a*c*d^2+1/b^2*x^3*c^2*d-4/b^5*a^3*d^3*x+9/b^4*a^2*c*d^2*x-6/b^3*a*c^2*d*x+1/b^2*c^3*x-1/2*a^4/b^5*x/(b*x^2+a)*d^3+3/2*a^3/b^4*x/(b*x^2+a)*c*d^2-3/2*a^2/b^3*x/(b*x^2+a)*c^2*d+1/2*a/b^2*x/(b*x^2+a)*c^3+9/2*a^4/b^5/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3-21/2*a^3/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2+15/2*a^2/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d-3/2*a/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3","B"
281,1,229,107,0.013000," ","int(x^3*(d*x^2+c)^3/(b*x^2+a)^2,x)","\frac{d^{3} x^{6}}{6 b^{2}}-\frac{a \,d^{3} x^{4}}{2 b^{3}}+\frac{3 c \,d^{2} x^{4}}{4 b^{2}}+\frac{3 a^{2} d^{3} x^{2}}{2 b^{4}}-\frac{3 a c \,d^{2} x^{2}}{b^{3}}+\frac{3 c^{2} d \,x^{2}}{2 b^{2}}-\frac{a^{4} d^{3}}{2 \left(b \,x^{2}+a \right) b^{5}}+\frac{3 a^{3} c \,d^{2}}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{2 a^{3} d^{3} \ln \left(b \,x^{2}+a \right)}{b^{5}}-\frac{3 a^{2} c^{2} d}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{9 a^{2} c \,d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}+\frac{a \,c^{3}}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a \,c^{2} d \ln \left(b \,x^{2}+a \right)}{b^{3}}+\frac{c^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/6*d^3*x^6/b^2-1/2*d^3/b^3*x^4*a+3/4*d^2/b^2*x^4*c+3/2*d^3/b^4*x^2*a^2-3*d^2/b^3*x^2*a*c+3/2*d/b^2*x^2*c^2-1/2/b^5*a^4/(b*x^2+a)*d^3+3/2/b^4*a^3/(b*x^2+a)*d^2*c-3/2/b^3*a^2/(b*x^2+a)*d*c^2+1/2/b^2*a/(b*x^2+a)*c^3-2/b^5*ln(b*x^2+a)*a^3*d^3+9/2/b^4*ln(b*x^2+a)*a^2*d^2*c-3/b^3*ln(b*x^2+a)*a*d*c^2+1/2/b^2*ln(b*x^2+a)*c^3","B"
282,1,247,129,0.011000," ","int(x^2*(d*x^2+c)^3/(b*x^2+a)^2,x)","\frac{d^{3} x^{5}}{5 b^{2}}-\frac{2 a \,d^{3} x^{3}}{3 b^{3}}+\frac{c \,d^{2} x^{3}}{b^{2}}+\frac{a^{3} d^{3} x}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{7 a^{3} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{4}}-\frac{3 a^{2} c \,d^{2} x}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{15 a^{2} c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}+\frac{3 a \,c^{2} d x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{9 a \,c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}-\frac{c^{3} x}{2 \left(b \,x^{2}+a \right) b}+\frac{c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}+\frac{3 a^{2} d^{3} x}{b^{4}}-\frac{6 a c \,d^{2} x}{b^{3}}+\frac{3 c^{2} d x}{b^{2}}"," ",0,"1/5*d^3/b^2*x^5-2/3*d^3/b^3*x^3*a+d^2/b^2*x^3*c+3*d^3/b^4*a^2*x-6*d^2/b^3*a*c*x+3*d/b^2*c^2*x+1/2/b^4*x/(b*x^2+a)*a^3*d^3-3/2/b^3*x/(b*x^2+a)*a^2*c*d^2+3/2/b^2*x/(b*x^2+a)*a*c^2*d-1/2/b*x/(b*x^2+a)*c^3-7/2/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^3*d^3+15/2/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^2*c*d^2-9/2/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*c^2*d+1/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3","A"
283,1,168,80,0.012000," ","int(x*(d*x^2+c)^3/(b*x^2+a)^2,x)","\frac{d^{3} x^{4}}{4 b^{2}}-\frac{a \,d^{3} x^{2}}{b^{3}}+\frac{3 c \,d^{2} x^{2}}{2 b^{2}}+\frac{a^{3} d^{3}}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{3 a^{2} c \,d^{2}}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{3 a^{2} d^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}+\frac{3 a \,c^{2} d}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a c \,d^{2} \ln \left(b \,x^{2}+a \right)}{b^{3}}-\frac{c^{3}}{2 \left(b \,x^{2}+a \right) b}+\frac{3 c^{2} d \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/4*d^3*x^4/b^2-d^3/b^3*a*x^2+3/2*d^2/b^2*c*x^2+1/2/b^4/(b*x^2+a)*a^3*d^3-3/2/b^3/(b*x^2+a)*a^2*d^2*c+3/2/b^2/(b*x^2+a)*a*d*c^2-1/2/b/(b*x^2+a)*c^3+3/2/b^4*ln(b*x^2+a)*d^3*a^2-3/b^3*ln(b*x^2+a)*d^2*a*c+3/2/b^2*ln(b*x^2+a)*d*c^2","B"
284,1,205,92,0.009000," ","int((d*x^2+c)^3/(b*x^2+a)^2,x)","\frac{d^{3} x^{3}}{3 b^{2}}-\frac{a^{2} d^{3} x}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{5 a^{2} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}+\frac{3 a c \,d^{2} x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{9 a c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}+\frac{c^{3} x}{2 \left(b \,x^{2}+a \right) a}+\frac{c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{3 c^{2} d x}{2 \left(b \,x^{2}+a \right) b}+\frac{3 c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}-\frac{2 a \,d^{3} x}{b^{3}}+\frac{3 c \,d^{2} x}{b^{2}}"," ",0,"1/3*d^3*x^3/b^2-2*d^3/b^3*a*x+3*d^2/b^2*c*x-1/2/b^3*x*a^2/(b*x^2+a)*d^3+3/2/b^2*x*a/(b*x^2+a)*c*d^2-3/2/b*x/(b*x^2+a)*c^2*d+1/2*x/a/(b*x^2+a)*c^3+5/2/b^3*a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3-9/2/b^2*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2+3/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3","B"
285,1,146,82,0.024000," ","int((d*x^2+c)^3/x/(b*x^2+a)^2,x)","\frac{d^{3} x^{2}}{2 b^{2}}-\frac{a^{2} d^{3}}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{3 a c \,d^{2}}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{a \,d^{3} \ln \left(b \,x^{2}+a \right)}{b^{3}}+\frac{c^{3}}{2 \left(b \,x^{2}+a \right) a}+\frac{c^{3} \ln \left(x \right)}{a^{2}}-\frac{c^{3} \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{3 c^{2} d}{2 \left(b \,x^{2}+a \right) b}+\frac{3 c \,d^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/2*d^3*x^2/b^2-1/2*a^2/b^3/(b*x^2+a)*d^3+3/2*a/b^2/(b*x^2+a)*d^2*c-3/2/b/(b*x^2+a)*d*c^2+1/2/a/(b*x^2+a)*c^3-a/b^3*ln(b*x^2+a)*d^3+3/2/b^2*ln(b*x^2+a)*d^2*c-1/2/a^2*ln(b*x^2+a)*c^3+c^3*ln(x)/a^2","A"
286,1,189,115,0.015000," ","int((d*x^2+c)^3/x^2/(b*x^2+a)^2,x)","\frac{a \,d^{3} x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a \,d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}+\frac{3 c^{2} d x}{2 \left(b \,x^{2}+a \right) a}+\frac{3 c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{b \,c^{3} x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b \,c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}-\frac{3 c \,d^{2} x}{2 \left(b \,x^{2}+a \right) b}+\frac{3 c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}+\frac{d^{3} x}{b^{2}}-\frac{c^{3}}{a^{2} x}"," ",0,"d^3/b^2*x+1/2*a/b^2*x/(b*x^2+a)*d^3-3/2/b*x/(b*x^2+a)*c*d^2+3/2/a*x/(b*x^2+a)*c^2*d-1/2/a^2*b*x/(b*x^2+a)*c^3-3/2*a/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3+3/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2+3/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d-3/2/a^2*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3-c^3/a^2/x","A"
287,1,156,92,0.015000," ","int((d*x^2+c)^3/x^3/(b*x^2+a)^2,x)","\frac{a \,d^{3}}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{3 c^{2} d}{2 \left(b \,x^{2}+a \right) a}-\frac{b \,c^{3}}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{3 c^{2} d \ln \left(x \right)}{a^{2}}-\frac{3 c^{2} d \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{2 b \,c^{3} \ln \left(x \right)}{a^{3}}+\frac{b \,c^{3} \ln \left(b \,x^{2}+a \right)}{a^{3}}-\frac{3 c \,d^{2}}{2 \left(b \,x^{2}+a \right) b}+\frac{d^{3} \ln \left(b \,x^{2}+a \right)}{2 b^{2}}-\frac{c^{3}}{2 a^{2} x^{2}}"," ",0,"1/2*a/b^2/(b*x^2+a)*d^3-3/2/b/(b*x^2+a)*d^2*c+3/2/a/(b*x^2+a)*d*c^2-1/2/a^2*b/(b*x^2+a)*c^3+1/2/b^2*ln(b*x^2+a)*d^3-3/2/a^2*ln(b*x^2+a)*d*c^2+1/a^3*b*ln(b*x^2+a)*c^3-1/2*c^3/a^2/x^2+3*c^2/a^2*ln(x)*d-2*c^3/a^3*ln(x)*b","A"
288,1,209,131,0.017000," ","int((d*x^2+c)^3/x^4/(b*x^2+a)^2,x)","\frac{3 c \,d^{2} x}{2 \left(b \,x^{2}+a \right) a}+\frac{3 c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{3 b \,c^{2} d x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{9 b \,c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}+\frac{b^{2} c^{3} x}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{5 b^{2} c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{3}}-\frac{d^{3} x}{2 \left(b \,x^{2}+a \right) b}+\frac{d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}-\frac{3 c^{2} d}{a^{2} x}+\frac{2 b \,c^{3}}{a^{3} x}-\frac{c^{3}}{3 a^{2} x^{3}}"," ",0,"-1/2/b*x/(b*x^2+a)*d^3+3/2/a*x/(b*x^2+a)*c*d^2-3/2/a^2*b*x/(b*x^2+a)*c^2*d+1/2/a^3*b^2*x/(b*x^2+a)*c^3+1/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3+3/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2-9/2/a^2*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d+5/2/a^3*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3-1/3*c^3/a^2/x^3-3*c^2/a^2/x*d+2*c^3/a^3/x*b","A"
289,1,144,89,0.013000," ","int(x^4/(b*x^2+a)^2/(d*x^2+c),x)","-\frac{a^{2} d x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) b}+\frac{a^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}\, b}+\frac{a c x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)}-\frac{3 a c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}}+\frac{c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right)^{2} \sqrt{c d}}"," ",0,"-1/2*a^2/(a*d-b*c)^2/b*x/(b*x^2+a)*d+1/2*a/(a*d-b*c)^2*x/(b*x^2+a)*c+1/2*a^2/(a*d-b*c)^2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-3/2*a/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c+c^2/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)","A"
290,1,95,68,0.013000," ","int(x^3/(b*x^2+a)^2/(d*x^2+c),x)","-\frac{a^{2} d}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) b}+\frac{a c}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)}+\frac{c \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2}}-\frac{c \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2}}"," ",0,"-1/2/(a*d-b*c)^2*a^2/b/(b*x^2+a)*d+1/2/(a*d-b*c)^2*a/(b*x^2+a)*c+1/2/(a*d-b*c)^2*c*ln(b*x^2+a)-1/2*c/(a*d-b*c)^2*ln(d*x^2+c)","A"
291,1,134,84,0.011000," ","int(x^2/(b*x^2+a)^2/(d*x^2+c),x)","\frac{a d x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)}+\frac{a d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}}-\frac{b c x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)}+\frac{b c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}}-\frac{c d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right)^{2} \sqrt{c d}}"," ",0,"1/2/(a*d-b*c)^2*x/(b*x^2+a)*a*d-1/2/(a*d-b*c)^2*x/(b*x^2+a)*b*c+1/2/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*d+1/2/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*b*c-c*d/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)","A"
292,1,90,64,0.013000," ","int(x/(b*x^2+a)^2/(d*x^2+c),x)","\frac{a d}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)}-\frac{b c}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)}-\frac{d \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2}}+\frac{d \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2}}"," ",0,"1/2/(a*d-b*c)^2/(b*x^2+a)*a*d-1/2*b/(a*d-b*c)^2/(b*x^2+a)*c-1/2/(a*d-b*c)^2*ln(b*x^2+a)*d+1/2*d/(a*d-b*c)^2*ln(d*x^2+c)","A"
293,1,144,88,0.010000," ","int(1/(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} c x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a}+\frac{b^{2} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}\, a}-\frac{b d x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)}-\frac{3 b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}}+\frac{d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right)^{2} \sqrt{c d}}"," ",0,"-1/2*b/(a*d-b*c)^2*x/(b*x^2+a)*d+1/2*b^2/(a*d-b*c)^2*x/a/(b*x^2+a)*c-3/2*b/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+1/2*b^2/(a*d-b*c)^2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c+d^2/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)","A"
294,1,139,93,0.017000," ","int(1/x/(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} c}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a}+\frac{b d \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{2} a}-\frac{b^{2} c \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2} a^{2}}-\frac{b d}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)}-\frac{d^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2} c}+\frac{\ln \left(x \right)}{a^{2} c}"," ",0,"-1/2*b/(a*d-b*c)^2/(b*x^2+a)*d+1/2*b^2/a/(a*d-b*c)^2/(b*x^2+a)*c+b/a/(a*d-b*c)^2*ln(b*x^2+a)*d-1/2*b^2/a^2/(a*d-b*c)^2*ln(b*x^2+a)*c-1/2*d^2/c/(a*d-b*c)^2*ln(d*x^2+c)+ln(x)/a^2/c","A"
295,1,169,122,0.016000," ","int(1/x^2/(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} d x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a}+\frac{5 b^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}\, a}-\frac{b^{3} c x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b^{3} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}\, a^{2}}-\frac{d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right)^{2} \sqrt{c d}\, c}-\frac{1}{a^{2} c x}"," ",0,"1/2*b^2/a/(a*d-b*c)^2*x/(b*x^2+a)*d-1/2*b^3/a^2/(a*d-b*c)^2*x/(b*x^2+a)*c+5/2*b^2/a/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-3/2*b^3/a^2/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c-1/c*d^3/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)-1/a^2/c/x","A"
296,1,170,118,0.020000," ","int(1/x^3/(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} d}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a}-\frac{b^{3} c}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b^{2} d \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2} a^{2}}+\frac{b^{3} c \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{2} a^{3}}+\frac{d^{3} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2} c^{2}}-\frac{d \ln \left(x \right)}{a^{2} c^{2}}-\frac{2 b \ln \left(x \right)}{a^{3} c}-\frac{1}{2 a^{2} c \,x^{2}}"," ",0,"1/2*b^2/a/(a*d-b*c)^2/(b*x^2+a)*d-1/2*b^3/a^2/(a*d-b*c)^2/(b*x^2+a)*c-3/2*b^2/a^2/(a*d-b*c)^2*ln(b*x^2+a)*d+b^3/a^3/(a*d-b*c)^2*ln(b*x^2+a)*c+1/2*d^3/c^2/(a*d-b*c)^2*ln(d*x^2+c)-1/2/a^2/c/x^2-1/a^2/c^2*ln(x)*d-2/a^3/c*ln(x)*b","A"
297,1,191,165,0.017000," ","int(1/x^4/(b*x^2+a)^2/(d*x^2+c),x)","-\frac{b^{3} d x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{2}}-\frac{7 b^{3} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}\, a^{2}}+\frac{b^{4} c x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{3}}+\frac{5 b^{4} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}\, a^{3}}+\frac{d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right)^{2} \sqrt{c d}\, c^{2}}+\frac{d}{a^{2} c^{2} x}+\frac{2 b}{a^{3} c x}-\frac{1}{3 a^{2} c \,x^{3}}"," ",0,"-1/2*b^3/a^2/(a*d-b*c)^2*x/(b*x^2+a)*d+1/2*b^4/a^3/(a*d-b*c)^2*x/(b*x^2+a)*c-7/2*b^3/a^2/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+5/2*b^4/a^3/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c+1/c^2*d^4/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)-1/3/a^2/c/x^3+1/a^2/c^2/x*d+2/a^3/c/x*b","A"
298,1,209,150,0.024000," ","int(1/x^5/(b*x^2+a)^2/(d*x^2+c),x)","-\frac{b^{3} d}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{2}}+\frac{b^{4} c}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{3}}+\frac{2 b^{3} d \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{2} a^{3}}-\frac{3 b^{4} c \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2} a^{4}}-\frac{d^{4} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2} c^{3}}+\frac{d^{2} \ln \left(x \right)}{a^{2} c^{3}}+\frac{2 b d \ln \left(x \right)}{a^{3} c^{2}}+\frac{3 b^{2} \ln \left(x \right)}{a^{4} c}+\frac{d}{2 a^{2} c^{2} x^{2}}+\frac{b}{a^{3} c \,x^{2}}-\frac{1}{4 a^{2} c \,x^{4}}"," ",0,"-1/2*b^3/a^2/(a*d-b*c)^2/(b*x^2+a)*d+1/2*b^4/a^3/(a*d-b*c)^2/(b*x^2+a)*c+2*b^3/a^3/(a*d-b*c)^2*ln(b*x^2+a)*d-3/2*b^4/a^4/(a*d-b*c)^2*ln(b*x^2+a)*c-1/2*d^4/c^3/(a*d-b*c)^2*ln(d*x^2+c)-1/4/a^2/c/x^4+1/2/a^2/c^2/x^2*d+1/a^3/c/x^2*b+1/a^2/c^3*ln(x)*d^2+2/a^3/c^2*ln(x)*b*d+3/a^4/c*ln(x)*b^2","A"
299,1,234,224,0.017000," ","int(1/x^6/(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{4} d x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{3}}+\frac{9 b^{4} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}\, a^{3}}-\frac{b^{5} c x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{4}}-\frac{7 b^{5} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}\, a^{4}}-\frac{d^{5} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right)^{2} \sqrt{c d}\, c^{3}}-\frac{d^{2}}{a^{2} c^{3} x}-\frac{2 b d}{a^{3} c^{2} x}-\frac{3 b^{2}}{a^{4} c x}+\frac{d}{3 a^{2} c^{2} x^{3}}+\frac{2 b}{3 a^{3} c \,x^{3}}-\frac{1}{5 a^{2} c \,x^{5}}"," ",0,"1/2*b^4/a^3/(a*d-b*c)^2*x/(b*x^2+a)*d-1/2*b^5/a^4/(a*d-b*c)^2*x/(b*x^2+a)*c+9/2*b^4/a^3/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-7/2*b^5/a^4/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c-1/c^3*d^5/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)-1/5/a^2/c/x^5+1/3/a^2/c^2/x^3*d+2/3/a^3/c/x^3*b-1/a^2/c^3/x*d^2-2/a^3/c^2/x*b*d-3/a^4/c/x*b^2","A"
300,1,268,199,0.030000," ","int(1/x^7/(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{4} d}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{3}}-\frac{b^{5} c}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a^{4}}-\frac{5 b^{4} d \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{2} a^{4}}+\frac{2 b^{5} c \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{2} a^{5}}+\frac{d^{5} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{2} c^{4}}-\frac{d^{3} \ln \left(x \right)}{a^{2} c^{4}}-\frac{2 b \,d^{2} \ln \left(x \right)}{a^{3} c^{3}}-\frac{3 b^{2} d \ln \left(x \right)}{a^{4} c^{2}}-\frac{4 b^{3} \ln \left(x \right)}{a^{5} c}-\frac{d^{2}}{2 a^{2} c^{3} x^{2}}-\frac{b d}{a^{3} c^{2} x^{2}}-\frac{3 b^{2}}{2 a^{4} c \,x^{2}}+\frac{d}{4 a^{2} c^{2} x^{4}}+\frac{b}{2 a^{3} c \,x^{4}}-\frac{1}{6 a^{2} c \,x^{6}}"," ",0,"1/2*b^4/a^3/(a*d-b*c)^2/(b*x^2+a)*d-1/2*b^5/a^4/(a*d-b*c)^2/(b*x^2+a)*c-5/2*b^4/a^4/(a*d-b*c)^2*ln(b*x^2+a)*d+2*b^5/a^5/(a*d-b*c)^2*ln(b*x^2+a)*c+1/2*d^5/c^4/(a*d-b*c)^2*ln(d*x^2+c)-1/6/a^2/c/x^6+1/4/a^2/c^2/x^4*d+1/2/a^3/c/x^4*b-1/2/a^2/c^3/x^2*d^2-1/a^3/c^2/x^2*b*d-3/2/a^4/c/x^2*b^2-1/a^2/c^4*ln(x)*d^3-2/a^3/c^3*ln(x)*d^2*b-3/a^4/c^2*ln(x)*d*b^2-4/a^5/c*ln(x)*b^3","A"
301,1,222,138,0.016000," ","int(x^4/(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a^{2} d x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{a^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}}-\frac{a b c x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{3 a b c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}}+\frac{a c d x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{3 a c d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}}-\frac{b \,c^{2} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{b \,c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}}"," ",0,"1/2*a^2/(a*d-b*c)^3*x/(b*x^2+a)*d-1/2*a/(a*d-b*c)^3*x/(b*x^2+a)*b*c+1/2*a^2/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+3/2*a/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*b*c+1/2*c/(a*d-b*c)^3*x/(d*x^2+c)*a*d-1/2*c^2/(a*d-b*c)^3*x/(d*x^2+c)*b-3/2*c/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*d-1/2*c^2/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b","A"
302,1,188,99,0.017000," ","int(x^3/(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a^{2} d}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{a b c}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{a c d}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{a d \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{3}}+\frac{a d \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3}}-\frac{b \,c^{2}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{b c \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{3}}+\frac{b c \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3}}"," ",0,"1/2/(a*d-b*c)^3*a^2/(b*x^2+a)*d-1/2*b/(a*d-b*c)^3*a/(b*x^2+a)*c-1/2/(a*d-b*c)^3*ln(b*x^2+a)*a*d-1/2*b/(a*d-b*c)^3*ln(b*x^2+a)*c+1/2*d/(a*d-b*c)^3*ln(d*x^2+c)*a+1/2/(a*d-b*c)^3*ln(d*x^2+c)*b*c+1/2*d/(a*d-b*c)^3*c/(d*x^2+c)*a-1/2/(a*d-b*c)^3*c^2/(d*x^2+c)*b","A"
303,1,222,125,0.019000," ","int(x^2/(b*x^2+a)^2/(d*x^2+c)^2,x)","-\frac{a b d x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{3 a b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}}-\frac{a \,d^{2} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{a \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}}+\frac{b^{2} c x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{b^{2} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}}+\frac{b c d x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{3 b c d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}}"," ",0,"-1/2*b/(a*d-b*c)^3*x/(b*x^2+a)*a*d+1/2*b^2/(a*d-b*c)^3*x/(b*x^2+a)*c-3/2*b/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*d-1/2*b^2/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c-1/2*d^2/(a*d-b*c)^3*x/(d*x^2+c)*a+1/2*d/(a*d-b*c)^3*x/(d*x^2+c)*b*c+1/2*d^2/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a+3/2*d/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b*c","A"
304,1,143,88,0.017000," ","int(x/(b*x^2+a)^2/(d*x^2+c)^2,x)","-\frac{a b d}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{a \,d^{2}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{b^{2} c}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{b c d}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{b d \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{3}}-\frac{b d \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{3}}"," ",0,"-1/2*b/(a*d-b*c)^3/(b*x^2+a)*a*d+1/2*b^2/(a*d-b*c)^3/(b*x^2+a)*c+b/(a*d-b*c)^3*ln(b*x^2+a)*d-d/(a*d-b*c)^3*b*ln(d*x^2+c)-1/2*d^2/(a*d-b*c)^3/(d*x^2+c)*a+1/2*d/(a*d-b*c)^3/(d*x^2+c)*b*c","A"
305,1,238,143,0.015000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a \,d^{3} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}+\frac{a \,d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}\, c}-\frac{b^{3} c x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a}-\frac{b^{3} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}\, a}+\frac{b^{2} d x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{5 b^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}}-\frac{b \,d^{2} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{5 b \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}}"," ",0,"1/2*b^2/(a*d-b*c)^3*x/(b*x^2+a)*d-1/2*b^3/(a*d-b*c)^3*x/a/(b*x^2+a)*c+5/2*b^2/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-1/2*b^3/(a*d-b*c)^3/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c+1/2*d^3/(a*d-b*c)^3/c*x/(d*x^2+c)*a-1/2*d^2/(a*d-b*c)^3*x/(d*x^2+c)*b+1/2*d^3/(a*d-b*c)^3/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a-5/2*d^2/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b","A"
306,1,225,133,0.032000," ","int(1/x/(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a \,d^{3}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}-\frac{a \,d^{3} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3} c^{2}}-\frac{b^{3} c}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a}-\frac{3 b^{2} d \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{3} a}+\frac{b^{3} c \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{3} a^{2}}+\frac{b^{2} d}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{3 b \,d^{2} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{3} c}-\frac{b \,d^{2}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{\ln \left(x \right)}{a^{2} c^{2}}"," ",0,"1/2*b^2/(a*d-b*c)^3/(b*x^2+a)*d-1/2*b^3/a/(a*d-b*c)^3/(b*x^2+a)*c-3/2*b^2/a/(a*d-b*c)^3*ln(b*x^2+a)*d+1/2*b^3/a^2/(a*d-b*c)^3*ln(b*x^2+a)*c-1/2*d^3/c^2/(a*d-b*c)^3*ln(d*x^2+c)*a+3/2*d^2/c/(a*d-b*c)^3*ln(d*x^2+c)*b+1/2*d^3/c/(a*d-b*c)^3/(d*x^2+c)*a-1/2*d^2/(a*d-b*c)^3/(d*x^2+c)*b+ln(x)/a^2/c^2","A"
307,1,261,192,0.019000," ","int(1/x^2/(b*x^2+a)^2/(d*x^2+c)^2,x)","-\frac{a \,d^{4} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{2}}-\frac{3 a \,d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{2}}-\frac{b^{3} d x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a}-\frac{7 b^{3} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}\, a}+\frac{b^{4} c x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a^{2}}+\frac{3 b^{4} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}\, a^{2}}+\frac{b \,d^{3} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}+\frac{7 b \,d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}\, c}-\frac{1}{a^{2} c^{2} x}"," ",0,"-1/2*b^3/a/(a*d-b*c)^3*x/(b*x^2+a)*d+1/2*b^4/a^2/(a*d-b*c)^3*x/(b*x^2+a)*c-7/2*b^3/a/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+3/2*b^4/a^2/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c-1/2*d^4/c^2/(a*d-b*c)^3*x/(d*x^2+c)*a+1/2*d^3/c/(a*d-b*c)^3*x/(d*x^2+c)*b-3/2*d^4/c^2/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a+7/2*d^3/c/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b-1/a^2/c^2/x","A"
308,1,254,150,0.029000," ","int(1/x^3/(b*x^2+a)^2/(d*x^2+c)^2,x)","-\frac{a \,d^{4}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{2}}+\frac{a \,d^{4} \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{3} c^{3}}-\frac{b^{3} d}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a}+\frac{b^{4} c}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a^{2}}+\frac{2 b^{3} d \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{3} a^{2}}-\frac{b^{4} c \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{3} a^{3}}+\frac{b \,d^{3}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}-\frac{2 b \,d^{3} \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{3} c^{2}}-\frac{2 d \ln \left(x \right)}{a^{2} c^{3}}-\frac{2 b \ln \left(x \right)}{a^{3} c^{2}}-\frac{1}{2 a^{2} c^{2} x^{2}}"," ",0,"-1/2*b^3/a/(a*d-b*c)^3/(b*x^2+a)*d+1/2*b^4/a^2/(a*d-b*c)^3/(b*x^2+a)*c+2*b^3/a^2/(a*d-b*c)^3*ln(b*x^2+a)*d-b^4/a^3/(a*d-b*c)^3*ln(b*x^2+a)*c+d^4/c^3/(a*d-b*c)^3*ln(d*x^2+c)*a-2*d^3/c^2/(a*d-b*c)^3*ln(d*x^2+c)*b-1/2*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)*a+1/2*d^3/c/(a*d-b*c)^3/(d*x^2+c)*b-1/2/a^2/c^2/x^2-2/a^2/c^3*ln(x)*d-2/a^3/c^2*ln(x)*b","A"
309,1,285,243,0.023000," ","int(1/x^4/(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a \,d^{5} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{3}}+\frac{5 a \,d^{5} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{3}}+\frac{b^{4} d x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a^{2}}+\frac{9 b^{4} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}\, a^{2}}-\frac{b^{5} c x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a^{3}}-\frac{5 b^{5} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}\, a^{3}}-\frac{b \,d^{4} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{2}}-\frac{9 b \,d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{2}}+\frac{2 d}{a^{2} c^{3} x}+\frac{2 b}{a^{3} c^{2} x}-\frac{1}{3 a^{2} c^{2} x^{3}}"," ",0,"1/2*b^4/a^2/(a*d-b*c)^3*x/(b*x^2+a)*d-1/2*b^5/a^3/(a*d-b*c)^3*x/(b*x^2+a)*c+9/2*b^4/a^2/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-5/2*b^5/a^3/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c+1/2*d^5/c^3/(a*d-b*c)^3*x/(d*x^2+c)*a-1/2*d^4/c^2/(a*d-b*c)^3*x/(d*x^2+c)*b+5/2*d^5/c^3/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a-9/2*d^4/c^2/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b-1/3/a^2/c^2/x^3+2/a^2/c^3/x*d+2/a^3/c^2/x*b","A"
310,1,388,181,0.017000," ","int(x^4/(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{5 a^{2} d^{3} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{a b c \,d^{2} x^{3}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{3 b^{2} c^{2} d \,x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{3 a^{2} c \,d^{2} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{a b \,c^{2} d x}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{5 b^{2} c^{3} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{a^{2} b d x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}-\frac{3 a^{2} b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}}+\frac{3 a^{2} d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}}+\frac{a \,b^{2} c x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}-\frac{3 a \,b^{2} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}}+\frac{9 a b c d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{c d}}+\frac{3 b^{2} c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}}"," ",0,"-1/2*a^2*b/(a*d-b*c)^4*x/(b*x^2+a)*d+1/2*a*b^2/(a*d-b*c)^4*x/(b*x^2+a)*c-3/2*a^2*b/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-3/2*a*b^2/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c-5/8/(a*d-b*c)^4/(d*x^2+c)^2*x^3*a^2*d^3+1/4/(a*d-b*c)^4/(d*x^2+c)^2*x^3*a*b*c*d^2+3/8/(a*d-b*c)^4/(d*x^2+c)^2*x^3*b^2*c^2*d-3/8/(a*d-b*c)^4/(d*x^2+c)^2*a^2*c*d^2*x-1/4/(a*d-b*c)^4/(d*x^2+c)^2*a*b*c^2*d*x+5/8/(a*d-b*c)^4/(d*x^2+c)^2*b^2*c^3*x+3/8/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2*d^2+9/4/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*c*d+3/8/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2*c^2","B"
311,1,283,132,0.019000," ","int(x^3/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{a^{2} c \,d^{2}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{a b \,c^{2} d}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{b^{2} c^{3}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{a^{2} b d}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}-\frac{a^{2} d^{2}}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)}+\frac{a \,b^{2} c}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{a b d \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{4}}-\frac{a b d \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{4}}+\frac{b^{2} c^{2}}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)}+\frac{b^{2} c \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{4}}-\frac{b^{2} c \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{4}}"," ",0,"-1/2*b/(a*d-b*c)^4*a^2/(b*x^2+a)*d+1/2*b^2/(a*d-b*c)^4*a/(b*x^2+a)*c+b/(a*d-b*c)^4*ln(b*x^2+a)*a*d+1/2*b^2/(a*d-b*c)^4*ln(b*x^2+a)*c+1/4*d^2/(a*d-b*c)^4*c/(d*x^2+c)^2*a^2-1/2*d/(a*d-b*c)^4*c^2/(d*x^2+c)^2*a*b+1/4/(a*d-b*c)^4*c^3/(d*x^2+c)^2*b^2-d/(a*d-b*c)^4*b*ln(d*x^2+c)*a-1/2/(a*d-b*c)^4*b^2*ln(d*x^2+c)*c-1/2*d^2/(a*d-b*c)^4/(d*x^2+c)*a^2+1/2/(a*d-b*c)^4/(d*x^2+c)*b^2*c^2","B"
312,1,391,174,0.017000," ","int(x^2/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{a^{2} d^{4} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}+\frac{3 a b \,d^{3} x^{3}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{7 b^{2} c \,d^{2} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{a^{2} d^{3} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{5 a b c \,d^{2} x}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{9 b^{2} c^{2} d x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{a^{2} d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}\, c}+\frac{a \,b^{2} d x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{5 a \,b^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}}-\frac{5 a b \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{c d}}-\frac{b^{3} c x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{b^{3} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}}-\frac{15 b^{2} c d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}}"," ",0,"1/2*b^2/(a*d-b*c)^4*x/(b*x^2+a)*a*d-1/2*b^3/(a*d-b*c)^4*x/(b*x^2+a)*c+5/2*b^2/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*d+1/2*b^3/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c+1/8*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^3*a^2+3/4*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^3*a*b-7/8*d^2/(a*d-b*c)^4/(d*x^2+c)^2*x^3*b^2*c+5/4*d^2/(a*d-b*c)^4/(d*x^2+c)^2*a*b*c*x-9/8*d/(a*d-b*c)^4/(d*x^2+c)^2*b^2*c^2*x-1/8*d^3/(a*d-b*c)^4/(d*x^2+c)^2*a^2*x+1/8*d^3/(a*d-b*c)^4/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-5/4*d^2/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-15/8*d/(a*d-b*c)^4*c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","B"
313,1,234,118,0.020000," ","int(x/(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{a^{2} d^{3}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{a b c \,d^{2}}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{b^{2} c^{2} d}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{a \,b^{2} d}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{a b \,d^{2}}{\left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)}-\frac{b^{3} c}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}-\frac{b^{2} c d}{\left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)}-\frac{3 b^{2} d \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{4}}+\frac{3 b^{2} d \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{4}}"," ",0,"1/2*b^2/(a*d-b*c)^4/(b*x^2+a)*a*d-1/2*b^3/(a*d-b*c)^4/(b*x^2+a)*c-3/2*b^2/(a*d-b*c)^4*ln(b*x^2+a)*d-1/4*d^3/(a*d-b*c)^4/(d*x^2+c)^2*a^2+1/2*d^2/(a*d-b*c)^4/(d*x^2+c)^2*a*b*c-1/4*d/(a*d-b*c)^4/(d*x^2+c)^2*b^2*c^2+3/2*d/(a*d-b*c)^4*ln(d*x^2+c)*b^2+d^2/(a*d-b*c)^4*b/(d*x^2+c)*a-d/(a*d-b*c)^4*b^2/(d*x^2+c)*c","A"
314,1,403,204,0.017000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{3 a^{2} d^{5} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{7 a b \,d^{4} x^{3}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}+\frac{11 b^{2} d^{3} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{5 a^{2} d^{4} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{9 a b \,d^{3} x}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{13 b^{2} c \,d^{2} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{3 a^{2} d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}\, c^{2}}-\frac{7 a b \,d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{c d}\, c}+\frac{b^{4} c x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a}+\frac{b^{4} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}\, a}-\frac{b^{3} d x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}-\frac{7 b^{3} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}}+\frac{35 b^{2} d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}}"," ",0,"-1/2*b^3/(a*d-b*c)^4*x/(b*x^2+a)*d+1/2*b^4/(a*d-b*c)^4/a*x/(b*x^2+a)*c-7/2*b^3/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+1/2*b^4/(a*d-b*c)^4/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c+3/8*d^5/(a*d-b*c)^4/(d*x^2+c)^2/c^2*x^3*a^2-7/4*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^3*a*b+11/8*d^3/(a*d-b*c)^4/(d*x^2+c)^2*b^2*x^3+5/8*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x*a^2-9/4*d^3/(a*d-b*c)^4/(d*x^2+c)^2*a*b*x+13/8*d^2/(a*d-b*c)^4/(d*x^2+c)^2*b^2*c*x+3/8*d^4/(a*d-b*c)^4/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-7/4*d^3/(a*d-b*c)^4/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+35/8*d^2/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","A"
315,1,374,182,0.026000," ","int(1/x/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{a^{2} d^{4}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{a b \,d^{3}}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{b^{2} c \,d^{2}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{a^{2} d^{4}}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right) c^{2}}-\frac{a^{2} d^{4} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{4} c^{3}}-\frac{2 a b \,d^{3}}{\left(a d -b c \right)^{4} \left(d \,x^{2}+c \right) c}+\frac{2 a b \,d^{3} \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{4} c^{2}}+\frac{b^{4} c}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a}+\frac{2 b^{3} d \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{4} a}-\frac{b^{4} c \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{4} a^{2}}-\frac{b^{3} d}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}-\frac{3 b^{2} d^{2} \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{4} c}+\frac{3 b^{2} d^{2}}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)}+\frac{\ln \left(x \right)}{a^{2} c^{3}}"," ",0,"-1/2*b^3/(a*d-b*c)^4/(b*x^2+a)*d+1/2*b^4/a/(a*d-b*c)^4/(b*x^2+a)*c+2*b^3/a/(a*d-b*c)^4*ln(b*x^2+a)*d-1/2*b^4/a^2/(a*d-b*c)^4*ln(b*x^2+a)*c+1/4*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*a^2-1/2*d^3/(a*d-b*c)^4/(d*x^2+c)^2*a*b+1/4*d^2*c/(a*d-b*c)^4/(d*x^2+c)^2*b^2-1/2*d^4/c^3/(a*d-b*c)^4*ln(d*x^2+c)*a^2+2*d^3/c^2/(a*d-b*c)^4*ln(d*x^2+c)*a*b-3*d^2/c/(a*d-b*c)^4*ln(d*x^2+c)*b^2+1/2*d^4/c^2/(a*d-b*c)^4/(d*x^2+c)*a^2-2*d^3/c/(a*d-b*c)^4/(d*x^2+c)*a*b+3/2*d^2/(a*d-b*c)^4/(d*x^2+c)*b^2+ln(x)/a^2/c^3","B"
316,1,428,269,0.023000," ","int(1/x^2/(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{7 a^{2} d^{6} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{11 a b \,d^{5} x^{3}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{15 b^{2} d^{4} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{9 a^{2} d^{5} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{13 a b \,d^{4} x}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{17 b^{2} d^{3} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{15 a^{2} d^{5} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}\, c^{3}}+\frac{27 a b \,d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{c d}\, c^{2}}+\frac{b^{4} d x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a}+\frac{9 b^{4} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}\, a}-\frac{b^{5} c x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b^{5} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}\, a^{2}}-\frac{63 b^{2} d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}\, c}-\frac{1}{a^{2} c^{3} x}"," ",0,"1/2*b^4/a/(a*d-b*c)^4*x/(b*x^2+a)*d-1/2*b^5/a^2/(a*d-b*c)^4*x/(b*x^2+a)*c+9/2*b^4/a/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-3/2*b^5/a^2/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c-7/8*d^6/c^3/(a*d-b*c)^4/(d*x^2+c)^2*x^3*a^2+11/4*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*x^3*a*b-15/8*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*x^3*b^2-9/8*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*a^2*x+13/4*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*a*b*x-17/8*d^3/(a*d-b*c)^4/(d*x^2+c)^2*b^2*x-15/8*d^5/c^3/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+27/4*d^4/c^2/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-63/8*d^3/c/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-1/a^2/c^3/x","A"
317,1,405,205,0.031000," ","int(1/x^3/(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{a^{2} d^{5}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{a b \,d^{4}}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{b^{2} d^{3}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{a^{2} d^{5}}{\left(a d -b c \right)^{4} \left(d \,x^{2}+c \right) c^{3}}+\frac{3 a^{2} d^{5} \ln \left(d \,x^{2}+c \right)}{2 \left(a d -b c \right)^{4} c^{4}}+\frac{3 a b \,d^{4}}{\left(a d -b c \right)^{4} \left(d \,x^{2}+c \right) c^{2}}-\frac{5 a b \,d^{4} \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{4} c^{3}}+\frac{b^{4} d}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a}-\frac{b^{5} c}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a^{2}}-\frac{5 b^{4} d \ln \left(b \,x^{2}+a \right)}{2 \left(a d -b c \right)^{4} a^{2}}+\frac{b^{5} c \ln \left(b \,x^{2}+a \right)}{\left(a d -b c \right)^{4} a^{3}}-\frac{2 b^{2} d^{3}}{\left(a d -b c \right)^{4} \left(d \,x^{2}+c \right) c}+\frac{5 b^{2} d^{3} \ln \left(d \,x^{2}+c \right)}{\left(a d -b c \right)^{4} c^{2}}-\frac{3 d \ln \left(x \right)}{a^{2} c^{4}}-\frac{2 b \ln \left(x \right)}{a^{3} c^{3}}-\frac{1}{2 a^{2} c^{3} x^{2}}"," ",0,"1/2*b^4/a/(a*d-b*c)^4/(b*x^2+a)*d-1/2*b^5/a^2/(a*d-b*c)^4/(b*x^2+a)*c-5/2*b^4/a^2/(a*d-b*c)^4*ln(b*x^2+a)*d+b^5/a^3/(a*d-b*c)^4*ln(b*x^2+a)*c-1/4*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*a^2+1/2*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*a*b-1/4*d^3/(a*d-b*c)^4/(d*x^2+c)^2*b^2+3/2*d^5/c^4/(a*d-b*c)^4*ln(d*x^2+c)*a^2-5*d^4/c^3/(a*d-b*c)^4*ln(d*x^2+c)*a*b+5*d^3/c^2/(a*d-b*c)^4*ln(d*x^2+c)*b^2-d^5/c^3/(a*d-b*c)^4/(d*x^2+c)*a^2+3*d^4/c^2/(a*d-b*c)^4/(d*x^2+c)*a*b-2*d^3/c/(a*d-b*c)^4/(d*x^2+c)*b^2-1/2/a^2/c^3/x^2-3/a^2/c^4*ln(x)*d-2/a^3/c^3*ln(x)*b","A"
318,1,455,347,0.026000," ","int(1/x^4/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{11 a^{2} d^{7} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{4}}-\frac{15 a b \,d^{6} x^{3}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{19 b^{2} d^{5} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{13 a^{2} d^{6} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{3}}-\frac{17 a b \,d^{5} x}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{21 b^{2} d^{4} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}+\frac{35 a^{2} d^{6} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}\, c^{4}}-\frac{55 a b \,d^{5} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{c d}\, c^{3}}-\frac{b^{5} d x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a^{2}}-\frac{11 b^{5} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}\, a^{2}}+\frac{b^{6} c x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a^{3}}+\frac{5 b^{6} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}\, a^{3}}+\frac{99 b^{2} d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}\, c^{2}}+\frac{3 d}{a^{2} c^{4} x}+\frac{2 b}{a^{3} c^{3} x}-\frac{1}{3 a^{2} c^{3} x^{3}}"," ",0,"-1/2*b^5/a^2/(a*d-b*c)^4*x/(b*x^2+a)*d+1/2*b^6/a^3/(a*d-b*c)^4*x/(b*x^2+a)*c-11/2*b^5/a^2/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+5/2*b^6/a^3/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c+11/8*d^7/c^4/(a*d-b*c)^4/(d*x^2+c)^2*x^3*a^2-15/4*d^6/c^3/(a*d-b*c)^4/(d*x^2+c)^2*x^3*a*b+19/8*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*x^3*b^2+13/8*d^6/c^3/(a*d-b*c)^4/(d*x^2+c)^2*a^2*x-17/4*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*a*b*x+21/8*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*b^2*x+35/8*d^6/c^4/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-55/4*d^5/c^3/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+99/8*d^4/c^2/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-1/3/a^2/c^3/x^3+3/a^2/c^4/x*d+2/a^3/c^3/x*b","A"
319,1,474,96,0.025000," ","int(x^m*(b*x^2+a)^3*(B*x^2+A),x)","\frac{\left(B \,b^{3} m^{4} x^{8}+16 B \,b^{3} m^{3} x^{8}+A \,b^{3} m^{4} x^{6}+3 B a \,b^{2} m^{4} x^{6}+86 B \,b^{3} m^{2} x^{8}+18 A \,b^{3} m^{3} x^{6}+54 B a \,b^{2} m^{3} x^{6}+176 B \,b^{3} m \,x^{8}+3 A a \,b^{2} m^{4} x^{4}+104 A \,b^{3} m^{2} x^{6}+3 B \,a^{2} b \,m^{4} x^{4}+312 B a \,b^{2} m^{2} x^{6}+105 B \,b^{3} x^{8}+60 A a \,b^{2} m^{3} x^{4}+222 A \,b^{3} m \,x^{6}+60 B \,a^{2} b \,m^{3} x^{4}+666 B a \,b^{2} m \,x^{6}+3 A \,a^{2} b \,m^{4} x^{2}+390 A a \,b^{2} m^{2} x^{4}+135 A \,b^{3} x^{6}+B \,a^{3} m^{4} x^{2}+390 B \,a^{2} b \,m^{2} x^{4}+405 B a \,b^{2} x^{6}+66 A \,a^{2} b \,m^{3} x^{2}+900 A a \,b^{2} m \,x^{4}+22 B \,a^{3} m^{3} x^{2}+900 B \,a^{2} b m \,x^{4}+A \,a^{3} m^{4}+492 A \,a^{2} b \,m^{2} x^{2}+567 A a \,b^{2} x^{4}+164 B \,a^{3} m^{2} x^{2}+567 B \,a^{2} b \,x^{4}+24 A \,a^{3} m^{3}+1374 A \,a^{2} b m \,x^{2}+458 B \,a^{3} m \,x^{2}+206 A \,a^{3} m^{2}+945 A \,a^{2} b \,x^{2}+315 B \,a^{3} x^{2}+744 A \,a^{3} m +945 A \,a^{3}\right) x^{m +1}}{\left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x^(1+m)*(B*b^3*m^4*x^8+16*B*b^3*m^3*x^8+A*b^3*m^4*x^6+3*B*a*b^2*m^4*x^6+86*B*b^3*m^2*x^8+18*A*b^3*m^3*x^6+54*B*a*b^2*m^3*x^6+176*B*b^3*m*x^8+3*A*a*b^2*m^4*x^4+104*A*b^3*m^2*x^6+3*B*a^2*b*m^4*x^4+312*B*a*b^2*m^2*x^6+105*B*b^3*x^8+60*A*a*b^2*m^3*x^4+222*A*b^3*m*x^6+60*B*a^2*b*m^3*x^4+666*B*a*b^2*m*x^6+3*A*a^2*b*m^4*x^2+390*A*a*b^2*m^2*x^4+135*A*b^3*x^6+B*a^3*m^4*x^2+390*B*a^2*b*m^2*x^4+405*B*a*b^2*x^6+66*A*a^2*b*m^3*x^2+900*A*a*b^2*m*x^4+22*B*a^3*m^3*x^2+900*B*a^2*b*m*x^4+A*a^3*m^4+492*A*a^2*b*m^2*x^2+567*A*a*b^2*x^4+164*B*a^3*m^2*x^2+567*B*a^2*b*x^4+24*A*a^3*m^3+1374*A*a^2*b*m*x^2+458*B*a^3*m*x^2+206*A*a^3*m^2+945*A*a^2*b*x^2+315*B*a^3*x^2+744*A*a^3*m+945*A*a^3)/(9+m)/(7+m)/(5+m)/(3+m)/(1+m)","B"
320,1,262,71,0.007000," ","int(x^m*(b*x^2+a)^2*(B*x^2+A),x)","\frac{\left(B \,b^{2} m^{3} x^{6}+9 B \,b^{2} m^{2} x^{6}+A \,b^{2} m^{3} x^{4}+2 B a b \,m^{3} x^{4}+23 B \,b^{2} m \,x^{6}+11 A \,b^{2} m^{2} x^{4}+22 B a b \,m^{2} x^{4}+15 B \,b^{2} x^{6}+2 A a b \,m^{3} x^{2}+31 A \,b^{2} m \,x^{4}+B \,a^{2} m^{3} x^{2}+62 B a b m \,x^{4}+26 A a b \,m^{2} x^{2}+21 A \,b^{2} x^{4}+13 B \,a^{2} m^{2} x^{2}+42 B a b \,x^{4}+A \,a^{2} m^{3}+94 A a b m \,x^{2}+47 B \,a^{2} m \,x^{2}+15 A \,a^{2} m^{2}+70 A a b \,x^{2}+35 B \,a^{2} x^{2}+71 A \,a^{2} m +105 a^{2} A \right) x^{m +1}}{\left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x^(m+1)*(B*b^2*m^3*x^6+9*B*b^2*m^2*x^6+A*b^2*m^3*x^4+2*B*a*b*m^3*x^4+23*B*b^2*m*x^6+11*A*b^2*m^2*x^4+22*B*a*b*m^2*x^4+15*B*b^2*x^6+2*A*a*b*m^3*x^2+31*A*b^2*m*x^4+B*a^2*m^3*x^2+62*B*a*b*m*x^4+26*A*a*b*m^2*x^2+21*A*b^2*x^4+13*B*a^2*m^2*x^2+42*B*a*b*x^4+A*a^2*m^3+94*A*a*b*m*x^2+47*B*a^2*m*x^2+15*A*a^2*m^2+70*A*a*b*x^2+35*B*a^2*x^2+71*A*a^2*m+105*A*a^2)/(m+7)/(m+5)/(m+3)/(m+1)","B"
321,1,110,45,0.004000," ","int(x^m*(b*x^2+a)*(B*x^2+A),x)","\frac{\left(B b \,m^{2} x^{4}+4 B b m \,x^{4}+A b \,m^{2} x^{2}+B a \,m^{2} x^{2}+3 B b \,x^{4}+6 A b m \,x^{2}+6 B a m \,x^{2}+A a \,m^{2}+5 A b \,x^{2}+5 B a \,x^{2}+8 A a m +15 A a \right) x^{m +1}}{\left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x^(m+1)*(B*b*m^2*x^4+4*B*b*m*x^4+A*b*m^2*x^2+B*a*m^2*x^2+3*B*b*x^4+6*A*b*m*x^2+6*B*a*m*x^2+A*a*m^2+5*A*b*x^2+5*B*a*x^2+8*A*a*m+15*A*a)/(m+5)/(m+3)/(m+1)","B"
322,0,0,64,0.141000," ","int(x^m*(B*x^2+A)/(b*x^2+a),x)","\int \frac{\left(B \,x^{2}+A \right) x^{m}}{b \,x^{2}+a}\, dx"," ",0,"int(x^m*(B*x^2+A)/(b*x^2+a),x)","F"
323,0,0,87,0.046000," ","int(x^m*(B*x^2+A)/(b*x^2+a)^2,x)","\int \frac{\left(B \,x^{2}+A \right) x^{m}}{\left(b \,x^{2}+a \right)^{2}}\, dx"," ",0,"int(x^m*(B*x^2+A)/(b*x^2+a)^2,x)","F"
324,0,0,87,0.063000," ","int(x^m*(B*x^2+A)/(b*x^2+a)^3,x)","\int \frac{\left(B \,x^{2}+A \right) x^{m}}{\left(b \,x^{2}+a \right)^{3}}\, dx"," ",0,"int(x^m*(B*x^2+A)/(b*x^2+a)^3,x)","F"
325,1,976,151,0.011000," ","int(x^m*(b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{\left(b^{2} d^{3} m^{5} x^{10}+25 b^{2} d^{3} m^{4} x^{10}+2 a b \,d^{3} m^{5} x^{8}+3 b^{2} c \,d^{2} m^{5} x^{8}+230 b^{2} d^{3} m^{3} x^{10}+54 a b \,d^{3} m^{4} x^{8}+81 b^{2} c \,d^{2} m^{4} x^{8}+950 b^{2} d^{3} m^{2} x^{10}+a^{2} d^{3} m^{5} x^{6}+6 a b c \,d^{2} m^{5} x^{6}+524 a b \,d^{3} m^{3} x^{8}+3 b^{2} c^{2} d \,m^{5} x^{6}+786 b^{2} c \,d^{2} m^{3} x^{8}+1689 b^{2} d^{3} m \,x^{10}+29 a^{2} d^{3} m^{4} x^{6}+174 a b c \,d^{2} m^{4} x^{6}+2244 a b \,d^{3} m^{2} x^{8}+87 b^{2} c^{2} d \,m^{4} x^{6}+3366 b^{2} c \,d^{2} m^{2} x^{8}+945 b^{2} d^{3} x^{10}+3 a^{2} c \,d^{2} m^{5} x^{4}+302 a^{2} d^{3} m^{3} x^{6}+6 a b \,c^{2} d \,m^{5} x^{4}+1812 a b c \,d^{2} m^{3} x^{6}+4082 a b \,d^{3} m \,x^{8}+b^{2} c^{3} m^{5} x^{4}+906 b^{2} c^{2} d \,m^{3} x^{6}+6123 b^{2} c \,d^{2} m \,x^{8}+93 a^{2} c \,d^{2} m^{4} x^{4}+1366 a^{2} d^{3} m^{2} x^{6}+186 a b \,c^{2} d \,m^{4} x^{4}+8196 a b c \,d^{2} m^{2} x^{6}+2310 a b \,d^{3} x^{8}+31 b^{2} c^{3} m^{4} x^{4}+4098 b^{2} c^{2} d \,m^{2} x^{6}+3465 b^{2} c \,d^{2} x^{8}+3 a^{2} c^{2} d \,m^{5} x^{2}+1050 a^{2} c \,d^{2} m^{3} x^{4}+2577 a^{2} d^{3} m \,x^{6}+2 a b \,c^{3} m^{5} x^{2}+2100 a b \,c^{2} d \,m^{3} x^{4}+15462 a b c \,d^{2} m \,x^{6}+350 b^{2} c^{3} m^{3} x^{4}+7731 b^{2} c^{2} d m \,x^{6}+99 a^{2} c^{2} d \,m^{4} x^{2}+5190 a^{2} c \,d^{2} m^{2} x^{4}+1485 a^{2} d^{3} x^{6}+66 a b \,c^{3} m^{4} x^{2}+10380 a b \,c^{2} d \,m^{2} x^{4}+8910 a b c \,d^{2} x^{6}+1730 b^{2} c^{3} m^{2} x^{4}+4455 b^{2} c^{2} d \,x^{6}+a^{2} c^{3} m^{5}+1218 a^{2} c^{2} d \,m^{3} x^{2}+10467 a^{2} c \,d^{2} m \,x^{4}+812 a b \,c^{3} m^{3} x^{2}+20934 a b \,c^{2} d m \,x^{4}+3489 b^{2} c^{3} m \,x^{4}+35 a^{2} c^{3} m^{4}+6786 a^{2} c^{2} d \,m^{2} x^{2}+6237 a^{2} c \,d^{2} x^{4}+4524 a b \,c^{3} m^{2} x^{2}+12474 a b \,c^{2} d \,x^{4}+2079 b^{2} c^{3} x^{4}+470 a^{2} c^{3} m^{3}+16059 a^{2} c^{2} d m \,x^{2}+10706 a b \,c^{3} m \,x^{2}+3010 a^{2} c^{3} m^{2}+10395 a^{2} c^{2} d \,x^{2}+6930 a b \,c^{3} x^{2}+9129 a^{2} c^{3} m +10395 a^{2} c^{3}\right) x^{m +1}}{\left(m +11\right) \left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x^(m+1)*(b^2*d^3*m^5*x^10+25*b^2*d^3*m^4*x^10+2*a*b*d^3*m^5*x^8+3*b^2*c*d^2*m^5*x^8+230*b^2*d^3*m^3*x^10+54*a*b*d^3*m^4*x^8+81*b^2*c*d^2*m^4*x^8+950*b^2*d^3*m^2*x^10+a^2*d^3*m^5*x^6+6*a*b*c*d^2*m^5*x^6+524*a*b*d^3*m^3*x^8+3*b^2*c^2*d*m^5*x^6+786*b^2*c*d^2*m^3*x^8+1689*b^2*d^3*m*x^10+29*a^2*d^3*m^4*x^6+174*a*b*c*d^2*m^4*x^6+2244*a*b*d^3*m^2*x^8+87*b^2*c^2*d*m^4*x^6+3366*b^2*c*d^2*m^2*x^8+945*b^2*d^3*x^10+3*a^2*c*d^2*m^5*x^4+302*a^2*d^3*m^3*x^6+6*a*b*c^2*d*m^5*x^4+1812*a*b*c*d^2*m^3*x^6+4082*a*b*d^3*m*x^8+b^2*c^3*m^5*x^4+906*b^2*c^2*d*m^3*x^6+6123*b^2*c*d^2*m*x^8+93*a^2*c*d^2*m^4*x^4+1366*a^2*d^3*m^2*x^6+186*a*b*c^2*d*m^4*x^4+8196*a*b*c*d^2*m^2*x^6+2310*a*b*d^3*x^8+31*b^2*c^3*m^4*x^4+4098*b^2*c^2*d*m^2*x^6+3465*b^2*c*d^2*x^8+3*a^2*c^2*d*m^5*x^2+1050*a^2*c*d^2*m^3*x^4+2577*a^2*d^3*m*x^6+2*a*b*c^3*m^5*x^2+2100*a*b*c^2*d*m^3*x^4+15462*a*b*c*d^2*m*x^6+350*b^2*c^3*m^3*x^4+7731*b^2*c^2*d*m*x^6+99*a^2*c^2*d*m^4*x^2+5190*a^2*c*d^2*m^2*x^4+1485*a^2*d^3*x^6+66*a*b*c^3*m^4*x^2+10380*a*b*c^2*d*m^2*x^4+8910*a*b*c*d^2*x^6+1730*b^2*c^3*m^2*x^4+4455*b^2*c^2*d*x^6+a^2*c^3*m^5+1218*a^2*c^2*d*m^3*x^2+10467*a^2*c*d^2*m*x^4+812*a*b*c^3*m^3*x^2+20934*a*b*c^2*d*m*x^4+3489*b^2*c^3*m*x^4+35*a^2*c^3*m^4+6786*a^2*c^2*d*m^2*x^2+6237*a^2*c*d^2*x^4+4524*a*b*c^3*m^2*x^2+12474*a*b*c^2*d*x^4+2079*b^2*c^3*x^4+470*a^2*c^3*m^3+16059*a^2*c^2*d*m*x^2+10706*a*b*c^3*m*x^2+3010*a^2*c^3*m^2+10395*a^2*c^2*d*x^2+6930*a*b*c^3*x^2+9129*a^2*c^3*m+10395*a^2*c^3)/(11+m)/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)","B"
326,1,569,109,0.009000," ","int(x^m*(b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{\left(b^{2} d^{2} m^{4} x^{8}+16 b^{2} d^{2} m^{3} x^{8}+2 a b \,d^{2} m^{4} x^{6}+2 b^{2} c d \,m^{4} x^{6}+86 b^{2} d^{2} m^{2} x^{8}+36 a b \,d^{2} m^{3} x^{6}+36 b^{2} c d \,m^{3} x^{6}+176 b^{2} d^{2} m \,x^{8}+a^{2} d^{2} m^{4} x^{4}+4 a b c d \,m^{4} x^{4}+208 a b \,d^{2} m^{2} x^{6}+b^{2} c^{2} m^{4} x^{4}+208 b^{2} c d \,m^{2} x^{6}+105 b^{2} d^{2} x^{8}+20 a^{2} d^{2} m^{3} x^{4}+80 a b c d \,m^{3} x^{4}+444 a b \,d^{2} m \,x^{6}+20 b^{2} c^{2} m^{3} x^{4}+444 b^{2} c d m \,x^{6}+2 a^{2} c d \,m^{4} x^{2}+130 a^{2} d^{2} m^{2} x^{4}+2 a b \,c^{2} m^{4} x^{2}+520 a b c d \,m^{2} x^{4}+270 a b \,d^{2} x^{6}+130 b^{2} c^{2} m^{2} x^{4}+270 b^{2} c d \,x^{6}+44 a^{2} c d \,m^{3} x^{2}+300 a^{2} d^{2} m \,x^{4}+44 a b \,c^{2} m^{3} x^{2}+1200 a b c d m \,x^{4}+300 b^{2} c^{2} m \,x^{4}+a^{2} c^{2} m^{4}+328 a^{2} c d \,m^{2} x^{2}+189 a^{2} d^{2} x^{4}+328 a b \,c^{2} m^{2} x^{2}+756 a b c d \,x^{4}+189 b^{2} c^{2} x^{4}+24 a^{2} c^{2} m^{3}+916 a^{2} c d m \,x^{2}+916 a b \,c^{2} m \,x^{2}+206 a^{2} c^{2} m^{2}+630 a^{2} c d \,x^{2}+630 a b \,c^{2} x^{2}+744 a^{2} c^{2} m +945 a^{2} c^{2}\right) x^{m +1}}{\left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x^(m+1)*(b^2*d^2*m^4*x^8+16*b^2*d^2*m^3*x^8+2*a*b*d^2*m^4*x^6+2*b^2*c*d*m^4*x^6+86*b^2*d^2*m^2*x^8+36*a*b*d^2*m^3*x^6+36*b^2*c*d*m^3*x^6+176*b^2*d^2*m*x^8+a^2*d^2*m^4*x^4+4*a*b*c*d*m^4*x^4+208*a*b*d^2*m^2*x^6+b^2*c^2*m^4*x^4+208*b^2*c*d*m^2*x^6+105*b^2*d^2*x^8+20*a^2*d^2*m^3*x^4+80*a*b*c*d*m^3*x^4+444*a*b*d^2*m*x^6+20*b^2*c^2*m^3*x^4+444*b^2*c*d*m*x^6+2*a^2*c*d*m^4*x^2+130*a^2*d^2*m^2*x^4+2*a*b*c^2*m^4*x^2+520*a*b*c*d*m^2*x^4+270*a*b*d^2*x^6+130*b^2*c^2*m^2*x^4+270*b^2*c*d*x^6+44*a^2*c*d*m^3*x^2+300*a^2*d^2*m*x^4+44*a*b*c^2*m^3*x^2+1200*a*b*c*d*m*x^4+300*b^2*c^2*m*x^4+a^2*c^2*m^4+328*a^2*c*d*m^2*x^2+189*a^2*d^2*x^4+328*a*b*c^2*m^2*x^2+756*a*b*c*d*x^4+189*b^2*c^2*x^4+24*a^2*c^2*m^3+916*a^2*c*d*m*x^2+916*a*b*c^2*m*x^2+206*a^2*c^2*m^2+630*a^2*c*d*x^2+630*a*b*c^2*x^2+744*a^2*c^2*m+945*a^2*c^2)/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)","B"
327,1,262,71,0.007000," ","int(x^m*(b*x^2+a)^2*(d*x^2+c),x)","\frac{\left(b^{2} d \,m^{3} x^{6}+9 b^{2} d \,m^{2} x^{6}+2 a b d \,m^{3} x^{4}+b^{2} c \,m^{3} x^{4}+23 b^{2} d m \,x^{6}+22 a b d \,m^{2} x^{4}+11 b^{2} c \,m^{2} x^{4}+15 b^{2} d \,x^{6}+a^{2} d \,m^{3} x^{2}+2 a b c \,m^{3} x^{2}+62 a b d m \,x^{4}+31 b^{2} c m \,x^{4}+13 a^{2} d \,m^{2} x^{2}+26 a b c \,m^{2} x^{2}+42 a b d \,x^{4}+21 b^{2} c \,x^{4}+a^{2} c \,m^{3}+47 a^{2} d m \,x^{2}+94 a b c m \,x^{2}+15 a^{2} c \,m^{2}+35 a^{2} d \,x^{2}+70 a b c \,x^{2}+71 a^{2} c m +105 a^{2} c \right) x^{m +1}}{\left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x^(m+1)*(b^2*d*m^3*x^6+9*b^2*d*m^2*x^6+2*a*b*d*m^3*x^4+b^2*c*m^3*x^4+23*b^2*d*m*x^6+22*a*b*d*m^2*x^4+11*b^2*c*m^2*x^4+15*b^2*d*x^6+a^2*d*m^3*x^2+2*a*b*c*m^3*x^2+62*a*b*d*m*x^4+31*b^2*c*m*x^4+13*a^2*d*m^2*x^2+26*a*b*c*m^2*x^2+42*a*b*d*x^4+21*b^2*c*x^4+a^2*c*m^3+47*a^2*d*m*x^2+94*a*b*c*m*x^2+15*a^2*c*m^2+35*a^2*d*x^2+70*a*b*c*x^2+71*a^2*c*m+105*a^2*c)/(m+7)/(m+5)/(m+3)/(m+1)","B"
328,0,0,92,0.062000," ","int(x^m*(b*x^2+a)^2/(d*x^2+c),x)","\int \frac{\left(b \,x^{2}+a \right)^{2} x^{m}}{d \,x^{2}+c}\, dx"," ",0,"int(x^m*(b*x^2+a)^2/(d*x^2+c),x)","F"
329,0,0,114,0.115000," ","int(x^m*(b*x^2+a)^2/(d*x^2+c)^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{2} x^{m}}{\left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^m*(b*x^2+a)^2/(d*x^2+c)^2,x)","F"
330,0,0,163,0.090000," ","int(x^m*(b*x^2+a)^2/(d*x^2+c)^3,x)","\int \frac{\left(b \,x^{2}+a \right)^{2} x^{m}}{\left(d \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(x^m*(b*x^2+a)^2/(d*x^2+c)^3,x)","F"
331,0,0,131,0.058000," ","int(x^m*(d*x^2+c)^3/(b*x^2+a),x)","\int \frac{\left(d \,x^{2}+c \right)^{3} x^{m}}{b \,x^{2}+a}\, dx"," ",0,"int(x^m*(d*x^2+c)^3/(b*x^2+a),x)","F"
332,0,0,92,0.087000," ","int(x^m*(d*x^2+c)^2/(b*x^2+a),x)","\int \frac{\left(d \,x^{2}+c \right)^{2} x^{m}}{b \,x^{2}+a}\, dx"," ",0,"int(x^m*(d*x^2+c)^2/(b*x^2+a),x)","F"
333,0,0,64,0.129000," ","int(x^m*(d*x^2+c)/(b*x^2+a),x)","\int \frac{\left(d \,x^{2}+c \right) x^{m}}{b \,x^{2}+a}\, dx"," ",0,"int(x^m*(d*x^2+c)/(b*x^2+a),x)","F"
334,0,0,98,0.069000," ","int(x^m/(b*x^2+a)/(d*x^2+c),x)","\int \frac{x^{m}}{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(x^m/(b*x^2+a)/(d*x^2+c),x)","F"
335,0,0,148,0.090000," ","int(x^m/(b*x^2+a)^2/(d*x^2+c),x)","\int \frac{x^{m}}{\left(b \,x^{2}+a \right)^{2} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(x^m/(b*x^2+a)^2/(d*x^2+c),x)","F"
336,0,0,224,0.057000," ","int(x^m/(b*x^2+a)^3/(d*x^2+c),x)","\int \frac{x^{m}}{\left(b \,x^{2}+a \right)^{3} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(x^m/(b*x^2+a)^3/(d*x^2+c),x)","F"
337,0,0,191,0.076000," ","int(x^m*(d*x^2+c)^3/(b*x^2+a)^2,x)","\int \frac{\left(d \,x^{2}+c \right)^{3} x^{m}}{\left(b \,x^{2}+a \right)^{2}}\, dx"," ",0,"int(x^m*(d*x^2+c)^3/(b*x^2+a)^2,x)","F"
338,0,0,114,0.059000," ","int(x^m*(d*x^2+c)^2/(b*x^2+a)^2,x)","\int \frac{\left(d \,x^{2}+c \right)^{2} x^{m}}{\left(b \,x^{2}+a \right)^{2}}\, dx"," ",0,"int(x^m*(d*x^2+c)^2/(b*x^2+a)^2,x)","F"
339,0,0,87,0.165000," ","int(x^m*(d*x^2+c)/(b*x^2+a)^2,x)","\int \frac{\left(d \,x^{2}+c \right) x^{m}}{\left(b \,x^{2}+a \right)^{2}}\, dx"," ",0,"int(x^m*(d*x^2+c)/(b*x^2+a)^2,x)","F"
340,0,0,148,0.000000," ","int(1/(b*x^2+a)^2/(d*x^2+c)*x^m,x)","\int \frac{x^{m}}{\left(b \,x^{2}+a \right)^{2} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(1/(b*x^2+a)^2/(d*x^2+c)*x^m,x)","F"
341,0,0,218,0.059000," ","int(x^m/(b*x^2+a)^2/(d*x^2+c)^2,x)","\int \frac{x^{m}}{\left(b \,x^{2}+a \right)^{2} \left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(x^m/(b*x^2+a)^2/(d*x^2+c)^2,x)","F"
342,0,0,311,0.115000," ","int(x^m/(b*x^2+a)^2/(d*x^2+c)^3,x)","\int \frac{x^{m}}{\left(b \,x^{2}+a \right)^{2} \left(d \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(x^m/(b*x^2+a)^2/(d*x^2+c)^3,x)","F"
343,1,32,27,0.006000," ","int(x^(7/2)*(b*x^2+a)*(B*x^2+A),x)","\frac{2 \left(117 B b \,x^{4}+153 A b \,x^{2}+153 B a \,x^{2}+221 A a \right) x^{\frac{9}{2}}}{1989}"," ",0,"2/1989*x^(9/2)*(117*B*b*x^4+153*A*b*x^2+153*B*a*x^2+221*A*a)","A"
344,1,32,27,0.006000," ","int(x^(5/2)*(b*x^2+a)*(B*x^2+A),x)","\frac{2 \left(77 B b \,x^{4}+105 A b \,x^{2}+105 B a \,x^{2}+165 A a \right) x^{\frac{7}{2}}}{1155}"," ",0,"2/1155*x^(7/2)*(77*B*b*x^4+105*A*b*x^2+105*B*a*x^2+165*A*a)","A"
345,1,32,27,0.004000," ","int(x^(3/2)*(b*x^2+a)*(B*x^2+A),x)","\frac{2 \left(45 B b \,x^{4}+65 A b \,x^{2}+65 B a \,x^{2}+117 A a \right) x^{\frac{5}{2}}}{585}"," ",0,"2/585*x^(5/2)*(45*B*b*x^4+65*A*b*x^2+65*B*a*x^2+117*A*a)","A"
346,1,32,27,0.005000," ","int((b*x^2+a)*(B*x^2+A)*x^(1/2),x)","\frac{2 \left(21 B b \,x^{4}+33 A b \,x^{2}+33 B a \,x^{2}+77 A a \right) x^{\frac{3}{2}}}{231}"," ",0,"2/231*x^(3/2)*(21*B*b*x^4+33*A*b*x^2+33*B*a*x^2+77*A*a)","A"
347,1,32,27,0.005000," ","int((b*x^2+a)*(B*x^2+A)/x^(1/2),x)","\frac{2 \left(5 B b \,x^{4}+9 A b \,x^{2}+9 B a \,x^{2}+45 A a \right) \sqrt{x}}{45}"," ",0,"2/45*x^(1/2)*(5*B*b*x^4+9*A*b*x^2+9*B*a*x^2+45*A*a)","A"
348,1,32,27,0.007000," ","int((b*x^2+a)*(B*x^2+A)/x^(3/2),x)","-\frac{2 \left(-3 B b \,x^{4}-7 A b \,x^{2}-7 B a \,x^{2}+21 A a \right)}{21 \sqrt{x}}"," ",0,"-2/21*(-3*B*b*x^4-7*A*b*x^2-7*B*a*x^2+21*A*a)/x^(1/2)","A"
349,1,32,27,0.004000," ","int((b*x^2+a)*(B*x^2+A)/x^(5/2),x)","-\frac{2 \left(-3 B b \,x^{4}-15 A b \,x^{2}-15 B a \,x^{2}+5 A a \right)}{15 x^{\frac{3}{2}}}"," ",0,"-2/15*(-3*B*b*x^4-15*A*b*x^2-15*B*a*x^2+5*A*a)/x^(3/2)","A"
350,1,32,27,0.004000," ","int((b*x^2+a)*(B*x^2+A)/x^(7/2),x)","-\frac{2 \left(-5 B b \,x^{4}+15 A b \,x^{2}+15 B a \,x^{2}+3 A a \right)}{15 x^{\frac{5}{2}}}"," ",0,"-2/15*(-5*B*b*x^4+15*A*b*x^2+15*B*a*x^2+3*A*a)/x^(5/2)","A"
351,1,56,47,0.008000," ","int(x^(7/2)*(b*x^2+a)^2*(B*x^2+A),x)","\frac{2 \left(663 B \,b^{2} x^{6}+819 A \,b^{2} x^{4}+1638 B a b \,x^{4}+2142 A a b \,x^{2}+1071 B \,a^{2} x^{2}+1547 a^{2} A \right) x^{\frac{9}{2}}}{13923}"," ",0,"2/13923*x^(9/2)*(663*B*b^2*x^6+819*A*b^2*x^4+1638*B*a*b*x^4+2142*A*a*b*x^2+1071*B*a^2*x^2+1547*A*a^2)","A"
352,1,56,47,0.006000," ","int(x^(5/2)*(b*x^2+a)^2*(B*x^2+A),x)","\frac{2 \left(1155 B \,b^{2} x^{6}+1463 A \,b^{2} x^{4}+2926 B a b \,x^{4}+3990 A a b \,x^{2}+1995 B \,a^{2} x^{2}+3135 a^{2} A \right) x^{\frac{7}{2}}}{21945}"," ",0,"2/21945*x^(7/2)*(1155*B*b^2*x^6+1463*A*b^2*x^4+2926*B*a*b*x^4+3990*A*a*b*x^2+1995*B*a^2*x^2+3135*A*a^2)","A"
353,1,56,47,0.008000," ","int(x^(3/2)*(b*x^2+a)^2*(B*x^2+A),x)","\frac{2 \left(585 B \,b^{2} x^{6}+765 A \,b^{2} x^{4}+1530 B a b \,x^{4}+2210 A a b \,x^{2}+1105 B \,a^{2} x^{2}+1989 a^{2} A \right) x^{\frac{5}{2}}}{9945}"," ",0,"2/9945*x^(5/2)*(585*B*b^2*x^6+765*A*b^2*x^4+1530*B*a*b*x^4+2210*A*a*b*x^2+1105*B*a^2*x^2+1989*A*a^2)","A"
354,1,56,47,0.005000," ","int((b*x^2+a)^2*(B*x^2+A)*x^(1/2),x)","\frac{2 \left(77 B \,b^{2} x^{6}+105 A \,b^{2} x^{4}+210 B a b \,x^{4}+330 A a b \,x^{2}+165 B \,a^{2} x^{2}+385 a^{2} A \right) x^{\frac{3}{2}}}{1155}"," ",0,"2/1155*x^(3/2)*(77*B*b^2*x^6+105*A*b^2*x^4+210*B*a*b*x^4+330*A*a*b*x^2+165*B*a^2*x^2+385*A*a^2)","A"
355,1,56,47,0.006000," ","int((b*x^2+a)^2*(B*x^2+A)/x^(1/2),x)","\frac{2 \left(45 B \,b^{2} x^{6}+65 A \,b^{2} x^{4}+130 B a b \,x^{4}+234 A a b \,x^{2}+117 B \,a^{2} x^{2}+585 a^{2} A \right) \sqrt{x}}{585}"," ",0,"2/585*x^(1/2)*(45*B*b^2*x^6+65*A*b^2*x^4+130*B*a*b*x^4+234*A*a*b*x^2+117*B*a^2*x^2+585*A*a^2)","A"
356,1,56,47,0.007000," ","int((b*x^2+a)^2*(B*x^2+A)/x^(3/2),x)","-\frac{2 \left(-21 B \,b^{2} x^{6}-33 A \,b^{2} x^{4}-66 B a b \,x^{4}-154 A a b \,x^{2}-77 B \,a^{2} x^{2}+231 a^{2} A \right)}{231 \sqrt{x}}"," ",0,"-2/231*(-21*B*b^2*x^6-33*A*b^2*x^4-66*B*a*b*x^4-154*A*a*b*x^2-77*B*a^2*x^2+231*A*a^2)/x^(1/2)","A"
357,1,56,47,0.006000," ","int((b*x^2+a)^2*(B*x^2+A)/x^(5/2),x)","-\frac{2 \left(-5 B \,b^{2} x^{6}-9 A \,b^{2} x^{4}-18 B a b \,x^{4}-90 A a b \,x^{2}-45 B \,a^{2} x^{2}+15 a^{2} A \right)}{45 x^{\frac{3}{2}}}"," ",0,"-2/45*(-5*B*b^2*x^6-9*A*b^2*x^4-18*B*a*b*x^4-90*A*a*b*x^2-45*B*a^2*x^2+15*A*a^2)/x^(3/2)","A"
358,1,56,47,0.007000," ","int((b*x^2+a)^2*(B*x^2+A)/x^(7/2),x)","-\frac{2 \left(-15 B \,b^{2} x^{6}-35 A \,b^{2} x^{4}-70 B a b \,x^{4}+210 A a b \,x^{2}+105 B \,a^{2} x^{2}+21 a^{2} A \right)}{105 x^{\frac{5}{2}}}"," ",0,"-2/105*(-15*B*b^2*x^6-35*A*b^2*x^4-70*B*a*b*x^4+210*A*a*b*x^2+105*B*a^2*x^2+21*A*a^2)/x^(5/2)","A"
359,1,80,65,0.008000," ","int(x^(7/2)*(b*x^2+a)^3*(B*x^2+A),x)","\frac{2 \left(13923 B \,b^{3} x^{8}+16575 x^{6} A \,b^{3}+49725 B a \,b^{2} x^{6}+61425 x^{4} A a \,b^{2}+61425 x^{4} B \,a^{2} b +80325 A \,a^{2} b \,x^{2}+26775 B \,a^{3} x^{2}+38675 A \,a^{3}\right) x^{\frac{9}{2}}}{348075}"," ",0,"2/348075*x^(9/2)*(13923*B*b^3*x^8+16575*A*b^3*x^6+49725*B*a*b^2*x^6+61425*A*a*b^2*x^4+61425*B*a^2*b*x^4+80325*A*a^2*b*x^2+26775*B*a^3*x^2+38675*A*a^3)","A"
360,1,80,65,0.006000," ","int(x^(5/2)*(b*x^2+a)^3*(B*x^2+A),x)","\frac{2 \left(7315 B \,b^{3} x^{8}+8855 x^{6} A \,b^{3}+26565 B a \,b^{2} x^{6}+33649 x^{4} A a \,b^{2}+33649 x^{4} B \,a^{2} b +45885 A \,a^{2} b \,x^{2}+15295 B \,a^{3} x^{2}+24035 A \,a^{3}\right) x^{\frac{7}{2}}}{168245}"," ",0,"2/168245*x^(7/2)*(7315*B*b^3*x^8+8855*A*b^3*x^6+26565*B*a*b^2*x^6+33649*A*a*b^2*x^4+33649*B*a^2*b*x^4+45885*A*a^2*b*x^2+15295*B*a^3*x^2+24035*A*a^3)","A"
361,1,80,65,0.007000," ","int(x^(3/2)*(b*x^2+a)^3*(B*x^2+A),x)","\frac{2 \left(3315 B \,b^{3} x^{8}+4095 x^{6} A \,b^{3}+12285 B a \,b^{2} x^{6}+16065 x^{4} A a \,b^{2}+16065 x^{4} B \,a^{2} b +23205 A \,a^{2} b \,x^{2}+7735 B \,a^{3} x^{2}+13923 A \,a^{3}\right) x^{\frac{5}{2}}}{69615}"," ",0,"2/69615*x^(5/2)*(3315*B*b^3*x^8+4095*A*b^3*x^6+12285*B*a*b^2*x^6+16065*A*a*b^2*x^4+16065*B*a^2*b*x^4+23205*A*a^2*b*x^2+7735*B*a^3*x^2+13923*A*a^3)","A"
362,1,80,65,0.007000," ","int((b*x^2+a)^3*(B*x^2+A)*x^(1/2),x)","\frac{2 \left(1155 B \,b^{3} x^{8}+1463 x^{6} A \,b^{3}+4389 B a \,b^{2} x^{6}+5985 x^{4} A a \,b^{2}+5985 x^{4} B \,a^{2} b +9405 A \,a^{2} b \,x^{2}+3135 B \,a^{3} x^{2}+7315 A \,a^{3}\right) x^{\frac{3}{2}}}{21945}"," ",0,"2/21945*x^(3/2)*(1155*B*b^3*x^8+1463*A*b^3*x^6+4389*B*a*b^2*x^6+5985*A*a*b^2*x^4+5985*B*a^2*b*x^4+9405*A*a^2*b*x^2+3135*B*a^3*x^2+7315*A*a^3)","A"
363,1,80,65,0.008000," ","int((b*x^2+a)^3*(B*x^2+A)/x^(1/2),x)","\frac{2 \left(195 B \,b^{3} x^{8}+255 x^{6} A \,b^{3}+765 B a \,b^{2} x^{6}+1105 x^{4} A a \,b^{2}+1105 x^{4} B \,a^{2} b +1989 A \,a^{2} b \,x^{2}+663 B \,a^{3} x^{2}+3315 A \,a^{3}\right) \sqrt{x}}{3315}"," ",0,"2/3315*x^(1/2)*(195*B*b^3*x^8+255*A*b^3*x^6+765*B*a*b^2*x^6+1105*A*a*b^2*x^4+1105*B*a^2*b*x^4+1989*A*a^2*b*x^2+663*B*a^3*x^2+3315*A*a^3)","A"
364,1,80,65,0.006000," ","int((b*x^2+a)^3*(B*x^2+A)/x^(3/2),x)","-\frac{2 \left(-77 B \,b^{3} x^{8}-105 x^{6} A \,b^{3}-315 B a \,b^{2} x^{6}-495 x^{4} A a \,b^{2}-495 x^{4} B \,a^{2} b -1155 A \,a^{2} b \,x^{2}-385 B \,a^{3} x^{2}+1155 A \,a^{3}\right)}{1155 \sqrt{x}}"," ",0,"-2/1155*(-77*B*b^3*x^8-105*A*b^3*x^6-315*B*a*b^2*x^6-495*A*a*b^2*x^4-495*B*a^2*b*x^4-1155*A*a^2*b*x^2-385*B*a^3*x^2+1155*A*a^3)/x^(1/2)","A"
365,1,80,65,0.016000," ","int((b*x^2+a)^3*(B*x^2+A)/x^(5/2),x)","-\frac{2 \left(-45 B \,b^{3} x^{8}-65 x^{6} A \,b^{3}-195 B a \,b^{2} x^{6}-351 x^{4} A a \,b^{2}-351 x^{4} B \,a^{2} b -1755 A \,a^{2} b \,x^{2}-585 B \,a^{3} x^{2}+195 A \,a^{3}\right)}{585 x^{\frac{3}{2}}}"," ",0,"-2/585*(-45*B*b^3*x^8-65*A*b^3*x^6-195*B*a*b^2*x^6-351*A*a*b^2*x^4-351*B*a^2*b*x^4-1755*A*a^2*b*x^2-585*B*a^3*x^2+195*A*a^3)/x^(3/2)","A"
366,1,80,65,0.006000," ","int((b*x^2+a)^3*(B*x^2+A)/x^(7/2),x)","-\frac{2 \left(-35 B \,b^{3} x^{8}-55 x^{6} A \,b^{3}-165 B a \,b^{2} x^{6}-385 x^{4} A a \,b^{2}-385 x^{4} B \,a^{2} b +1155 A \,a^{2} b \,x^{2}+385 B \,a^{3} x^{2}+77 A \,a^{3}\right)}{385 x^{\frac{5}{2}}}"," ",0,"-2/385*(-35*B*b^3*x^8-55*A*b^3*x^6-165*B*a*b^2*x^6-385*A*a*b^2*x^4-385*B*a^2*b*x^4+1155*A*a^2*b*x^2+385*B*a^3*x^2+77*A*a^3)/x^(5/2)","A"
367,1,330,199,0.022000," ","int(x^(7/2)*(B*x^2+A)/(b*x^2+a),x)","\frac{2 B \,x^{\frac{9}{2}}}{9 b}+\frac{2 A \,x^{\frac{5}{2}}}{5 b}-\frac{2 B a \,x^{\frac{5}{2}}}{5 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A a \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \,a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \,a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \,a^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b^{3}}-\frac{2 A a \sqrt{x}}{b^{2}}+\frac{2 B \,a^{2} \sqrt{x}}{b^{3}}"," ",0,"2/9*B*x^(9/2)/b+2/5/b*A*x^(5/2)-2/5/b^2*B*x^(5/2)*a-2/b^2*a*A*x^(1/2)+2/b^3*a^2*B*x^(1/2)+1/2*a/b^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*a/b^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4*a/b^2*(a/b)^(1/4)*2^(1/2)*A*ln((x+(a/b)^(1/4)*x^(1/2)*2^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*x^(1/2)*2^(1/2)+(a/b)^(1/2)))-1/2*a^2/b^3*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*a^2/b^3*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/4*a^2/b^3*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*x^(1/2)*2^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*x^(1/2)*2^(1/2)+(a/b)^(1/2)))","A"
368,1,308,182,0.010000," ","int(x^(5/2)*(B*x^2+A)/(b*x^2+a),x)","\frac{2 B \,x^{\frac{7}{2}}}{7 b}+\frac{2 A \,x^{\frac{3}{2}}}{3 b}-\frac{2 B a \,x^{\frac{3}{2}}}{3 b^{2}}-\frac{\sqrt{2}\, A a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, A a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, A a \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{\sqrt{2}\, B \,a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{\sqrt{2}\, B \,a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{\sqrt{2}\, B \,a^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}"," ",0,"2/7*B*x^(7/2)/b+2/3/b*x^(3/2)*A-2/3/b^2*x^(3/2)*B*a-1/4*a/b^2/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*a/b^2/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*a/b^2/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4*a^2/b^3/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*a^2/b^3/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*a^2/b^3/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)","A"
369,1,299,182,0.009000," ","int(x^(3/2)*(B*x^2+A)/(b*x^2+a),x)","\frac{2 B \,x^{\frac{5}{2}}}{5 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B a \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b^{2}}+\frac{2 A \sqrt{x}}{b}-\frac{2 B a \sqrt{x}}{b^{2}}"," ",0,"2/5*B*x^(5/2)/b+2/b*A*x^(1/2)-2/b^2*B*a*x^(1/2)-1/4/b*(a/b)^(1/4)*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2/b*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2/b*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4/b^2*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*a+1/2/b^2*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*a+1/2/b^2*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*a","A"
370,1,280,166,0.010000," ","int((B*x^2+A)*x^(1/2)/(b*x^2+a),x)","\frac{2 B \,x^{\frac{3}{2}}}{3 b}+\frac{\sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, A \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{\sqrt{2}\, B a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, B a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, B a \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}"," ",0,"2/3*B*x^(3/2)/b+1/4/b/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2/b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2/b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/4/b^2/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*a-1/2/b^2/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*a-1/2/b^2/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*a","A"
371,1,277,166,0.007000," ","int((B*x^2+A)/(b*x^2+a)/x^(1/2),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b}+\frac{2 B \sqrt{x}}{b}"," ",0,"2*B*x^(1/2)/b+1/2*(a/b)^(1/4)/a*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4*(a/b)^(1/4)/a*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*(a/b)^(1/4)/a*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2/b*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/4/b*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2/b*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)","A"
372,1,277,166,0.012000," ","int((B*x^2+A)/x^(3/2)/(b*x^2+a),x)","-\frac{\sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, A \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, B \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{2 A}{a \sqrt{x}}"," ",0,"-1/2/a/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/4/a/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2/a/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2/b/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4/b/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2/b/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-2*A/a/x^(1/2)","A"
373,1,280,166,0.010000," ","int((B*x^2+A)/x^(5/2)/(b*x^2+a),x)","-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A b \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a}-\frac{2 A}{3 a \,x^{\frac{3}{2}}}"," ",0,"-1/4/a^2*(a/b)^(1/4)*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b-1/2/a^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b-1/2/a^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b+1/4/a*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2/a*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2/a*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-2/3*A/a/x^(3/2)","A"
374,1,299,182,0.015000," ","int((B*x^2+A)/x^(7/2)/(b*x^2+a),x)","\frac{\sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, A b \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{\sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, B \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{2 A b}{a^{2} \sqrt{x}}-\frac{2 B}{a \sqrt{x}}-\frac{2 A}{5 a \,x^{\frac{5}{2}}}"," ",0,"1/2/a^2/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b+1/2/a^2/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b+1/4/a^2/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b-1/2/a/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2/a/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/4/a/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-2/5*A/a/x^(5/2)+2/a^2/x^(1/2)*A*b-2/a/x^(1/2)*B","A"
375,1,339,226,0.017000," ","int(x^(7/2)*(B*x^2+A)/(b*x^2+a)^2,x)","\frac{2 B \,x^{\frac{5}{2}}}{5 b^{2}}+\frac{A a \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{B \,a^{2} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{3}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{2}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B a \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{3}}+\frac{2 A \sqrt{x}}{b^{2}}-\frac{4 B a \sqrt{x}}{b^{3}}"," ",0,"2/5/b^2*B*x^(5/2)+2/b^2*A*x^(1/2)-4/b^3*B*a*x^(1/2)+1/2*a/b^2*x^(1/2)/(b*x^2+a)*A-1/2*a^2/b^3*x^(1/2)/(b*x^2+a)*B-5/8/b^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-5/8/b^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-5/16/b^2*(a/b)^(1/4)*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+9/8*a/b^3*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+9/8*a/b^3*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+9/16*a/b^3*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))","A"
376,1,317,209,0.017000," ","int(x^(5/2)*(B*x^2+A)/(b*x^2+a)^2,x)","-\frac{A \,x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b}+\frac{B a \,x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{2 B \,x^{\frac{3}{2}}}{3 b^{2}}+\frac{3 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, A \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{7 \sqrt{2}\, B a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{7 \sqrt{2}\, B a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{7 \sqrt{2}\, B a \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}"," ",0,"2/3*B*x^(3/2)/b^2-1/2/b*x^(3/2)/(b*x^2+a)*A+1/2/b^2*x^(3/2)/(b*x^2+a)*B*a-7/16/b^3/(a/b)^(1/4)*2^(1/2)*B*a*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-7/8/b^3/(a/b)^(1/4)*2^(1/2)*B*a*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-7/8/b^3/(a/b)^(1/4)*2^(1/2)*B*a*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/16/b^2/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+3/8/b^2/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+3/8/b^2/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)","A"
377,1,323,204,0.017000," ","int(x^(3/2)*(B*x^2+A)/(b*x^2+a)^2,x)","-\frac{A \sqrt{x}}{2 \left(b \,x^{2}+a \right) b}+\frac{B a \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a b}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{2}}+\frac{2 B \sqrt{x}}{b^{2}}"," ",0,"2*B/b^2*x^(1/2)-1/2/b*x^(1/2)/(b*x^2+a)*A+1/2/b^2*x^(1/2)/(b*x^2+a)*B*a+1/8/b*(a/b)^(1/4)/a*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/8/b*(a/b)^(1/4)/a*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/16/b*(a/b)^(1/4)/a*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-5/8/b^2*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-5/8/b^2*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-5/16/b^2*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))","A"
378,1,305,185,0.017000," ","int((B*x^2+A)*x^(1/2)/(b*x^2+a)^2,x)","\frac{\sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, A \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{3 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, B \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{\left(A b -B a \right) x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a b}"," ",0,"1/2*(A*b-B*a)*x^(3/2)/a/b/(b*x^2+a)+1/8/a/b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/8/a/b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/16/a/b/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+3/8/b^2/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+3/8/b^2/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/16/b^2/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))","A"
379,1,305,185,0.014000," ","int((B*x^2+A)/(b*x^2+a)^2/x^(1/2),x)","\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a b}+\frac{\left(A b -B a \right) \sqrt{x}}{2 \left(b \,x^{2}+a \right) a b}"," ",0,"1/2*(A*b-B*a)*x^(1/2)/a/b/(b*x^2+a)+3/8/a^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+3/8/a^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/16/a^2*(a/b)^(1/4)*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/8/a/b*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/8/a/b*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/16/a/b*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))","A"
380,1,323,208,0.019000," ","int((B*x^2+A)/x^(3/2)/(b*x^2+a)^2,x)","-\frac{A b \,x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{B \,x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a}-\frac{5 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, A \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, B \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}-\frac{2 A}{a^{2} \sqrt{x}}"," ",0,"-1/2/a^2*x^(3/2)/(b*x^2+a)*A*b+1/2/a*x^(3/2)/(b*x^2+a)*B-5/16/a^2/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-5/8/a^2/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-5/8/a^2/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/16/a/b/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/8/a/b/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/8/a/b/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-2*A/a^2/x^(1/2)","A"
381,1,317,209,0.019000," ","int((B*x^2+A)/x^(5/2)/(b*x^2+a)^2,x)","-\frac{A b \sqrt{x}}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{B \sqrt{x}}{2 \left(b \,x^{2}+a \right) a}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{3}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{3}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A b \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a^{2}}-\frac{2 A}{3 a^{2} x^{\frac{3}{2}}}"," ",0,"-1/2/a^2*x^(1/2)/(b*x^2+a)*A*b+1/2/a*x^(1/2)/(b*x^2+a)*B-7/8/a^3*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b-7/16/a^3*(a/b)^(1/4)*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b-7/8/a^3*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b+3/8/a^2*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/16/a^2*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+3/8/a^2*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-2/3*A/a^2/x^(3/2)","A"
382,1,339,226,0.020000," ","int((B*x^2+A)/x^(7/2)/(b*x^2+a)^2,x)","\frac{A \,b^{2} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a^{3}}-\frac{B b \,x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{9 \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{9 \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{9 \sqrt{2}\, A b \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{5 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, B \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{4 A b}{a^{3} \sqrt{x}}-\frac{2 B}{a^{2} \sqrt{x}}-\frac{2 A}{5 a^{2} x^{\frac{5}{2}}}"," ",0,"1/2/a^3*b^2*x^(3/2)/(b*x^2+a)*A-1/2/a^2*b*x^(3/2)/(b*x^2+a)*B+9/16/a^3*b/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+9/8/a^3*b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+9/8/a^3*b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-5/16/a^2/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-5/8/a^2/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-5/8/a^2/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-2/5*A/a^2/x^(5/2)+4/a^3/x^(1/2)*A*b-2/a^2/x^(1/2)*B","A"
383,1,363,232,0.021000," ","int(x^(7/2)*(B*x^2+A)/(b*x^2+a)^3,x)","-\frac{9 A \,x^{\frac{5}{2}}}{16 \left(b \,x^{2}+a \right)^{2} b}+\frac{17 B a \,x^{\frac{5}{2}}}{16 \left(b \,x^{2}+a \right)^{2} b^{2}}-\frac{5 A a \sqrt{x}}{16 \left(b \,x^{2}+a \right)^{2} b^{2}}+\frac{13 B \,a^{2} \sqrt{x}}{16 \left(b \,x^{2}+a \right)^{2} b^{3}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 a \,b^{2}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 a \,b^{2}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 a \,b^{2}}-\frac{45 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 b^{3}}-\frac{45 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 b^{3}}-\frac{45 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 b^{3}}+\frac{2 B \sqrt{x}}{b^{3}}"," ",0,"2*B/b^3*x^(1/2)-9/16/b/(b*x^2+a)^2*x^(5/2)*A+17/16/b^2/(b*x^2+a)^2*x^(5/2)*a*B-5/16/b^2/(b*x^2+a)^2*A*x^(1/2)*a+13/16/b^3/(b*x^2+a)^2*B*x^(1/2)*a^2+5/64/b^2*(a/b)^(1/4)/a*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+5/64/b^2*(a/b)^(1/4)/a*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+5/128/b^2*(a/b)^(1/4)/a*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-45/64/b^3*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-45/64/b^3*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-45/128/b^3*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))","A"
384,1,325,213,0.020000," ","int(x^(5/2)*(B*x^2+A)/(b*x^2+a)^3,x)","\frac{3 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, A \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{21 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{21 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{21 \sqrt{2}\, B \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{\frac{\left(3 A b -11 B a \right) x^{\frac{7}{2}}}{16 a b}-\frac{\left(A b +7 B a \right) x^{\frac{3}{2}}}{16 b^{2}}}{\left(b \,x^{2}+a \right)^{2}}"," ",0,"2*(1/32*(3*A*b-11*B*a)/a/b*x^(7/2)-1/32*(A*b+7*B*a)/b^2*x^(3/2))/(b*x^2+a)^2+3/64/b^2/a/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+3/64/b^2/a/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/128/b^2/a/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+21/64/b^3/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+21/64/b^3/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+21/128/b^3/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))","A"
385,1,334,218,0.017000," ","int(x^(3/2)*(B*x^2+A)/(b*x^2+a)^3,x)","\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 a^{2} b}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 a \,b^{2}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 a \,b^{2}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 a \,b^{2}}+\frac{\frac{\left(A b -9 B a \right) x^{\frac{5}{2}}}{16 a b}-\frac{\left(3 A b +5 B a \right) \sqrt{x}}{16 b^{2}}}{\left(b \,x^{2}+a \right)^{2}}"," ",0,"2*(1/32*(A*b-9*B*a)/a/b*x^(5/2)-1/32*(3*A*b+5*B*a)/b^2*x^(1/2))/(b*x^2+a)^2+3/64/b/a^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/128/b/a^2*(a/b)^(1/4)*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+3/64/b/a^2*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+5/64/b^2/a*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+5/128/b^2/a*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+5/64/b^2/a*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)","A"
386,1,335,218,0.020000," ","int((B*x^2+A)*x^(1/2)/(b*x^2+a)^3,x)","\frac{5 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, A \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{3 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, B \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{\frac{\left(5 A b +3 B a \right) x^{\frac{7}{2}}}{16 a^{2}}+\frac{\left(9 A b -B a \right) x^{\frac{3}{2}}}{16 a b}}{\left(b \,x^{2}+a \right)^{2}}"," ",0,"2*(1/32*(5*A*b+3*B*a)/a^2*x^(7/2)+1/32*(9*A*b-B*a)/a/b*x^(3/2))/(b*x^2+a)^2+5/64/a^2/b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+5/128/a^2/b/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+5/64/a^2/b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+3/64/a/b^2/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/128/a/b^2/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+3/64/a/b^2/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)","A"
387,1,325,213,0.019000," ","int((B*x^2+A)/(b*x^2+a)^3/x^(1/2),x)","\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 a^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 a^{2} b}+\frac{\frac{\left(7 A b +B a \right) x^{\frac{5}{2}}}{16 a^{2}}+\frac{\left(11 A b -3 B a \right) \sqrt{x}}{16 a b}}{\left(b \,x^{2}+a \right)^{2}}"," ",0,"2*(1/32*(7*A*b+B*a)/a^2*x^(5/2)+1/32*(11*A*b-3*B*a)/a/b*x^(1/2))/(b*x^2+a)^2+21/128/a^3*(a/b)^(1/4)*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+21/64/a^3*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+21/64/a^3*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/128/a^2/b*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+3/64/a^2/b*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+3/64/a^2/b*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)","A"
388,1,363,238,0.023000," ","int((B*x^2+A)/x^(3/2)/(b*x^2+a)^3,x)","-\frac{13 A \,b^{2} x^{\frac{7}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a^{3}}+\frac{5 B b \,x^{\frac{7}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a^{2}}-\frac{17 A b \,x^{\frac{3}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{9 B \,x^{\frac{3}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a}-\frac{45 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{45 \sqrt{2}\, A \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{45 \sqrt{2}\, A \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{5 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, B \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}-\frac{2 A}{a^{3} \sqrt{x}}"," ",0,"-13/16/a^3/(b*x^2+a)^2*x^(7/2)*b^2*A+5/16/a^2/(b*x^2+a)^2*x^(7/2)*b*B-17/16/a^2/(b*x^2+a)^2*A*x^(3/2)*b+9/16/a/(b*x^2+a)^2*B*x^(3/2)-45/128/a^3/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-45/64/a^3/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-45/64/a^3/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+5/128/a^2/b/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+5/64/a^2/b/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+5/64/a^2/b/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-2*A/a^3/x^(1/2)","A"
389,1,357,238,0.020000," ","int((B*x^2+A)/x^(5/2)/(b*x^2+a)^3,x)","-\frac{15 A \,b^{2} x^{\frac{5}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a^{3}}+\frac{7 B b \,x^{\frac{5}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a^{2}}-\frac{19 A b \sqrt{x}}{16 \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{11 B \sqrt{x}}{16 \left(b \,x^{2}+a \right)^{2} a}-\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 a^{4}}-\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 a^{4}}-\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, A b \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 a^{4}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, B \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 a^{3}}-\frac{2 A}{3 a^{3} x^{\frac{3}{2}}}"," ",0,"-15/16/a^3/(b*x^2+a)^2*x^(5/2)*b^2*A+7/16/a^2/(b*x^2+a)^2*x^(5/2)*b*B-19/16/a^2/(b*x^2+a)^2*A*x^(1/2)*b+11/16/a/(b*x^2+a)^2*B*x^(1/2)-77/64/a^4*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b-77/128/a^4*(a/b)^(1/4)*2^(1/2)*A*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b-77/64/a^4*(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b+21/64/a^3*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+21/128/a^3*(a/b)^(1/4)*2^(1/2)*B*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+21/64/a^3*(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-2/3*A/a^3/x^(3/2)","A"
390,1,381,255,0.026000," ","int((B*x^2+A)/x^(7/2)/(b*x^2+a)^3,x)","\frac{21 A \,b^{3} x^{\frac{7}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a^{4}}-\frac{13 B \,b^{2} x^{\frac{7}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a^{3}}+\frac{25 A \,b^{2} x^{\frac{3}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a^{3}}-\frac{17 B b \,x^{\frac{3}{2}}}{16 \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{117 \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{4}}+\frac{117 \sqrt{2}\, A b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{4}}+\frac{117 \sqrt{2}\, A b \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{4}}-\frac{45 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{45 \sqrt{2}\, B \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{45 \sqrt{2}\, B \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{6 A b}{a^{4} \sqrt{x}}-\frac{2 B}{a^{3} \sqrt{x}}-\frac{2 A}{5 a^{3} x^{\frac{5}{2}}}"," ",0,"21/16/a^4*b^3/(b*x^2+a)^2*x^(7/2)*A-13/16/a^3*b^2/(b*x^2+a)^2*x^(7/2)*B+25/16/a^3*b^2/(b*x^2+a)^2*A*x^(3/2)-17/16/a^2*b/(b*x^2+a)^2*B*x^(3/2)+117/128/a^4*b/(a/b)^(1/4)*2^(1/2)*A*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+117/64/a^4*b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+117/64/a^4*b/(a/b)^(1/4)*2^(1/2)*A*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-45/128/a^3/(a/b)^(1/4)*2^(1/2)*B*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-45/64/a^3/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-45/64/a^3/(a/b)^(1/4)*2^(1/2)*B*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-2/5*A/a^3/x^(5/2)+6/a^4/x^(1/2)*A*b-2/a^3/x^(1/2)*B","A"
391,1,56,47,0.007000," ","int(x^(7/2)*(b*x^2+a)^2*(d*x^2+c),x)","\frac{2 \left(663 b^{2} d \,x^{6}+1638 a b d \,x^{4}+819 b^{2} c \,x^{4}+1071 a^{2} d \,x^{2}+2142 a b c \,x^{2}+1547 a^{2} c \right) x^{\frac{9}{2}}}{13923}"," ",0,"2/13923*x^(9/2)*(663*b^2*d*x^6+1638*a*b*d*x^4+819*b^2*c*x^4+1071*a^2*d*x^2+2142*a*b*c*x^2+1547*a^2*c)","A"
392,1,56,47,0.006000," ","int(x^(5/2)*(b*x^2+a)^2*(d*x^2+c),x)","\frac{2 \left(1155 b^{2} d \,x^{6}+2926 a b d \,x^{4}+1463 b^{2} c \,x^{4}+1995 a^{2} d \,x^{2}+3990 a b c \,x^{2}+3135 a^{2} c \right) x^{\frac{7}{2}}}{21945}"," ",0,"2/21945*x^(7/2)*(1155*b^2*d*x^6+2926*a*b*d*x^4+1463*b^2*c*x^4+1995*a^2*d*x^2+3990*a*b*c*x^2+3135*a^2*c)","A"
393,1,56,47,0.008000," ","int(x^(3/2)*(b*x^2+a)^2*(d*x^2+c),x)","\frac{2 \left(585 b^{2} d \,x^{6}+1530 a b d \,x^{4}+765 b^{2} c \,x^{4}+1105 a^{2} d \,x^{2}+2210 a b c \,x^{2}+1989 a^{2} c \right) x^{\frac{5}{2}}}{9945}"," ",0,"2/9945*x^(5/2)*(585*b^2*d*x^6+1530*a*b*d*x^4+765*b^2*c*x^4+1105*a^2*d*x^2+2210*a*b*c*x^2+1989*a^2*c)","A"
394,1,56,47,0.007000," ","int((b*x^2+a)^2*(d*x^2+c)*x^(1/2),x)","\frac{2 \left(77 b^{2} d \,x^{6}+210 a b d \,x^{4}+105 b^{2} c \,x^{4}+165 a^{2} d \,x^{2}+330 a b c \,x^{2}+385 a^{2} c \right) x^{\frac{3}{2}}}{1155}"," ",0,"2/1155*x^(3/2)*(77*b^2*d*x^6+210*a*b*d*x^4+105*b^2*c*x^4+165*a^2*d*x^2+330*a*b*c*x^2+385*a^2*c)","A"
395,1,56,47,0.006000," ","int((b*x^2+a)^2*(d*x^2+c)/x^(1/2),x)","\frac{2 \left(45 b^{2} d \,x^{6}+130 a b d \,x^{4}+65 b^{2} c \,x^{4}+117 a^{2} d \,x^{2}+234 a b c \,x^{2}+585 a^{2} c \right) \sqrt{x}}{585}"," ",0,"2/585*x^(1/2)*(45*b^2*d*x^6+130*a*b*d*x^4+65*b^2*c*x^4+117*a^2*d*x^2+234*a*b*c*x^2+585*a^2*c)","A"
396,1,56,47,0.009000," ","int((b*x^2+a)^2*(d*x^2+c)/x^(3/2),x)","-\frac{2 \left(-21 b^{2} d \,x^{6}-66 a b d \,x^{4}-33 b^{2} c \,x^{4}-77 a^{2} d \,x^{2}-154 a b c \,x^{2}+231 a^{2} c \right)}{231 \sqrt{x}}"," ",0,"-2/231*(-21*b^2*d*x^6-66*a*b*d*x^4-33*b^2*c*x^4-77*a^2*d*x^2-154*a*b*c*x^2+231*a^2*c)/x^(1/2)","A"
397,1,56,47,0.006000," ","int((b*x^2+a)^2*(d*x^2+c)/x^(5/2),x)","-\frac{2 \left(-5 b^{2} d \,x^{6}-18 a b d \,x^{4}-9 b^{2} c \,x^{4}-45 a^{2} d \,x^{2}-90 a b c \,x^{2}+15 a^{2} c \right)}{45 x^{\frac{3}{2}}}"," ",0,"-2/45*(-5*b^2*d*x^6-18*a*b*d*x^4-9*b^2*c*x^4-45*a^2*d*x^2-90*a*b*c*x^2+15*a^2*c)/x^(3/2)","A"
398,1,56,47,0.007000," ","int((b*x^2+a)^2*(d*x^2+c)/x^(7/2),x)","-\frac{2 \left(-15 b^{2} d \,x^{6}-70 a b d \,x^{4}-35 b^{2} c \,x^{4}+105 a^{2} d \,x^{2}+210 a b c \,x^{2}+21 a^{2} c \right)}{105 x^{\frac{5}{2}}}"," ",0,"-2/105*(-15*b^2*d*x^6-70*a*b*d*x^4-35*b^2*c*x^4+105*a^2*d*x^2+210*a*b*c*x^2+21*a^2*c)/x^(5/2)","A"
399,1,97,77,0.007000," ","int(x^(7/2)*(b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{2 \left(13923 b^{2} d^{2} x^{8}+33150 a b \,d^{2} x^{6}+33150 b^{2} c d \,x^{6}+20475 a^{2} d^{2} x^{4}+81900 a b c d \,x^{4}+20475 b^{2} c^{2} x^{4}+53550 a^{2} c d \,x^{2}+53550 a b \,c^{2} x^{2}+38675 a^{2} c^{2}\right) x^{\frac{9}{2}}}{348075}"," ",0,"2/348075*x^(9/2)*(13923*b^2*d^2*x^8+33150*a*b*d^2*x^6+33150*b^2*c*d*x^6+20475*a^2*d^2*x^4+81900*a*b*c*d*x^4+20475*b^2*c^2*x^4+53550*a^2*c*d*x^2+53550*a*b*c^2*x^2+38675*a^2*c^2)","A"
400,1,97,77,0.007000," ","int(x^(5/2)*(b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{2 \left(21945 b^{2} d^{2} x^{8}+53130 a b \,d^{2} x^{6}+53130 b^{2} c d \,x^{6}+33649 a^{2} d^{2} x^{4}+134596 a b c d \,x^{4}+33649 b^{2} c^{2} x^{4}+91770 a^{2} c d \,x^{2}+91770 a b \,c^{2} x^{2}+72105 a^{2} c^{2}\right) x^{\frac{7}{2}}}{504735}"," ",0,"2/504735*x^(7/2)*(21945*b^2*d^2*x^8+53130*a*b*d^2*x^6+53130*b^2*c*d*x^6+33649*a^2*d^2*x^4+134596*a*b*c*d*x^4+33649*b^2*c^2*x^4+91770*a^2*c*d*x^2+91770*a*b*c^2*x^2+72105*a^2*c^2)","A"
401,1,97,77,0.007000," ","int(x^(3/2)*(b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{2 \left(3315 b^{2} d^{2} x^{8}+8190 a b \,d^{2} x^{6}+8190 b^{2} c d \,x^{6}+5355 a^{2} d^{2} x^{4}+21420 a b c d \,x^{4}+5355 b^{2} c^{2} x^{4}+15470 a^{2} c d \,x^{2}+15470 a b \,c^{2} x^{2}+13923 a^{2} c^{2}\right) x^{\frac{5}{2}}}{69615}"," ",0,"2/69615*x^(5/2)*(3315*b^2*d^2*x^8+8190*a*b*d^2*x^6+8190*b^2*c*d*x^6+5355*a^2*d^2*x^4+21420*a*b*c*d*x^4+5355*b^2*c^2*x^4+15470*a^2*c*d*x^2+15470*a*b*c^2*x^2+13923*a^2*c^2)","A"
402,1,97,77,0.008000," ","int((b*x^2+a)^2*(d*x^2+c)^2*x^(1/2),x)","\frac{2 \left(1155 b^{2} d^{2} x^{8}+2926 a b \,d^{2} x^{6}+2926 b^{2} c d \,x^{6}+1995 a^{2} d^{2} x^{4}+7980 a b c d \,x^{4}+1995 b^{2} c^{2} x^{4}+6270 a^{2} c d \,x^{2}+6270 a b \,c^{2} x^{2}+7315 a^{2} c^{2}\right) x^{\frac{3}{2}}}{21945}"," ",0,"2/21945*x^(3/2)*(1155*b^2*d^2*x^8+2926*a*b*d^2*x^6+2926*b^2*c*d*x^6+1995*a^2*d^2*x^4+7980*a*b*c*d*x^4+1995*b^2*c^2*x^4+6270*a^2*c*d*x^2+6270*a*b*c^2*x^2+7315*a^2*c^2)","A"
403,1,97,77,0.008000," ","int((b*x^2+a)^2*(d*x^2+c)^2/x^(1/2),x)","\frac{2 \left(585 b^{2} d^{2} x^{8}+1530 a b \,d^{2} x^{6}+1530 b^{2} c d \,x^{6}+1105 a^{2} d^{2} x^{4}+4420 a b c d \,x^{4}+1105 b^{2} c^{2} x^{4}+3978 a^{2} c d \,x^{2}+3978 a b \,c^{2} x^{2}+9945 a^{2} c^{2}\right) \sqrt{x}}{9945}"," ",0,"2/9945*x^(1/2)*(585*b^2*d^2*x^8+1530*a*b*d^2*x^6+1530*b^2*c*d*x^6+1105*a^2*d^2*x^4+4420*a*b*c*d*x^4+1105*b^2*c^2*x^4+3978*a^2*c*d*x^2+3978*a*b*c^2*x^2+9945*a^2*c^2)","A"
404,1,97,77,0.007000," ","int((b*x^2+a)^2*(d*x^2+c)^2/x^(3/2),x)","-\frac{2 \left(-77 b^{2} d^{2} x^{8}-210 a b \,d^{2} x^{6}-210 b^{2} c d \,x^{6}-165 a^{2} d^{2} x^{4}-660 a b c d \,x^{4}-165 b^{2} c^{2} x^{4}-770 a^{2} c d \,x^{2}-770 a b \,c^{2} x^{2}+1155 a^{2} c^{2}\right)}{1155 \sqrt{x}}"," ",0,"-2/1155*(-77*b^2*d^2*x^8-210*a*b*d^2*x^6-210*b^2*c*d*x^6-165*a^2*d^2*x^4-660*a*b*c*d*x^4-165*b^2*c^2*x^4-770*a^2*c*d*x^2-770*a*b*c^2*x^2+1155*a^2*c^2)/x^(1/2)","A"
405,1,97,77,0.009000," ","int((b*x^2+a)^2*(d*x^2+c)^2/x^(5/2),x)","-\frac{2 \left(-45 b^{2} d^{2} x^{8}-130 a b \,d^{2} x^{6}-130 b^{2} c d \,x^{6}-117 a^{2} d^{2} x^{4}-468 a b c d \,x^{4}-117 b^{2} c^{2} x^{4}-1170 a^{2} c d \,x^{2}-1170 a b \,c^{2} x^{2}+195 a^{2} c^{2}\right)}{585 x^{\frac{3}{2}}}"," ",0,"-2/585*(-45*b^2*d^2*x^8-130*a*b*d^2*x^6-130*b^2*c*d*x^6-117*a^2*d^2*x^4-468*a*b*c*d*x^4-117*b^2*c^2*x^4-1170*a^2*c*d*x^2-1170*a*b*c^2*x^2+195*a^2*c^2)/x^(3/2)","A"
406,1,97,77,0.007000," ","int((b*x^2+a)^2*(d*x^2+c)^2/x^(7/2),x)","-\frac{2 \left(-105 b^{2} d^{2} x^{8}-330 a b \,d^{2} x^{6}-330 b^{2} c d \,x^{6}-385 a^{2} d^{2} x^{4}-1540 a b c d \,x^{4}-385 b^{2} c^{2} x^{4}+2310 a^{2} c d \,x^{2}+2310 a b \,c^{2} x^{2}+231 a^{2} c^{2}\right)}{1155 x^{\frac{5}{2}}}"," ",0,"-2/1155*(-105*b^2*d^2*x^8-330*a*b*d^2*x^6-330*b^2*c*d*x^6-385*a^2*d^2*x^4-1540*a*b*c*d*x^4-385*b^2*c^2*x^4+2310*a^2*c*d*x^2+2310*a*b*c^2*x^2+231*a^2*c^2)/x^(5/2)","A"
407,1,138,115,0.008000," ","int(x^(7/2)*(b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{2 \left(348075 b^{2} d^{3} x^{10}+807534 a b \,d^{3} x^{8}+1211301 b^{2} c \,d^{2} x^{8}+480675 a^{2} d^{3} x^{6}+2884050 a b c \,d^{2} x^{6}+1442025 b^{2} c^{2} d \,x^{6}+1781325 a^{2} c \,d^{2} x^{4}+3562650 a b \,c^{2} d \,x^{4}+593775 b^{2} c^{3} x^{4}+2329425 a^{2} c^{2} d \,x^{2}+1552950 a b \,c^{3} x^{2}+1121575 a^{2} c^{3}\right) x^{\frac{9}{2}}}{10094175}"," ",0,"2/10094175*x^(9/2)*(348075*b^2*d^3*x^10+807534*a*b*d^3*x^8+1211301*b^2*c*d^2*x^8+480675*a^2*d^3*x^6+2884050*a*b*c*d^2*x^6+1442025*b^2*c^2*d*x^6+1781325*a^2*c*d^2*x^4+3562650*a*b*c^2*d*x^4+593775*b^2*c^3*x^4+2329425*a^2*c^2*d*x^2+1552950*a*b*c^3*x^2+1121575*a^2*c^3)","A"
408,1,138,115,0.007000," ","int(x^(5/2)*(b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{2 \left(168245 b^{2} d^{3} x^{10}+395010 a b \,d^{3} x^{8}+592515 b^{2} c \,d^{2} x^{8}+239085 a^{2} d^{3} x^{6}+1434510 a b c \,d^{2} x^{6}+717255 b^{2} c^{2} d \,x^{6}+908523 a^{2} c \,d^{2} x^{4}+1817046 a b \,c^{2} d \,x^{4}+302841 b^{2} c^{3} x^{4}+1238895 a^{2} c^{2} d \,x^{2}+825930 a b \,c^{3} x^{2}+648945 a^{2} c^{3}\right) x^{\frac{7}{2}}}{4542615}"," ",0,"2/4542615*x^(7/2)*(168245*b^2*d^3*x^10+395010*a*b*d^3*x^8+592515*b^2*c*d^2*x^8+239085*a^2*d^3*x^6+1434510*a*b*c*d^2*x^6+717255*b^2*c^2*d*x^6+908523*a^2*c*d^2*x^4+1817046*a*b*c^2*d*x^4+302841*b^2*c^3*x^4+1238895*a^2*c^2*d*x^2+825930*a*b*c^3*x^2+648945*a^2*c^3)","A"
409,1,138,115,0.010000," ","int(x^(3/2)*(b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{2 \left(13923 b^{2} d^{3} x^{10}+33150 a b \,d^{3} x^{8}+49725 b^{2} c \,d^{2} x^{8}+20475 a^{2} d^{3} x^{6}+122850 a b c \,d^{2} x^{6}+61425 b^{2} c^{2} d \,x^{6}+80325 a^{2} c \,d^{2} x^{4}+160650 a b \,c^{2} d \,x^{4}+26775 b^{2} c^{3} x^{4}+116025 a^{2} c^{2} d \,x^{2}+77350 a b \,c^{3} x^{2}+69615 a^{2} c^{3}\right) x^{\frac{5}{2}}}{348075}"," ",0,"2/348075*x^(5/2)*(13923*b^2*d^3*x^10+33150*a*b*d^3*x^8+49725*b^2*c*d^2*x^8+20475*a^2*d^3*x^6+122850*a*b*c*d^2*x^6+61425*b^2*c^2*d*x^6+80325*a^2*c*d^2*x^4+160650*a*b*c^2*d*x^4+26775*b^2*c^3*x^4+116025*a^2*c^2*d*x^2+77350*a*b*c^3*x^2+69615*a^2*c^3)","A"
410,1,138,115,0.009000," ","int((b*x^2+a)^2*(d*x^2+c)^3*x^(1/2),x)","\frac{2 \left(21945 b^{2} d^{3} x^{10}+53130 a b \,d^{3} x^{8}+79695 b^{2} c \,d^{2} x^{8}+33649 a^{2} d^{3} x^{6}+201894 a b c \,d^{2} x^{6}+100947 b^{2} c^{2} d \,x^{6}+137655 a^{2} c \,d^{2} x^{4}+275310 a b \,c^{2} d \,x^{4}+45885 b^{2} c^{3} x^{4}+216315 a^{2} c^{2} d \,x^{2}+144210 a b \,c^{3} x^{2}+168245 a^{2} c^{3}\right) x^{\frac{3}{2}}}{504735}"," ",0,"2/504735*x^(3/2)*(21945*b^2*d^3*x^10+53130*a*b*d^3*x^8+79695*b^2*c*d^2*x^8+33649*a^2*d^3*x^6+201894*a*b*c*d^2*x^6+100947*b^2*c^2*d*x^6+137655*a^2*c*d^2*x^4+275310*a*b*c^2*d*x^4+45885*b^2*c^3*x^4+216315*a^2*c^2*d*x^2+144210*a*b*c^3*x^2+168245*a^2*c^3)","A"
411,1,138,115,0.009000," ","int((b*x^2+a)^2*(d*x^2+c)^3/x^(1/2),x)","\frac{2 \left(3315 b^{2} d^{3} x^{10}+8190 a b \,d^{3} x^{8}+12285 b^{2} c \,d^{2} x^{8}+5355 a^{2} d^{3} x^{6}+32130 a b c \,d^{2} x^{6}+16065 b^{2} c^{2} d \,x^{6}+23205 a^{2} c \,d^{2} x^{4}+46410 a b \,c^{2} d \,x^{4}+7735 b^{2} c^{3} x^{4}+41769 a^{2} c^{2} d \,x^{2}+27846 a b \,c^{3} x^{2}+69615 a^{2} c^{3}\right) \sqrt{x}}{69615}"," ",0,"2/69615*x^(1/2)*(3315*b^2*d^3*x^10+8190*a*b*d^3*x^8+12285*b^2*c*d^2*x^8+5355*a^2*d^3*x^6+32130*a*b*c*d^2*x^6+16065*b^2*c^2*d*x^6+23205*a^2*c*d^2*x^4+46410*a*b*c^2*d*x^4+7735*b^2*c^3*x^4+41769*a^2*c^2*d*x^2+27846*a*b*c^3*x^2+69615*a^2*c^3)","A"
412,1,138,115,0.007000," ","int((b*x^2+a)^2*(d*x^2+c)^3/x^(3/2),x)","-\frac{2 \left(-1155 b^{2} d^{3} x^{10}-2926 a b \,d^{3} x^{8}-4389 b^{2} c \,d^{2} x^{8}-1995 a^{2} d^{3} x^{6}-11970 a b c \,d^{2} x^{6}-5985 b^{2} c^{2} d \,x^{6}-9405 a^{2} c \,d^{2} x^{4}-18810 a b \,c^{2} d \,x^{4}-3135 b^{2} c^{3} x^{4}-21945 a^{2} c^{2} d \,x^{2}-14630 a b \,c^{3} x^{2}+21945 a^{2} c^{3}\right)}{21945 \sqrt{x}}"," ",0,"-2/21945*(-1155*b^2*d^3*x^10-2926*a*b*d^3*x^8-4389*b^2*c*d^2*x^8-1995*a^2*d^3*x^6-11970*a*b*c*d^2*x^6-5985*b^2*c^2*d*x^6-9405*a^2*c*d^2*x^4-18810*a*b*c^2*d*x^4-3135*b^2*c^3*x^4-21945*a^2*c^2*d*x^2-14630*a*b*c^3*x^2+21945*a^2*c^3)/x^(1/2)","A"
413,1,138,115,0.010000," ","int((b*x^2+a)^2*(d*x^2+c)^3/x^(5/2),x)","-\frac{2 \left(-585 b^{2} d^{3} x^{10}-1530 a b \,d^{3} x^{8}-2295 b^{2} c \,d^{2} x^{8}-1105 a^{2} d^{3} x^{6}-6630 a b c \,d^{2} x^{6}-3315 b^{2} c^{2} d \,x^{6}-5967 a^{2} c \,d^{2} x^{4}-11934 a b \,c^{2} d \,x^{4}-1989 b^{2} c^{3} x^{4}-29835 a^{2} c^{2} d \,x^{2}-19890 a b \,c^{3} x^{2}+3315 a^{2} c^{3}\right)}{9945 x^{\frac{3}{2}}}"," ",0,"-2/9945*(-585*b^2*d^3*x^10-1530*a*b*d^3*x^8-2295*b^2*c*d^2*x^8-1105*a^2*d^3*x^6-6630*a*b*c*d^2*x^6-3315*b^2*c^2*d*x^6-5967*a^2*c*d^2*x^4-11934*a*b*c^2*d*x^4-1989*b^2*c^3*x^4-29835*a^2*c^2*d*x^2-19890*a*b*c^3*x^2+3315*a^2*c^3)/x^(3/2)","A"
414,1,138,115,0.009000," ","int((b*x^2+a)^2*(d*x^2+c)^3/x^(7/2),x)","-\frac{2 \left(-77 b^{2} d^{3} x^{10}-210 a b \,d^{3} x^{8}-315 b^{2} c \,d^{2} x^{8}-165 a^{2} d^{3} x^{6}-990 a b c \,d^{2} x^{6}-495 b^{2} c^{2} d \,x^{6}-1155 a^{2} c \,d^{2} x^{4}-2310 a b \,c^{2} d \,x^{4}-385 b^{2} c^{3} x^{4}+3465 a^{2} c^{2} d \,x^{2}+2310 a b \,c^{3} x^{2}+231 a^{2} c^{3}\right)}{1155 x^{\frac{5}{2}}}"," ",0,"-2/1155*(-77*b^2*d^3*x^10-210*a*b*d^3*x^8-315*b^2*c*d^2*x^8-165*a^2*d^3*x^6-990*a*b*c*d^2*x^6-495*b^2*c^2*d*x^6-1155*a^2*c*d^2*x^4-2310*a*b*c^2*d*x^4-385*b^2*c^3*x^4+3465*a^2*c^2*d*x^2+2310*a*b*c^3*x^2+231*a^2*c^3)/x^(5/2)","A"
415,1,545,230,0.020000," ","int(x^(7/2)*(b*x^2+a)^2/(d*x^2+c),x)","\frac{2 b^{2} x^{\frac{13}{2}}}{13 d}+\frac{4 a b \,x^{\frac{9}{2}}}{9 d}-\frac{2 b^{2} c \,x^{\frac{9}{2}}}{9 d^{2}}+\frac{2 a^{2} x^{\frac{5}{2}}}{5 d}-\frac{4 a b c \,x^{\frac{5}{2}}}{5 d^{2}}+\frac{2 b^{2} c^{2} x^{\frac{5}{2}}}{5 d^{3}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 d^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 d^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 d^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{d^{3}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{d^{3}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,c^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{2 d^{3}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 d^{4}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 d^{4}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{3} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 d^{4}}-\frac{2 a^{2} c \sqrt{x}}{d^{2}}+\frac{4 a b \,c^{2} \sqrt{x}}{d^{3}}-\frac{2 b^{2} c^{3} \sqrt{x}}{d^{4}}"," ",0,"2/13*b^2*x^(13/2)/d+4/9/d*x^(9/2)*a*b-2/9/d^2*x^(9/2)*b^2*c+2/5/d*x^(5/2)*a^2-4/5/d^2*x^(5/2)*a*b*c+2/5/d^3*x^(5/2)*b^2*c^2-2/d^2*a^2*c*x^(1/2)+4/d^3*a*b*c^2*x^(1/2)-2/d^4*b^2*c^3*x^(1/2)+1/4*c/d^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*x^(1/2)*2^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*x^(1/2)*2^(1/2)+(c/d)^(1/2)))*a^2-1/2*c^2/d^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*x^(1/2)*2^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*x^(1/2)*2^(1/2)+(c/d)^(1/2)))*a*b+1/4*c^3/d^4*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*x^(1/2)*2^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*x^(1/2)*2^(1/2)+(c/d)^(1/2)))*b^2+1/2*c/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-c^2/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+1/2*c^3/d^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+1/2*c/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-c^2/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+1/2*c^3/d^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2","B"
416,1,504,211,0.012000," ","int(x^(5/2)*(b*x^2+a)^2/(d*x^2+c),x)","\frac{2 b^{2} x^{\frac{11}{2}}}{11 d}+\frac{4 a b \,x^{\frac{7}{2}}}{7 d}-\frac{2 b^{2} c \,x^{\frac{7}{2}}}{7 d^{2}}+\frac{2 a^{2} x^{\frac{3}{2}}}{3 d}-\frac{4 a b c \,x^{\frac{3}{2}}}{3 d^{2}}+\frac{2 b^{2} c^{2} x^{\frac{3}{2}}}{3 d^{3}}-\frac{\sqrt{2}\, a^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{\sqrt{2}\, a^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{\sqrt{2}\, a^{2} c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{\sqrt{2}\, a b \,c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{\left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{\sqrt{2}\, a b \,c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{\left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{\sqrt{2}\, a b \,c^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}-\frac{\sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{4}}-\frac{\sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{4}}-\frac{\sqrt{2}\, b^{2} c^{3} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{4}}"," ",0,"2/11*b^2*x^(11/2)/d+4/7/d*x^(7/2)*a*b-2/7/d^2*x^(7/2)*b^2*c+2/3/d*x^(3/2)*a^2-4/3/d^2*x^(3/2)*a*b*c+2/3/d^3*x^(3/2)*b^2*c^2-1/2*c/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+c^2/d^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-1/2*c^3/d^4/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-1/2*c/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+c^2/d^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-1/2*c^3/d^4/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-1/4*c/d^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+1/2*c^2/d^3/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-1/4*c^3/d^4/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","B"
417,1,495,211,0.013000," ","int(x^(3/2)*(b*x^2+a)^2/(d*x^2+c),x)","\frac{2 b^{2} x^{\frac{9}{2}}}{9 d}+\frac{4 a b \,x^{\frac{5}{2}}}{5 d}-\frac{2 b^{2} c \,x^{\frac{5}{2}}}{5 d^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{d^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{d^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{2 d^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 d^{3}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 d^{3}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 d^{3}}+\frac{2 a^{2} \sqrt{x}}{d}-\frac{4 a b c \sqrt{x}}{d^{2}}+\frac{2 b^{2} c^{2} \sqrt{x}}{d^{3}}"," ",0,"2/9*b^2*x^(9/2)/d+4/5/d*x^(5/2)*a*b-2/5/d^2*x^(5/2)*b^2*c+2/d*a^2*x^(1/2)-4/d^2*a*b*c*x^(1/2)+2/d^3*b^2*c^2*x^(1/2)-1/4/d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+1/2/d^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b*c-1/4/d^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2*c^2-1/2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+1/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b*c-1/2/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2*c^2-1/2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+1/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b*c-1/2/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2*c^2","B"
418,1,461,193,0.011000," ","int((b*x^2+a)^2*x^(1/2)/(d*x^2+c),x)","\frac{2 b^{2} x^{\frac{7}{2}}}{7 d}+\frac{4 a b \,x^{\frac{3}{2}}}{3 d}-\frac{2 b^{2} c \,x^{\frac{3}{2}}}{3 d^{2}}+\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{\sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{\sqrt{2}\, a b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{\left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{\sqrt{2}\, a b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{\left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{\sqrt{2}\, a b c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{\sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{\sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{\sqrt{2}\, b^{2} c^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}"," ",0,"2/7*b^2*x^(7/2)/d+4/3*b/d*x^(3/2)*a-2/3*b^2/d^2*x^(3/2)*c+1/4/d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-1/2/d^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b*c+1/4/d^3/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2*c^2+1/2/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-1/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b*c+1/2/d^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2*c^2+1/2/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-1/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b*c+1/2/d^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2*c^2","B"
419,1,452,193,0.011000," ","int((b*x^2+a)^2/(d*x^2+c)/x^(1/2),x)","\frac{2 b^{2} x^{\frac{5}{2}}}{5 d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 c}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{2 d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 d^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 d^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 d^{2}}+\frac{4 a b \sqrt{x}}{d}-\frac{2 b^{2} c \sqrt{x}}{d^{2}}"," ",0,"2/5*b^2*x^(5/2)/d+4*b/d*a*x^(1/2)-2*b^2/d^2*c*x^(1/2)+1/4*(c/d)^(1/4)/c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-1/2/d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+1/4/d^2*(c/d)^(1/4)*c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+1/2*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-1/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+1/2/d^2*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+1/2*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-1/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+1/2/d^2*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2","B"
420,1,439,187,0.015000," ","int((b*x^2+a)^2/x^(3/2)/(d*x^2+c),x)","\frac{2 b^{2} x^{\frac{3}{2}}}{3 d}-\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{\left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{\sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{\left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{\sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{\sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{\sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{\sqrt{2}\, b^{2} c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{2 a^{2}}{c \sqrt{x}}"," ",0,"2/3*b^2*x^(3/2)/d-1/2/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+1/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-1/2*c/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-1/4/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+1/2/d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-1/4*c/d^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2-1/2/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+1/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-1/2*c/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-2*a^2/c/x^(1/2)","B"
421,1,439,187,0.014000," ","int((b*x^2+a)^2/x^(5/2)/(d*x^2+c),x)","-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 c^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 c^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 c^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{2 c}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 d}+\frac{2 b^{2} \sqrt{x}}{d}-\frac{2 a^{2}}{3 c \,x^{\frac{3}{2}}}"," ",0,"2*b^2*x^(1/2)/d-1/2/c^2*d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+1/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-1/2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-1/4/c^2*d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+1/2/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-1/4/d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2-1/2/c^2*d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+1/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-1/2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-2/3*a^2/c/x^(3/2)","B"
422,1,452,194,0.017000," ","int((b*x^2+a)^2/x^(7/2)/(d*x^2+c),x)","\frac{\sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{\sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{\sqrt{2}\, a^{2} d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{\left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{\left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{\sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{2 a^{2} d}{c^{2} \sqrt{x}}-\frac{4 a b}{c \sqrt{x}}-\frac{2 a^{2}}{5 c \,x^{\frac{5}{2}}}"," ",0,"1/4/c^2*d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-1/2/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+1/4/d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+1/2/c^2*d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-1/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+1/2/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+1/2/c^2*d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-1/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+1/2/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-2/5*a^2/c/x^(5/2)+2*a^2/c^2/x^(1/2)*d-4*a/c/x^(1/2)*b","B"
423,1,461,194,0.015000," ","int((b*x^2+a)^2/x^(9/2)/(d*x^2+c),x)","\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 c^{3}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 c^{3}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 c^{3}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{c^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{c^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{2 c^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 c}+\frac{2 a^{2} d}{3 c^{2} x^{\frac{3}{2}}}-\frac{4 a b}{3 c \,x^{\frac{3}{2}}}-\frac{2 a^{2}}{7 c \,x^{\frac{7}{2}}}"," ",0,"1/2/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2*d^2-1/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b*d+1/2/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+1/4/c^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2*d^2-1/2/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b*d+1/4/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+1/2/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2*d^2-1/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b*d+1/2/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-2/7*a^2/c/x^(7/2)+2/3*a^2/c^2/x^(3/2)*d-4/3*a/c/x^(3/2)*b","B"
424,1,495,211,0.016000," ","int((d*x^2+c)^2/x^(11/2)/(b*x^2+a),x)","-\frac{\sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, b c d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{\sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{\sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{\sqrt{2}\, b^{2} c^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{2 d^{2}}{a \sqrt{x}}+\frac{4 b c d}{a^{2} \sqrt{x}}-\frac{2 b^{2} c^{2}}{a^{3} \sqrt{x}}-\frac{4 c d}{5 a \,x^{\frac{5}{2}}}+\frac{2 b \,c^{2}}{5 a^{2} x^{\frac{5}{2}}}-\frac{2 c^{2}}{9 a \,x^{\frac{9}{2}}}"," ",0,"-1/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^2+1/a^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b*c*d-1/2/a^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b^2*c^2-1/4/a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^2+1/2/a^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b*c*d-1/4/a^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b^2*c^2-1/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^2+1/a^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b*c*d-1/2/a^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b^2*c^2-2/9*c^2/a/x^(9/2)-2/a/x^(1/2)*d^2+4/a^2/x^(1/2)*b*c*d-2/a^3/x^(1/2)*b^2*c^2-4/5*c/a/x^(5/2)*d+2/5*c^2/a^2/x^(5/2)*b","B"
425,1,563,287,0.021000," ","int(x^(7/2)*(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{2 b^{2} x^{\frac{9}{2}}}{9 d^{2}}+\frac{4 a b \,x^{\frac{5}{2}}}{5 d^{2}}-\frac{4 b^{2} c \,x^{\frac{5}{2}}}{5 d^{3}}+\frac{a^{2} c \sqrt{x}}{2 \left(d \,x^{2}+c \right) d^{2}}-\frac{a b \,c^{2} \sqrt{x}}{\left(d \,x^{2}+c \right) d^{3}}+\frac{b^{2} c^{3} \sqrt{x}}{2 \left(d \,x^{2}+c \right) d^{4}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 d^{2}}+\frac{9 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 d^{3}}+\frac{9 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 d^{3}}+\frac{9 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{8 d^{3}}-\frac{13 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 d^{4}}-\frac{13 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 d^{4}}-\frac{13 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 d^{4}}+\frac{2 a^{2} \sqrt{x}}{d^{2}}-\frac{8 a b c \sqrt{x}}{d^{3}}+\frac{6 b^{2} c^{2} \sqrt{x}}{d^{4}}"," ",0,"2/9*b^2*x^(9/2)/d^2+4/5/d^2*x^(5/2)*a*b-4/5/d^3*x^(5/2)*b^2*c+2/d^2*a^2*x^(1/2)-8/d^3*a*b*c*x^(1/2)+6/d^4*b^2*c^2*x^(1/2)+1/2*c/d^2*x^(1/2)/(d*x^2+c)*a^2-c^2/d^3*x^(1/2)/(d*x^2+c)*a*b+1/2*c^3/d^4*x^(1/2)/(d*x^2+c)*b^2-5/8/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+9/4*c/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-13/8*c^2/d^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-5/16/d^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+9/8*c/d^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-13/16*c^2/d^4*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2-5/8/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+9/4*c/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-13/8*c^2/d^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2","A"
426,1,523,262,0.020000," ","int(x^(5/2)*(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{2 b^{2} x^{\frac{7}{2}}}{7 d^{2}}-\frac{a^{2} x^{\frac{3}{2}}}{2 \left(d \,x^{2}+c \right) d}+\frac{a b c \,x^{\frac{3}{2}}}{\left(d \,x^{2}+c \right) d^{2}}-\frac{b^{2} c^{2} x^{\frac{3}{2}}}{2 \left(d \,x^{2}+c \right) d^{3}}+\frac{4 a b \,x^{\frac{3}{2}}}{3 d^{2}}-\frac{4 b^{2} c \,x^{\frac{3}{2}}}{3 d^{3}}+\frac{3 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{3 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{3 \sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{7 \sqrt{2}\, a b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}-\frac{7 \sqrt{2}\, a b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}-\frac{7 \sqrt{2}\, a b c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{11 \sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{4}}+\frac{11 \sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{4}}+\frac{11 \sqrt{2}\, b^{2} c^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{4}}"," ",0,"2/7*b^2*x^(7/2)/d^2+4/3*b/d^2*x^(3/2)*a-4/3*b^2/d^3*x^(3/2)*c-1/2/d*x^(3/2)/(d*x^2+c)*a^2+1/d^2*x^(3/2)/(d*x^2+c)*a*b*c-1/2/d^3*x^(3/2)/(d*x^2+c)*b^2*c^2-7/8/d^3/(c/d)^(1/4)*2^(1/2)*a*b*c*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-7/4/d^3/(c/d)^(1/4)*2^(1/2)*a*b*c*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-7/4/d^3/(c/d)^(1/4)*2^(1/2)*a*b*c*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+11/16/d^4/(c/d)^(1/4)*2^(1/2)*b^2*c^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+11/8/d^4/(c/d)^(1/4)*2^(1/2)*b^2*c^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+11/8/d^4/(c/d)^(1/4)*2^(1/2)*b^2*c^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+3/16/d^2/(c/d)^(1/4)*2^(1/2)*a^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+3/8/d^2/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+3/8/d^2/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)","A"
427,1,523,262,0.020000," ","int(x^(3/2)*(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{2 b^{2} x^{\frac{5}{2}}}{5 d^{2}}-\frac{a^{2} \sqrt{x}}{2 \left(d \,x^{2}+c \right) d}+\frac{a b c \sqrt{x}}{\left(d \,x^{2}+c \right) d^{2}}-\frac{b^{2} c^{2} \sqrt{x}}{2 \left(d \,x^{2}+c \right) d^{3}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 c d}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{8 d^{2}}+\frac{9 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 d^{3}}+\frac{9 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 d^{3}}+\frac{9 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 d^{3}}+\frac{4 a b \sqrt{x}}{d^{2}}-\frac{4 b^{2} c \sqrt{x}}{d^{3}}"," ",0,"2/5*b^2*x^(5/2)/d^2+4*b/d^2*a*x^(1/2)-4*b^2/d^3*c*x^(1/2)-1/2/d*x^(1/2)/(d*x^2+c)*a^2+1/d^2*x^(1/2)/(d*x^2+c)*a*b*c-1/2/d^3*x^(1/2)/(d*x^2+c)*b^2*c^2+1/8/d*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-5/4/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+9/8/d^3*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+1/16/d*(c/d)^(1/4)/c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-5/8/d^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+9/16/d^3*(c/d)^(1/4)*c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+1/8/d*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-5/4/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+9/8/d^3*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2","A"
428,1,499,230,0.019000," ","int((b*x^2+a)^2*x^(1/2)/(d*x^2+c)^2,x)","\frac{a^{2} x^{\frac{3}{2}}}{2 \left(d \,x^{2}+c \right) c}-\frac{a b \,x^{\frac{3}{2}}}{\left(d \,x^{2}+c \right) d}+\frac{b^{2} c \,x^{\frac{3}{2}}}{2 \left(d \,x^{2}+c \right) d^{2}}+\frac{2 b^{2} x^{\frac{3}{2}}}{3 d^{2}}+\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c d}+\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c d}+\frac{\sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(\frac{c}{d}\right)^{\frac{1}{4}} c d}+\frac{3 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{3 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{3 \sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{7 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}-\frac{7 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}-\frac{7 \sqrt{2}\, b^{2} c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}"," ",0,"2/3*b^2*x^(3/2)/d^2+1/2/c*x^(3/2)/(d*x^2+c)*a^2-1/d*x^(3/2)/(d*x^2+c)*a*b+1/2/d^2*c*x^(3/2)/(d*x^2+c)*b^2+1/16/d/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+3/8/d^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-7/16/d^3*c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+1/8/d/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+3/4/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-7/8/d^3*c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+1/8/d/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+3/4/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-7/8/d^3*c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2","B"
429,1,496,234,0.018000," ","int((b*x^2+a)^2/(d*x^2+c)^2/x^(1/2),x)","\frac{a^{2} \sqrt{x}}{2 \left(d \,x^{2}+c \right) c}-\frac{a b \sqrt{x}}{\left(d \,x^{2}+c \right) d}+\frac{b^{2} c \sqrt{x}}{2 \left(d \,x^{2}+c \right) d^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 c^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{8 c d}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 d^{2}}+\frac{2 b^{2} \sqrt{x}}{d^{2}}"," ",0,"2*b^2*x^(1/2)/d^2+1/2/c*x^(1/2)/(d*x^2+c)*a^2-1/d*x^(1/2)/(d*x^2+c)*a*b+1/2/d^2*c*x^(1/2)/(d*x^2+c)*b^2+3/16/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+1/8/d/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-5/16/d^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+3/8/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+1/4/d/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-5/8/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+3/8/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+1/4/d/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-5/8/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2","B"
430,1,495,255,0.020000," ","int((b*x^2+a)^2/x^(3/2)/(d*x^2+c)^2,x)","-\frac{a^{2} d \,x^{\frac{3}{2}}}{2 \left(d \,x^{2}+c \right) c^{2}}+\frac{a b \,x^{\frac{3}{2}}}{\left(d \,x^{2}+c \right) c}-\frac{b^{2} x^{\frac{3}{2}}}{2 \left(d \,x^{2}+c \right) d}-\frac{5 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{5 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{5 \sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{\sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} c d}+\frac{\sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} c d}+\frac{\sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c d}+\frac{3 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{3 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{3 \sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}-\frac{2 a^{2}}{c^{2} \sqrt{x}}"," ",0,"-1/2/c^2*d*x^(3/2)/(d*x^2+c)*a^2+1/c*x^(3/2)/(d*x^2+c)*a*b-1/2/d*x^(3/2)/(d*x^2+c)*b^2-5/8/c^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+1/4/c/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+3/8/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-5/16/c^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+1/8/c/d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+3/16/d^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2-5/8/c^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+1/4/c/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+3/8/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-2*a^2/c^2/x^(1/2)","A"
431,1,498,252,0.021000," ","int((b*x^2+a)^2/x^(5/2)/(d*x^2+c)^2,x)","-\frac{a^{2} d \sqrt{x}}{2 \left(d \,x^{2}+c \right) c^{2}}+\frac{a b \sqrt{x}}{\left(d \,x^{2}+c \right) c}-\frac{b^{2} \sqrt{x}}{2 \left(d \,x^{2}+c \right) d}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 c^{3}}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 c^{3}}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 c^{3}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{8 c^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 c d}-\frac{2 a^{2}}{3 c^{2} x^{\frac{3}{2}}}"," ",0,"-1/2/c^2*d*x^(1/2)/(d*x^2+c)*a^2+1/c*x^(1/2)/(d*x^2+c)*a*b-1/2/d*x^(1/2)/(d*x^2+c)*b^2-7/8/c^3*d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+3/4/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+1/8/c/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-7/8/c^3*d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+3/4/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+1/8/c/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-7/16/c^3*d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+3/8/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+1/16/c/d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2-2/3*a^2/c^2/x^(3/2)","A"
432,1,524,279,0.025000," ","int((b*x^2+a)^2/x^(7/2)/(d*x^2+c)^2,x)","\frac{a^{2} d^{2} x^{\frac{3}{2}}}{2 \left(d \,x^{2}+c \right) c^{3}}-\frac{a b d \,x^{\frac{3}{2}}}{\left(d \,x^{2}+c \right) c^{2}}+\frac{b^{2} x^{\frac{3}{2}}}{2 \left(d \,x^{2}+c \right) c}+\frac{9 \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{9 \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{9 \sqrt{2}\, a^{2} d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{5 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{5 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{5 \sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c d}+\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{c}{d}\right)^{\frac{1}{4}} c d}+\frac{\sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(\frac{c}{d}\right)^{\frac{1}{4}} c d}+\frac{4 a^{2} d}{c^{3} \sqrt{x}}-\frac{4 a b}{c^{2} \sqrt{x}}-\frac{2 a^{2}}{5 c^{2} x^{\frac{5}{2}}}"," ",0,"1/2/c^3*x^(3/2)/(d*x^2+c)*a^2*d^2-1/c^2*x^(3/2)/(d*x^2+c)*a*b*d+1/2/c*x^(3/2)/(d*x^2+c)*b^2+9/16/c^3*d/(c/d)^(1/4)*2^(1/2)*a^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+9/8/c^3*d/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+9/8/c^3*d/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-5/8/c^2/(c/d)^(1/4)*2^(1/2)*a*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-5/4/c^2/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-5/4/c^2/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+1/16/c/d/(c/d)^(1/4)*2^(1/2)*b^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+1/8/c/d/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+1/8/c/d/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/5*a^2/c^2/x^(5/2)+4*a^2/c^3/x^(1/2)*d-4*a/c^2/x^(1/2)*b","A"
433,1,590,352,0.025000," ","int(x^(7/2)*(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{9 a^{2} x^{\frac{5}{2}}}{16 \left(d \,x^{2}+c \right)^{2} d}+\frac{17 a b c \,x^{\frac{5}{2}}}{8 \left(d \,x^{2}+c \right)^{2} d^{2}}-\frac{25 b^{2} c^{2} x^{\frac{5}{2}}}{16 \left(d \,x^{2}+c \right)^{2} d^{3}}-\frac{5 a^{2} c \sqrt{x}}{16 \left(d \,x^{2}+c \right)^{2} d^{2}}+\frac{13 a b \,c^{2} \sqrt{x}}{8 \left(d \,x^{2}+c \right)^{2} d^{3}}-\frac{21 b^{2} c^{3} \sqrt{x}}{16 \left(d \,x^{2}+c \right)^{2} d^{4}}+\frac{2 b^{2} x^{\frac{5}{2}}}{5 d^{3}}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 c \,d^{2}}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 c \,d^{2}}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 c \,d^{2}}-\frac{45 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 d^{3}}-\frac{45 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 d^{3}}-\frac{45 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 d^{3}}+\frac{117 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 d^{4}}+\frac{117 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 d^{4}}+\frac{117 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 d^{4}}+\frac{4 a b \sqrt{x}}{d^{3}}-\frac{6 b^{2} c \sqrt{x}}{d^{4}}"," ",0,"2/5*b^2/d^3*x^(5/2)+4*b/d^3*a*x^(1/2)-6*b^2/d^4*c*x^(1/2)-9/16/d/(d*x^2+c)^2*x^(5/2)*a^2+17/8/d^2/(d*x^2+c)^2*x^(5/2)*a*b*c-25/16/d^3/(d*x^2+c)^2*x^(5/2)*b^2*c^2-5/16/d^2/(d*x^2+c)^2*x^(1/2)*a^2*c+13/8/d^3/(d*x^2+c)^2*x^(1/2)*a*b*c^2-21/16/d^4/(d*x^2+c)^2*x^(1/2)*b^2*c^3+5/64/d^2*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-45/32/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+117/64/d^4*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+5/128/d^2*(c/d)^(1/4)/c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-45/64/d^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+117/128/d^4*(c/d)^(1/4)*c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+5/64/d^2*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-45/32/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+117/64/d^4*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2","A"
434,1,562,317,0.026000," ","int(x^(5/2)*(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{3 a^{2} x^{\frac{7}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c}-\frac{11 a b \,x^{\frac{7}{2}}}{8 \left(d \,x^{2}+c \right)^{2} d}+\frac{19 b^{2} c \,x^{\frac{7}{2}}}{16 \left(d \,x^{2}+c \right)^{2} d^{2}}-\frac{a^{2} x^{\frac{3}{2}}}{16 \left(d \,x^{2}+c \right)^{2} d}-\frac{7 a b c \,x^{\frac{3}{2}}}{8 \left(d \,x^{2}+c \right)^{2} d^{2}}+\frac{15 b^{2} c^{2} x^{\frac{3}{2}}}{16 \left(d \,x^{2}+c \right)^{2} d^{3}}+\frac{2 b^{2} x^{\frac{3}{2}}}{3 d^{3}}+\frac{3 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c \,d^{2}}+\frac{3 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c \,d^{2}}+\frac{3 \sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(\frac{c}{d}\right)^{\frac{1}{4}} c \,d^{2}}+\frac{21 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{21 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{21 \sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}-\frac{77 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{4}}-\frac{77 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{4}}-\frac{77 \sqrt{2}\, b^{2} c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{4}}"," ",0,"2/3*b^2/d^3*x^(3/2)+3/16/(d*x^2+c)^2/c*x^(7/2)*a^2-11/8/d/(d*x^2+c)^2*x^(7/2)*a*b+19/16/d^2/(d*x^2+c)^2*c*x^(7/2)*b^2-1/16/d/(d*x^2+c)^2*x^(3/2)*a^2-7/8/d^2/(d*x^2+c)^2*x^(3/2)*a*b*c+15/16/d^3/(d*x^2+c)^2*x^(3/2)*b^2*c^2+3/64/d^2/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+21/32/d^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-77/64/d^4*c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+3/64/d^2/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+21/32/d^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-77/64/d^4*c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+3/128/d^2/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+21/64/d^3/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-77/128/d^4*c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
435,1,568,318,0.023000," ","int(x^(3/2)*(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{a^{2} x^{\frac{5}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c}-\frac{9 a b \,x^{\frac{5}{2}}}{8 \left(d \,x^{2}+c \right)^{2} d}+\frac{17 b^{2} c \,x^{\frac{5}{2}}}{16 \left(d \,x^{2}+c \right)^{2} d^{2}}-\frac{3 a^{2} \sqrt{x}}{16 \left(d \,x^{2}+c \right)^{2} d}-\frac{5 a b c \sqrt{x}}{8 \left(d \,x^{2}+c \right)^{2} d^{2}}+\frac{13 b^{2} c^{2} \sqrt{x}}{16 \left(d \,x^{2}+c \right)^{2} d^{3}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 c^{2} d}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 c \,d^{2}}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 c \,d^{2}}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 c \,d^{2}}-\frac{45 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 d^{3}}-\frac{45 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 d^{3}}-\frac{45 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 d^{3}}+\frac{2 b^{2} \sqrt{x}}{d^{3}}"," ",0,"2*b^2/d^3*x^(1/2)+1/16/(d*x^2+c)^2/c*x^(5/2)*a^2-9/8/d/(d*x^2+c)^2*x^(5/2)*a*b+17/16/d^2/(d*x^2+c)^2*c*x^(5/2)*b^2-3/16/d/(d*x^2+c)^2*x^(1/2)*a^2-5/8/d^2/(d*x^2+c)^2*x^(1/2)*a*b*c+13/16/d^3/(d*x^2+c)^2*x^(1/2)*b^2*c^2+3/64/d/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+5/32/d^2/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-45/64/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+3/128/d/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+5/64/d^2/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-45/128/d^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+3/64/d/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+5/32/d^2/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-45/64/d^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2","A"
436,1,514,284,0.023000," ","int((b*x^2+a)^2*x^(1/2)/(d*x^2+c)^3,x)","\frac{5 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2} d}+\frac{5 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2} d}+\frac{5 \sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2} d}+\frac{3 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(\frac{c}{d}\right)^{\frac{1}{4}} c \,d^{2}}+\frac{3 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(\frac{c}{d}\right)^{\frac{1}{4}} c \,d^{2}}+\frac{3 \sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c \,d^{2}}+\frac{21 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{21 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{21 \sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{3}}+\frac{\frac{\left(5 a^{2} d^{2}+6 a b c d -11 b^{2} c^{2}\right) x^{\frac{7}{2}}}{16 c^{2} d}+\frac{\left(9 a^{2} d^{2}-2 a b c d -7 b^{2} c^{2}\right) x^{\frac{3}{2}}}{16 c \,d^{2}}}{\left(d \,x^{2}+c \right)^{2}}"," ",0,"2*(1/32*(5*a^2*d^2+6*a*b*c*d-11*b^2*c^2)/c^2/d*x^(7/2)+1/32*(9*a^2*d^2-2*a*b*c*d-7*b^2*c^2)/c/d^2*x^(3/2))/(d*x^2+c)^2+5/64/d/c^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+3/32/d^2/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+21/64/d^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+5/64/d/c^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+3/32/d^2/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+21/64/d^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+5/128/d/c^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+3/64/d^2/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+21/128/d^3/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
437,1,514,284,0.021000," ","int((b*x^2+a)^2/(d*x^2+c)^3/x^(1/2),x)","\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 c^{3}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 c^{2} d}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 c \,d^{2}}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 c \,d^{2}}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 c \,d^{2}}+\frac{\frac{\left(7 a^{2} d^{2}+2 a b c d -9 b^{2} c^{2}\right) x^{\frac{5}{2}}}{16 c^{2} d}+\frac{\left(11 a^{2} d^{2}-6 a b c d -5 b^{2} c^{2}\right) \sqrt{x}}{16 c \,d^{2}}}{\left(d \,x^{2}+c \right)^{2}}"," ",0,"2*(1/32*(7*a^2*d^2+2*a*b*c*d-9*b^2*c^2)/c^2/d*x^(5/2)+1/32*(11*a^2*d^2-6*a*b*c*d-5*b^2*c^2)/c/d^2*x^(1/2))/(d*x^2+c)^2+21/64/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+3/32/c^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+5/64/c/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+21/128/c^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+3/64/c^2/d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+5/128/c/d^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+21/64/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+3/32/c^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+5/64/c/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2","A"
438,1,568,317,0.025000," ","int((b*x^2+a)^2/x^(3/2)/(d*x^2+c)^3,x)","-\frac{13 a^{2} d^{2} x^{\frac{7}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{5 a b d \,x^{\frac{7}{2}}}{8 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{3 b^{2} x^{\frac{7}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c}-\frac{17 a^{2} d \,x^{\frac{3}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{9 a b \,x^{\frac{3}{2}}}{8 \left(d \,x^{2}+c \right)^{2} c}-\frac{b^{2} x^{\frac{3}{2}}}{16 \left(d \,x^{2}+c \right)^{2} d}-\frac{45 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{45 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{45 \sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{5 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2} d}+\frac{5 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2} d}+\frac{5 \sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2} d}+\frac{3 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c \,d^{2}}+\frac{3 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c \,d^{2}}+\frac{3 \sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(\frac{c}{d}\right)^{\frac{1}{4}} c \,d^{2}}-\frac{2 a^{2}}{c^{3} \sqrt{x}}"," ",0,"-13/16/c^3/(d*x^2+c)^2*x^(7/2)*a^2*d^2+5/8/c^2/(d*x^2+c)^2*x^(7/2)*a*b*d+3/16/c/(d*x^2+c)^2*x^(7/2)*b^2-17/16/c^2/(d*x^2+c)^2*d*x^(3/2)*a^2+9/8/c/(d*x^2+c)^2*x^(3/2)*a*b-1/16/(d*x^2+c)^2/d*x^(3/2)*b^2-45/64/c^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+5/32/c^2/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+3/64/c/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-45/64/c^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+5/32/c^2/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+3/64/c/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-45/128/c^3/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+5/64/c^2/d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+3/128/c/d^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2-2*a^2/c^3/x^(1/2)","A"
439,1,562,318,0.023000," ","int((b*x^2+a)^2/x^(5/2)/(d*x^2+c)^3,x)","-\frac{15 a^{2} d^{2} x^{\frac{5}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{7 a b d \,x^{\frac{5}{2}}}{8 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{b^{2} x^{\frac{5}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c}-\frac{19 a^{2} d \sqrt{x}}{16 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{11 a b \sqrt{x}}{8 \left(d \,x^{2}+c \right)^{2} c}-\frac{3 b^{2} \sqrt{x}}{16 \left(d \,x^{2}+c \right)^{2} d}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 c^{4}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 c^{4}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 c^{4}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 c^{3}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 c^{2} d}-\frac{2 a^{2}}{3 c^{3} x^{\frac{3}{2}}}"," ",0,"-15/16/c^3/(d*x^2+c)^2*x^(5/2)*a^2*d^2+7/8/c^2/(d*x^2+c)^2*x^(5/2)*a*b*d+1/16/c/(d*x^2+c)^2*x^(5/2)*b^2-19/16/c^2/(d*x^2+c)^2*d*x^(1/2)*a^2+11/8/c/(d*x^2+c)^2*x^(1/2)*a*b-3/16/(d*x^2+c)^2/d*x^(1/2)*b^2-77/64/c^4*d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+21/32/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+3/64/c^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-77/128/c^4*d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+21/64/c^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+3/128/c^2/d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2-77/64/c^4*d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+21/32/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+3/64/c^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-2/3*a^2/c^3/x^(3/2)","A"
440,1,590,351,0.028000," ","int((b*x^2+a)^2/x^(7/2)/(d*x^2+c)^3,x)","\frac{21 a^{2} d^{3} x^{\frac{7}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c^{4}}-\frac{13 a b \,d^{2} x^{\frac{7}{2}}}{8 \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{5 b^{2} d \,x^{\frac{7}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{25 a^{2} d^{2} x^{\frac{3}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c^{3}}-\frac{17 a b d \,x^{\frac{3}{2}}}{8 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{9 b^{2} x^{\frac{3}{2}}}{16 \left(d \,x^{2}+c \right)^{2} c}+\frac{117 \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{4}}+\frac{117 \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{4}}+\frac{117 \sqrt{2}\, a^{2} d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{4}}-\frac{45 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{45 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{45 \sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{5 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2} d}+\frac{5 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2} d}+\frac{5 \sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2} d}+\frac{6 a^{2} d}{c^{4} \sqrt{x}}-\frac{4 a b}{c^{3} \sqrt{x}}-\frac{2 a^{2}}{5 c^{3} x^{\frac{5}{2}}}"," ",0,"21/16/c^4/(d*x^2+c)^2*x^(7/2)*a^2*d^3-13/8/c^3/(d*x^2+c)^2*x^(7/2)*a*b*d^2+5/16/c^2/(d*x^2+c)^2*x^(7/2)*b^2*d+25/16/c^3/(d*x^2+c)^2*x^(3/2)*a^2*d^2-17/8/c^2/(d*x^2+c)^2*x^(3/2)*a*b*d+9/16/c/(d*x^2+c)^2*x^(3/2)*b^2+117/128/c^4*d/(c/d)^(1/4)*2^(1/2)*a^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+117/64/c^4*d/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+117/64/c^4*d/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-45/64/c^3/(c/d)^(1/4)*2^(1/2)*a*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-45/32/c^3/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-45/32/c^3/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+5/128/c^2/d/(c/d)^(1/4)*2^(1/2)*b^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+5/64/c^2/d/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+5/64/c^2/d/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/5*a^2/c^3/x^(5/2)+6*a^2/c^4/x^(1/2)*d-4*a/c^3/x^(1/2)*b","A"
441,1,721,245,0.014000," ","int(x^(5/2)*(d*x^2+c)^3/(b*x^2+a),x)","\frac{2 d^{3} x^{\frac{15}{2}}}{15 b}-\frac{2 a \,d^{3} x^{\frac{11}{2}}}{11 b^{2}}+\frac{6 c \,d^{2} x^{\frac{11}{2}}}{11 b}+\frac{2 a^{2} d^{3} x^{\frac{7}{2}}}{7 b^{3}}-\frac{6 a c \,d^{2} x^{\frac{7}{2}}}{7 b^{2}}+\frac{6 c^{2} d \,x^{\frac{7}{2}}}{7 b}-\frac{2 a^{3} d^{3} x^{\frac{3}{2}}}{3 b^{4}}+\frac{2 a^{2} c \,d^{2} x^{\frac{3}{2}}}{b^{3}}-\frac{2 a \,c^{2} d \,x^{\frac{3}{2}}}{b^{2}}+\frac{2 c^{3} x^{\frac{3}{2}}}{3 b}+\frac{\sqrt{2}\, a^{4} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{5}}+\frac{\sqrt{2}\, a^{4} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{5}}+\frac{\sqrt{2}\, a^{4} d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{5}}-\frac{3 \sqrt{2}\, a^{3} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}-\frac{3 \sqrt{2}\, a^{3} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}-\frac{3 \sqrt{2}\, a^{3} c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}+\frac{3 \sqrt{2}\, a^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{3 \sqrt{2}\, a^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{3 \sqrt{2}\, a^{2} c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{\sqrt{2}\, a \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a \,c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}"," ",0,"2/15*d^3*x^(15/2)/b-2/11/b^2*x^(11/2)*a*d^3+6/11/b*x^(11/2)*c*d^2+2/7/b^3*x^(7/2)*a^2*d^3-6/7/b^2*x^(7/2)*a*c*d^2+6/7/b*x^(7/2)*c^2*d-2/3/b^4*x^(3/2)*a^3*d^3+2/b^3*x^(3/2)*a^2*c*d^2-2/b^2*x^(3/2)*a*c^2*d+2/3/b*x^(3/2)*c^3+1/2*a^4/b^5/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3-3/2*a^3/b^4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2+3/2*a^2/b^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d-1/2*a/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3+1/4*a^4/b^5/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3-3/4*a^3/b^4/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2+3/4*a^2/b^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d-1/4*a/b^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3+1/2*a^4/b^5/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3-3/2*a^3/b^4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2+3/2*a^2/b^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d-1/2*a/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3","B"
442,1,712,245,0.013000," ","int(x^(3/2)*(d*x^2+c)^3/(b*x^2+a),x)","\frac{2 d^{3} x^{\frac{13}{2}}}{13 b}-\frac{2 a \,d^{3} x^{\frac{9}{2}}}{9 b^{2}}+\frac{2 c \,d^{2} x^{\frac{9}{2}}}{3 b}+\frac{2 a^{2} d^{3} x^{\frac{5}{2}}}{5 b^{3}}-\frac{6 a c \,d^{2} x^{\frac{5}{2}}}{5 b^{2}}+\frac{6 c^{2} d \,x^{\frac{5}{2}}}{5 b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{4}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{4}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b^{4}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{3}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{3}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b}-\frac{2 a^{3} d^{3} \sqrt{x}}{b^{4}}+\frac{6 a^{2} c \,d^{2} \sqrt{x}}{b^{3}}-\frac{6 a \,c^{2} d \sqrt{x}}{b^{2}}+\frac{2 c^{3} \sqrt{x}}{b}"," ",0,"2/13*d^3*x^(13/2)/b-2/9/b^2*x^(9/2)*a*d^3+2/3/b*x^(9/2)*c*d^2+2/5/b^3*x^(5/2)*a^2*d^3-6/5/b^2*x^(5/2)*a*c*d^2+6/5/b*x^(5/2)*c^2*d-2/b^4*a^3*d^3*x^(1/2)+6/b^3*a^2*c*d^2*x^(1/2)-6/b^2*a*c^2*d*x^(1/2)+2/b*c^3*x^(1/2)+1/4/b^4*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*a^3*d^3-3/4/b^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*a^2*c*d^2+3/4/b^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*a*c^2*d-1/4/b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3+1/2/b^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*a^3*d^3-3/2/b^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*a^2*c*d^2+3/2/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*a*c^2*d-1/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3+1/2/b^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*a^3*d^3-3/2/b^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*a^2*c*d^2+3/2/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*a*c^2*d-1/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3","B"
443,1,659,227,0.013000," ","int((d*x^2+c)^3*x^(1/2)/(b*x^2+a),x)","\frac{2 d^{3} x^{\frac{11}{2}}}{11 b}-\frac{2 a \,d^{3} x^{\frac{7}{2}}}{7 b^{2}}+\frac{6 c \,d^{2} x^{\frac{7}{2}}}{7 b}+\frac{2 a^{2} d^{3} x^{\frac{3}{2}}}{3 b^{3}}-\frac{2 a c \,d^{2} x^{\frac{3}{2}}}{b^{2}}+\frac{2 c^{2} d \,x^{\frac{3}{2}}}{b}-\frac{\sqrt{2}\, a^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}-\frac{\sqrt{2}\, a^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}-\frac{\sqrt{2}\, a^{3} d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}+\frac{3 \sqrt{2}\, a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{3 \sqrt{2}\, a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{3 \sqrt{2}\, a^{2} c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{3 \sqrt{2}\, a \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{3 \sqrt{2}\, a \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{3 \sqrt{2}\, a \,c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{\sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}"," ",0,"2/11*d^3*x^(11/2)/b-2/7*d^3/b^2*x^(7/2)*a+6/7*d^2/b*x^(7/2)*c+2/3*d^3/b^3*x^(3/2)*a^2-2*d^2/b^2*x^(3/2)*a*c+2*d/b*x^(3/2)*c^2-1/2/b^4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*a^3*d^3+3/2/b^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*a^2*c*d^2-3/2/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*a*c^2*d+1/2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3-1/2/b^4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*a^3*d^3+3/2/b^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*a^2*c*d^2-3/2/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*a*c^2*d+1/2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3-1/4/b^4/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*a^3*d^3+3/4/b^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*a^2*c*d^2-3/4/b^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*a*c^2*d+1/4/b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3","B"
444,1,650,227,0.012000," ","int((d*x^2+c)^3/(b*x^2+a)/x^(1/2),x)","\frac{2 d^{3} x^{\frac{9}{2}}}{9 b}-\frac{2 a \,d^{3} x^{\frac{5}{2}}}{5 b^{2}}+\frac{6 c \,d^{2} x^{\frac{5}{2}}}{5 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b}+\frac{2 a^{2} d^{3} \sqrt{x}}{b^{3}}-\frac{6 a c \,d^{2} \sqrt{x}}{b^{2}}+\frac{6 c^{2} d \sqrt{x}}{b}"," ",0,"2/9*d^3*x^(9/2)/b-2/5*d^3/b^2*x^(5/2)*a+6/5*d^2/b*x^(5/2)*c+2*d^3/b^3*a^2*x^(1/2)-6*d^2/b^2*a*c*x^(1/2)+6*d/b*c^2*x^(1/2)-1/2/b^3*(a/b)^(1/4)*a^2*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3+3/2/b^2*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2-3/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d+1/2*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3-1/2/b^3*(a/b)^(1/4)*a^2*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3+3/2/b^2*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2-3/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d+1/2*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3-1/4/b^3*(a/b)^(1/4)*a^2*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3+3/4/b^2*(a/b)^(1/4)*a*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2-3/4/b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d+1/4*(a/b)^(1/4)/a*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3","B"
445,1,622,207,0.015000," ","int((d*x^2+c)^3/x^(3/2)/(b*x^2+a),x)","\frac{2 d^{3} x^{\frac{7}{2}}}{7 b}-\frac{2 a \,d^{3} x^{\frac{3}{2}}}{3 b^{2}}+\frac{2 c \,d^{2} x^{\frac{3}{2}}}{b}+\frac{\sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{\sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{\sqrt{2}\, a^{2} d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{3 \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{3 \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{3 \sqrt{2}\, a c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{3 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{3 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{3 \sqrt{2}\, c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{2 c^{3}}{a \sqrt{x}}"," ",0,"2/7*d^3*x^(7/2)/b-2/3*d^3/b^2*x^(3/2)*a+2*d^2/b*x^(3/2)*c+1/4*a^2/b^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3-3/4*a/b^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2+3/4/b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d-1/4/a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3+1/2*a^2/b^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3-3/2*a/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2+3/2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d-1/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3+1/2*a^2/b^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3-3/2*a/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2+3/2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d-1/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3-2*c^3/a/x^(1/2)","B"
446,1,616,207,0.016000," ","int((d*x^2+c)^3/x^(5/2)/(b*x^2+a),x)","\frac{2 d^{3} x^{\frac{5}{2}}}{5 b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a^{2}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b}-\frac{2 a \,d^{3} \sqrt{x}}{b^{2}}+\frac{6 c \,d^{2} \sqrt{x}}{b}-\frac{2 c^{3}}{3 a \,x^{\frac{3}{2}}}"," ",0,"2/5*d^3*x^(5/2)/b-2*d^3/b^2*a*x^(1/2)+6*d^2/b*c*x^(1/2)+1/2*a/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3-3/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2+3/2/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d-1/2/a^2*b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3+1/4*a/b^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3-3/4/b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2+3/4/a*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d-1/4/a^2*b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3+1/2*a/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3-3/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2+3/2/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d-1/2/a^2*b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3-2/3*c^3/a/x^(3/2)","B"
447,1,616,206,0.017000," ","int((d*x^2+c)^3/x^(7/2)/(b*x^2+a),x)","\frac{2 d^{3} x^{\frac{3}{2}}}{3 b}-\frac{\sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a \,d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{3 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{3 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{3 \sqrt{2}\, c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, b \,c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{3 \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{3 \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{3 \sqrt{2}\, c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{6 c^{2} d}{a \sqrt{x}}+\frac{2 b \,c^{3}}{a^{2} \sqrt{x}}-\frac{2 c^{3}}{5 a \,x^{\frac{5}{2}}}"," ",0,"2/3*d^3*x^(3/2)/b-1/2*a/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3+3/2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2-3/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d+1/2/a^2*b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3-1/4*a/b^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3+3/4/b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2-3/4/a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d+1/4/a^2*b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3-1/2*a/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3+3/2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2-3/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d+1/2/a^2*b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3-2/5*c^3/a/x^(5/2)-6*c^2/a/x^(1/2)*d+2*c^3/a^2/x^(1/2)*b","B"
448,1,622,206,0.019000," ","int((d*x^2+c)^3/x^(9/2)/(b*x^2+a),x)","\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a^{2}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a^{2}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a^{3}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a^{3}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 b}+\frac{2 d^{3} \sqrt{x}}{b}-\frac{2 c^{2} d}{a \,x^{\frac{3}{2}}}+\frac{2 b \,c^{3}}{3 a^{2} x^{\frac{3}{2}}}-\frac{2 c^{3}}{7 a \,x^{\frac{7}{2}}}"," ",0,"2*d^3*x^(1/2)/b-1/4/b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3+3/4/a*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2-3/4/a^2*b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d+1/4/a^3*b^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3-1/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3+3/2/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2-3/2/a^2*b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d+1/2/a^3*b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3-1/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3+3/2/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2-3/2/a^2*b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d+1/2/a^3*b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3-2/7*c^3/a/x^(7/2)-2*c^2/a/x^(3/2)*d+2/3*c^3/a^2/x^(3/2)*b","B"
449,1,650,226,0.016000," ","int((d*x^2+c)^3/x^(11/2)/(b*x^2+a),x)","-\frac{3 \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{3 \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{3 \sqrt{2}\, c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{3 \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{3 \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{3 \sqrt{2}\, b \,c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{\sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{\sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{\sqrt{2}\, b^{2} c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{\sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{6 c \,d^{2}}{a \sqrt{x}}+\frac{6 b \,c^{2} d}{a^{2} \sqrt{x}}-\frac{2 b^{2} c^{3}}{a^{3} \sqrt{x}}-\frac{6 c^{2} d}{5 a \,x^{\frac{5}{2}}}+\frac{2 b \,c^{3}}{5 a^{2} x^{\frac{5}{2}}}-\frac{2 c^{3}}{9 a \,x^{\frac{9}{2}}}"," ",0,"1/2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3-3/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2+3/2/a^2*b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d-1/2/a^3*b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3+1/2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3-3/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2+3/2/a^2*b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d-1/2/a^3*b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3+1/4/b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3-3/4/a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2+3/4/a^2*b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d-1/4/a^3*b^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3-2/9*c^3/a/x^(9/2)-6*c/a/x^(1/2)*d^2+6*c^2/a^2/x^(1/2)*b*d-2*c^3/a^3/x^(1/2)*b^2-6/5*c^2/a/x^(5/2)*d+2/5*c^3/a^2/x^(5/2)*b","B"
450,1,659,226,0.016000," ","int((d*x^2+c)^3/x^(13/2)/(b*x^2+a),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a^{2}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a^{2}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a^{4}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a^{4}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a^{4}}-\frac{2 c \,d^{2}}{a \,x^{\frac{3}{2}}}+\frac{2 b \,c^{2} d}{a^{2} x^{\frac{3}{2}}}-\frac{2 b^{2} c^{3}}{3 a^{3} x^{\frac{3}{2}}}-\frac{6 c^{2} d}{7 a \,x^{\frac{7}{2}}}+\frac{2 b \,c^{3}}{7 a^{2} x^{\frac{7}{2}}}-\frac{2 c^{3}}{11 a \,x^{\frac{11}{2}}}"," ",0,"1/2/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3-3/2/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b*c*d^2+3/2/a^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b^2*c^2*d-1/2/a^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b^3*c^3+1/4/a*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3-3/4/a^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b*c*d^2+3/4/a^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b^2*c^2*d-1/4/a^4*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b^3*c^3+1/2/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3-3/2/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b*c*d^2+3/2/a^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b^2*c^2*d-1/2/a^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b^3*c^3-2/11*c^3/a/x^(11/2)-2*c/a/x^(3/2)*d^2+2*c^2/a^2/x^(3/2)*b*d-2/3*c^3/a^3/x^(3/2)*b^2-6/7*c^2/a/x^(7/2)*d+2/7*c^3/a^2/x^(7/2)*b","B"
451,1,712,244,0.018000," ","int((d*x^2+c)^3/x^(15/2)/(b*x^2+a),x)","-\frac{\sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{3 \sqrt{2}\, b c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{3 \sqrt{2}\, b c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{3 \sqrt{2}\, b c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{3 \sqrt{2}\, b^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{3 \sqrt{2}\, b^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{3 \sqrt{2}\, b^{2} c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{\sqrt{2}\, b^{3} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{4}}+\frac{\sqrt{2}\, b^{3} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{4}}+\frac{\sqrt{2}\, b^{3} c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{4}}-\frac{2 d^{3}}{a \sqrt{x}}+\frac{6 b c \,d^{2}}{a^{2} \sqrt{x}}-\frac{6 b^{2} c^{2} d}{a^{3} \sqrt{x}}+\frac{2 b^{3} c^{3}}{a^{4} \sqrt{x}}-\frac{6 c \,d^{2}}{5 a \,x^{\frac{5}{2}}}+\frac{6 b \,c^{2} d}{5 a^{2} x^{\frac{5}{2}}}-\frac{2 b^{2} c^{3}}{5 a^{3} x^{\frac{5}{2}}}-\frac{2 c^{2} d}{3 a \,x^{\frac{9}{2}}}+\frac{2 b \,c^{3}}{9 a^{2} x^{\frac{9}{2}}}-\frac{2 c^{3}}{13 a \,x^{\frac{13}{2}}}"," ",0,"-1/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3+3/2/a^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b*c*d^2-3/2/a^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b^2*c^2*d+1/2/a^4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b^3*c^3-1/2/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3+3/2/a^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b*c*d^2-3/2/a^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b^2*c^2*d+1/2/a^4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b^3*c^3-1/4/a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3+3/4/a^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b*c*d^2-3/4/a^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b^2*c^2*d+1/4/a^4/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b^3*c^3-2/13*c^3/a/x^(13/2)-2/a/x^(1/2)*d^3+6/a^2/x^(1/2)*c*d^2*b-6/a^3/x^(1/2)*c^2*d*b^2+2/a^4/x^(1/2)*c^3*b^3-6/5*c/a/x^(5/2)*d^2+6/5*c^2/a^2/x^(5/2)*b*d-2/5*c^3/a^3/x^(5/2)*b^2-2/3*c^2/a/x^(9/2)*d+2/9*c^3/a^2/x^(9/2)*b","B"
452,1,804,317,0.021000," ","int(x^(7/2)*(d*x^2+c)^3/(b*x^2+a)^2,x)","\frac{2 d^{3} x^{\frac{13}{2}}}{13 b^{2}}-\frac{4 a \,d^{3} x^{\frac{9}{2}}}{9 b^{3}}+\frac{2 c \,d^{2} x^{\frac{9}{2}}}{3 b^{2}}+\frac{6 a^{2} d^{3} x^{\frac{5}{2}}}{5 b^{4}}-\frac{12 a c \,d^{2} x^{\frac{5}{2}}}{5 b^{3}}+\frac{6 c^{2} d \,x^{\frac{5}{2}}}{5 b^{2}}-\frac{a^{4} d^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{5}}+\frac{3 a^{3} c \,d^{2} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{3 a^{2} c^{2} d \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{a \,c^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{17 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{5}}+\frac{17 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{5}}+\frac{17 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{5}}-\frac{39 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{4}}-\frac{39 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{4}}-\frac{39 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{4}}+\frac{27 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{3}}+\frac{27 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{3}}+\frac{27 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{3}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{2}}-\frac{8 a^{3} d^{3} \sqrt{x}}{b^{5}}+\frac{18 a^{2} c \,d^{2} \sqrt{x}}{b^{4}}-\frac{12 a \,c^{2} d \sqrt{x}}{b^{3}}+\frac{2 c^{3} \sqrt{x}}{b^{2}}"," ",0,"-39/8*a^2/b^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2+27/8*a/b^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d-39/8*a^2/b^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2+27/16*a/b^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d+27/8*a/b^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d-39/16*a^2/b^4*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2+2/13*d^3*x^(13/2)/b^2+6/5/b^2*x^(5/2)*c^2*d-8/b^5*a^3*d^3*x^(1/2)+6/5/b^4*x^(5/2)*a^2*d^3+3/2*a^3/b^4*x^(1/2)/(b*x^2+a)*c*d^2-3/2*a^2/b^3*x^(1/2)/(b*x^2+a)*c^2*d+17/8*a^3/b^5*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3+17/8*a^3/b^5*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3+17/16*a^3/b^5*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3-4/9/b^3*x^(9/2)*a*d^3+2/3/b^2*x^(9/2)*c*d^2-12/b^3*a*c^2*d*x^(1/2)-1/2*a^4/b^5*x^(1/2)/(b*x^2+a)*d^3+1/2*a/b^2*x^(1/2)/(b*x^2+a)*c^3-5/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3-5/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3-5/16/b^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3+18/b^4*a^2*c*d^2*x^(1/2)-12/5/b^3*x^(5/2)*a*c*d^2+2/b^2*c^3*x^(1/2)","B"
453,1,748,286,0.023000," ","int(x^(5/2)*(d*x^2+c)^3/(b*x^2+a)^2,x)","\frac{2 d^{3} x^{\frac{11}{2}}}{11 b^{2}}-\frac{4 a \,d^{3} x^{\frac{7}{2}}}{7 b^{3}}+\frac{6 c \,d^{2} x^{\frac{7}{2}}}{7 b^{2}}+\frac{a^{3} d^{3} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{3 a^{2} c \,d^{2} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{3 a \,c^{2} d \,x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{c^{3} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b}+\frac{2 a^{2} d^{3} x^{\frac{3}{2}}}{b^{4}}-\frac{4 a c \,d^{2} x^{\frac{3}{2}}}{b^{3}}+\frac{2 c^{2} d \,x^{\frac{3}{2}}}{b^{2}}-\frac{15 \sqrt{2}\, a^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{5}}-\frac{15 \sqrt{2}\, a^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{5}}-\frac{15 \sqrt{2}\, a^{3} d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{5}}+\frac{33 \sqrt{2}\, a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}+\frac{33 \sqrt{2}\, a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}+\frac{33 \sqrt{2}\, a^{2} c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}-\frac{21 \sqrt{2}\, a \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{21 \sqrt{2}\, a \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{21 \sqrt{2}\, a \,c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{3 \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}"," ",0,"2/11*d^3*x^(11/2)/b^2-4/7*d^3/b^3*x^(7/2)*a+6/7*d^2/b^2*x^(7/2)*c+2*d^3/b^4*x^(3/2)*a^2-4*d^2/b^3*x^(3/2)*a*c+2*d/b^2*x^(3/2)*c^2+1/2/b^4*x^(3/2)/(b*x^2+a)*a^3*d^3-3/2/b^3*x^(3/2)/(b*x^2+a)*a^2*c*d^2+3/2/b^2*x^(3/2)/(b*x^2+a)*a*c^2*d-1/2/b*x^(3/2)/(b*x^2+a)*c^3-15/16/b^5/(a/b)^(1/4)*2^(1/2)*a^3*d^3*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-15/8/b^5/(a/b)^(1/4)*2^(1/2)*a^3*d^3*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-15/8/b^5/(a/b)^(1/4)*2^(1/2)*a^3*d^3*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+33/16/b^4/(a/b)^(1/4)*2^(1/2)*a^2*c*d^2*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+33/8/b^4/(a/b)^(1/4)*2^(1/2)*a^2*c*d^2*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+33/8/b^4/(a/b)^(1/4)*2^(1/2)*a^2*c*d^2*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-21/16/b^3/(a/b)^(1/4)*2^(1/2)*a*c^2*d*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-21/8/b^3/(a/b)^(1/4)*2^(1/2)*a*c^2*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-21/8/b^3/(a/b)^(1/4)*2^(1/2)*a*c^2*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/16/b^2/(a/b)^(1/4)*2^(1/2)*c^3*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+3/8/b^2/(a/b)^(1/4)*2^(1/2)*c^3*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+3/8/b^2/(a/b)^(1/4)*2^(1/2)*c^3*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)","B"
454,1,748,298,0.020000," ","int(x^(3/2)*(d*x^2+c)^3/(b*x^2+a)^2,x)","\frac{2 d^{3} x^{\frac{9}{2}}}{9 b^{2}}-\frac{4 a \,d^{3} x^{\frac{5}{2}}}{5 b^{3}}+\frac{6 c \,d^{2} x^{\frac{5}{2}}}{5 b^{2}}+\frac{a^{3} d^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{3 a^{2} c \,d^{2} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{3 a \,c^{2} d \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{c^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b}-\frac{13 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{4}}-\frac{13 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{4}}-\frac{13 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{4}}+\frac{27 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{3}}+\frac{27 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{3}}+\frac{27 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{3}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a b}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{2}}+\frac{6 a^{2} d^{3} \sqrt{x}}{b^{4}}-\frac{12 a c \,d^{2} \sqrt{x}}{b^{3}}+\frac{6 c^{2} d \sqrt{x}}{b^{2}}"," ",0,"2/9*d^3/b^2*x^(9/2)-4/5*d^3/b^3*x^(5/2)*a+6/5*d^2/b^2*x^(5/2)*c+6*d^3/b^4*a^2*x^(1/2)-12*d^2/b^3*a*c*x^(1/2)+6*d/b^2*c^2*x^(1/2)+1/2/b^4*x^(1/2)/(b*x^2+a)*a^3*d^3-3/2/b^3*x^(1/2)/(b*x^2+a)*a^2*c*d^2+3/2/b^2*x^(1/2)/(b*x^2+a)*a*c^2*d-1/2/b*x^(1/2)/(b*x^2+a)*c^3-13/16/b^4*(a/b)^(1/4)*a^2*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3+27/16/b^3*(a/b)^(1/4)*a*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2-15/16/b^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d+1/16/b*(a/b)^(1/4)/a*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3-13/8/b^4*(a/b)^(1/4)*a^2*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3+27/8/b^3*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2-15/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d+1/8/b*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3-13/8/b^4*(a/b)^(1/4)*a^2*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3+27/8/b^3*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2-15/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d+1/8/b*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3","B"
455,1,706,292,0.020000," ","int((d*x^2+c)^3*x^(1/2)/(b*x^2+a)^2,x)","\frac{2 d^{3} x^{\frac{7}{2}}}{7 b^{2}}-\frac{a^{2} d^{3} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{3 a c \,d^{2} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{c^{3} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a}-\frac{3 c^{2} d \,x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b}-\frac{4 a \,d^{3} x^{\frac{3}{2}}}{3 b^{3}}+\frac{2 c \,d^{2} x^{\frac{3}{2}}}{b^{2}}+\frac{11 \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}+\frac{11 \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}+\frac{11 \sqrt{2}\, a^{2} d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{4}}-\frac{21 \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{21 \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{21 \sqrt{2}\, a c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{\sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{9 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{9 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{9 \sqrt{2}\, c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}"," ",0,"2/7*d^3/b^2*x^(7/2)-4/3*d^3/b^3*x^(3/2)*a+2*d^2/b^2*x^(3/2)*c-1/2/b^3*a^2*x^(3/2)/(b*x^2+a)*d^3+3/2/b^2*a*x^(3/2)/(b*x^2+a)*c*d^2-3/2/b*x^(3/2)/(b*x^2+a)*c^2*d+1/2/a*x^(3/2)/(b*x^2+a)*c^3+11/8/b^4*a^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3-21/8/b^3*a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2+9/8/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d+1/8/b/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3+11/8/b^4*a^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3-21/8/b^3*a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2+9/8/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d+1/8/b/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3+11/16/b^4*a^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3-21/16/b^3*a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2+9/16/b^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d+1/16/b/a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3","B"
456,1,697,258,0.022000," ","int((d*x^2+c)^3/(b*x^2+a)^2/x^(1/2),x)","\frac{2 d^{3} x^{\frac{5}{2}}}{5 b^{2}}-\frac{a^{2} d^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{3 a c \,d^{2} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{c^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) a}-\frac{3 c^{2} d \sqrt{x}}{2 \left(b \,x^{2}+a \right) b}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{2}}-\frac{4 a \,d^{3} \sqrt{x}}{b^{3}}+\frac{6 c \,d^{2} \sqrt{x}}{b^{2}}"," ",0,"2/5*d^3*x^(5/2)/b^2-4*d^3/b^3*a*x^(1/2)+6*d^2/b^2*c*x^(1/2)-1/2/b^3*a^2*x^(1/2)/(b*x^2+a)*d^3+3/2/b^2*a*x^(1/2)/(b*x^2+a)*c*d^2-3/2/b*x^(1/2)/(b*x^2+a)*c^2*d+1/2/a*x^(1/2)/(b*x^2+a)*c^3+9/16/b^3*a*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3-15/16/b^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2+3/16/b/a*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d+3/16/a^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3+9/8/b^3*a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3-15/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2+3/8/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d+3/8/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3+9/8/b^3*a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3-15/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2+3/8/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d+3/8/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3","B"
457,1,682,284,0.024000," ","int((d*x^2+c)^3/x^(3/2)/(b*x^2+a)^2,x)","\frac{a \,d^{3} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{3 c^{2} d \,x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a}-\frac{b \,c^{3} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 c \,d^{2} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b}+\frac{2 d^{3} x^{\frac{3}{2}}}{3 b^{2}}-\frac{7 \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{7 \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{7 \sqrt{2}\, a \,d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{3 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{3 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{3 \sqrt{2}\, c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}-\frac{5 \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{9 \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{9 \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{9 \sqrt{2}\, c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{2 c^{3}}{a^{2} \sqrt{x}}"," ",0,"2/3*d^3*x^(3/2)/b^2+1/2*a/b^2*x^(3/2)/(b*x^2+a)*d^3-3/2/b*x^(3/2)/(b*x^2+a)*c*d^2+3/2/a*x^(3/2)/(b*x^2+a)*c^2*d-1/2/a^2*b*x^(3/2)/(b*x^2+a)*c^3-7/16*a/b^3/(a/b)^(1/4)*2^(1/2)*d^3*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-7/8*a/b^3/(a/b)^(1/4)*2^(1/2)*d^3*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-7/8*a/b^3/(a/b)^(1/4)*2^(1/2)*d^3*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/16/a/b/(a/b)^(1/4)*2^(1/2)*c^2*d*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+3/8/a/b/(a/b)^(1/4)*2^(1/2)*c^2*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+3/8/a/b/(a/b)^(1/4)*2^(1/2)*c^2*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-5/16/a^2/(a/b)^(1/4)*2^(1/2)*c^3*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-5/8/a^2/(a/b)^(1/4)*2^(1/2)*c^3*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-5/8/a^2/(a/b)^(1/4)*2^(1/2)*c^3*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+9/16/b^2/(a/b)^(1/4)*2^(1/2)*c*d^2*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+9/8/b^2/(a/b)^(1/4)*2^(1/2)*c*d^2*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+9/8/b^2/(a/b)^(1/4)*2^(1/2)*c*d^2*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-2*c^3/a^2/x^(1/2)","B"
458,1,682,283,0.023000," ","int((d*x^2+c)^3/x^(5/2)/(b*x^2+a)^2,x)","\frac{a \,d^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{3 c^{2} d \sqrt{x}}{2 \left(b \,x^{2}+a \right) a}-\frac{b \,c^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 c \,d^{2} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a b}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{2}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{2}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a^{2}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{3}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{3}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a^{3}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 b^{2}}+\frac{2 d^{3} \sqrt{x}}{b^{2}}-\frac{2 c^{3}}{3 a^{2} x^{\frac{3}{2}}}"," ",0,"2*d^3/b^2*x^(1/2)+1/2*a/b^2*x^(1/2)/(b*x^2+a)*d^3-3/2/b*x^(1/2)/(b*x^2+a)*c*d^2+3/2/a*x^(1/2)/(b*x^2+a)*c^2*d-1/2/a^2*b*x^(1/2)/(b*x^2+a)*c^3-5/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3+3/8/a/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2+9/8/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d-7/8/a^3*b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3-5/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3+3/8/a/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2+9/8/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d-7/8/a^3*b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3-5/16/b^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3+3/16/a/b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2+9/16/a^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d-7/16/a^3*b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3-2/3*c^3/a^2/x^(3/2)","B"
459,1,697,292,0.025000," ","int((d*x^2+c)^3/x^(7/2)/(b*x^2+a)^2,x)","\frac{3 c \,d^{2} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a}-\frac{3 b \,c^{2} d \,x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{b^{2} c^{3} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) a^{3}}-\frac{d^{3} x^{\frac{3}{2}}}{2 \left(b \,x^{2}+a \right) b}+\frac{3 \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{3 \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{3 \sqrt{2}\, c \,d^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}-\frac{15 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{15 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{15 \sqrt{2}\, c^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{9 \sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{9 \sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{9 \sqrt{2}\, b \,c^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{3 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, d^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{6 c^{2} d}{a^{2} \sqrt{x}}+\frac{4 b \,c^{3}}{a^{3} \sqrt{x}}-\frac{2 c^{3}}{5 a^{2} x^{\frac{5}{2}}}"," ",0,"-1/2/b*x^(3/2)/(b*x^2+a)*d^3+3/2/a*x^(3/2)/(b*x^2+a)*c*d^2-3/2/a^2*b*x^(3/2)/(b*x^2+a)*c^2*d+1/2/a^3*b^2*x^(3/2)/(b*x^2+a)*c^3+3/8/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3+3/8/a/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2-15/8/a^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d+9/8/a^3*b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3+3/8/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3+3/8/a/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2-15/8/a^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d+9/8/a^3*b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3+3/16/b^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3+3/16/a/b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2-15/16/a^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d+9/16/a^3*b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3-2/5*c^3/a^2/x^(5/2)-6*c^2/a^2/x^(1/2)*d+4*c^3/a^3/x^(1/2)*b","B"
460,1,706,292,0.022000," ","int((d*x^2+c)^3/x^(9/2)/(b*x^2+a)^2,x)","\frac{3 c \,d^{2} \sqrt{x}}{2 \left(b \,x^{2}+a \right) a}-\frac{3 b \,c^{2} d \sqrt{x}}{2 \left(b \,x^{2}+a \right) a^{2}}+\frac{b^{2} c^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) a^{3}}-\frac{d^{3} \sqrt{x}}{2 \left(b \,x^{2}+a \right) b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a b}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{2}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{2}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a^{2}}-\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{3}}-\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{3}}-\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a^{3}}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{4}}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{4}}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 a^{4}}-\frac{2 c^{2} d}{a^{2} x^{\frac{3}{2}}}+\frac{4 b \,c^{3}}{3 a^{3} x^{\frac{3}{2}}}-\frac{2 c^{3}}{7 a^{2} x^{\frac{7}{2}}}"," ",0,"-1/2/b*x^(1/2)/(b*x^2+a)*d^3+3/2/a*x^(1/2)/(b*x^2+a)*c*d^2-3/2/a^2*b*x^(1/2)/(b*x^2+a)*c^2*d+1/2/a^3*b^2*x^(1/2)/(b*x^2+a)*c^3+1/8/a/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d^3+9/8/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c*d^2-21/8/a^3*b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^2*d+11/8/a^4*b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c^3+1/8/a/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d^3+9/8/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c*d^2-21/8/a^3*b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^2*d+11/8/a^4*b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c^3+1/16/a/b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d^3+9/16/a^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c*d^2-21/16/a^3*b*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^2*d+11/16/a^4*b^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c^3-2/7*c^3/a^2/x^(7/2)-2*c^2/a^2/x^(3/2)*d+4/3*c^3/a^3/x^(3/2)*b","B"
461,1,351,340,0.015000," ","int(x^(9/2)/(b*x^2+a)/(d*x^2+c),x)","-\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{\sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{\sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{\sqrt{2}\, c^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{2 x^{\frac{3}{2}}}{3 b d}"," ",0,"2/3*x^(3/2)/b/d-1/4*a^2/b^2/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*a^2/b^2/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*a^2/b^2/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4*c^2/d^2/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+1/2*c^2/d^2/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+1/2*c^2/d^2/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)","A"
462,1,339,340,0.017000," ","int(x^(7/2)/(b*x^2+a)/(d*x^2+c),x)","-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right) b}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(a d -b c \right) d}+\frac{2 \sqrt{x}}{b d}"," ",0,"2*x^(1/2)/b/d-1/4/b*a/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2/b*a/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2/b*a/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4/d*c/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+1/2/d*c/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+1/2/d*c/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)","A"
463,1,328,329,0.013000," ","int(x^(5/2)/(b*x^2+a)/(d*x^2+c),x)","\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, a \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{\sqrt{2}\, c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} d}"," ",0,"1/4*a/(a*d-b*c)/b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*a/(a*d-b*c)/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*a/(a*d-b*c)/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/4*c/(a*d-b*c)/d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-1/2*c/(a*d-b*c)/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-1/2*c/(a*d-b*c)/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)","A"
464,1,304,329,0.013000," ","int(x^(3/2)/(b*x^2+a)/(d*x^2+c),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 a d -2 b c}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 a d -2 b c}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 a d -4 b c}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(a d -b c \right)}"," ",0,"1/4/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/4/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-1/2/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-1/2/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)","A"
465,1,304,329,0.013000," ","int(x^(1/2)/(b*x^2+a)/(d*x^2+c),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}}}"," ",0,"-1/4/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+1/2/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+1/2/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)","A"
466,1,328,329,0.013000," ","int(1/(b*x^2+a)/(d*x^2+c)/x^(1/2),x)","-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right) a}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(a d -b c \right) c}"," ",0,"-1/4*b/(a*d-b*c)*(a/b)^(1/4)/a*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*b/(a*d-b*c)*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*b/(a*d-b*c)*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4*d/(a*d-b*c)*(c/d)^(1/4)/c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+1/2*d/(a*d-b*c)*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+1/2*d/(a*d-b*c)*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)","A"
467,1,339,340,0.016000," ","int(1/x^(3/2)/(b*x^2+a)/(d*x^2+c),x)","\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{2}{a c \sqrt{x}}"," ",0,"1/4*b/a/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*b/a/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*b/a/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/4*d/c/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-1/2*d/c/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-1/2*d/c/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/a/c/x^(1/2)","A"
468,1,351,340,0.016000," ","int(1/x^(5/2)/(b*x^2+a)/(d*x^2+c),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) a^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) a^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right) a^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) c^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) c^{2}}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(a d -b c \right) c^{2}}-\frac{2}{3 a c \,x^{\frac{3}{2}}}"," ",0,"1/4/a^2*b^2/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2/a^2*b^2/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2/a^2*b^2/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/4/c^2*d^2/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-1/2/c^2*d^2/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-1/2/c^2*d^2/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/3/a/c/x^(3/2)","A"
469,1,375,358,0.020000," ","int(1/x^(7/2)/(b*x^2+a)/(d*x^2+c),x)","-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{\sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{\sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{\sqrt{2}\, d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{2 d}{a \,c^{2} \sqrt{x}}+\frac{2 b}{a^{2} c \sqrt{x}}-\frac{2}{5 a c \,x^{\frac{5}{2}}}"," ",0,"-1/4*b^2/a^2/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*b^2/a^2/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*b^2/a^2/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/4*d^2/c^2/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+1/2*d^2/c^2/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+1/2*d^2/c^2/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/5/a/c/x^(5/2)+2/a/c^2/x^(1/2)*d+2/a^2/c/x^(1/2)*b","A"
470,1,582,423,0.020000," ","int(x^(11/2)/(b*x^2+a)/(d*x^2+c)^2,x)","-\frac{a \,c^{2} \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) d}+\frac{b \,c^{3} \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) d^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2} b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2} b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2} b}+\frac{9 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} d}+\frac{9 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} d}+\frac{9 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} d}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,c^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} d^{2}}+\frac{2 \sqrt{x}}{b \,d^{2}}"," ",0,"2/b/d^2*x^(1/2)-1/4/b*a^2/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2/b*a^2/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2/b*a^2/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/2*c^2/d/(a*d-b*c)^2*x^(1/2)/(d*x^2+c)*a+1/2*c^3/d^2/(a*d-b*c)^2*x^(1/2)/(d*x^2+c)*b+9/8*c/d/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a-5/8*c^2/d^2/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b+9/8*c/d/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a-5/8*c^2/d^2/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b+9/16*c/d/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a-5/16*c^2/d^2/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b","A"
471,1,566,393,0.019000," ","int(x^(9/2)/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}-\frac{b \,c^{2} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) d}+\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, a^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{7 \sqrt{2}\, a c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{7 \sqrt{2}\, a c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{7 \sqrt{2}\, a c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{3 \sqrt{2}\, b \,c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{3 \sqrt{2}\, b \,c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}+\frac{3 \sqrt{2}\, b \,c^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} d^{2}}"," ",0,"1/4*a^2/(a*d-b*c)^2/b/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*a^2/(a*d-b*c)^2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*a^2/(a*d-b*c)^2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/2*c/(a*d-b*c)^2*x^(3/2)/(d*x^2+c)*a-1/2*c^2/(a*d-b*c)^2/d*x^(3/2)/(d*x^2+c)*b-7/8*c/(a*d-b*c)^2/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a+3/8*c^2/(a*d-b*c)^2/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b-7/8*c/(a*d-b*c)^2/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a+3/8*c^2/(a*d-b*c)^2/d^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b-7/16*c/(a*d-b*c)^2/d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a+3/16*c^2/(a*d-b*c)^2/d^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b","A"
472,1,533,389,0.018000," ","int(x^(7/2)/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a c \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}-\frac{b \,c^{2} \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) d}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} d}"," ",0,"1/4*a/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*a/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*a/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/2*c/(a*d-b*c)^2*x^(1/2)/(d*x^2+c)*a-1/2*c^2/(a*d-b*c)^2/d*x^(1/2)/(d*x^2+c)*b-5/8/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a+1/8*c/(a*d-b*c)^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b-5/16/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a+1/16*c/(a*d-b*c)^2/d*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b-5/8/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a+1/8*c/(a*d-b*c)^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b","A"
473,1,528,385,0.018000," ","int(x^(5/2)/(b*x^2+a)/(d*x^2+c)^2,x)","-\frac{a d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{b c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}-\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, a \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, a \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{\sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} d}+\frac{\sqrt{2}\, b c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} d}"," ",0,"-1/4*a/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*a/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*a/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/2/(a*d-b*c)^2*x^(3/2)/(d*x^2+c)*a*d+1/2/(a*d-b*c)^2*x^(3/2)/(d*x^2+c)*b*c+3/16/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*a*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+3/8/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+3/8/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+1/16/(a*d-b*c)^2/d/(c/d)^(1/4)*2^(1/2)*b*c*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+1/8/(a*d-b*c)^2/d/(c/d)^(1/4)*2^(1/2)*b*c*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+1/8/(a*d-b*c)^2/d/(c/d)^(1/4)*2^(1/2)*b*c*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)","A"
474,1,528,385,0.019000," ","int(x^(3/2)/(b*x^2+a)/(d*x^2+c)^2,x)","-\frac{a d \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{b c \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} c}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2}}"," ",0,"-1/4*b/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*b/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*b/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/2/(a*d-b*c)^2*x^(1/2)/(d*x^2+c)*a*d+1/2/(a*d-b*c)^2*x^(1/2)/(d*x^2+c)*b*c+1/16/(a*d-b*c)^2*(c/d)^(1/4)/c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*d+3/16/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b+1/8/(a*d-b*c)^2*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*d+3/8/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b+1/8/(a*d-b*c)^2*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*d+3/8/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b","A"
475,1,533,393,0.018000," ","int(x^(1/2)/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a \,d^{2} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c}-\frac{b d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{\sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, b \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}}"," ",0,"1/4*b/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*b/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*b/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/2*d^2/(a*d-b*c)^2/c*x^(3/2)/(d*x^2+c)*a-1/2*d/(a*d-b*c)^2*x^(3/2)/(d*x^2+c)*b+1/8*d/(a*d-b*c)^2/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a-5/8/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b+1/8*d/(a*d-b*c)^2/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a-5/8/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b+1/16*d/(a*d-b*c)^2/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a-5/16/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b","A"
476,1,566,393,0.018000," ","int(1/(b*x^2+a)/(d*x^2+c)^2/x^(1/2),x)","\frac{a \,d^{2} \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c}-\frac{b d \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} c^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2} a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2} a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2} a}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} c}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} c}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} c}"," ",0,"1/4*b^2/(a*d-b*c)^2*(a/b)^(1/4)/a*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*b^2/(a*d-b*c)^2*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*b^2/(a*d-b*c)^2*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/2*d^2/(a*d-b*c)^2/c*x^(1/2)/(d*x^2+c)*a-1/2*d/(a*d-b*c)^2*x^(1/2)/(d*x^2+c)*b+3/16*d^2/(a*d-b*c)^2/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a-7/16*d/(a*d-b*c)^2/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b+3/8*d^2/(a*d-b*c)^2/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a-7/8*d/(a*d-b*c)^2/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b+3/8*d^2/(a*d-b*c)^2/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a-7/8*d/(a*d-b*c)^2/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b","A"
477,1,582,423,0.023000," ","int(1/x^(3/2)/(b*x^2+a)/(d*x^2+c)^2,x)","-\frac{a \,d^{3} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c^{2}}+\frac{b \,d^{2} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c}-\frac{5 \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{5 \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{5 \sqrt{2}\, a \,d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{9 \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{9 \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{9 \sqrt{2}\, b d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{2}{a \,c^{2} \sqrt{x}}"," ",0,"-1/4*b^2/a/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*b^2/a/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*b^2/a/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/2*d^3/c^2/(a*d-b*c)^2*x^(3/2)/(d*x^2+c)*a+1/2*d^2/c/(a*d-b*c)^2*x^(3/2)/(d*x^2+c)*b-5/16*d^2/c^2/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*a*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-5/8*d^2/c^2/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-5/8*d^2/c^2/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+9/16*d/c/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+9/8*d/c/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+9/8*d/c/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/a/c^2/x^(1/2)","A"
478,1,588,423,0.021000," ","int(1/x^(5/2)/(b*x^2+a)/(d*x^2+c)^2,x)","-\frac{a \,d^{3} \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c^{2}}+\frac{b \,d^{2} \sqrt{x}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} c^{3}}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} c^{3}}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} c^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2} a^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2} a^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2} a^{2}}+\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} c^{2}}+\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} c^{2}}+\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} c^{2}}-\frac{2}{3 a \,c^{2} x^{\frac{3}{2}}}"," ",0,"-1/4/a^2*b^3/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2/a^2*b^3/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2/a^2*b^3/(a*d-b*c)^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/2*d^3/c^2/(a*d-b*c)^2*x^(1/2)/(d*x^2+c)*a+1/2*d^2/c/(a*d-b*c)^2*x^(1/2)/(d*x^2+c)*b-7/8*d^3/c^3/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a+11/8*d^2/c^2/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b-7/16*d^3/c^3/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a+11/16*d^2/c^2/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b-7/8*d^3/c^3/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a+11/8*d^2/c^2/(a*d-b*c)^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b-2/3/a/c^2/x^(3/2)","A"
479,1,612,467,0.025000," ","int(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a \,d^{4} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c^{3}}-\frac{b \,d^{3} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c^{2}}+\frac{9 \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{9 \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{9 \sqrt{2}\, a \,d^{3} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{\sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{\sqrt{2}\, b^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{13 \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{13 \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{13 \sqrt{2}\, b \,d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{4 d}{a \,c^{3} \sqrt{x}}+\frac{2 b}{a^{2} c^{2} \sqrt{x}}-\frac{2}{5 a \,c^{2} x^{\frac{5}{2}}}"," ",0,"1/4*b^3/a^2/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*b^3/a^2/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*b^3/a^2/(a*d-b*c)^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/2*d^4/c^3/(a*d-b*c)^2*x^(3/2)/(d*x^2+c)*a-1/2*d^3/c^2/(a*d-b*c)^2*x^(3/2)/(d*x^2+c)*b+9/16*d^3/c^3/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*a*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+9/8*d^3/c^3/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+9/8*d^3/c^3/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-13/16*d^2/c^2/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-13/8*d^2/c^2/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-13/8*d^2/c^2/(a*d-b*c)^2/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/5/a/c^2/x^(5/2)+4/a/c^3/x^(1/2)*d+2/a^2/c^2/x^(1/2)*b","A"
480,1,839,484,0.021000," ","int(x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x)","-\frac{9 a^{2} d^{2} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{5 a b c d \,x^{\frac{5}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{b^{2} c^{2} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{5 a^{2} c d \sqrt{x}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{a b \,c^{2} \sqrt{x}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{3 b^{2} c^{3} \sqrt{x}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} d}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} c}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} c}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} c}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{3}}+\frac{15 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{3}}+\frac{15 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{3}}+\frac{15 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{3}}-\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} d}-\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} d}-\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} d}"," ",0,"-1/4*a*b/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*a*b/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*a*b/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-9/16/(a*d-b*c)^3/(d*x^2+c)^2*x^(5/2)*a^2*d^2+5/8/(a*d-b*c)^3/(d*x^2+c)^2*x^(5/2)*a*b*c*d-1/16/(a*d-b*c)^3/(d*x^2+c)^2*x^(5/2)*b^2*c^2-5/16/(a*d-b*c)^3/(d*x^2+c)^2*c*d*x^(1/2)*a^2+1/8/(a*d-b*c)^3/(d*x^2+c)^2*c^2*x^(1/2)*a*b+3/16/(a*d-b*c)^3/(d*x^2+c)^2*c^3/d*x^(1/2)*b^2+5/64/(a*d-b*c)^3*d*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+15/32/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-3/64/(a*d-b*c)^3/d*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+5/64/(a*d-b*c)^3*d*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+15/32/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-3/64/(a*d-b*c)^3/d*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+5/128/(a*d-b*c)^3*d*(c/d)^(1/4)/c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+15/64/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-3/128/(a*d-b*c)^3/d*(c/d)^(1/4)*c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
481,1,839,481,0.023000," ","int(x^(5/2)/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{3 a^{2} d^{3} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}+\frac{a b \,d^{2} x^{\frac{7}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{5 b^{2} c d \,x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{a^{2} d^{2} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{5 a b c d \,x^{\frac{3}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{9 b^{2} c^{2} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{3 \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{3 \sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{3 \sqrt{2}\, a^{2} d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{15 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{15 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{15 \sqrt{2}\, a b \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{5 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{5 \sqrt{2}\, b^{2} c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} d}"," ",0,"1/4*a*b/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*a*b/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*a*b/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/16/(a*d-b*c)^3/(d*x^2+c)^2*d^3/c*x^(7/2)*a^2+1/8/(a*d-b*c)^3/(d*x^2+c)^2*d^2*x^(7/2)*a*b-5/16/(a*d-b*c)^3/(d*x^2+c)^2*d*c*x^(7/2)*b^2-1/16/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*a^2*d^2+5/8/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*a*b*c*d-9/16/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*b^2*c^2+3/64/(a*d-b*c)^3/c*d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-15/32/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-5/64/(a*d-b*c)^3*c/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+3/128/(a*d-b*c)^3/c*d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-15/64/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-5/128/(a*d-b*c)^3*c/d/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+3/64/(a*d-b*c)^3/c*d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-15/32/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-5/64/(a*d-b*c)^3*c/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2","A"
482,1,848,480,0.021000," ","int(x^(3/2)/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{a^{2} d^{3} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}+\frac{3 a b \,d^{2} x^{\frac{5}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{7 b^{2} c d \,x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{3 a^{2} d^{2} \sqrt{x}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{7 a b c d \sqrt{x}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{11 b^{2} c^{2} \sqrt{x}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} c^{2}}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{3} c}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{3} c}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{3} c}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{3}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{3}}-\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3}}-\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{3}}-\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3}}"," ",0,"1/4*b^2/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*b^2/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*b^2/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/16/(a*d-b*c)^3/(d*x^2+c)^2*d^3/c*x^(5/2)*a^2+3/8/(a*d-b*c)^3/(d*x^2+c)^2*d^2*x^(5/2)*a*b-7/16/(a*d-b*c)^3/(d*x^2+c)^2*d*c*x^(5/2)*b^2+7/8/(a*d-b*c)^3/(d*x^2+c)^2*x^(1/2)*a*b*c*d-11/16/(a*d-b*c)^3/(d*x^2+c)^2*x^(1/2)*b^2*c^2-3/16/(a*d-b*c)^3/(d*x^2+c)^2*x^(1/2)*a^2*d^2+3/64/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2*d^2-7/32/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b*d-21/64/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+3/64/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2*d^2-7/32/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b*d-21/64/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+3/128/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2*d^2-7/64/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b*d-21/128/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
483,1,855,486,0.022000," ","int(x^(1/2)/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{5 a^{2} d^{4} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{9 a b \,d^{3} x^{\frac{7}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}+\frac{13 b^{2} d^{2} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{9 a^{2} d^{3} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{13 a b \,d^{2} x^{\frac{3}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{17 b^{2} c d \,x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{5 \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{5 \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{5 \sqrt{2}\, a^{2} d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{9 \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{9 \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{9 \sqrt{2}\, a b d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{45 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{45 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{45 \sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}"," ",0,"-1/4*b^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*b^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*b^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+5/16*d^4/(a*d-b*c)^3/(d*x^2+c)^2/c^2*x^(7/2)*a^2-9/8*d^3/(a*d-b*c)^3/(d*x^2+c)^2/c*x^(7/2)*a*b+13/16*d^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(7/2)*b^2+9/16*d^3/(a*d-b*c)^3/(d*x^2+c)^2/c*x^(3/2)*a^2-13/8*d^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*a*b+17/16*d/(a*d-b*c)^3/(d*x^2+c)^2*c*x^(3/2)*b^2+5/64*d^2/(a*d-b*c)^3/c^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-9/32*d/(a*d-b*c)^3/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+45/64/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+5/128*d^2/(a*d-b*c)^3/c^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-9/64*d/(a*d-b*c)^3/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+45/128/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2+5/64*d^2/(a*d-b*c)^3/c^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-9/32*d/(a*d-b*c)^3/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+45/64/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2","A"
484,1,882,486,0.020000," ","int(1/(b*x^2+a)/(d*x^2+c)^3/x^(1/2),x)","\frac{7 a^{2} d^{4} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{11 a b \,d^{3} x^{\frac{5}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}+\frac{15 b^{2} d^{2} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{11 a^{2} d^{3} \sqrt{x}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{15 a b \,d^{2} \sqrt{x}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{19 b^{2} c d \sqrt{x}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} c^{3}}-\frac{33 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{3} c^{2}}-\frac{33 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{3} c^{2}}-\frac{33 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{3} c^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{3} a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{3} a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{3} a}+\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} c}+\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} c}+\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} c}"," ",0,"-1/4*b^3/(a*d-b*c)^3*(a/b)^(1/4)/a*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*b^3/(a*d-b*c)^3*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*b^3/(a*d-b*c)^3*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+7/16*d^4/(a*d-b*c)^3/(d*x^2+c)^2/c^2*x^(5/2)*a^2-11/8*d^3/(a*d-b*c)^3/(d*x^2+c)^2/c*x^(5/2)*a*b+15/16*d^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(5/2)*b^2+11/16*d^3/(a*d-b*c)^3/(d*x^2+c)^2/c*x^(1/2)*a^2-15/8*d^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(1/2)*a*b+19/16*d/(a*d-b*c)^3/(d*x^2+c)^2*c*x^(1/2)*b^2+21/64*d^3/(a*d-b*c)^3/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-33/32*d^2/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+77/64*d/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+21/64*d^3/(a*d-b*c)^3/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-33/32*d^2/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+77/64*d/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+21/128*d^3/(a*d-b*c)^3/c^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-33/64*d^2/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+77/128*d/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
485,1,900,530,0.027000," ","int(1/x^(3/2)/(b*x^2+a)/(d*x^2+c)^3,x)","-\frac{13 a^{2} d^{5} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{17 a b \,d^{4} x^{\frac{7}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{21 b^{2} d^{3} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{17 a^{2} d^{4} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{21 a b \,d^{3} x^{\frac{3}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{25 b^{2} d^{2} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{45 \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{45 \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{45 \sqrt{2}\, a^{2} d^{3} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{65 \sqrt{2}\, a b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{65 \sqrt{2}\, a b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{65 \sqrt{2}\, a b \,d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{\sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b^{3} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{117 \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{117 \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{117 \sqrt{2}\, b^{2} d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{2}{a \,c^{3} \sqrt{x}}"," ",0,"1/4*b^3/a/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2*b^3/a/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2*b^3/a/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-13/16*d^5/c^3/(a*d-b*c)^3/(d*x^2+c)^2*x^(7/2)*a^2+17/8*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(7/2)*a*b-21/16*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*x^(7/2)*b^2-17/16*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*a^2+21/8*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*a*b-25/16*d^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*b^2-45/128*d^3/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-45/64*d^3/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-45/64*d^3/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+65/64*d^2/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+65/32*d^2/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+65/32*d^2/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-117/128*d/c/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-117/64*d/c/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-117/64*d/c/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/a/c^3/x^(1/2)","A"
486,1,906,530,0.028000," ","int(1/x^(5/2)/(b*x^2+a)/(d*x^2+c)^3,x)","-\frac{15 a^{2} d^{5} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{19 a b \,d^{4} x^{\frac{5}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{23 b^{2} d^{3} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{19 a^{2} d^{4} \sqrt{x}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{23 a b \,d^{3} \sqrt{x}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{27 b^{2} d^{2} \sqrt{x}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} c^{4}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} c^{4}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{4} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} c^{4}}+\frac{105 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{3} c^{3}}+\frac{105 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{3} c^{3}}+\frac{105 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{3} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{3} c^{3}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{3} a^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{3} a^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{3} a^{2}}-\frac{165 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} c^{2}}-\frac{165 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} c^{2}}-\frac{165 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} c^{2}}-\frac{2}{3 a \,c^{3} x^{\frac{3}{2}}}"," ",0,"1/4/a^2*b^4/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+1/2/a^2*b^4/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+1/2/a^2*b^4/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-15/16*d^5/c^3/(a*d-b*c)^3/(d*x^2+c)^2*x^(5/2)*a^2+19/8*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(5/2)*a*b-23/16*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*x^(5/2)*b^2-19/16*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(1/2)*a^2+23/8*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*x^(1/2)*a*b-27/16*d^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(1/2)*b^2-77/64*d^4/c^4/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+105/32*d^3/c^3/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-165/64*d^2/c^2/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-77/64*d^4/c^4/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+105/32*d^3/c^3/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-165/64*d^2/c^2/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-77/128*d^4/c^4/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+105/64*d^3/c^3/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-165/128*d^2/c^2/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2-2/3/a/c^3/x^(3/2)","A"
487,1,933,588,0.028000," ","int(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{21 a^{2} d^{6} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{4}}-\frac{25 a b \,d^{5} x^{\frac{7}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{29 b^{2} d^{4} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{25 a^{2} d^{5} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{3}}-\frac{29 a b \,d^{4} x^{\frac{3}{2}}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{33 b^{2} d^{3} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}+\frac{117 \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{4}}+\frac{117 \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{4}}+\frac{117 \sqrt{2}\, a^{2} d^{4} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{4}}-\frac{153 \sqrt{2}\, a b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{153 \sqrt{2}\, a b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{153 \sqrt{2}\, a b \,d^{3} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{\sqrt{2}\, b^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{\sqrt{2}\, b^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{\sqrt{2}\, b^{4} \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{4 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{221 \sqrt{2}\, b^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{221 \sqrt{2}\, b^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{221 \sqrt{2}\, b^{2} d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{6 d}{a \,c^{4} \sqrt{x}}+\frac{2 b}{a^{2} c^{3} \sqrt{x}}-\frac{2}{5 a \,c^{3} x^{\frac{5}{2}}}"," ",0,"-1/4*b^4/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*b^4/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1/2*b^4/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+21/16*d^6/c^4/(a*d-b*c)^3/(d*x^2+c)^2*x^(7/2)*a^2-25/8*d^5/c^3/(a*d-b*c)^3/(d*x^2+c)^2*x^(7/2)*a*b+29/16*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(7/2)*b^2+25/16*d^5/c^3/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*a^2-29/8*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*a*b+33/16*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*b^2+117/128*d^4/c^4/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+117/64*d^4/c^4/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+117/64*d^4/c^4/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-153/64*d^3/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-153/32*d^3/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-153/32*d^3/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+221/128*d^2/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+221/64*d^2/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+221/64*d^2/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/5/a/c^3/x^(5/2)+6/a/c^4/x^(1/2)*d+2/a^2/c^3/x^(1/2)*b","A"
488,1,740,472,0.023000," ","int(x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a^{2} d \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{a b c \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{a c d \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{b \,c^{2} \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3}}-\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3}}-\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3}}-\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3}}"," ",0,"1/2*a^2/(a*d-b*c)^3*x^(1/2)/(b*x^2+a)*d-1/2*a/(a*d-b*c)^3*x^(1/2)/(b*x^2+a)*b*c+3/8*a/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d+5/8/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*b*c+3/8*a/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d+5/8/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*b*c+3/16*a/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d+5/16/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*b*c+1/2*c/(a*d-b*c)^3*x^(1/2)/(d*x^2+c)*a*d-1/2*c^2/(a*d-b*c)^3*x^(1/2)/(d*x^2+c)*b-5/8/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*d-3/8*c/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b-5/8/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*d-3/8*c/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b-5/16/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*d-3/16*c/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b","A"
489,1,740,459,0.023000," ","int(x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x)","-\frac{a b d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{a \,d^{2} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{b^{2} c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{b c d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{5 \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, a d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, a d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{5 \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{5 \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, b c \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{5 \sqrt{2}\, b c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}"," ",0,"-1/2*b/(a*d-b*c)^3*x^(3/2)/(b*x^2+a)*a*d+1/2*b^2/(a*d-b*c)^3*x^(3/2)/(b*x^2+a)*c-5/16/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*a*d*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-5/8/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*a*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-5/8/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*a*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-3/16*b/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-3/8*b/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-3/8*b/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/2*d^2/(a*d-b*c)^3*x^(3/2)/(d*x^2+c)*a+1/2*d/(a*d-b*c)^3*x^(3/2)/(d*x^2+c)*b*c+5/16/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*c*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+5/8/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*c*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+5/8/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*c*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+3/16*d/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+3/8*d/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+3/8*d/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)","A"
490,1,770,451,0.021000," ","int(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^2,x)","-\frac{a b d \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{a \,d^{2} \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{b^{2} c \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{b c d \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} c}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} a}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3}}+\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3}}+\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3}}+\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3}}"," ",0,"-1/2*b/(a*d-b*c)^3*x^(1/2)/(b*x^2+a)*a*d+1/2*b^2/(a*d-b*c)^3*x^(1/2)/(b*x^2+a)*c-7/8*b/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d-1/8*b^2/(a*d-b*c)^3*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c-7/16*b/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d-1/16*b^2/(a*d-b*c)^3*(a/b)^(1/4)/a*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c-7/8*b/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d-1/8*b^2/(a*d-b*c)^3*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c-1/2*d^2/(a*d-b*c)^3*x^(1/2)/(d*x^2+c)*a+1/2*d/(a*d-b*c)^3*x^(1/2)/(d*x^2+c)*b*c+1/8*d^2/(a*d-b*c)^3*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a+7/8*d/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b+1/8*d^2/(a*d-b*c)^3*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a+7/8*d/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b+1/16*d^2/(a*d-b*c)^3*(c/d)^(1/4)/c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a+7/16*d/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b","A"
491,1,778,472,0.024000," ","int(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a \,d^{3} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}-\frac{b^{3} c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a}+\frac{b^{2} d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{b \,d^{2} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{\sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a \,d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, b^{2} c \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{9 \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{9 \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{9 \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{9 \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{9 \sqrt{2}\, b d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{9 \sqrt{2}\, b d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}}}"," ",0,"1/2*b^2/(a*d-b*c)^3*x^(3/2)/(b*x^2+a)*d-1/2*b^3/(a*d-b*c)^3/a*x^(3/2)/(b*x^2+a)*c+9/8*b/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d-1/8*b^2/(a*d-b*c)^3/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c+9/16*b/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d-1/16*b^2/(a*d-b*c)^3/a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c+9/8*b/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d-1/8*b^2/(a*d-b*c)^3/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c+1/2*d^3/(a*d-b*c)^3/c*x^(3/2)/(d*x^2+c)*a-1/2*d^2/(a*d-b*c)^3*x^(3/2)/(d*x^2+c)*b+1/8*d^2/(a*d-b*c)^3/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a-9/8*d/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b+1/8*d^2/(a*d-b*c)^3/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a-9/8*d/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b+1/16*d^2/(a*d-b*c)^3/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a-9/16*d/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b","A"
492,1,808,476,0.025000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^2/x^(1/2),x)","\frac{a \,d^{3} \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}-\frac{b^{3} c \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a}+\frac{b^{2} d \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}-\frac{b \,d^{2} \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} c^{2}}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} a}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} a}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} a}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} a^{2}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} a^{2}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} a^{2}}-\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} c}-\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} c}-\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} c}"," ",0,"1/2*b^2/(a*d-b*c)^3*x^(1/2)/(b*x^2+a)*d-1/2*b^3/(a*d-b*c)^3/a*x^(1/2)/(b*x^2+a)*c+11/8*b^2/(a*d-b*c)^3/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d-3/8*b^3/(a*d-b*c)^3/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c+11/16*b^2/(a*d-b*c)^3/a*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d-3/16*b^3/(a*d-b*c)^3/a^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c+11/8*b^2/(a*d-b*c)^3/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d-3/8*b^3/(a*d-b*c)^3/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c+1/2*d^3/(a*d-b*c)^3/c*x^(1/2)/(d*x^2+c)*a-1/2*d^2/(a*d-b*c)^3*x^(1/2)/(d*x^2+c)*b+3/16*d^3/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a-11/16*d^2/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b+3/8*d^3/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a-11/8*d^2/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b+3/8*d^3/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a-11/8*d^2/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b","A"
493,1,825,520,0.027000," ","int(1/x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^2,x)","-\frac{a \,d^{4} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{2}}-\frac{b^{3} d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a}+\frac{b^{4} c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a^{2}}+\frac{b \,d^{3} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}-\frac{5 \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{5 \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{5 \sqrt{2}\, a \,d^{3} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{13 \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{13 \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{13 \sqrt{2}\, b^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{5 \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{5 \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{5 \sqrt{2}\, b^{3} c \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{13 \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{13 \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{13 \sqrt{2}\, b \,d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{2}{a^{2} c^{2} \sqrt{x}}"," ",0,"-1/2*b^3/a/(a*d-b*c)^3*x^(3/2)/(b*x^2+a)*d+1/2*b^4/a^2/(a*d-b*c)^3*x^(3/2)/(b*x^2+a)*c-13/16*b^2/a/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*d*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-13/8*b^2/a/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-13/8*b^2/a/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+5/16*b^3/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+5/8*b^3/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+5/8*b^3/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-1/2*d^4/c^2/(a*d-b*c)^3*x^(3/2)/(d*x^2+c)*a+1/2*d^3/c/(a*d-b*c)^3*x^(3/2)/(d*x^2+c)*b-5/16*d^3/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-5/8*d^3/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-5/8*d^3/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+13/16*d^2/c/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+13/8*d^2/c/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+13/8*d^2/c/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/a^2/c^2/x^(1/2)","A"
494,1,825,520,0.027000," ","int(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x)","-\frac{a \,d^{4} \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{2}}-\frac{b^{3} d \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a}+\frac{b^{4} c \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a^{2}}+\frac{b \,d^{3} \sqrt{x}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} c^{3}}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} c^{3}}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{4} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} c^{3}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} a^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} a^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} a^{2}}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} a^{3}}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} a^{3}}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} a^{3}}+\frac{15 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} c^{2}}+\frac{15 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} c^{2}}+\frac{15 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{3} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} c^{2}}-\frac{2}{3 a^{2} c^{2} x^{\frac{3}{2}}}"," ",0,"-1/2*b^3/a/(a*d-b*c)^3*x^(1/2)/(b*x^2+a)*d+1/2*b^4/a^2/(a*d-b*c)^3*x^(1/2)/(b*x^2+a)*c-15/8*b^3/a^2/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d+7/8*b^4/a^3/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c-15/8*b^3/a^2/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d+7/8*b^4/a^3/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c-15/16*b^3/a^2/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d+7/16*b^4/a^3/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c-1/2*d^4/c^2/(a*d-b*c)^3*x^(1/2)/(d*x^2+c)*a+1/2*d^3/c/(a*d-b*c)^3*x^(1/2)/(d*x^2+c)*b-7/8*d^4/c^3/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a+15/8*d^3/c^2/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b-7/16*d^4/c^3/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a+15/16*d^3/c^2/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b-7/8*d^4/c^3/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a+15/8*d^3/c^2/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b-2/3/a^2/c^2/x^(3/2)","A"
495,1,849,571,0.031000," ","int(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a \,d^{5} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{3}}+\frac{b^{4} d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a^{2}}-\frac{b^{5} c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a^{3}}-\frac{b \,d^{4} x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c^{2}}+\frac{9 \sqrt{2}\, a \,d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{9 \sqrt{2}\, a \,d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{9 \sqrt{2}\, a \,d^{4} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{17 \sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{17 \sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{17 \sqrt{2}\, b^{3} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{9 \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{9 \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{9 \sqrt{2}\, b^{4} c \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}-\frac{17 \sqrt{2}\, b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{17 \sqrt{2}\, b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{17 \sqrt{2}\, b \,d^{3} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{16 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{4 d}{a^{2} c^{3} \sqrt{x}}+\frac{4 b}{a^{3} c^{2} \sqrt{x}}-\frac{2}{5 a^{2} c^{2} x^{\frac{5}{2}}}"," ",0,"1/2*b^4/a^2/(a*d-b*c)^3*x^(3/2)/(b*x^2+a)*d-1/2*b^5/a^3/(a*d-b*c)^3*x^(3/2)/(b*x^2+a)*c+17/16*b^3/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*d*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+17/8*b^3/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+17/8*b^3/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-9/16*b^4/a^3/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-9/8*b^4/a^3/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-9/8*b^4/a^3/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/2*d^5/c^3/(a*d-b*c)^3*x^(3/2)/(d*x^2+c)*a-1/2*d^4/c^2/(a*d-b*c)^3*x^(3/2)/(d*x^2+c)*b+9/16*d^4/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+9/8*d^4/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+9/8*d^4/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-17/16*d^3/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-17/8*d^3/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-17/8*d^3/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/5/a^2/c^2/x^(5/2)+4/a^2/c^3/x^(1/2)*d+4/a^3/c^2/x^(1/2)*b","A"
496,1,1066,562,0.026000," ","int(x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{9 a^{2} d^{3} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{a b c \,d^{2} x^{\frac{5}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{7 b^{2} c^{2} d \,x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{5 a^{2} c \,d^{2} \sqrt{x}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{3 a b \,c^{2} d \sqrt{x}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{11 b^{2} c^{3} \sqrt{x}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{a^{2} b d \sqrt{x}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{a \,b^{2} c \sqrt{x}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} c}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} c}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} c}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4}}+\frac{35 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{4}}+\frac{35 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{4}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4}}+\frac{35 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{4}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4}}"," ",0,"-1/2*a^2*b/(a*d-b*c)^4*x^(1/2)/(b*x^2+a)*d+1/2*a*b^2/(a*d-b*c)^4*x^(1/2)/(b*x^2+a)*c-7/8*a*b/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d-5/8*b^2/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c-7/8*a*b/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d-5/8*b^2/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c-7/16*a*b/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d-5/16*b^2/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c-9/16/(a*d-b*c)^4/(d*x^2+c)^2*x^(5/2)*a^2*d^3+1/8/(a*d-b*c)^4/(d*x^2+c)^2*x^(5/2)*a*b*c*d^2+7/16/(a*d-b*c)^4/(d*x^2+c)^2*x^(5/2)*b^2*c^2*d-5/16/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*a^2*c*d^2-3/8/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*a*b*c^2*d+11/16/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*b^2*c^3+5/64/(a*d-b*c)^4*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2*d^2+35/32/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b*d+21/64/(a*d-b*c)^4*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+5/64/(a*d-b*c)^4*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2*d^2+35/32/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b*d+21/64/(a*d-b*c)^4*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+5/128/(a*d-b*c)^4*(c/d)^(1/4)/c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2*d^2+35/64/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b*d+21/128/(a*d-b*c)^4*(c/d)^(1/4)*c*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
497,1,1067,547,0.026000," ","int(x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{3 a^{2} d^{4} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}+\frac{5 a b \,d^{3} x^{\frac{7}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{13 b^{2} c \,d^{2} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{a^{2} d^{3} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{9 a b c \,d^{2} x^{\frac{3}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{17 b^{2} c^{2} d \,x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{a \,b^{2} d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}-\frac{b^{3} c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{3 \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{3 \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{3 \sqrt{2}\, a^{2} d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{9 \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{9 \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{27 \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{27 \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{9 \sqrt{2}\, a b d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{27 \sqrt{2}\, a b d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{45 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{45 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, b^{2} c \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{45 \sqrt{2}\, b^{2} c \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}}}"," ",0,"1/2*b^2/(a*d-b*c)^4*x^(3/2)/(b*x^2+a)*a*d-1/2*b^3/(a*d-b*c)^4*x^(3/2)/(b*x^2+a)*c+9/16*b/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*a*d*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+9/8*b/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*a*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+9/8*b/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*a*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/16*b^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*c*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+3/8*b^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+3/8*b^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+3/16*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^(7/2)*a^2+5/8*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(7/2)*a*b-13/16*d^2/(a*d-b*c)^4/(d*x^2+c)^2*c*x^(7/2)*b^2-1/16*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*a^2+9/8*d^2/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*a*b*c-17/16*d/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*b^2*c^2+3/64*d^2/(a*d-b*c)^4/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-27/32*d/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-45/64/(a*d-b*c)^4*c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+3/64*d^2/(a*d-b*c)^4/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-27/32*d/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-45/64/(a*d-b*c)^4*c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+3/128*d^2/(a*d-b*c)^4/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-27/64*d/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-45/128/(a*d-b*c)^4*c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
498,1,1094,547,0.027000," ","int(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{a^{2} d^{4} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}+\frac{7 a b \,d^{3} x^{\frac{5}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{15 b^{2} c \,d^{2} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{3 a^{2} d^{3} \sqrt{x}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{11 a b c \,d^{2} \sqrt{x}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}-\frac{19 b^{2} c^{2} d \sqrt{x}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{a \,b^{2} d \sqrt{x}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}-\frac{b^{3} c \sqrt{x}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} c^{2}}-\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{4} c}-\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{4} c}-\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{4} c}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} a}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4}}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4}}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4}}"," ",0,"1/2*b^2/(a*d-b*c)^4*x^(1/2)/(b*x^2+a)*a*d-1/2*b^3/(a*d-b*c)^4*x^(1/2)/(b*x^2+a)*c+11/8*b^2/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d+1/8*b^3/(a*d-b*c)^4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c+11/8*b^2/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d+1/8*b^3/(a*d-b*c)^4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c+11/16*b^2/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d+1/16*b^3/(a*d-b*c)^4*(a/b)^(1/4)/a*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c+1/16*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^(5/2)*a^2+7/8*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(5/2)*a*b-15/16*d^2/(a*d-b*c)^4/(d*x^2+c)^2*c*x^(5/2)*b^2+11/8*d^2/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*a*b*c-19/16*d/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*b^2*c^2-3/16*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*a^2+3/64*d^3/(a*d-b*c)^4/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-11/32*d^2/(a*d-b*c)^4/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-77/64*d/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+3/64*d^3/(a*d-b*c)^4/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-11/32*d^2/(a*d-b*c)^4/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-77/64*d/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+3/128*d^3/(a*d-b*c)^4/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-11/64*d^2/(a*d-b*c)^4/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-77/128*d/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
499,1,1100,583,0.029000," ","int(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{5 a^{2} d^{5} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{13 a b \,d^{4} x^{\frac{7}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}+\frac{21 b^{2} d^{3} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{9 a^{2} d^{4} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{17 a b \,d^{3} x^{\frac{3}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{25 b^{2} c \,d^{2} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{b^{4} c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a}-\frac{b^{3} d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{5 \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{5 \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{5 \sqrt{2}\, a^{2} d^{3} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}-\frac{13 \sqrt{2}\, a b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{13 \sqrt{2}\, a b \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{13 \sqrt{2}\, a b \,d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b^{3} c \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{13 \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{13 \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{117 \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{117 \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{13 \sqrt{2}\, b^{2} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{117 \sqrt{2}\, b^{2} d \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}}}"," ",0,"-1/2*b^3/(a*d-b*c)^4*x^(3/2)/(b*x^2+a)*d+1/2*b^4/(a*d-b*c)^4/a*x^(3/2)/(b*x^2+a)*c-13/8*b^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d+1/8*b^3/(a*d-b*c)^4/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c-13/16*b^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d+1/16*b^3/(a*d-b*c)^4/a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c-13/8*b^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d+1/8*b^3/(a*d-b*c)^4/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c+5/16*d^5/(a*d-b*c)^4/(d*x^2+c)^2/c^2*x^(7/2)*a^2-13/8*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^(7/2)*a*b+21/16*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(7/2)*b^2+9/16*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^(3/2)*a^2-17/8*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*a*b+25/16*d^2/(a*d-b*c)^4/(d*x^2+c)^2*c*x^(3/2)*b^2+5/64*d^3/(a*d-b*c)^4/c^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-13/32*d^2/(a*d-b*c)^4/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+117/64*d/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+5/64*d^3/(a*d-b*c)^4/c^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-13/32*d^2/(a*d-b*c)^4/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+117/64*d/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+5/128*d^3/(a*d-b*c)^4/c^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-13/64*d^2/(a*d-b*c)^4/c/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+117/128*d/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
500,1,1124,583,0.026000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^3/x^(1/2),x)","\frac{7 a^{2} d^{5} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{15 a b \,d^{4} x^{\frac{5}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}+\frac{23 b^{2} d^{3} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{11 a^{2} d^{4} \sqrt{x}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{19 a b \,d^{3} \sqrt{x}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{27 b^{2} c \,d^{2} \sqrt{x}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{b^{4} c \sqrt{x}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a}-\frac{b^{3} d \sqrt{x}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{4} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} c^{3}}-\frac{45 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{4} c^{2}}-\frac{45 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{4} c^{2}}-\frac{45 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{3} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{4} c^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} a}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} a}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} a}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} a^{2}}+\frac{165 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} c}+\frac{165 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} c}+\frac{165 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} c}"," ",0,"-1/2*b^3/(a*d-b*c)^4*x^(1/2)/(b*x^2+a)*d+1/2*b^4/(a*d-b*c)^4/a*x^(1/2)/(b*x^2+a)*c-15/8*b^3/(a*d-b*c)^4/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d+3/8*b^4/(a*d-b*c)^4/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c-15/8*b^3/(a*d-b*c)^4/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d+3/8*b^4/(a*d-b*c)^4/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c-15/16*b^3/(a*d-b*c)^4/a*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d+3/16*b^4/(a*d-b*c)^4/a^2*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c+7/16*d^5/(a*d-b*c)^4/(d*x^2+c)^2/c^2*x^(5/2)*a^2-15/8*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^(5/2)*a*b+23/16*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(5/2)*b^2+11/16*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^(1/2)*a^2-19/8*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*a*b+27/16*d^2/(a*d-b*c)^4/(d*x^2+c)^2*c*x^(1/2)*b^2+21/64*d^4/(a*d-b*c)^4/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-45/32*d^3/(a*d-b*c)^4/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+165/64*d^2/(a*d-b*c)^4/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2+21/64*d^4/(a*d-b*c)^4/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-45/32*d^3/(a*d-b*c)^4/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+165/64*d^2/(a*d-b*c)^4/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+21/128*d^4/(a*d-b*c)^4/c^3*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-45/64*d^3/(a*d-b*c)^4/c^2*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+165/128*d^2/(a*d-b*c)^4/c*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2","A"
501,1,1143,645,0.036000," ","int(1/x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{13 a^{2} d^{6} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{21 a b \,d^{5} x^{\frac{7}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{29 b^{2} d^{4} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{17 a^{2} d^{5} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{25 a b \,d^{4} x^{\frac{3}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{33 b^{2} d^{3} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{b^{4} d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a}-\frac{b^{5} c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a^{2}}-\frac{45 \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{45 \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{45 \sqrt{2}\, a^{2} d^{4} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}+\frac{85 \sqrt{2}\, a b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{85 \sqrt{2}\, a b \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{85 \sqrt{2}\, a b \,d^{3} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{17 \sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{17 \sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{17 \sqrt{2}\, b^{3} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{5 \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, b^{4} c \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{221 \sqrt{2}\, b^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{221 \sqrt{2}\, b^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{221 \sqrt{2}\, b^{2} d^{2} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{2}{a^{2} c^{3} \sqrt{x}}"," ",0,"1/2*b^4/a/(a*d-b*c)^4*x^(3/2)/(b*x^2+a)*d-1/2*b^5/a^2/(a*d-b*c)^4*x^(3/2)/(b*x^2+a)*c+17/16*b^3/a/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*d*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+17/8*b^3/a/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+17/8*b^3/a/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-5/16*b^4/a^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*c*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-5/8*b^4/a^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-5/8*b^4/a^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-13/16*d^6/c^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(7/2)*a^2+21/8*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*x^(7/2)*a*b-29/16*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*x^(7/2)*b^2-17/16*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*a^2+25/8*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*a*b-33/16*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*b^2-45/128*d^4/c^3/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-45/64*d^4/c^3/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-45/64*d^4/c^3/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+85/64*d^3/c^2/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+85/32*d^3/c^2/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+85/32*d^3/c^2/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-221/128*d^2/c/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*b^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-221/64*d^2/c/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-221/64*d^2/c/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/a^2/c^3/x^(1/2)","A"
502,1,1143,645,0.033000," ","int(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^3,x)","-\frac{15 a^{2} d^{6} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{23 a b \,d^{5} x^{\frac{5}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{31 b^{2} d^{4} x^{\frac{5}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{19 a^{2} d^{5} \sqrt{x}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{27 a b \,d^{4} \sqrt{x}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{35 b^{2} d^{3} \sqrt{x}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{b^{4} d \sqrt{x}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a}-\frac{b^{5} c \sqrt{x}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a^{2}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} c^{4}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} c^{4}}-\frac{77 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{5} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} c^{4}}+\frac{133 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{4} c^{3}}+\frac{133 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{4} c^{3}}+\frac{133 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{4} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{4} c^{3}}+\frac{19 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} a^{2}}+\frac{19 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} a^{2}}+\frac{19 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} a^{2}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{5} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} a^{3}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{5} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} a^{3}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{5} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} a^{3}}-\frac{285 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} c^{2}}-\frac{285 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} c^{2}}-\frac{285 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{3} \ln \left(\frac{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} c^{2}}-\frac{2}{3 a^{2} c^{3} x^{\frac{3}{2}}}"," ",0,"1/2*b^4/a/(a*d-b*c)^4*x^(1/2)/(b*x^2+a)*d-1/2*b^5/a^2/(a*d-b*c)^4*x^(1/2)/(b*x^2+a)*c+19/8*b^4/a^2/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d-7/8*b^5/a^3/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c+19/8*b^4/a^2/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d-7/8*b^5/a^3/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c+19/16*b^4/a^2/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d-7/16*b^5/a^3/(a*d-b*c)^4*(a/b)^(1/4)*2^(1/2)*ln((x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c-15/16*d^6/c^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(5/2)*a^2+23/8*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*x^(5/2)*a*b-31/16*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*x^(5/2)*b^2-19/16*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*a^2+27/8*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*a*b-35/16*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(1/2)*b^2-77/64*d^5/c^4/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2+133/32*d^4/c^3/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b-285/64*d^3/c^2/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2-77/128*d^5/c^4/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2+133/64*d^4/c^3/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b-285/128*d^3/c^2/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*ln((x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*b^2-77/64*d^5/c^4/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2+133/32*d^4/c^3/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b-285/64*d^3/c^2/(a*d-b*c)^4*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b^2-2/3/a^2/c^3/x^(3/2)","A"
503,1,1170,717,0.040000," ","int(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{21 a^{2} d^{7} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{4}}-\frac{29 a b \,d^{6} x^{\frac{7}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{3}}+\frac{37 b^{2} d^{5} x^{\frac{7}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{25 a^{2} d^{6} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{3}}-\frac{33 a b \,d^{5} x^{\frac{3}{2}}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{41 b^{2} d^{4} x^{\frac{3}{2}}}{16 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{b^{5} d \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a^{2}}+\frac{b^{6} c \,x^{\frac{3}{2}}}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a^{3}}+\frac{117 \sqrt{2}\, a^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{4}}+\frac{117 \sqrt{2}\, a^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{4}}+\frac{117 \sqrt{2}\, a^{2} d^{5} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{4}}-\frac{189 \sqrt{2}\, a b \,d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{32 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{189 \sqrt{2}\, a b \,d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{32 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{189 \sqrt{2}\, a b \,d^{4} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{3}}-\frac{21 \sqrt{2}\, b^{4} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{21 \sqrt{2}\, b^{4} d \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}-\frac{21 \sqrt{2}\, b^{4} d \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2}}+\frac{9 \sqrt{2}\, b^{5} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{9 \sqrt{2}\, b^{5} c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{9 \sqrt{2}\, b^{5} c \ln \left(\frac{x -\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}{x +\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{a}{b}}}\right)}{16 \left(a d -b c \right)^{4} \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3}}+\frac{357 \sqrt{2}\, b^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{357 \sqrt{2}\, b^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{357 \sqrt{2}\, b^{2} d^{3} \ln \left(\frac{x -\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}{x +\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{c}{d}}}\right)}{128 \left(a d -b c \right)^{4} \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{6 d}{a^{2} c^{4} \sqrt{x}}+\frac{4 b}{a^{3} c^{3} \sqrt{x}}-\frac{2}{5 a^{2} c^{3} x^{\frac{5}{2}}}"," ",0,"6/a^2/c^4/x^(1/2)*d+4/a^3/c^3/x^(1/2)*b+41/16*d^4/c/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*b^2-1/2*b^5/a^2/(a*d-b*c)^4*x^(3/2)/(b*x^2+a)*d+1/2*b^6/a^3/(a*d-b*c)^4*x^(3/2)/(b*x^2+a)*c+21/16*d^7/c^4/(a*d-b*c)^4/(d*x^2+c)^2*x^(7/2)*a^2+37/16*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*x^(7/2)*b^2+25/16*d^6/c^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*a^2-189/64*d^4/c^3/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a*b*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-21/16*b^4/a^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*d*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))-21/8*b^4/a^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-21/8*b^4/a^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+9/16*b^5/a^3/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*c*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))+9/8*b^5/a^3/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+9/8*b^5/a^3/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-29/8*d^6/c^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(7/2)*a*b-33/8*d^5/c^2/(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*a*b+117/128*d^5/c^4/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+117/64*d^5/c^4/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+117/64*d^5/c^4/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+357/128*d^3/c^2/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*b^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+357/64*d^3/c^2/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+357/64*d^3/c^2/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-189/32*d^4/c^3/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-189/32*d^4/c^3/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/5/a^2/c^3/x^(5/2)","A"
504,1,77,87,0.008000," ","int(x^5*(B*x^2+A)*(b*x^2+a)^(1/2),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} \left(35 B \,x^{6} b^{3}+45 A \,b^{3} x^{4}-30 B a \,b^{2} x^{4}-36 A a \,b^{2} x^{2}+24 B \,a^{2} b \,x^{2}+24 A \,a^{2} b -16 B \,a^{3}\right)}{315 b^{4}}"," ",0,"1/315*(b*x^2+a)^(3/2)*(35*B*b^3*x^6+45*A*b^3*x^4-30*B*a*b^2*x^4-36*A*a*b^2*x^2+24*B*a^2*b*x^2+24*A*a^2*b-16*B*a^3)/b^4","A"
505,1,181,131,0.016000," ","int(x^4*(B*x^2+A)*(b*x^2+a)^(1/2),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,x^{5}}{8 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,x^{3}}{6 b}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B a \,x^{3}}{48 b^{2}}+\frac{A \,a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{5}{2}}}-\frac{5 B \,a^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{7}{2}}}+\frac{\sqrt{b \,x^{2}+a}\, A \,a^{2} x}{16 b^{2}}-\frac{5 \sqrt{b \,x^{2}+a}\, B \,a^{3} x}{128 b^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A a x}{8 b^{2}}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,a^{2} x}{64 b^{3}}"," ",0,"1/8*B*x^5*(b*x^2+a)^(3/2)/b-5/48*B*a/b^2*x^3*(b*x^2+a)^(3/2)+5/64*B*a^2/b^3*x*(b*x^2+a)^(3/2)-5/128*B*a^3/b^3*x*(b*x^2+a)^(1/2)-5/128*B*a^4/b^(7/2)*ln(x*b^(1/2)+(b*x^2+a)^(1/2))+1/6*A*x^3*(b*x^2+a)^(3/2)/b-1/8*A*a/b^2*x*(b*x^2+a)^(3/2)+1/16*A*a^2/b^2*x*(b*x^2+a)^(1/2)+1/16*A*a^3/b^(5/2)*ln(x*b^(1/2)+(b*x^2+a)^(1/2))","A"
506,1,53,61,0.007000," ","int(x^3*(B*x^2+A)*(b*x^2+a)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} \left(-15 B \,b^{2} x^{4}-21 A \,b^{2} x^{2}+12 B a b \,x^{2}+14 a b A -8 a^{2} B \right)}{105 b^{3}}"," ",0,"-1/105*(b*x^2+a)^(3/2)*(-15*B*b^2*x^4-21*A*b^2*x^2+12*B*a*b*x^2+14*A*a*b-8*B*a^2)/b^3","A"
507,1,139,102,0.009000," ","int(x^2*(B*x^2+A)*(b*x^2+a)^(1/2),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,x^{3}}{6 b}-\frac{A \,a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{3}{2}}}+\frac{B \,a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{5}{2}}}-\frac{\sqrt{b \,x^{2}+a}\, A a x}{8 b}+\frac{\sqrt{b \,x^{2}+a}\, B \,a^{2} x}{16 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A x}{4 b}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B a x}{8 b^{2}}"," ",0,"1/6*B*x^3*(b*x^2+a)^(3/2)/b-1/8*B*a/b^2*x*(b*x^2+a)^(3/2)+1/16*B*a^2/b^2*x*(b*x^2+a)^(1/2)+1/16*B*a^3/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/4*A*x*(b*x^2+a)^(3/2)/b-1/8*A*a/b*x*(b*x^2+a)^(1/2)-1/8*A*a^2/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
508,1,31,38,0.005000," ","int(x*(B*x^2+A)*(b*x^2+a)^(1/2),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} \left(3 B b \,x^{2}+5 A b -2 B a \right)}{15 b^{2}}"," ",0,"1/15*(b*x^2+a)^(3/2)*(3*B*b*x^2+5*A*b-2*B*a)/b^2","A"
509,1,96,71,0.006000," ","int((B*x^2+A)*(b*x^2+a)^(1/2),x)","\frac{A a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 \sqrt{b}}-\frac{B \,a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{3}{2}}}+\frac{\sqrt{b \,x^{2}+a}\, A x}{2}-\frac{\sqrt{b \,x^{2}+a}\, B a x}{8 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B x}{4 b}"," ",0,"1/4*B*x*(b*x^2+a)^(3/2)/b-1/8*B*a/b*x*(b*x^2+a)^(1/2)-1/8*B*a^2/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*A*x*(b*x^2+a)^(1/2)+1/2*A*a/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
510,1,57,47,0.009000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x,x)","-A \sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)+\sqrt{b \,x^{2}+a}\, A +\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B}{3 b}"," ",0,"1/3*B*(b*x^2+a)^(3/2)/b-A*ln((2*a+2*a^(1/2)*(b*x^2+a)^(1/2))/x)*a^(1/2)+A*(b*x^2+a)^(1/2)","A"
511,1,93,70,0.010000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^2,x)","A \sqrt{b}\, \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)+\frac{B a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 \sqrt{b}}+\frac{\sqrt{b \,x^{2}+a}\, A b x}{a}+\frac{\sqrt{b \,x^{2}+a}\, B x}{2}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A}{a x}"," ",0,"1/2*x*B*(b*x^2+a)^(1/2)+1/2*B*a/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-A*(b*x^2+a)^(3/2)/a/x+A*b/a*x*(b*x^2+a)^(1/2)+A*b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
512,1,106,68,0.010000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^3,x)","-\frac{A b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 \sqrt{a}}-B \sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)+\frac{\sqrt{b \,x^{2}+a}\, A b}{2 a}+\sqrt{b \,x^{2}+a}\, B -\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A}{2 a \,x^{2}}"," ",0,"-1/2*A*(b*x^2+a)^(3/2)/a/x^2-1/2*A*b/a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+1/2*A*b/a*(b*x^2+a)^(1/2)-B*a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+B*(b*x^2+a)^(1/2)","A"
513,1,75,54,0.011000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^4,x)","B \sqrt{b}\, \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)+\frac{\sqrt{b \,x^{2}+a}\, B b x}{a}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B}{a x}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A}{3 a \,x^{3}}"," ",0,"-B/a/x*(b*x^2+a)^(3/2)+B*b/a*x*(b*x^2+a)^(1/2)+B*b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-1/3*A*(b*x^2+a)^(3/2)/a/x^3","A"
514,1,153,72,0.013000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^5,x)","\frac{A \,b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{3}{2}}}-\frac{B b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 \sqrt{a}}-\frac{\sqrt{b \,x^{2}+a}\, A \,b^{2}}{8 a^{2}}+\frac{\sqrt{b \,x^{2}+a}\, B b}{2 a}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A b}{8 a^{2} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B}{2 a \,x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A}{4 a \,x^{4}}"," ",0,"-1/4*A*(b*x^2+a)^(3/2)/a/x^4+1/8*A*b/a^2/x^2*(b*x^2+a)^(3/2)+1/8*A*b^2/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/8*A*b^2/a^2*(b*x^2+a)^(1/2)-1/2*B/a/x^2*(b*x^2+a)^(3/2)-1/2*B*b/a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+1/2*B*b/a*(b*x^2+a)^(1/2)","B"
515,1,37,45,0.006000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^6,x)","-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} \left(-2 A b \,x^{2}+5 B a \,x^{2}+3 A a \right)}{15 a^{2} x^{5}}"," ",0,"-1/15*(b*x^2+a)^(3/2)*(-2*A*b*x^2+5*B*a*x^2+3*A*a)/x^5/a^2","A"
516,1,197,100,0.013000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^7,x)","-\frac{A \,b^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{16 a^{\frac{5}{2}}}+\frac{B \,b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{3}{2}}}+\frac{\sqrt{b \,x^{2}+a}\, A \,b^{3}}{16 a^{3}}-\frac{\sqrt{b \,x^{2}+a}\, B \,b^{2}}{8 a^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{2}}{16 a^{3} x^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B b}{8 a^{2} x^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A b}{8 a^{2} x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B}{4 a \,x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A}{6 a \,x^{6}}"," ",0,"-1/4*B/a/x^4*(b*x^2+a)^(3/2)+1/8*B*b/a^2/x^2*(b*x^2+a)^(3/2)+1/8*B*b^2/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/8*B*b^2/a^2*(b*x^2+a)^(1/2)-1/6*A*(b*x^2+a)^(3/2)/a/x^6+1/8*A*b/a^2/x^4*(b*x^2+a)^(3/2)-1/16*A*b^2/a^3/x^2*(b*x^2+a)^(3/2)-1/16*A*b^3/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+1/16*A*b^3/a^3*(b*x^2+a)^(1/2)","A"
517,1,59,72,0.005000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^8,x)","-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} \left(8 A \,b^{2} x^{4}-14 B a b \,x^{4}-12 A a b \,x^{2}+21 B \,a^{2} x^{2}+15 a^{2} A \right)}{105 a^{3} x^{7}}"," ",0,"-1/105*(b*x^2+a)^(3/2)*(8*A*b^2*x^4-14*B*a*b*x^4-12*A*a*b*x^2+21*B*a^2*x^2+15*A*a^2)/x^7/a^3","A"
518,1,239,132,0.021000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^9,x)","\frac{5 A \,b^{4} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{128 a^{\frac{7}{2}}}-\frac{B \,b^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{16 a^{\frac{5}{2}}}-\frac{5 \sqrt{b \,x^{2}+a}\, A \,b^{4}}{128 a^{4}}+\frac{\sqrt{b \,x^{2}+a}\, B \,b^{3}}{16 a^{3}}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{3}}{128 a^{4} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{2}}{16 a^{3} x^{2}}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{2}}{64 a^{3} x^{4}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B b}{8 a^{2} x^{4}}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A b}{48 a^{2} x^{6}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B}{6 a \,x^{6}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A}{8 a \,x^{8}}"," ",0,"-1/8*A*(b*x^2+a)^(3/2)/a/x^8+5/48*A*b/a^2/x^6*(b*x^2+a)^(3/2)-5/64*A*b^2/a^3/x^4*(b*x^2+a)^(3/2)+5/128*A*b^3/a^4/x^2*(b*x^2+a)^(3/2)+5/128*A*b^4/a^(7/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-5/128*A*b^4/a^4*(b*x^2+a)^(1/2)-1/6*B/a/x^6*(b*x^2+a)^(3/2)+1/8*B*b/a^2/x^4*(b*x^2+a)^(3/2)-1/16*B*b^2/a^3/x^2*(b*x^2+a)^(3/2)-1/16*B*b^3/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+1/16*B*b^3/a^3*(b*x^2+a)^(1/2)","A"
519,1,83,101,0.009000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^10,x)","-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} \left(-16 A \,b^{3} x^{6}+24 B a \,b^{2} x^{6}+24 x^{4} A a \,b^{2}-36 B \,a^{2} b \,x^{4}-30 A \,a^{2} b \,x^{2}+45 B \,a^{3} x^{2}+35 A \,a^{3}\right)}{315 a^{4} x^{9}}"," ",0,"-1/315*(b*x^2+a)^(3/2)*(-16*A*b^3*x^6+24*B*a*b^2*x^6+24*A*a*b^2*x^4-36*B*a^2*b*x^4-30*A*a^2*b*x^2+45*B*a^3*x^2+35*A*a^3)/x^9/a^4","A"
520,1,281,161,0.034000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^11,x)","-\frac{7 A \,b^{5} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{256 a^{\frac{9}{2}}}+\frac{5 B \,b^{4} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{128 a^{\frac{7}{2}}}+\frac{7 \sqrt{b \,x^{2}+a}\, A \,b^{5}}{256 a^{5}}-\frac{5 \sqrt{b \,x^{2}+a}\, B \,b^{4}}{128 a^{4}}-\frac{7 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{4}}{256 a^{5} x^{2}}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{3}}{128 a^{4} x^{2}}+\frac{7 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{3}}{128 a^{4} x^{4}}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{2}}{64 a^{3} x^{4}}-\frac{7 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{2}}{96 a^{3} x^{6}}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B b}{48 a^{2} x^{6}}+\frac{7 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A b}{80 a^{2} x^{8}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B}{8 a \,x^{8}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A}{10 a \,x^{10}}"," ",0,"-1/10*A*(b*x^2+a)^(3/2)/a/x^10+7/80*A*b/a^2/x^8*(b*x^2+a)^(3/2)-7/96*A*b^2/a^3/x^6*(b*x^2+a)^(3/2)+7/128*A*b^3/a^4/x^4*(b*x^2+a)^(3/2)-7/256*A*b^4/a^5/x^2*(b*x^2+a)^(3/2)-7/256*A*b^5/a^(9/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+7/256*A*b^5/a^5*(b*x^2+a)^(1/2)-1/8*B/a/x^8*(b*x^2+a)^(3/2)+5/48*B*b/a^2/x^6*(b*x^2+a)^(3/2)-5/64*B*b^2/a^3/x^4*(b*x^2+a)^(3/2)+5/128*B*b^3/a^4/x^2*(b*x^2+a)^(3/2)+5/128*B*b^4/a^(7/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-5/128*B*b^4/a^4*(b*x^2+a)^(1/2)","A"
521,1,77,87,0.008000," ","int(x^5*(b*x^2+a)^(3/2)*(B*x^2+A),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} \left(315 B \,x^{6} b^{3}+385 A \,b^{3} x^{4}-210 B a \,b^{2} x^{4}-220 A a \,b^{2} x^{2}+120 B \,a^{2} b \,x^{2}+88 A \,a^{2} b -48 B \,a^{3}\right)}{3465 b^{4}}"," ",0,"1/3465*(b*x^2+a)^(5/2)*(315*B*b^3*x^6+385*A*b^3*x^4-210*B*a*b^2*x^4-220*A*a*b^2*x^2+120*B*a^2*b*x^2+88*A*a^2*b-48*B*a^3)/b^4","A"
522,1,219,160,0.014000," ","int(x^4*(b*x^2+a)^(3/2)*(B*x^2+A),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,x^{5}}{10 b}+\frac{3 A \,a^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{5}{2}}}-\frac{3 B \,a^{5} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{256 b^{\frac{7}{2}}}+\frac{3 \sqrt{b \,x^{2}+a}\, A \,a^{3} x}{128 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,x^{3}}{8 b}-\frac{3 \sqrt{b \,x^{2}+a}\, B \,a^{4} x}{256 b^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B a \,x^{3}}{16 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,a^{2} x}{64 b^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,a^{3} x}{128 b^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A a x}{16 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,a^{2} x}{32 b^{3}}"," ",0,"1/10*B*x^5*(b*x^2+a)^(5/2)/b-1/16*B*a/b^2*x^3*(b*x^2+a)^(5/2)+1/32*B*a^2/b^3*x*(b*x^2+a)^(5/2)-1/128*B*a^3/b^3*x*(b*x^2+a)^(3/2)-3/256*B*a^4/b^3*x*(b*x^2+a)^(1/2)-3/256*B*a^5/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/8*A*x^3*(b*x^2+a)^(5/2)/b-1/16*A*a/b^2*x*(b*x^2+a)^(5/2)+1/64*A*a^2/b^2*x*(b*x^2+a)^(3/2)+3/128*A*a^3/b^2*x*(b*x^2+a)^(1/2)+3/128*A*a^4/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
523,1,53,61,0.007000," ","int(x^3*(b*x^2+a)^(3/2)*(B*x^2+A),x)","-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} \left(-35 B \,b^{2} x^{4}-45 A \,b^{2} x^{2}+20 B a b \,x^{2}+18 a b A -8 a^{2} B \right)}{315 b^{3}}"," ",0,"-1/315*(b*x^2+a)^(5/2)*(-35*B*b^2*x^4-45*A*b^2*x^2+20*B*a*b*x^2+18*A*a*b-8*B*a^2)/b^3","A"
524,1,177,131,0.010000," ","int(x^2*(b*x^2+a)^(3/2)*(B*x^2+A),x)","-\frac{A \,a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{3}{2}}}+\frac{3 B \,a^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{5}{2}}}-\frac{\sqrt{b \,x^{2}+a}\, A \,a^{2} x}{16 b}+\frac{3 \sqrt{b \,x^{2}+a}\, B \,a^{3} x}{128 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,x^{3}}{8 b}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A a x}{24 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,a^{2} x}{64 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A x}{6 b}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B a x}{16 b^{2}}"," ",0,"1/8*B*x^3*(b*x^2+a)^(5/2)/b-1/16*B*a/b^2*x*(b*x^2+a)^(5/2)+1/64*B*a^2/b^2*x*(b*x^2+a)^(3/2)+3/128*B*a^3/b^2*x*(b*x^2+a)^(1/2)+3/128*B*a^4/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/6*A*x*(b*x^2+a)^(5/2)/b-1/24*A*a/b*x*(b*x^2+a)^(3/2)-1/16*A*a^2/b*x*(b*x^2+a)^(1/2)-1/16*A*a^3/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
525,1,31,38,0.004000," ","int(x*(b*x^2+a)^(3/2)*(B*x^2+A),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} \left(5 B b \,x^{2}+7 A b -2 B a \right)}{35 b^{2}}"," ",0,"1/35*(b*x^2+a)^(5/2)*(5*B*b*x^2+7*A*b-2*B*a)/b^2","A"
526,1,131,98,0.007000," ","int((b*x^2+a)^(3/2)*(B*x^2+A),x)","\frac{3 A \,a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 \sqrt{b}}-\frac{B \,a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{3}{2}}}+\frac{3 \sqrt{b \,x^{2}+a}\, A a x}{8}-\frac{\sqrt{b \,x^{2}+a}\, B \,a^{2} x}{16 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A x}{4}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B a x}{24 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B x}{6 b}"," ",0,"1/6*B*x*(b*x^2+a)^(5/2)/b-1/24*B*a/b*x*(b*x^2+a)^(3/2)-1/16*B*a^2/b*x*(b*x^2+a)^(1/2)-1/16*B*a^3/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/4*A*x*(b*x^2+a)^(3/2)+3/8*A*a*x*(b*x^2+a)^(1/2)+3/8*A*a^2/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
527,1,70,60,0.011000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x,x)","-A \,a^{\frac{3}{2}} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)+\sqrt{b \,x^{2}+a}\, A a +\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A}{3}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B}{5 b}"," ",0,"1/5*B*(b*x^2+a)^(5/2)/b+1/3*A*(b*x^2+a)^(3/2)-A*a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+a*A*(b*x^2+a)^(1/2)","A"
528,1,125,91,0.010000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^2,x)","\frac{3 A a \sqrt{b}\, \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2}+\frac{3 B \,a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 \sqrt{b}}+\frac{3 \sqrt{b \,x^{2}+a}\, A b x}{2}+\frac{3 \sqrt{b \,x^{2}+a}\, B a x}{8}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A b x}{a}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B x}{4}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A}{a x}"," ",0,"1/4*x*B*(b*x^2+a)^(3/2)+3/8*B*a*x*(b*x^2+a)^(1/2)+3/8*B*a^2/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-A*(b*x^2+a)^(5/2)/a/x+A*b/a*x*(b*x^2+a)^(3/2)+3/2*A*b*x*(b*x^2+a)^(1/2)+3/2*A*b^(1/2)*a*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
529,1,132,90,0.010000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^3,x)","-\frac{3 A \sqrt{a}\, b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2}-B \,a^{\frac{3}{2}} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)+\frac{3 \sqrt{b \,x^{2}+a}\, A b}{2}+\sqrt{b \,x^{2}+a}\, B a +\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A b}{2 a}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B}{3}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A}{2 a \,x^{2}}"," ",0,"-1/2*A*(b*x^2+a)^(5/2)/a/x^2+1/2*A*b/a*(b*x^2+a)^(3/2)-3/2*A*b*a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+3/2*A*b*(b*x^2+a)^(1/2)+1/3*B*(b*x^2+a)^(3/2)-B*a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+B*(b*x^2+a)^(1/2)*a","A"
530,1,168,99,0.012000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^4,x)","A \,b^{\frac{3}{2}} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)+\frac{3 B a \sqrt{b}\, \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2}+\frac{\sqrt{b \,x^{2}+a}\, A \,b^{2} x}{a}+\frac{3 \sqrt{b \,x^{2}+a}\, B b x}{2}+\frac{2 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{2} x}{3 a^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B b x}{a}-\frac{2 \left(b \,x^{2}+a \right)^{\frac{5}{2}} A b}{3 a^{2} x}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B}{a x}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A}{3 a \,x^{3}}"," ",0,"-B/a/x*(b*x^2+a)^(5/2)+B*b/a*x*(b*x^2+a)^(3/2)+3/2*B*b*x*(b*x^2+a)^(1/2)+3/2*B*b^(1/2)*a*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-1/3*A*(b*x^2+a)^(5/2)/a/x^3-2/3*A*b/a^2/x*(b*x^2+a)^(5/2)+2/3*A*b^2/a^2*x*(b*x^2+a)^(3/2)+A*b^2/a*x*(b*x^2+a)^(1/2)+A*b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
531,1,184,95,0.012000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^5,x)","-\frac{3 A \,b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 \sqrt{a}}-\frac{3 B \sqrt{a}\, b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2}+\frac{3 \sqrt{b \,x^{2}+a}\, A \,b^{2}}{8 a}+\frac{3 \sqrt{b \,x^{2}+a}\, B b}{2}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{2}}{8 a^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B b}{2 a}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A b}{8 a^{2} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B}{2 a \,x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A}{4 a \,x^{4}}"," ",0,"-1/2*B/a/x^2*(b*x^2+a)^(5/2)+1/2*B*b/a*(b*x^2+a)^(3/2)-3/2*B*b*a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+3/2*B*b*(b*x^2+a)^(1/2)-1/4*A*(b*x^2+a)^(5/2)/a/x^4-1/8*A*b/a^2/x^2*(b*x^2+a)^(5/2)+1/8*A*b^2/a^2*(b*x^2+a)^(3/2)-3/8*A*b^2/a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+3/8*A*b^2/a*(b*x^2+a)^(1/2)","A"
532,1,115,70,0.010000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^6,x)","B \,b^{\frac{3}{2}} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)+\frac{\sqrt{b \,x^{2}+a}\, B \,b^{2} x}{a}+\frac{2 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{2} x}{3 a^{2}}-\frac{2 \left(b \,x^{2}+a \right)^{\frac{5}{2}} B b}{3 a^{2} x}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B}{3 a \,x^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A}{5 a \,x^{5}}"," ",0,"-1/5*A*(b*x^2+a)^(5/2)/a/x^5-1/3*B/a/x^3*(b*x^2+a)^(5/2)-2/3*B*b/a^2/x*(b*x^2+a)^(5/2)+2/3*B*b^2/a^2*x*(b*x^2+a)^(3/2)+B*b^2/a*x*(b*x^2+a)^(1/2)+B*b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
533,1,233,100,0.014000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^7,x)","\frac{A \,b^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{16 a^{\frac{3}{2}}}-\frac{3 B \,b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 \sqrt{a}}-\frac{\sqrt{b \,x^{2}+a}\, A \,b^{3}}{16 a^{2}}+\frac{3 \sqrt{b \,x^{2}+a}\, B \,b^{2}}{8 a}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{3}}{48 a^{3}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{2}}{8 a^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{2}}{48 a^{3} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B b}{8 a^{2} x^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A b}{24 a^{2} x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B}{4 a \,x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A}{6 a \,x^{6}}"," ",0,"-1/6*A*(b*x^2+a)^(5/2)/a/x^6+1/24*A*b/a^2/x^4*(b*x^2+a)^(5/2)+1/48*A*b^2/a^3/x^2*(b*x^2+a)^(5/2)-1/48*A*b^3/a^3*(b*x^2+a)^(3/2)+1/16*A*b^3/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/16*A*b^3/a^2*(b*x^2+a)^(1/2)-1/4*B/a/x^4*(b*x^2+a)^(5/2)-1/8*B*b/a^2/x^2*(b*x^2+a)^(5/2)+1/8*B*b^2/a^2*(b*x^2+a)^(3/2)-3/8*B*b^2/a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+3/8*B*b^2/a*(b*x^2+a)^(1/2)","B"
534,1,37,45,0.006000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^8,x)","-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} \left(-2 A b \,x^{2}+7 B a \,x^{2}+5 A a \right)}{35 a^{2} x^{7}}"," ",0,"-1/35*(b*x^2+a)^(5/2)*(-2*A*b*x^2+7*B*a*x^2+5*A*a)/x^7/a^2","A"
535,1,275,132,0.021000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^9,x)","-\frac{3 A \,b^{4} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{128 a^{\frac{5}{2}}}+\frac{B \,b^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{16 a^{\frac{3}{2}}}+\frac{3 \sqrt{b \,x^{2}+a}\, A \,b^{4}}{128 a^{3}}-\frac{\sqrt{b \,x^{2}+a}\, B \,b^{3}}{16 a^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{4}}{128 a^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{3}}{48 a^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{3}}{128 a^{4} x^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,b^{2}}{48 a^{3} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{2}}{64 a^{3} x^{4}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B b}{24 a^{2} x^{4}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A b}{16 a^{2} x^{6}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B}{6 a \,x^{6}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A}{8 a \,x^{8}}"," ",0,"-1/6*B/a/x^6*(b*x^2+a)^(5/2)+1/24*B*b/a^2/x^4*(b*x^2+a)^(5/2)+1/48*B*b^2/a^3/x^2*(b*x^2+a)^(5/2)-1/48*B*b^3/a^3*(b*x^2+a)^(3/2)+1/16*B*b^3/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/16*B*b^3/a^2*(b*x^2+a)^(1/2)-1/8*A*(b*x^2+a)^(5/2)/a/x^8+1/16*A*b/a^2/x^6*(b*x^2+a)^(5/2)-1/64*A*b^2/a^3/x^4*(b*x^2+a)^(5/2)-1/128*A*b^3/a^4/x^2*(b*x^2+a)^(5/2)+1/128*A*b^4/a^4*(b*x^2+a)^(3/2)-3/128*A*b^4/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+3/128*A*b^4/a^3*(b*x^2+a)^(1/2)","B"
536,1,59,72,0.007000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^10,x)","-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} \left(8 A \,b^{2} x^{4}-18 B a b \,x^{4}-20 A a b \,x^{2}+45 B \,a^{2} x^{2}+35 a^{2} A \right)}{315 a^{3} x^{9}}"," ",0,"-1/315*(b*x^2+a)^(5/2)*(8*A*b^2*x^4-18*B*a*b*x^4-20*A*a*b*x^2+45*B*a^2*x^2+35*A*a^2)/x^9/a^3","A"
537,1,317,156,0.036000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/x^11,x)","\frac{3 A \,b^{5} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{256 a^{\frac{7}{2}}}-\frac{3 B \,b^{4} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{128 a^{\frac{5}{2}}}-\frac{3 \sqrt{b \,x^{2}+a}\, A \,b^{5}}{256 a^{4}}+\frac{3 \sqrt{b \,x^{2}+a}\, B \,b^{4}}{128 a^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{5}}{256 a^{5}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{4}}{128 a^{4}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{4}}{256 a^{5} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,b^{3}}{128 a^{4} x^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{3}}{128 a^{4} x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,b^{2}}{64 a^{3} x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{2}}{32 a^{3} x^{6}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B b}{16 a^{2} x^{6}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A b}{16 a^{2} x^{8}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B}{8 a \,x^{8}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A}{10 a \,x^{10}}"," ",0,"-1/10*A*(b*x^2+a)^(5/2)/a/x^10+1/16*A*b/a^2/x^8*(b*x^2+a)^(5/2)-1/32*A*b^2/a^3/x^6*(b*x^2+a)^(5/2)+1/128*A*b^3/a^4/x^4*(b*x^2+a)^(5/2)+1/256*A*b^4/a^5/x^2*(b*x^2+a)^(5/2)-1/256*A*b^5/a^5*(b*x^2+a)^(3/2)+3/256*A*b^5/a^(7/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-3/256*A*b^5/a^4*(b*x^2+a)^(1/2)-1/8*B/a/x^8*(b*x^2+a)^(5/2)+1/16*B*b/a^2/x^6*(b*x^2+a)^(5/2)-1/64*B*b^2/a^3/x^4*(b*x^2+a)^(5/2)-1/128*B*b^3/a^4/x^2*(b*x^2+a)^(5/2)+1/128*B*b^4/a^4*(b*x^2+a)^(3/2)-3/128*B*b^4/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+3/128*B*b^4/a^3*(b*x^2+a)^(1/2)","B"
538,1,77,87,0.009000," ","int(x^5*(b*x^2+a)^(5/2)*(B*x^2+A),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} \left(693 B \,x^{6} b^{3}+819 A \,b^{3} x^{4}-378 B a \,b^{2} x^{4}-364 A a \,b^{2} x^{2}+168 B \,a^{2} b \,x^{2}+104 A \,a^{2} b -48 B \,a^{3}\right)}{9009 b^{4}}"," ",0,"1/9009*(b*x^2+a)^(7/2)*(693*B*b^3*x^6+819*A*b^3*x^4-378*B*a*b^2*x^4-364*A*a*b^2*x^2+168*B*a^2*b*x^2+104*A*a^2*b-48*B*a^3)/b^4","A"
539,1,257,189,0.018000," ","int(x^4*(b*x^2+a)^(5/2)*(B*x^2+A),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B \,x^{5}}{12 b}+\frac{3 A \,a^{5} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{256 b^{\frac{5}{2}}}-\frac{5 B \,a^{6} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{1024 b^{\frac{7}{2}}}+\frac{3 \sqrt{b \,x^{2}+a}\, A \,a^{4} x}{256 b^{2}}-\frac{5 \sqrt{b \,x^{2}+a}\, B \,a^{5} x}{1024 b^{3}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,a^{3} x}{128 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A \,x^{3}}{10 b}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,a^{4} x}{1536 b^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B a \,x^{3}}{24 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,a^{2} x}{160 b^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,a^{3} x}{384 b^{3}}-\frac{3 \left(b \,x^{2}+a \right)^{\frac{7}{2}} A a x}{80 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B \,a^{2} x}{64 b^{3}}"," ",0,"1/12*B*x^5*(b*x^2+a)^(7/2)/b-1/24*B*a/b^2*x^3*(b*x^2+a)^(7/2)+1/64*B*a^2/b^3*x*(b*x^2+a)^(7/2)-1/384*B*a^3/b^3*x*(b*x^2+a)^(5/2)-5/1536*B*a^4/b^3*x*(b*x^2+a)^(3/2)-5/1024*B*a^5/b^3*x*(b*x^2+a)^(1/2)-5/1024*B*a^6/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/10*A*x^3*(b*x^2+a)^(7/2)/b-3/80*A*a/b^2*x*(b*x^2+a)^(7/2)+1/160*A*a^2/b^2*x*(b*x^2+a)^(5/2)+1/128*A*a^3/b^2*x*(b*x^2+a)^(3/2)+3/256*A*a^4/b^2*x*(b*x^2+a)^(1/2)+3/256*A*a^5/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
540,1,53,61,0.006000," ","int(x^3*(b*x^2+a)^(5/2)*(B*x^2+A),x)","-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} \left(-63 B \,b^{2} x^{4}-77 A \,b^{2} x^{2}+28 B a b \,x^{2}+22 a b A -8 a^{2} B \right)}{693 b^{3}}"," ",0,"-1/693*(b*x^2+a)^(7/2)*(-63*B*b^2*x^4-77*A*b^2*x^2+28*B*a*b*x^2+22*A*a*b-8*B*a^2)/b^3","A"
541,1,215,160,0.007000," ","int(x^2*(b*x^2+a)^(5/2)*(B*x^2+A),x)","-\frac{5 A \,a^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{3}{2}}}+\frac{3 B \,a^{5} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{256 b^{\frac{5}{2}}}-\frac{5 \sqrt{b \,x^{2}+a}\, A \,a^{3} x}{128 b}+\frac{3 \sqrt{b \,x^{2}+a}\, B \,a^{4} x}{256 b^{2}}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,a^{2} x}{192 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,a^{3} x}{128 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B \,x^{3}}{10 b}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A a x}{48 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,a^{2} x}{160 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A x}{8 b}-\frac{3 \left(b \,x^{2}+a \right)^{\frac{7}{2}} B a x}{80 b^{2}}"," ",0,"1/10*B*x^3*(b*x^2+a)^(7/2)/b-3/80*B*a/b^2*x*(b*x^2+a)^(7/2)+1/160*B*a^2/b^2*x*(b*x^2+a)^(5/2)+1/128*B*a^3/b^2*x*(b*x^2+a)^(3/2)+3/256*B*a^4/b^2*x*(b*x^2+a)^(1/2)+3/256*B*a^5/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/8*A*x*(b*x^2+a)^(7/2)/b-1/48*A*a/b*x*(b*x^2+a)^(5/2)-5/192*A*a^2/b*x*(b*x^2+a)^(3/2)-5/128*A*a^3/b*x*(b*x^2+a)^(1/2)-5/128*A*a^4/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
542,1,31,38,0.003000," ","int(x*(b*x^2+a)^(5/2)*(B*x^2+A),x)","\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} \left(7 B b \,x^{2}+9 A b -2 B a \right)}{63 b^{2}}"," ",0,"1/63*(b*x^2+a)^(7/2)*(7*B*b*x^2+9*A*b-2*B*a)/b^2","A"
543,1,166,125,0.006000," ","int((b*x^2+a)^(5/2)*(B*x^2+A),x)","\frac{5 A \,a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 \sqrt{b}}-\frac{5 B \,a^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{3}{2}}}+\frac{5 \sqrt{b \,x^{2}+a}\, A \,a^{2} x}{16}-\frac{5 \sqrt{b \,x^{2}+a}\, B \,a^{3} x}{128 b}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A a x}{24}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,a^{2} x}{192 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A x}{6}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B a x}{48 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B x}{8 b}"," ",0,"1/8*B*x*(b*x^2+a)^(7/2)/b-1/48*B*a/b*x*(b*x^2+a)^(5/2)-5/192*B*a^2/b*x*(b*x^2+a)^(3/2)-5/128*B*a^3/b*x*(b*x^2+a)^(1/2)-5/128*B*a^4/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/6*A*x*(b*x^2+a)^(5/2)+5/24*A*a*x*(b*x^2+a)^(3/2)+5/16*A*a^2*x*(b*x^2+a)^(1/2)+5/16*A*a^3/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
544,1,85,75,0.008000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x,x)","-A \,a^{\frac{5}{2}} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)+\sqrt{b \,x^{2}+a}\, A \,a^{2}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A a}{3}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A}{5}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B}{7 b}"," ",0,"1/7*B*(b*x^2+a)^(7/2)/b+1/5*A*(b*x^2+a)^(5/2)+1/3*a*A*(b*x^2+a)^(3/2)-A*a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+a^2*A*(b*x^2+a)^(1/2)","A"
545,1,158,114,0.010000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^2,x)","\frac{15 A \,a^{2} \sqrt{b}\, \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8}+\frac{5 B \,a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 \sqrt{b}}+\frac{15 \sqrt{b \,x^{2}+a}\, A a b x}{8}+\frac{5 \sqrt{b \,x^{2}+a}\, B \,a^{2} x}{16}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A b x}{4}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B a x}{24}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A b x}{a}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B x}{6}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A}{a x}"," ",0,"1/6*x*B*(b*x^2+a)^(5/2)+5/24*B*a*x*(b*x^2+a)^(3/2)+5/16*B*a^2*x*(b*x^2+a)^(1/2)+5/16*B*a^3/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-A*(b*x^2+a)^(7/2)/a/x+A*b/a*x*(b*x^2+a)^(5/2)+5/4*A*b*x*(b*x^2+a)^(3/2)+15/8*A*b*a*x*(b*x^2+a)^(1/2)+15/8*A*b^(1/2)*a^2*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
546,1,161,111,0.010000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^3,x)","-\frac{5 A \,a^{\frac{3}{2}} b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2}-B \,a^{\frac{5}{2}} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)+\frac{5 \sqrt{b \,x^{2}+a}\, A a b}{2}+\sqrt{b \,x^{2}+a}\, B \,a^{2}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A b}{6}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} B a}{3}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A b}{2 a}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B}{5}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A}{2 a \,x^{2}}"," ",0,"-1/2*A*(b*x^2+a)^(7/2)/a/x^2+1/2*A*b/a*(b*x^2+a)^(5/2)+5/6*A*b*(b*x^2+a)^(3/2)-5/2*A*b*a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+5/2*A*b*a*(b*x^2+a)^(1/2)+1/5*B*(b*x^2+a)^(5/2)+1/3*B*a*(b*x^2+a)^(3/2)-B*a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+B*(b*x^2+a)^(1/2)*a^2","A"
547,1,204,122,0.012000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^4,x)","\frac{5 A a \,b^{\frac{3}{2}} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2}+\frac{15 B \,a^{2} \sqrt{b}\, \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8}+\frac{5 \sqrt{b \,x^{2}+a}\, A \,b^{2} x}{2}+\frac{15 \sqrt{b \,x^{2}+a}\, B a b x}{8}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{2} x}{3 a}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B b x}{4}+\frac{4 \left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{2} x}{3 a^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B b x}{a}-\frac{4 \left(b \,x^{2}+a \right)^{\frac{7}{2}} A b}{3 a^{2} x}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B}{a x}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A}{3 a \,x^{3}}"," ",0,"-B/a/x*(b*x^2+a)^(7/2)+B*b/a*x*(b*x^2+a)^(5/2)+5/4*B*b*x*(b*x^2+a)^(3/2)+15/8*B*b*a*x*(b*x^2+a)^(1/2)+15/8*B*b^(1/2)*a^2*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-1/3*A*(b*x^2+a)^(7/2)/a/x^3-4/3*A*b/a^2/x*(b*x^2+a)^(7/2)+4/3*A*b^2/a^2*x*(b*x^2+a)^(5/2)+5/3*A*b^2/a*x*(b*x^2+a)^(3/2)+5/2*A*b^2*x*(b*x^2+a)^(1/2)+5/2*A*b^(3/2)*a*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
548,1,213,119,0.011000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^5,x)","-\frac{15 A \sqrt{a}\, b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8}-\frac{5 B \,a^{\frac{3}{2}} b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2}+\frac{15 \sqrt{b \,x^{2}+a}\, A \,b^{2}}{8}+\frac{5 \sqrt{b \,x^{2}+a}\, B a b}{2}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{2}}{8 a}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B b}{6}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{2}}{8 a^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B b}{2 a}-\frac{3 \left(b \,x^{2}+a \right)^{\frac{7}{2}} A b}{8 a^{2} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B}{2 a \,x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A}{4 a \,x^{4}}"," ",0,"-1/2*B/a/x^2*(b*x^2+a)^(7/2)+1/2*B*b/a*(b*x^2+a)^(5/2)+5/6*B*b*(b*x^2+a)^(3/2)-5/2*B*b*a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+5/2*B*b*a*(b*x^2+a)^(1/2)-1/4*A*(b*x^2+a)^(7/2)/a/x^4-3/8*A*b/a^2/x^2*(b*x^2+a)^(7/2)+3/8*A*b^2/a^2*(b*x^2+a)^(5/2)+5/8*A*b^2/a*(b*x^2+a)^(3/2)-15/8*A*b^2*a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+15/8*A*b^2*(b*x^2+a)^(1/2)","A"
549,1,251,128,0.013000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^6,x)","A \,b^{\frac{5}{2}} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)+\frac{5 B a \,b^{\frac{3}{2}} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2}+\frac{\sqrt{b \,x^{2}+a}\, A \,b^{3} x}{a}+\frac{5 \sqrt{b \,x^{2}+a}\, B \,b^{2} x}{2}+\frac{2 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{3} x}{3 a^{2}}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{2} x}{3 a}+\frac{8 \left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{3} x}{15 a^{3}}+\frac{4 \left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,b^{2} x}{3 a^{2}}-\frac{8 \left(b \,x^{2}+a \right)^{\frac{7}{2}} A \,b^{2}}{15 a^{3} x}-\frac{4 \left(b \,x^{2}+a \right)^{\frac{7}{2}} B b}{3 a^{2} x}-\frac{2 \left(b \,x^{2}+a \right)^{\frac{7}{2}} A b}{15 a^{2} x^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B}{3 a \,x^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A}{5 a \,x^{5}}"," ",0,"-1/5*A*(b*x^2+a)^(7/2)/a/x^5-2/15*A*b/a^2/x^3*(b*x^2+a)^(7/2)-8/15*A*b^2/a^3/x*(b*x^2+a)^(7/2)+8/15*A*b^3/a^3*x*(b*x^2+a)^(5/2)+2/3*A*b^3/a^2*x*(b*x^2+a)^(3/2)+A*b^3/a*x*(b*x^2+a)^(1/2)+A*b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-1/3*B/a/x^3*(b*x^2+a)^(7/2)-4/3*B*b/a^2/x*(b*x^2+a)^(7/2)+4/3*B*b^2/a^2*x*(b*x^2+a)^(5/2)+5/3*B*b^2/a*x*(b*x^2+a)^(3/2)+5/2*B*b^2*x*(b*x^2+a)^(1/2)+5/2*B*b^(3/2)*a*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
550,1,266,125,0.015000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^7,x)","-\frac{5 A \,b^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{16 \sqrt{a}}-\frac{15 B \sqrt{a}\, b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8}+\frac{5 \sqrt{b \,x^{2}+a}\, A \,b^{3}}{16 a}+\frac{15 \sqrt{b \,x^{2}+a}\, B \,b^{2}}{8}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{3}}{48 a^{2}}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{2}}{8 a}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{3}}{16 a^{3}}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,b^{2}}{8 a^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A \,b^{2}}{16 a^{3} x^{2}}-\frac{3 \left(b \,x^{2}+a \right)^{\frac{7}{2}} B b}{8 a^{2} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A b}{24 a^{2} x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B}{4 a \,x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A}{6 a \,x^{6}}"," ",0,"-1/6*A*(b*x^2+a)^(7/2)/a/x^6-1/24*A*b/a^2/x^4*(b*x^2+a)^(7/2)-1/16*A*b^2/a^3/x^2*(b*x^2+a)^(7/2)+1/16*A*b^3/a^3*(b*x^2+a)^(5/2)+5/48*A*b^3/a^2*(b*x^2+a)^(3/2)-5/16*A*b^3/a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+5/16*A*b^3/a*(b*x^2+a)^(1/2)-1/4*B/a/x^4*(b*x^2+a)^(7/2)-3/8*B*b/a^2/x^2*(b*x^2+a)^(7/2)+3/8*B*b^2/a^2*(b*x^2+a)^(5/2)+5/8*B*b^2/a*(b*x^2+a)^(3/2)-15/8*B*b^2*a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+15/8*B*b^2*(b*x^2+a)^(1/2)","B"
551,1,155,88,0.017000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^8,x)","B \,b^{\frac{5}{2}} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)+\frac{\sqrt{b \,x^{2}+a}\, B \,b^{3} x}{a}+\frac{2 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{3} x}{3 a^{2}}+\frac{8 \left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,b^{3} x}{15 a^{3}}-\frac{8 \left(b \,x^{2}+a \right)^{\frac{7}{2}} B \,b^{2}}{15 a^{3} x}-\frac{2 \left(b \,x^{2}+a \right)^{\frac{7}{2}} B b}{15 a^{2} x^{3}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B}{5 a \,x^{5}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A}{7 a \,x^{7}}"," ",0,"-1/5*B/a/x^5*(b*x^2+a)^(7/2)-2/15*B*b/a^2/x^3*(b*x^2+a)^(7/2)-8/15*B*b^2/a^3/x*(b*x^2+a)^(7/2)+8/15*B*b^3/a^3*x*(b*x^2+a)^(5/2)+2/3*B*b^3/a^2*x*(b*x^2+a)^(3/2)+B*b^3/a*x*(b*x^2+a)^(1/2)+B*b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-1/7*A*(b*x^2+a)^(7/2)/a/x^7","A"
552,1,311,128,0.022000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^9,x)","\frac{5 A \,b^{4} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{128 a^{\frac{3}{2}}}-\frac{5 B \,b^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{16 \sqrt{a}}-\frac{5 \sqrt{b \,x^{2}+a}\, A \,b^{4}}{128 a^{2}}+\frac{5 \sqrt{b \,x^{2}+a}\, B \,b^{3}}{16 a}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{4}}{384 a^{3}}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{3}}{48 a^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{4}}{128 a^{4}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,b^{3}}{16 a^{3}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A \,b^{3}}{128 a^{4} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B \,b^{2}}{16 a^{3} x^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A \,b^{2}}{192 a^{3} x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B b}{24 a^{2} x^{4}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A b}{48 a^{2} x^{6}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B}{6 a \,x^{6}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A}{8 a \,x^{8}}"," ",0,"-1/6*B/a/x^6*(b*x^2+a)^(7/2)-1/24*B*b/a^2/x^4*(b*x^2+a)^(7/2)-1/16*B*b^2/a^3/x^2*(b*x^2+a)^(7/2)+1/16*B*b^3/a^3*(b*x^2+a)^(5/2)+5/48*B*b^3/a^2*(b*x^2+a)^(3/2)-5/16*B*b^3/a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+5/16*B*b^3/a*(b*x^2+a)^(1/2)-1/8*A*(b*x^2+a)^(7/2)/a/x^8+1/48*A*b/a^2/x^6*(b*x^2+a)^(7/2)+1/192*A*b^2/a^3/x^4*(b*x^2+a)^(7/2)+1/128*A*b^3/a^4/x^2*(b*x^2+a)^(7/2)-1/128*A*b^4/a^4*(b*x^2+a)^(5/2)-5/384*A*b^4/a^3*(b*x^2+a)^(3/2)+5/128*A*b^4/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-5/128*A*b^4/a^2*(b*x^2+a)^(1/2)","B"
553,1,37,45,0.006000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^10,x)","-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} \left(-2 A b \,x^{2}+9 B a \,x^{2}+7 A a \right)}{63 a^{2} x^{9}}"," ",0,"-1/63*(b*x^2+a)^(7/2)*(-2*A*b*x^2+9*B*a*x^2+7*A*a)/x^9/a^2","A"
554,1,353,161,0.043000," ","int((b*x^2+a)^(5/2)*(B*x^2+A)/x^11,x)","-\frac{3 A \,b^{5} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{256 a^{\frac{5}{2}}}+\frac{5 B \,b^{4} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{128 a^{\frac{3}{2}}}+\frac{3 \sqrt{b \,x^{2}+a}\, A \,b^{5}}{256 a^{3}}-\frac{5 \sqrt{b \,x^{2}+a}\, B \,b^{4}}{128 a^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} A \,b^{5}}{256 a^{4}}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} B \,b^{4}}{384 a^{3}}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{5}{2}} A \,b^{5}}{1280 a^{5}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} B \,b^{4}}{128 a^{4}}-\frac{3 \left(b \,x^{2}+a \right)^{\frac{7}{2}} A \,b^{4}}{1280 a^{5} x^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B \,b^{3}}{128 a^{4} x^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A \,b^{3}}{640 a^{4} x^{4}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B \,b^{2}}{192 a^{3} x^{4}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A \,b^{2}}{160 a^{3} x^{6}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B b}{48 a^{2} x^{6}}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{7}{2}} A b}{80 a^{2} x^{8}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} B}{8 a \,x^{8}}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} A}{10 a \,x^{10}}"," ",0,"-1/10*A*(b*x^2+a)^(7/2)/a/x^10+3/80*A*b/a^2/x^8*(b*x^2+a)^(7/2)-1/160*A*b^2/a^3/x^6*(b*x^2+a)^(7/2)-1/640*A*b^3/a^4/x^4*(b*x^2+a)^(7/2)-3/1280*A*b^4/a^5/x^2*(b*x^2+a)^(7/2)+3/1280*A*b^5/a^5*(b*x^2+a)^(5/2)+1/256*A*b^5/a^4*(b*x^2+a)^(3/2)-3/256*A*b^5/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+3/256*A*b^5/a^3*(b*x^2+a)^(1/2)-1/8*B/a/x^8*(b*x^2+a)^(7/2)+1/48*B*b/a^2/x^6*(b*x^2+a)^(7/2)+1/192*B*b^2/a^3/x^4*(b*x^2+a)^(7/2)+1/128*B*b^3/a^4/x^2*(b*x^2+a)^(7/2)-1/128*B*b^4/a^4*(b*x^2+a)^(5/2)-5/384*B*b^4/a^3*(b*x^2+a)^(3/2)+5/128*B*b^4/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-5/128*B*b^4/a^2*(b*x^2+a)^(1/2)","B"
555,1,77,86,0.007000," ","int(x^5*(B*x^2+A)/(b*x^2+a)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \left(15 B \,x^{6} b^{3}+21 A \,b^{3} x^{4}-18 B a \,b^{2} x^{4}-28 A a \,b^{2} x^{2}+24 B \,a^{2} b \,x^{2}+56 A \,a^{2} b -48 B \,a^{3}\right)}{105 b^{4}}"," ",0,"1/105*(b*x^2+a)^(1/2)*(15*B*b^3*x^6+21*A*b^3*x^4-18*B*a*b^2*x^4-28*A*a*b^2*x^2+24*B*a^2*b*x^2+56*A*a^2*b-48*B*a^3)/b^4","A"
556,1,143,102,0.010000," ","int(x^4*(B*x^2+A)/(b*x^2+a)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, B \,x^{5}}{6 b}+\frac{\sqrt{b \,x^{2}+a}\, A \,x^{3}}{4 b}-\frac{5 \sqrt{b \,x^{2}+a}\, B a \,x^{3}}{24 b^{2}}+\frac{3 A \,a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{5}{2}}}-\frac{5 B \,a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{7}{2}}}-\frac{3 \sqrt{b \,x^{2}+a}\, A a x}{8 b^{2}}+\frac{5 \sqrt{b \,x^{2}+a}\, B \,a^{2} x}{16 b^{3}}"," ",0,"1/6*B*x^5*(b*x^2+a)^(1/2)/b-5/24*B*a/b^2*x^3*(b*x^2+a)^(1/2)+5/16*B*a^2/b^3*x*(b*x^2+a)^(1/2)-5/16*B*a^3/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/4*A*x^3/b*(b*x^2+a)^(1/2)-3/8*A*a/b^2*x*(b*x^2+a)^(1/2)+3/8*A*a^2/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
557,1,53,61,0.007000," ","int(x^3*(B*x^2+A)/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \left(-3 B \,b^{2} x^{4}-5 A \,b^{2} x^{2}+4 B a b \,x^{2}+10 a b A -8 a^{2} B \right)}{15 b^{3}}"," ",0,"-1/15*(b*x^2+a)^(1/2)*(-3*B*b^2*x^4-5*A*b^2*x^2+4*B*a*b*x^2+10*A*a*b-8*B*a^2)/b^3","A"
558,1,101,73,0.008000," ","int(x^2*(B*x^2+A)/(b*x^2+a)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, B \,x^{3}}{4 b}-\frac{A a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{3}{2}}}+\frac{3 B \,a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{5}{2}}}+\frac{\sqrt{b \,x^{2}+a}\, A x}{2 b}-\frac{3 \sqrt{b \,x^{2}+a}\, B a x}{8 b^{2}}"," ",0,"1/4*B*x^3*(b*x^2+a)^(1/2)/b-3/8*B*a/b^2*x*(b*x^2+a)^(1/2)+3/8*B*a^2/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*A*x/b*(b*x^2+a)^(1/2)-1/2*A*a/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
559,1,30,37,0.006000," ","int(x*(B*x^2+A)/(b*x^2+a)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \left(B b \,x^{2}+3 A b -2 B a \right)}{3 b^{2}}"," ",0,"1/3*(b*x^2+a)^(1/2)*(B*b*x^2+3*A*b-2*B*a)/b^2","A"
560,1,62,46,0.005000," ","int((B*x^2+A)/(b*x^2+a)^(1/2),x)","\frac{A \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{\sqrt{b}}-\frac{B a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{3}{2}}}+\frac{\sqrt{b \,x^{2}+a}\, B x}{2 b}"," ",0,"1/2*B*x*(b*x^2+a)^(1/2)/b-1/2*B*a/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+A*ln(b^(1/2)*x+(b*x^2+a)^(1/2))/b^(1/2)","A"
561,1,45,35,0.008000," ","int((B*x^2+A)/x/(b*x^2+a)^(1/2),x)","-\frac{A \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\sqrt{a}}+\frac{\sqrt{b \,x^{2}+a}\, B}{b}"," ",0,"B*(b*x^2+a)^(1/2)/b-A/a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
562,1,41,39,0.010000," ","int((B*x^2+A)/x^2/(b*x^2+a)^(1/2),x)","\frac{B \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{\sqrt{b}}-\frac{\sqrt{b \,x^{2}+a}\, A}{a x}"," ",0,"B*ln(b^(1/2)*x+(b*x^2+a)^(1/2))/b^(1/2)-A*(b*x^2+a)^(1/2)/a/x","A"
563,1,79,46,0.010000," ","int((B*x^2+A)/x^3/(b*x^2+a)^(1/2),x)","\frac{A b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{3}{2}}}-\frac{B \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\sqrt{a}}-\frac{\sqrt{b \,x^{2}+a}\, A}{2 a \,x^{2}}"," ",0,"-1/2*A*(b*x^2+a)^(1/2)/a/x^2+1/2*A*b/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-B/a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
564,1,36,45,0.006000," ","int((B*x^2+A)/x^4/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \left(-2 A b \,x^{2}+3 B a \,x^{2}+A a \right)}{3 a^{2} x^{3}}"," ",0,"-1/3*(b*x^2+a)^(1/2)*(-2*A*b*x^2+3*B*a*x^2+A*a)/x^3/a^2","A"
565,1,119,74,0.010000," ","int((B*x^2+A)/x^5/(b*x^2+a)^(1/2),x)","-\frac{3 A \,b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{5}{2}}}+\frac{B b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{3}{2}}}+\frac{3 \sqrt{b \,x^{2}+a}\, A b}{8 a^{2} x^{2}}-\frac{\sqrt{b \,x^{2}+a}\, B}{2 a \,x^{2}}-\frac{\sqrt{b \,x^{2}+a}\, A}{4 a \,x^{4}}"," ",0,"-1/2*B/a/x^2*(b*x^2+a)^(1/2)+1/2*B*b/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/4*A*(b*x^2+a)^(1/2)/a/x^4+3/8*A*b/a^2/x^2*(b*x^2+a)^(1/2)-3/8*A*b^2/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
566,1,59,72,0.006000," ","int((B*x^2+A)/x^6/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \left(8 A \,b^{2} x^{4}-10 B a b \,x^{4}-4 A a b \,x^{2}+5 B \,a^{2} x^{2}+3 a^{2} A \right)}{15 a^{3} x^{5}}"," ",0,"-1/15*(b*x^2+a)^(1/2)*(8*A*b^2*x^4-10*B*a*b*x^4-4*A*a*b*x^2+5*B*a^2*x^2+3*A*a^2)/x^5/a^3","A"
567,1,161,103,0.015000," ","int((B*x^2+A)/x^7/(b*x^2+a)^(1/2),x)","\frac{5 A \,b^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{16 a^{\frac{7}{2}}}-\frac{3 B \,b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{5}{2}}}-\frac{5 \sqrt{b \,x^{2}+a}\, A \,b^{2}}{16 a^{3} x^{2}}+\frac{3 \sqrt{b \,x^{2}+a}\, B b}{8 a^{2} x^{2}}+\frac{5 \sqrt{b \,x^{2}+a}\, A b}{24 a^{2} x^{4}}-\frac{\sqrt{b \,x^{2}+a}\, B}{4 a \,x^{4}}-\frac{\sqrt{b \,x^{2}+a}\, A}{6 a \,x^{6}}"," ",0,"-1/4*B/a/x^4*(b*x^2+a)^(1/2)+3/8*B*b/a^2/x^2*(b*x^2+a)^(1/2)-3/8*B*b^2/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/6*A*(b*x^2+a)^(1/2)/a/x^6+5/24*A*b/a^2/x^4*(b*x^2+a)^(1/2)-5/16*A*b^2/a^3/x^2*(b*x^2+a)^(1/2)+5/16*A*b^3/a^(7/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
568,1,83,101,0.006000," ","int((B*x^2+A)/x^8/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \left(-48 A \,b^{3} x^{6}+56 B a \,b^{2} x^{6}+24 x^{4} A a \,b^{2}-28 B \,a^{2} b \,x^{4}-18 A \,a^{2} b \,x^{2}+21 B \,a^{3} x^{2}+15 A \,a^{3}\right)}{105 a^{4} x^{7}}"," ",0,"-1/105*(b*x^2+a)^(1/2)*(-48*A*b^3*x^6+56*B*a*b^2*x^6+24*A*a*b^2*x^4-28*B*a^2*b*x^4-18*A*a^2*b*x^2+21*B*a^3*x^2+15*A*a^3)/x^7/a^4","A"
569,1,185,128,0.019000," ","int(x^6*(B*x^2+A)/(b*x^2+a)^(3/2),x)","\frac{B \,x^{7}}{6 \sqrt{b \,x^{2}+a}\, b}+\frac{A \,x^{5}}{4 \sqrt{b \,x^{2}+a}\, b}-\frac{7 B a \,x^{5}}{24 \sqrt{b \,x^{2}+a}\, b^{2}}-\frac{5 A a \,x^{3}}{8 \sqrt{b \,x^{2}+a}\, b^{2}}+\frac{35 B \,a^{2} x^{3}}{48 \sqrt{b \,x^{2}+a}\, b^{3}}-\frac{15 A \,a^{2} x}{8 \sqrt{b \,x^{2}+a}\, b^{3}}+\frac{35 B \,a^{3} x}{16 \sqrt{b \,x^{2}+a}\, b^{4}}+\frac{15 A \,a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{7}{2}}}-\frac{35 B \,a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{9}{2}}}"," ",0,"1/6*B*x^7/b/(b*x^2+a)^(1/2)-7/24*B*a/b^2*x^5/(b*x^2+a)^(1/2)+35/48*B*a^2/b^3*x^3/(b*x^2+a)^(1/2)+35/16*B*a^3/b^4*x/(b*x^2+a)^(1/2)-35/16*B*a^3/b^(9/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/4*A*x^5/b/(b*x^2+a)^(1/2)-5/8*A*a/b^2*x^3/(b*x^2+a)^(1/2)-15/8*A*a^2/b^3*x/(b*x^2+a)^(1/2)+15/8*A*a^2/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
570,1,77,87,0.006000," ","int(x^5*(B*x^2+A)/(b*x^2+a)^(3/2),x)","-\frac{-3 B \,x^{6} b^{3}-5 A \,b^{3} x^{4}+6 B a \,b^{2} x^{4}+20 A a \,b^{2} x^{2}-24 B \,a^{2} b \,x^{2}+40 A \,a^{2} b -48 B \,a^{3}}{15 \sqrt{b \,x^{2}+a}\, b^{4}}"," ",0,"-1/15*(-3*B*b^3*x^6-5*A*b^3*x^4+6*B*a*b^2*x^4+20*A*a*b^2*x^2-24*B*a^2*b*x^2+40*A*a^2*b-48*B*a^3)/(b*x^2+a)^(1/2)/b^4","A"
571,1,141,99,0.011000," ","int(x^4*(B*x^2+A)/(b*x^2+a)^(3/2),x)","\frac{B \,x^{5}}{4 \sqrt{b \,x^{2}+a}\, b}+\frac{A \,x^{3}}{2 \sqrt{b \,x^{2}+a}\, b}-\frac{5 B a \,x^{3}}{8 \sqrt{b \,x^{2}+a}\, b^{2}}+\frac{3 A a x}{2 \sqrt{b \,x^{2}+a}\, b^{2}}-\frac{15 B \,a^{2} x}{8 \sqrt{b \,x^{2}+a}\, b^{3}}-\frac{3 A a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{5}{2}}}+\frac{15 B \,a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{7}{2}}}"," ",0,"1/4*B*x^5/b/(b*x^2+a)^(1/2)-5/8*B*a/b^2*x^3/(b*x^2+a)^(1/2)-15/8*B*a^2/b^3*x/(b*x^2+a)^(1/2)+15/8*B*a^2/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*A*x^3/b/(b*x^2+a)^(1/2)+3/2*A*a/b^2*x/(b*x^2+a)^(1/2)-3/2*A*a/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
572,1,52,59,0.005000," ","int(x^3*(B*x^2+A)/(b*x^2+a)^(3/2),x)","\frac{B \,b^{2} x^{4}+3 A \,b^{2} x^{2}-4 B a b \,x^{2}+6 a b A -8 a^{2} B}{3 \sqrt{b \,x^{2}+a}\, b^{3}}"," ",0,"1/3*(B*b^2*x^4+3*A*b^2*x^2-4*B*a*b*x^2+6*A*a*b-8*B*a^2)/(b*x^2+a)^(1/2)/b^3","A"
573,1,97,69,0.010000," ","int(x^2*(B*x^2+A)/(b*x^2+a)^(3/2),x)","\frac{B \,x^{3}}{2 \sqrt{b \,x^{2}+a}\, b}-\frac{A x}{\sqrt{b \,x^{2}+a}\, b}+\frac{3 B a x}{2 \sqrt{b \,x^{2}+a}\, b^{2}}+\frac{A \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{3}{2}}}-\frac{3 B a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{5}{2}}}"," ",0,"1/2*B*x^3/b/(b*x^2+a)^(1/2)+3/2*B*a/b^2*x/(b*x^2+a)^(1/2)-3/2*B*a/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-A*x/b/(b*x^2+a)^(1/2)+A/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
574,1,30,36,0.004000," ","int(x*(B*x^2+A)/(b*x^2+a)^(3/2),x)","-\frac{-B b \,x^{2}+A b -2 B a}{\sqrt{b \,x^{2}+a}\, b^{2}}"," ",0,"-(-B*b*x^2+A*b-2*B*a)/(b*x^2+a)^(1/2)/b^2","A"
575,1,54,46,0.007000," ","int((B*x^2+A)/(b*x^2+a)^(3/2),x)","\frac{A x}{\sqrt{b \,x^{2}+a}\, a}-\frac{B x}{\sqrt{b \,x^{2}+a}\, b}+\frac{B \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{3}{2}}}"," ",0,"-B*x/b/(b*x^2+a)^(1/2)+B/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+A*x/a/(b*x^2+a)^(1/2)","A"
576,1,60,45,0.010000," ","int((B*x^2+A)/x/(b*x^2+a)^(3/2),x)","-\frac{A \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{a^{\frac{3}{2}}}+\frac{A}{\sqrt{b \,x^{2}+a}\, a}-\frac{B}{\sqrt{b \,x^{2}+a}\, b}"," ",0,"-B/b/(b*x^2+a)^(1/2)+A/a/(b*x^2+a)^(1/2)-A/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
577,1,36,43,0.005000," ","int((B*x^2+A)/x^2/(b*x^2+a)^(3/2),x)","-\frac{2 A b \,x^{2}-B a \,x^{2}+A a}{\sqrt{b \,x^{2}+a}\, a^{2} x}"," ",0,"-(2*A*b*x^2-B*a*x^2+A*a)/(b*x^2+a)^(1/2)/x/a^2","A"
578,1,109,70,0.010000," ","int((B*x^2+A)/x^3/(b*x^2+a)^(3/2),x)","\frac{3 A b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{5}{2}}}-\frac{B \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{a^{\frac{3}{2}}}-\frac{3 A b}{2 \sqrt{b \,x^{2}+a}\, a^{2}}+\frac{B}{\sqrt{b \,x^{2}+a}\, a}-\frac{A}{2 \sqrt{b \,x^{2}+a}\, a \,x^{2}}"," ",0,"-1/2*A/a/x^2/(b*x^2+a)^(1/2)-3/2*A*b/a^2/(b*x^2+a)^(1/2)+3/2*A*b/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+B/a/(b*x^2+a)^(1/2)-B/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
579,1,58,70,0.007000," ","int((B*x^2+A)/x^4/(b*x^2+a)^(3/2),x)","-\frac{-8 A \,b^{2} x^{4}+6 B a b \,x^{4}-4 A a b \,x^{2}+3 B \,a^{2} x^{2}+a^{2} A}{3 \sqrt{b \,x^{2}+a}\, a^{3} x^{3}}"," ",0,"-1/3*(-8*A*b^2*x^4+6*B*a*b*x^4-4*A*a*b*x^2+3*B*a^2*x^2+A*a^2)/(b*x^2+a)^(1/2)/x^3/a^3","A"
580,1,153,98,0.012000," ","int((B*x^2+A)/x^5/(b*x^2+a)^(3/2),x)","-\frac{15 A \,b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{7}{2}}}+\frac{3 B b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{5}{2}}}+\frac{15 A \,b^{2}}{8 \sqrt{b \,x^{2}+a}\, a^{3}}-\frac{3 B b}{2 \sqrt{b \,x^{2}+a}\, a^{2}}+\frac{5 A b}{8 \sqrt{b \,x^{2}+a}\, a^{2} x^{2}}-\frac{B}{2 \sqrt{b \,x^{2}+a}\, a \,x^{2}}-\frac{A}{4 \sqrt{b \,x^{2}+a}\, a \,x^{4}}"," ",0,"-1/2*B/a/x^2/(b*x^2+a)^(1/2)-3/2*B*b/a^2/(b*x^2+a)^(1/2)+3/2*B*b/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/4*A/a/x^4/(b*x^2+a)^(1/2)+5/8*A*b/a^2/x^2/(b*x^2+a)^(1/2)+15/8*A*b^2/a^3/(b*x^2+a)^(1/2)-15/8*A*b^2/a^(7/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
581,1,83,99,0.007000," ","int((B*x^2+A)/x^6/(b*x^2+a)^(3/2),x)","-\frac{48 A \,b^{3} x^{6}-40 B a \,b^{2} x^{6}+24 x^{4} A a \,b^{2}-20 B \,a^{2} b \,x^{4}-6 A \,a^{2} b \,x^{2}+5 B \,a^{3} x^{2}+3 A \,a^{3}}{15 \sqrt{b \,x^{2}+a}\, a^{4} x^{5}}"," ",0,"-1/15*(48*A*b^3*x^6-40*B*a*b^2*x^6+24*A*a*b^2*x^4-20*B*a^2*b*x^4-6*A*a^2*b*x^2+5*B*a^3*x^2+3*A*a^3)/(b*x^2+a)^(1/2)/x^5/a^4","A"
582,1,197,129,0.014000," ","int((B*x^2+A)/x^7/(b*x^2+a)^(3/2),x)","\frac{35 A \,b^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{16 a^{\frac{9}{2}}}-\frac{15 B \,b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{7}{2}}}-\frac{35 A \,b^{3}}{16 \sqrt{b \,x^{2}+a}\, a^{4}}+\frac{15 B \,b^{2}}{8 \sqrt{b \,x^{2}+a}\, a^{3}}-\frac{35 A \,b^{2}}{48 \sqrt{b \,x^{2}+a}\, a^{3} x^{2}}+\frac{5 B b}{8 \sqrt{b \,x^{2}+a}\, a^{2} x^{2}}+\frac{7 A b}{24 \sqrt{b \,x^{2}+a}\, a^{2} x^{4}}-\frac{B}{4 \sqrt{b \,x^{2}+a}\, a \,x^{4}}-\frac{A}{6 \sqrt{b \,x^{2}+a}\, a \,x^{6}}"," ",0,"-1/4*B/a/x^4/(b*x^2+a)^(1/2)+5/8*B*b/a^2/x^2/(b*x^2+a)^(1/2)+15/8*B*b^2/a^3/(b*x^2+a)^(1/2)-15/8*B*b^2/a^(7/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/6*A/a/x^6/(b*x^2+a)^(1/2)+7/24*A*b/a^2/x^4/(b*x^2+a)^(1/2)-35/48*A*b^2/a^3/x^2/(b*x^2+a)^(1/2)-35/16*A*b^3/a^4/(b*x^2+a)^(1/2)+35/16*A*b^3/a^(9/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
583,1,107,128,0.007000," ","int((B*x^2+A)/x^8/(b*x^2+a)^(3/2),x)","-\frac{-128 A \,b^{4} x^{8}+112 B a \,b^{3} x^{8}-64 A a \,b^{3} x^{6}+56 B \,a^{2} b^{2} x^{6}+16 A \,a^{2} b^{2} x^{4}-14 B \,a^{3} b \,x^{4}-8 A \,a^{3} b \,x^{2}+7 B \,a^{4} x^{2}+5 A \,a^{4}}{35 \sqrt{b \,x^{2}+a}\, a^{5} x^{7}}"," ",0,"-1/35*(-128*A*b^4*x^8+112*B*a*b^3*x^8-64*A*a*b^3*x^6+56*B*a^2*b^2*x^6+16*A*a^2*b^2*x^4-14*B*a^3*b*x^4-8*A*a^3*b*x^2+7*B*a^4*x^2+5*A*a^4)/(b*x^2+a)^(1/2)/x^7/a^5","A"
584,1,101,112,0.007000," ","int(x^7*(B*x^2+A)/(b*x^2+a)^(5/2),x)","-\frac{-3 x^{8} B \,b^{4}-5 A \,b^{4} x^{6}+8 B a \,b^{3} x^{6}+30 A a \,b^{3} x^{4}-48 B \,a^{2} b^{2} x^{4}+120 A \,a^{2} b^{2} x^{2}-192 B \,a^{3} b \,x^{2}+80 A \,a^{3} b -128 B \,a^{4}}{15 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{5}}"," ",0,"-1/15*(-3*B*b^4*x^8-5*A*b^4*x^6+8*B*a*b^3*x^6+30*A*a*b^3*x^4-48*B*a^2*b^2*x^4+120*A*a^2*b^2*x^2-192*B*a^3*b*x^2+80*A*a^3*b-128*B*a^4)/(b*x^2+a)^(3/2)/b^5","A"
585,1,181,125,0.020000," ","int(x^6*(B*x^2+A)/(b*x^2+a)^(5/2),x)","\frac{B \,x^{7}}{4 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}+\frac{A \,x^{5}}{2 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}-\frac{7 B a \,x^{5}}{8 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}+\frac{5 A a \,x^{3}}{6 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}-\frac{35 B \,a^{2} x^{3}}{24 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{3}}+\frac{5 A a x}{2 \sqrt{b \,x^{2}+a}\, b^{3}}-\frac{35 B \,a^{2} x}{8 \sqrt{b \,x^{2}+a}\, b^{4}}-\frac{5 A a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{7}{2}}}+\frac{35 B \,a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{9}{2}}}"," ",0,"1/4*B*x^7/b/(b*x^2+a)^(3/2)-7/8*B*a/b^2*x^5/(b*x^2+a)^(3/2)-35/24*B*a^2/b^3*x^3/(b*x^2+a)^(3/2)-35/8*B*a^2/b^4*x/(b*x^2+a)^(1/2)+35/8*B*a^2/b^(9/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*A*x^5/b/(b*x^2+a)^(3/2)+5/6*A*a/b^2*x^3/(b*x^2+a)^(3/2)+5/2*A*a/b^3*x/(b*x^2+a)^(1/2)-5/2*A*a/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
586,1,76,85,0.007000," ","int(x^5*(B*x^2+A)/(b*x^2+a)^(5/2),x)","\frac{B \,x^{6} b^{3}+3 A \,b^{3} x^{4}-6 B a \,b^{2} x^{4}+12 A a \,b^{2} x^{2}-24 B \,a^{2} b \,x^{2}+8 A \,a^{2} b -16 B \,a^{3}}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{4}}"," ",0,"1/3*(B*b^3*x^6+3*A*b^3*x^4-6*B*a*b^2*x^4+12*A*a*b^2*x^2-24*B*a^2*b*x^2+8*A*a^2*b-16*B*a^3)/(b*x^2+a)^(3/2)/b^4","A"
587,1,134,94,0.010000," ","int(x^4*(B*x^2+A)/(b*x^2+a)^(5/2),x)","\frac{B \,x^{5}}{2 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}-\frac{A \,x^{3}}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}+\frac{5 B a \,x^{3}}{6 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}-\frac{A x}{\sqrt{b \,x^{2}+a}\, b^{2}}+\frac{5 B a x}{2 \sqrt{b \,x^{2}+a}\, b^{3}}+\frac{A \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{5}{2}}}-\frac{5 B a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{7}{2}}}"," ",0,"1/2*B*x^5/b/(b*x^2+a)^(3/2)+5/6*B*a/b^2*x^3/(b*x^2+a)^(3/2)+5/2*B*a/b^3*x/(b*x^2+a)^(1/2)-5/2*B*a/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-1/3*A*x^3/b/(b*x^2+a)^(3/2)-A/b^2*x/(b*x^2+a)^(1/2)+A/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
588,1,53,60,0.006000," ","int(x^3*(B*x^2+A)/(b*x^2+a)^(5/2),x)","-\frac{-3 B \,b^{2} x^{4}+3 A \,b^{2} x^{2}-12 B a b \,x^{2}+2 a b A -8 a^{2} B}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{3}}"," ",0,"-1/3*(-3*B*b^2*x^4+3*A*b^2*x^2-12*B*a*b*x^2+2*A*a*b-8*B*a^2)/(b*x^2+a)^(3/2)/b^3","A"
589,1,92,65,0.010000," ","int(x^2*(B*x^2+A)/(b*x^2+a)^(5/2),x)","-\frac{B \,x^{3}}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}-\frac{A x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}+\frac{A x}{3 \sqrt{b \,x^{2}+a}\, a b}-\frac{B x}{\sqrt{b \,x^{2}+a}\, b^{2}}+\frac{B \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{5}{2}}}"," ",0,"-1/3*B*x^3/b/(b*x^2+a)^(3/2)-B*x/b^2/(b*x^2+a)^(1/2)+B/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-1/3*A/b*x/(b*x^2+a)^(3/2)+1/3*A/a/b*x/(b*x^2+a)^(1/2)","A"
590,1,30,38,0.004000," ","int(x*(B*x^2+A)/(b*x^2+a)^(5/2),x)","-\frac{3 B b \,x^{2}+A b +2 B a}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}"," ",0,"-1/3*(3*B*b*x^2+A*b+2*B*a)/(b*x^2+a)^(3/2)/b^2","A"
591,1,34,39,0.005000," ","int((B*x^2+A)/(b*x^2+a)^(5/2),x)","\frac{\left(2 A b \,x^{2}+B a \,x^{2}+3 A a \right) x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2}}"," ",0,"1/3*x*(2*A*b*x^2+B*a*x^2+3*A*a)/(b*x^2+a)^(3/2)/a^2","A"
592,1,75,60,0.010000," ","int((B*x^2+A)/x/(b*x^2+a)^(5/2),x)","\frac{A}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a}-\frac{B}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}-\frac{A \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{a^{\frac{5}{2}}}+\frac{A}{\sqrt{b \,x^{2}+a}\, a^{2}}"," ",0,"-1/3*B/b/(b*x^2+a)^(3/2)+1/3*A/a/(b*x^2+a)^(3/2)+A/a^2/(b*x^2+a)^(1/2)-A/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
593,1,59,67,0.005000," ","int((B*x^2+A)/x^2/(b*x^2+a)^(5/2),x)","-\frac{8 A \,b^{2} x^{4}-2 B a b \,x^{4}+12 A a b \,x^{2}-3 B \,a^{2} x^{2}+3 a^{2} A}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{3} x}"," ",0,"-1/3*(8*A*b^2*x^4-2*B*a*b*x^4+12*A*a*b*x^2-3*B*a^2*x^2+3*A*a^2)/(b*x^2+a)^(3/2)/x/a^3","A"
594,1,140,93,0.018000," ","int((B*x^2+A)/x^3/(b*x^2+a)^(5/2),x)","-\frac{5 A b}{6 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2}}+\frac{B}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a}+\frac{5 A b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{7}{2}}}-\frac{B \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{a^{\frac{5}{2}}}-\frac{5 A b}{2 \sqrt{b \,x^{2}+a}\, a^{3}}+\frac{B}{\sqrt{b \,x^{2}+a}\, a^{2}}-\frac{A}{2 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,x^{2}}"," ",0,"-1/2*A/a/x^2/(b*x^2+a)^(3/2)-5/6*A*b/a^2/(b*x^2+a)^(3/2)-5/2*A*b/a^3/(b*x^2+a)^(1/2)+5/2*A*b/a^(7/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+1/3*B/a/(b*x^2+a)^(3/2)+B/a^2/(b*x^2+a)^(1/2)-B/a^(5/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
595,1,82,94,0.007000," ","int((B*x^2+A)/x^4/(b*x^2+a)^(5/2),x)","-\frac{-16 A \,b^{3} x^{6}+8 B a \,b^{2} x^{6}-24 x^{4} A a \,b^{2}+12 B \,a^{2} b \,x^{4}-6 A \,a^{2} b \,x^{2}+3 B \,a^{3} x^{2}+A \,a^{3}}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{4} x^{3}}"," ",0,"-1/3*(-16*A*b^3*x^6+8*B*a*b^2*x^6-24*A*a*b^2*x^4+12*B*a^2*b*x^4-6*A*a^2*b*x^2+3*B*a^3*x^2+A*a^3)/(b*x^2+a)^(3/2)/x^3/a^4","A"
596,1,187,122,0.013000," ","int((B*x^2+A)/x^5/(b*x^2+a)^(5/2),x)","\frac{35 A \,b^{2}}{24 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{3}}-\frac{5 B b}{6 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2}}-\frac{35 A \,b^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{9}{2}}}+\frac{5 B b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{7}{2}}}+\frac{35 A \,b^{2}}{8 \sqrt{b \,x^{2}+a}\, a^{4}}-\frac{5 B b}{2 \sqrt{b \,x^{2}+a}\, a^{3}}+\frac{7 A b}{8 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} x^{2}}-\frac{B}{2 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,x^{2}}-\frac{A}{4 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,x^{4}}"," ",0,"-1/4*A/a/x^4/(b*x^2+a)^(3/2)+7/8*A*b/a^2/x^2/(b*x^2+a)^(3/2)+35/24*A*b^2/a^3/(b*x^2+a)^(3/2)+35/8*A*b^2/a^4/(b*x^2+a)^(1/2)-35/8*A*b^2/a^(9/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/2*B/a/x^2/(b*x^2+a)^(3/2)-5/6*B*b/a^2/(b*x^2+a)^(3/2)-5/2*B*b/a^3/(b*x^2+a)^(1/2)+5/2*B*b/a^(7/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
597,1,107,126,0.007000," ","int((B*x^2+A)/x^6/(b*x^2+a)^(5/2),x)","-\frac{128 A \,b^{4} x^{8}-80 B a \,b^{3} x^{8}+192 A a \,b^{3} x^{6}-120 B \,a^{2} b^{2} x^{6}+48 A \,a^{2} b^{2} x^{4}-30 B \,a^{3} b \,x^{4}-8 A \,a^{3} b \,x^{2}+5 B \,a^{4} x^{2}+3 A \,a^{4}}{15 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{5} x^{5}}"," ",0,"-1/15*(128*A*b^4*x^8-80*B*a*b^3*x^8+192*A*a*b^3*x^6-120*B*a^2*b^2*x^6+48*A*a^2*b^2*x^4-30*B*a^3*b*x^4-8*A*a^3*b*x^2+5*B*a^4*x^2+3*A*a^4)/(b*x^2+a)^(3/2)/x^5/a^5","A"
598,1,149,137,0.008000," ","int(x^5*(b*x^2+a)^2*(d*x^2+c)^(1/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} \left(315 b^{2} x^{8} d^{4}+770 a b \,d^{4} x^{6}-280 b^{2} c \,d^{3} x^{6}+495 a^{2} d^{4} x^{4}-660 a b c \,d^{3} x^{4}+240 b^{2} c^{2} d^{2} x^{4}-396 a^{2} c \,d^{3} x^{2}+528 a b \,c^{2} d^{2} x^{2}-192 b^{2} c^{3} d \,x^{2}+264 a^{2} c^{2} d^{2}-352 a b \,c^{3} d +128 b^{2} c^{4}\right)}{3465 d^{5}}"," ",0,"1/3465*(d*x^2+c)^(3/2)*(315*b^2*d^4*x^8+770*a*b*d^4*x^6-280*b^2*c*d^3*x^6+495*a^2*d^4*x^4-660*a*b*c*d^3*x^4+240*b^2*c^2*d^2*x^4-396*a^2*c*d^3*x^2+528*a*b*c^2*d^2*x^2-192*b^2*c^3*d*x^2+264*a^2*c^2*d^2-352*a*b*c^3*d+128*b^2*c^4)/d^5","A"
599,1,108,98,0.008000," ","int(x^3*(b*x^2+a)^2*(d*x^2+c)^(1/2),x)","-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} \left(-35 b^{2} x^{6} d^{3}-90 a b \,d^{3} x^{4}+30 b^{2} c \,d^{2} x^{4}-63 a^{2} d^{3} x^{2}+72 a b c \,d^{2} x^{2}-24 b^{2} c^{2} d \,x^{2}+42 a^{2} c \,d^{2}-48 a b \,c^{2} d +16 b^{2} c^{3}\right)}{315 d^{4}}"," ",0,"-1/315*(d*x^2+c)^(3/2)*(-35*b^2*d^3*x^6-90*a*b*d^3*x^4+30*b^2*c*d^2*x^4-63*a^2*d^3*x^2+72*a*b*c*d^2*x^2-24*b^2*c^2*d*x^2+42*a^2*c*d^2-48*a*b*c^2*d+16*b^2*c^3)/d^4","A"
600,1,69,65,0.007000," ","int(x*(b*x^2+a)^2*(d*x^2+c)^(1/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} \left(15 b^{2} x^{4} d^{2}+42 a b \,d^{2} x^{2}-12 b^{2} c d \,x^{2}+35 a^{2} d^{2}-28 a b c d +8 b^{2} c^{2}\right)}{105 d^{3}}"," ",0,"1/105*(d*x^2+c)^(3/2)*(15*b^2*d^2*x^4+42*a*b*d^2*x^2-12*b^2*c*d*x^2+35*a^2*d^2-28*a*b*c*d+8*b^2*c^2)/d^3","A"
601,1,100,76,0.013000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x,x)","-a^{2} \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} x^{2}}{5 d}+\sqrt{d \,x^{2}+c}\, a^{2}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b}{3 d}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c}{15 d^{2}}"," ",0,"1/5*b^2*x^2*(d*x^2+c)^(3/2)/d-2/15*b^2*c/d^2*(d*x^2+c)^(3/2)+2/3*a*b*(d*x^2+c)^(3/2)/d-c^(1/2)*ln((2*c+2*c^(1/2)*(d*x^2+c)^(1/2))/x)*a^2+a^2*(d*x^2+c)^(1/2)","A"
602,1,132,89,0.014000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^3,x)","-\frac{a^{2} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 \sqrt{c}}-2 a b \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+\frac{\sqrt{d \,x^{2}+c}\, a^{2} d}{2 c}+2 \sqrt{d \,x^{2}+c}\, a b +\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2}}{3 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2}}{2 c \,x^{2}}"," ",0,"1/3*b^2*(d*x^2+c)^(3/2)/d-1/2*a^2*(d*x^2+c)^(3/2)/c/x^2-1/2*a^2*d/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/2*a^2*d/c*(d*x^2+c)^(1/2)-2*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)*a*b+2*(d*x^2+c)^(1/2)*a*b","A"
603,1,207,123,0.016000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^5,x)","\frac{a^{2} d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{8 c^{\frac{3}{2}}}-\frac{a b d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{\sqrt{c}}-b^{2} \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)-\frac{\sqrt{d \,x^{2}+c}\, a^{2} d^{2}}{8 c^{2}}+\frac{\sqrt{d \,x^{2}+c}\, a b d}{c}+\sqrt{d \,x^{2}+c}\, b^{2}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d}{8 c^{2} x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b}{c \,x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2}}{4 c \,x^{4}}"," ",0,"-1/4*a^2*(d*x^2+c)^(3/2)/c/x^4+1/8*a^2*d/c^2/x^2*(d*x^2+c)^(3/2)+1/8*a^2*d^2/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/8*a^2*d^2/c^2*(d*x^2+c)^(1/2)-a*b/c/x^2*(d*x^2+c)^(3/2)-a*b*d/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+a*b*d/c*(d*x^2+c)^(1/2)-c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)*b^2+(d*x^2+c)^(1/2)*b^2","A"
604,1,281,129,0.017000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^7,x)","-\frac{a^{2} d^{3} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{16 c^{\frac{5}{2}}}+\frac{a b \,d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{4 c^{\frac{3}{2}}}-\frac{b^{2} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 \sqrt{c}}+\frac{\sqrt{d \,x^{2}+c}\, a^{2} d^{3}}{16 c^{3}}-\frac{\sqrt{d \,x^{2}+c}\, a b \,d^{2}}{4 c^{2}}+\frac{\sqrt{d \,x^{2}+c}\, b^{2} d}{2 c}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d^{2}}{16 c^{3} x^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b d}{4 c^{2} x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2}}{2 c \,x^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d}{8 c^{2} x^{4}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b}{2 c \,x^{4}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2}}{6 c \,x^{6}}"," ",0,"-1/6*a^2*(d*x^2+c)^(3/2)/c/x^6+1/8*a^2*d/c^2/x^4*(d*x^2+c)^(3/2)-1/16*a^2*d^2/c^3/x^2*(d*x^2+c)^(3/2)-1/16*a^2*d^3/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/16*a^2*d^3/c^3*(d*x^2+c)^(1/2)-1/2*a*b/c/x^4*(d*x^2+c)^(3/2)+1/4*a*b*d/c^2/x^2*(d*x^2+c)^(3/2)+1/4*a*b*d^2/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/4*a*b*d^2/c^2*(d*x^2+c)^(1/2)-1/2*b^2/c/x^2*(d*x^2+c)^(3/2)-1/2*b^2*d/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/2*b^2*d/c*(d*x^2+c)^(1/2)","B"
605,1,259,167,0.015000," ","int(x^2*(b*x^2+a)^2*(d*x^2+c)^(1/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} x^{5}}{8 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b \,x^{3}}{3 d}-\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c \,x^{3}}{48 d^{2}}-\frac{a^{2} c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 d^{\frac{3}{2}}}+\frac{a b \,c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 d^{\frac{5}{2}}}-\frac{5 b^{2} c^{4} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{128 d^{\frac{7}{2}}}-\frac{\sqrt{d \,x^{2}+c}\, a^{2} c x}{8 d}+\frac{\sqrt{d \,x^{2}+c}\, a b \,c^{2} x}{8 d^{2}}-\frac{5 \sqrt{d \,x^{2}+c}\, b^{2} c^{3} x}{128 d^{3}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} x}{4 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b c x}{4 d^{2}}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c^{2} x}{64 d^{3}}"," ",0,"1/8*b^2*x^5*(d*x^2+c)^(3/2)/d-5/48*b^2*c/d^2*x^3*(d*x^2+c)^(3/2)+5/64*b^2*c^2/d^3*x*(d*x^2+c)^(3/2)-5/128*b^2*c^3/d^3*x*(d*x^2+c)^(1/2)-5/128*b^2*c^4/d^(7/2)*ln(x*d^(1/2)+(d*x^2+c)^(1/2))+1/3*a*b*x^3*(d*x^2+c)^(3/2)/d-1/4*a*b*c/d^2*x*(d*x^2+c)^(3/2)+1/8*a*b*c^2/d^2*x*(d*x^2+c)^(1/2)+1/8*a*b*c^3/d^(5/2)*ln(x*d^(1/2)+(d*x^2+c)^(1/2))+1/4*a^2*x*(d*x^2+c)^(3/2)/d-1/8*a^2*c/d*x*(d*x^2+c)^(1/2)-1/8*a^2*c^2/d^(3/2)*ln(x*d^(1/2)+(d*x^2+c)^(1/2))","A"
606,1,190,129,0.009000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} x^{3}}{6 d}+\frac{a^{2} c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 \sqrt{d}}-\frac{a b \,c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{4 d^{\frac{3}{2}}}+\frac{b^{2} c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{16 d^{\frac{5}{2}}}+\frac{\sqrt{d \,x^{2}+c}\, a^{2} x}{2}-\frac{\sqrt{d \,x^{2}+c}\, a b c x}{4 d}+\frac{\sqrt{d \,x^{2}+c}\, b^{2} c^{2} x}{16 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b x}{2 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c x}{8 d^{2}}"," ",0,"1/6*b^2*x^3*(d*x^2+c)^(3/2)/d-1/8*b^2*c/d^2*x*(d*x^2+c)^(3/2)+1/16*b^2*c^2/d^2*x*(d*x^2+c)^(1/2)+1/16*b^2*c^3/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/2*a*b*x*(d*x^2+c)^(3/2)/d-1/4*a*b*c/d*x*(d*x^2+c)^(1/2)-1/4*a*b*c^2/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/2*a^2*x*(d*x^2+c)^(1/2)+1/2*a^2*c/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
607,1,163,115,0.013000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^2,x)","a^{2} \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+\frac{a b c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{\sqrt{d}}-\frac{b^{2} c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 d^{\frac{3}{2}}}+\frac{\sqrt{d \,x^{2}+c}\, a^{2} d x}{c}+\sqrt{d \,x^{2}+c}\, a b x -\frac{\sqrt{d \,x^{2}+c}\, b^{2} c x}{8 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} x}{4 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2}}{c x}"," ",0,"1/4*b^2*x*(d*x^2+c)^(3/2)/d-1/8*b^2*c/d*x*(d*x^2+c)^(1/2)-1/8*b^2*c^2/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+a*b*x*(d*x^2+c)^(1/2)+a*b*c/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-a^2*(d*x^2+c)^(3/2)/c/x+a^2*d/c*x*(d*x^2+c)^(1/2)+a^2*d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
608,1,122,93,0.013000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^4,x)","2 a b \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+\frac{b^{2} c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 \sqrt{d}}+\frac{2 \sqrt{d \,x^{2}+c}\, a b d x}{c}+\frac{\sqrt{d \,x^{2}+c}\, b^{2} x}{2}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b}{c x}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2}}{3 c \,x^{3}}"," ",0,"1/2*x*b^2*(d*x^2+c)^(1/2)+1/2*b^2*c/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2*a*b*(d*x^2+c)^(3/2)/c/x+2*a*b*d/c*x*(d*x^2+c)^(1/2)+2*a*b*d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/3*a^2*(d*x^2+c)^(3/2)/c/x^3","A"
609,1,123,87,0.015000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^6,x)","b^{2} \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+\frac{\sqrt{d \,x^{2}+c}\, b^{2} d x}{c}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2}}{c x}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d}{15 c^{2} x^{3}}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b}{3 c \,x^{3}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2}}{5 c \,x^{5}}"," ",0,"-1/5*a^2*(d*x^2+c)^(3/2)/c/x^5+2/15*a^2*d/c^2/x^3*(d*x^2+c)^(3/2)-b^2/c/x*(d*x^2+c)^(3/2)+b^2*d/c*x*(d*x^2+c)^(1/2)+b^2*d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2/3*a*b/c/x^3*(d*x^2+c)^(3/2)","A"
610,1,78,87,0.008000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^8,x)","-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} \left(8 a^{2} d^{2} x^{4}-28 a b c d \,x^{4}+35 b^{2} c^{2} x^{4}-12 a^{2} c d \,x^{2}+42 a b \,c^{2} x^{2}+15 a^{2} c^{2}\right)}{105 c^{3} x^{7}}"," ",0,"-1/105*(d*x^2+c)^(3/2)*(8*a^2*d^2*x^4-28*a*b*c*d*x^4+35*b^2*c^2*x^4-12*a^2*c*d*x^2+42*a*b*c^2*x^2+15*a^2*c^2)/x^7/c^3","A"
611,1,117,127,0.008000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^10,x)","-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} \left(-16 a^{2} d^{3} x^{6}+48 a b c \,d^{2} x^{6}-42 b^{2} c^{2} d \,x^{6}+24 a^{2} c \,d^{2} x^{4}-72 a b \,c^{2} d \,x^{4}+63 b^{2} c^{3} x^{4}-30 a^{2} c^{2} d \,x^{2}+90 a b \,c^{3} x^{2}+35 a^{2} c^{3}\right)}{315 c^{4} x^{9}}"," ",0,"-1/315*(d*x^2+c)^(3/2)*(-16*a^2*d^3*x^6+48*a*b*c*d^2*x^6-42*b^2*c^2*d*x^6+24*a^2*c*d^2*x^4-72*a*b*c^2*d*x^4+63*b^2*c^3*x^4-30*a^2*c^2*d*x^2+90*a*b*c^3*x^2+35*a^2*c^3)/x^9/c^4","A"
612,1,158,169,0.007000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^12,x)","-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} \left(128 a^{2} d^{4} x^{8}-352 a b c \,d^{3} x^{8}+264 b^{2} c^{2} d^{2} x^{8}-192 a^{2} c \,d^{3} x^{6}+528 a b \,c^{2} d^{2} x^{6}-396 b^{2} c^{3} d \,x^{6}+240 a^{2} c^{2} d^{2} x^{4}-660 a b \,c^{3} d \,x^{4}+495 b^{2} c^{4} x^{4}-280 a^{2} c^{3} d \,x^{2}+770 a b \,c^{4} x^{2}+315 a^{2} c^{4}\right)}{3465 c^{5} x^{11}}"," ",0,"-1/3465*(d*x^2+c)^(3/2)*(128*a^2*d^4*x^8-352*a*b*c*d^3*x^8+264*b^2*c^2*d^2*x^8-192*a^2*c*d^3*x^6+528*a*b*c^2*d^2*x^6-396*b^2*c^3*d*x^6+240*a^2*c^2*d^2*x^4-660*a*b*c^3*d*x^4+495*b^2*c^4*x^4-280*a^2*c^3*d*x^2+770*a*b*c^4*x^2+315*a^2*c^4)/x^11/c^5","A"
613,1,389,249,0.024000," ","int(x^4*(b*x^2+a)^2*(d*x^2+c)^(3/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} x^{7}}{12 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b \,x^{5}}{5 d}-\frac{7 \left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c \,x^{5}}{120 d^{2}}+\frac{3 a^{2} c^{4} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{128 d^{\frac{5}{2}}}-\frac{3 a b \,c^{5} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{128 d^{\frac{7}{2}}}+\frac{7 b^{2} c^{6} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{1024 d^{\frac{9}{2}}}+\frac{3 \sqrt{d \,x^{2}+c}\, a^{2} c^{3} x}{128 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} x^{3}}{8 d}-\frac{3 \sqrt{d \,x^{2}+c}\, a b \,c^{4} x}{128 d^{3}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b c \,x^{3}}{8 d^{2}}+\frac{7 \sqrt{d \,x^{2}+c}\, b^{2} c^{5} x}{1024 d^{4}}+\frac{7 \left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c^{2} x^{3}}{192 d^{3}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c^{2} x}{64 d^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b \,c^{3} x}{64 d^{3}}+\frac{7 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c^{4} x}{1536 d^{4}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} c x}{16 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b \,c^{2} x}{16 d^{3}}-\frac{7 \left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c^{3} x}{384 d^{4}}"," ",0,"1/12*b^2*x^7*(d*x^2+c)^(5/2)/d-7/120*b^2*c/d^2*x^5*(d*x^2+c)^(5/2)+7/192*b^2*c^2/d^3*x^3*(d*x^2+c)^(5/2)-7/384*b^2*c^3/d^4*x*(d*x^2+c)^(5/2)+7/1536*b^2*c^4/d^4*x*(d*x^2+c)^(3/2)+7/1024*b^2*c^5/d^4*x*(d*x^2+c)^(1/2)+7/1024*b^2*c^6/d^(9/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/5*a*b*x^5*(d*x^2+c)^(5/2)/d-1/8*a*b*c/d^2*x^3*(d*x^2+c)^(5/2)+1/16*a*b*c^2/d^3*x*(d*x^2+c)^(5/2)-1/64*a*b*c^3/d^3*x*(d*x^2+c)^(3/2)-3/128*a*b*c^4/d^3*x*(d*x^2+c)^(1/2)-3/128*a*b*c^5/d^(7/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/8*a^2*x^3*(d*x^2+c)^(5/2)/d-1/16*a^2*c/d^2*x*(d*x^2+c)^(5/2)+1/64*a^2*c^2/d^2*x*(d*x^2+c)^(3/2)+3/128*a^2*c^3/d^2*x*(d*x^2+c)^(1/2)+3/128*a^2*c^4/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
614,1,108,98,0.010000," ","int(x^3*(b*x^2+a)^2*(d*x^2+c)^(3/2),x)","-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} \left(-315 b^{2} x^{6} d^{3}-770 a b \,d^{3} x^{4}+210 b^{2} c \,d^{2} x^{4}-495 a^{2} d^{3} x^{2}+440 a b c \,d^{2} x^{2}-120 b^{2} c^{2} d \,x^{2}+198 a^{2} c \,d^{2}-176 a b \,c^{2} d +48 b^{2} c^{3}\right)}{3465 d^{4}}"," ",0,"-1/3465*(d*x^2+c)^(5/2)*(-315*b^2*d^3*x^6-770*a*b*d^3*x^4+210*b^2*c*d^2*x^4-495*a^2*d^3*x^2+440*a*b*c*d^2*x^2-120*b^2*c^2*d*x^2+198*a^2*c*d^2-176*a*b*c^2*d+48*b^2*c^3)/d^4","A"
615,1,321,207,0.013000," ","int(x^2*(b*x^2+a)^2*(d*x^2+c)^(3/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} x^{5}}{10 d}-\frac{a^{2} c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{16 d^{\frac{3}{2}}}+\frac{3 a b \,c^{4} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{64 d^{\frac{5}{2}}}-\frac{3 b^{2} c^{5} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{256 d^{\frac{7}{2}}}-\frac{\sqrt{d \,x^{2}+c}\, a^{2} c^{2} x}{16 d}+\frac{3 \sqrt{d \,x^{2}+c}\, a b \,c^{3} x}{64 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b \,x^{3}}{4 d}-\frac{3 \sqrt{d \,x^{2}+c}\, b^{2} c^{4} x}{256 d^{3}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c \,x^{3}}{16 d^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c x}{24 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b \,c^{2} x}{32 d^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c^{3} x}{128 d^{3}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} x}{6 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b c x}{8 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c^{2} x}{32 d^{3}}"," ",0,"1/10*b^2*x^5*(d*x^2+c)^(5/2)/d-1/16*b^2*c/d^2*x^3*(d*x^2+c)^(5/2)+1/32*b^2*c^2/d^3*x*(d*x^2+c)^(5/2)-1/128*b^2*c^3/d^3*x*(d*x^2+c)^(3/2)-3/256*b^2*c^4/d^3*x*(d*x^2+c)^(1/2)-3/256*b^2*c^5/d^(7/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/4*a*b*x^3*(d*x^2+c)^(5/2)/d-1/8*a*b*c/d^2*x*(d*x^2+c)^(5/2)+1/32*a*b*c^2/d^2*x*(d*x^2+c)^(3/2)+3/64*a*b*c^3/d^2*x*(d*x^2+c)^(1/2)+3/64*a*b*c^4/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/6*a^2*x*(d*x^2+c)^(5/2)/d-1/24*a^2*c/d*x*(d*x^2+c)^(3/2)-1/16*a^2*c^2/d*x*(d*x^2+c)^(1/2)-1/16*a^2*c^3/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
616,1,69,65,0.009000," ","int(x*(b*x^2+a)^2*(d*x^2+c)^(3/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} \left(35 b^{2} x^{4} d^{2}+90 a b \,d^{2} x^{2}-20 b^{2} c d \,x^{2}+63 a^{2} d^{2}-36 a b c d +8 b^{2} c^{2}\right)}{315 d^{3}}"," ",0,"1/315*(d*x^2+c)^(5/2)*(35*b^2*d^2*x^4+90*a*b*d^2*x^2-20*b^2*c*d*x^2+63*a^2*d^2-36*a*b*c*d+8*b^2*c^2)/d^3","A"
617,1,249,172,0.009000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2),x)","\frac{3 a^{2} c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 \sqrt{d}}-\frac{a b \,c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 d^{\frac{3}{2}}}+\frac{3 b^{2} c^{4} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{128 d^{\frac{5}{2}}}+\frac{3 \sqrt{d \,x^{2}+c}\, a^{2} c x}{8}-\frac{\sqrt{d \,x^{2}+c}\, a b \,c^{2} x}{8 d}+\frac{3 \sqrt{d \,x^{2}+c}\, b^{2} c^{3} x}{128 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} x^{3}}{8 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} x}{4}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b c x}{12 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c^{2} x}{64 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b x}{3 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c x}{16 d^{2}}"," ",0,"1/8*b^2*x^3*(d*x^2+c)^(5/2)/d-1/16*b^2*c/d^2*x*(d*x^2+c)^(5/2)+1/64*b^2*c^2/d^2*x*(d*x^2+c)^(3/2)+3/128*b^2*c^3/d^2*x*(d*x^2+c)^(1/2)+3/128*b^2*c^4/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/3*a*b*x*(d*x^2+c)^(5/2)/d-1/12*a*b*c/d*x*(d*x^2+c)^(3/2)-1/8*a*b*c^2/d*x*(d*x^2+c)^(1/2)-1/8*a*b*c^3/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/4*a^2*x*(d*x^2+c)^(3/2)+3/8*a^2*c*x*(d*x^2+c)^(1/2)+3/8*a^2*c^2/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
618,1,115,91,0.011000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/x,x)","-a^{2} c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+\sqrt{d \,x^{2}+c}\, a^{2} c +\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} x^{2}}{7 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2}}{3}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a b}{5 d}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c}{35 d^{2}}"," ",0,"1/7*b^2*x^2*(d*x^2+c)^(5/2)/d-2/35*b^2*c/d^2*(d*x^2+c)^(5/2)+2/5*a*b*(d*x^2+c)^(5/2)/d+1/3*a^2*(d*x^2+c)^(3/2)-a^2*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+a^2*c*(d*x^2+c)^(1/2)","A"
619,1,221,153,0.013000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^2,x)","\frac{3 a^{2} c \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2}+\frac{3 a b \,c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{4 \sqrt{d}}-\frac{b^{2} c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{16 d^{\frac{3}{2}}}+\frac{3 \sqrt{d \,x^{2}+c}\, a^{2} d x}{2}+\frac{3 \sqrt{d \,x^{2}+c}\, a b c x}{4}-\frac{\sqrt{d \,x^{2}+c}\, b^{2} c^{2} x}{16 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d x}{c}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b x}{2}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c x}{24 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} x}{6 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2}}{c x}"," ",0,"1/6*b^2*x*(d*x^2+c)^(5/2)/d-1/24*b^2*c/d*x*(d*x^2+c)^(3/2)-1/16*b^2*c^2/d*x*(d*x^2+c)^(1/2)-1/16*b^2*c^3/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/2*a*b*x*(d*x^2+c)^(3/2)+3/4*a*b*c*x*(d*x^2+c)^(1/2)+3/4*a*b*c^2/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-a^2*(d*x^2+c)^(5/2)/c/x+a^2*d/c*x*(d*x^2+c)^(3/2)+3/2*a^2*d*x*(d*x^2+c)^(1/2)+3/2*a^2*d^(1/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
620,1,161,112,0.013000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^3,x)","-\frac{3 a^{2} \sqrt{c}\, d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2}-2 a b \,c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+\frac{3 \sqrt{d \,x^{2}+c}\, a^{2} d}{2}+2 \sqrt{d \,x^{2}+c}\, a b c +\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d}{2 c}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b}{3}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2}}{5 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2}}{2 c \,x^{2}}"," ",0,"1/5*b^2*(d*x^2+c)^(5/2)/d-1/2*a^2*(d*x^2+c)^(5/2)/c/x^2+1/2*a^2*d/c*(d*x^2+c)^(3/2)-3/2*a^2*d*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+3/2*a^2*d*(d*x^2+c)^(1/2)+2/3*a*b*(d*x^2+c)^(3/2)-2*a*b*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+2*a*b*(d*x^2+c)^(1/2)*c","A"
621,1,241,160,0.015000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^4,x)","a^{2} d^{\frac{3}{2}} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+3 a b c \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+\frac{3 b^{2} c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 \sqrt{d}}+\frac{\sqrt{d \,x^{2}+c}\, a^{2} d^{2} x}{c}+3 \sqrt{d \,x^{2}+c}\, a b d x +\frac{3 \sqrt{d \,x^{2}+c}\, b^{2} c x}{8}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d^{2} x}{3 c^{2}}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b d x}{c}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} x}{4}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d}{3 c^{2} x}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a b}{c x}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2}}{3 c \,x^{3}}"," ",0,"1/4*x*b^2*(d*x^2+c)^(3/2)+3/8*b^2*c*x*(d*x^2+c)^(1/2)+3/8*b^2*c^2/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2*a*b/c/x*(d*x^2+c)^(5/2)+2*a*b*d/c*x*(d*x^2+c)^(3/2)+3*a*b*d*x*(d*x^2+c)^(1/2)+3*a*b*d^(1/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/3*a^2*(d*x^2+c)^(5/2)/c/x^3-2/3*a^2*d/c^2/x*(d*x^2+c)^(5/2)+2/3*a^2*d^2/c^2*x*(d*x^2+c)^(3/2)+a^2*d^2/c*x*(d*x^2+c)^(1/2)+a^2*d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
622,1,256,157,0.014000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^5,x)","-\frac{3 a^{2} d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{8 \sqrt{c}}-3 a b \sqrt{c}\, d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)-b^{2} c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+\frac{3 \sqrt{d \,x^{2}+c}\, a^{2} d^{2}}{8 c}+3 \sqrt{d \,x^{2}+c}\, a b d +\sqrt{d \,x^{2}+c}\, b^{2} c +\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d^{2}}{8 c^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b d}{c}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2}}{3}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d}{8 c^{2} x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b}{c \,x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2}}{4 c \,x^{4}}"," ",0,"-1/4*a^2*(d*x^2+c)^(5/2)/c/x^4-1/8*a^2*d/c^2/x^2*(d*x^2+c)^(5/2)+1/8*a^2*d^2/c^2*(d*x^2+c)^(3/2)-3/8*a^2*d^2/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+3/8*a^2*d^2/c*(d*x^2+c)^(1/2)-a*b/c/x^2*(d*x^2+c)^(5/2)+a*b*d/c*(d*x^2+c)^(3/2)-3*a*b*d*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+3*a*b*d*(d*x^2+c)^(1/2)+1/3*b^2*(d*x^2+c)^(3/2)-b^2*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+b^2*(d*x^2+c)^(1/2)*c","A"
623,1,203,123,0.016000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^6,x)","2 a b \,d^{\frac{3}{2}} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+\frac{3 b^{2} c \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2}+\frac{2 \sqrt{d \,x^{2}+c}\, a b \,d^{2} x}{c}+\frac{3 \sqrt{d \,x^{2}+c}\, b^{2} d x}{2}+\frac{4 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b \,d^{2} x}{3 c^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} d x}{c}-\frac{4 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a b d}{3 c^{2} x}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2}}{c x}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a b}{3 c \,x^{3}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2}}{5 c \,x^{5}}"," ",0,"-1/5*a^2*(d*x^2+c)^(5/2)/c/x^5-b^2/c/x*(d*x^2+c)^(5/2)+b^2*d/c*x*(d*x^2+c)^(3/2)+3/2*b^2*d*x*(d*x^2+c)^(1/2)+3/2*b^2*d^(1/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2/3*a*b*(d*x^2+c)^(5/2)/c/x^3-4/3*a*b*d/c^2/x*(d*x^2+c)^(5/2)+4/3*a*b*d^2/c^2*x*(d*x^2+c)^(3/2)+2*a*b*d^2/c*x*(d*x^2+c)^(1/2)+2*a*b*d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
624,1,335,163,0.016000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^7,x)","\frac{a^{2} d^{3} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{16 c^{\frac{3}{2}}}-\frac{3 a b \,d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{4 \sqrt{c}}-\frac{3 b^{2} \sqrt{c}\, d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2}-\frac{\sqrt{d \,x^{2}+c}\, a^{2} d^{3}}{16 c^{2}}+\frac{3 \sqrt{d \,x^{2}+c}\, a b \,d^{2}}{4 c}+\frac{3 \sqrt{d \,x^{2}+c}\, b^{2} d}{2}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d^{3}}{48 c^{3}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b \,d^{2}}{4 c^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} d}{2 c}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d^{2}}{48 c^{3} x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b d}{4 c^{2} x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2}}{2 c \,x^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d}{24 c^{2} x^{4}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b}{2 c \,x^{4}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2}}{6 c \,x^{6}}"," ",0,"-1/6*a^2*(d*x^2+c)^(5/2)/c/x^6+1/24*a^2*d/c^2/x^4*(d*x^2+c)^(5/2)+1/48*a^2*d^2/c^3/x^2*(d*x^2+c)^(5/2)-1/48*a^2*d^3/c^3*(d*x^2+c)^(3/2)+1/16*a^2*d^3/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/16*a^2*d^3/c^2*(d*x^2+c)^(1/2)-1/2*a*b/c/x^4*(d*x^2+c)^(5/2)-1/4*a*b*d/c^2/x^2*(d*x^2+c)^(5/2)+1/4*a*b*d^2/c^2*(d*x^2+c)^(3/2)-3/4*a*b*d^2/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+3/4*a*b*d^2/c*(d*x^2+c)^(1/2)-1/2*b^2/c/x^2*(d*x^2+c)^(5/2)+1/2*b^2*d/c*(d*x^2+c)^(3/2)-3/2*b^2*d*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+3/2*b^2*d*(d*x^2+c)^(1/2)","B"
625,1,108,98,0.009000," ","int(x^3*(b*x^2+a)^2*(d*x^2+c)^(5/2),x)","-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} \left(-693 b^{2} x^{6} d^{3}-1638 a b \,d^{3} x^{4}+378 b^{2} c \,d^{2} x^{4}-1001 a^{2} d^{3} x^{2}+728 a b c \,d^{2} x^{2}-168 b^{2} c^{2} d \,x^{2}+286 a^{2} c \,d^{2}-208 a b \,c^{2} d +48 b^{2} c^{3}\right)}{9009 d^{4}}"," ",0,"-1/9009*(d*x^2+c)^(7/2)*(-693*b^2*d^3*x^6-1638*a*b*d^3*x^4+378*b^2*c*d^2*x^4-1001*a^2*d^3*x^2+728*a*b*c*d^2*x^2-168*b^2*c^2*d*x^2+286*a^2*c*d^2-208*a*b*c^2*d+48*b^2*c^3)/d^4","A"
626,1,383,249,0.020000," ","int(x^2*(b*x^2+a)^2*(d*x^2+c)^(5/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2} x^{5}}{12 d}-\frac{5 a^{2} c^{4} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{128 d^{\frac{3}{2}}}+\frac{3 a b \,c^{5} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{128 d^{\frac{5}{2}}}-\frac{5 b^{2} c^{6} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{1024 d^{\frac{7}{2}}}-\frac{5 \sqrt{d \,x^{2}+c}\, a^{2} c^{3} x}{128 d}+\frac{3 \sqrt{d \,x^{2}+c}\, a b \,c^{4} x}{128 d^{2}}-\frac{5 \sqrt{d \,x^{2}+c}\, b^{2} c^{5} x}{1024 d^{3}}-\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c^{2} x}{192 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a b \,c^{3} x}{64 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a b \,x^{3}}{5 d}-\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c^{4} x}{1536 d^{3}}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2} c \,x^{3}}{24 d^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} c x}{48 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b \,c^{2} x}{80 d^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c^{3} x}{384 d^{3}}+\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2} x}{8 d}-\frac{3 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a b c x}{40 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2} c^{2} x}{64 d^{3}}"," ",0,"1/12*b^2*x^5*(d*x^2+c)^(7/2)/d-1/24*b^2*c/d^2*x^3*(d*x^2+c)^(7/2)+1/64*b^2*c^2/d^3*x*(d*x^2+c)^(7/2)-1/384*b^2*c^3/d^3*x*(d*x^2+c)^(5/2)-5/1536*b^2*c^4/d^3*x*(d*x^2+c)^(3/2)-5/1024*b^2*c^5/d^3*x*(d*x^2+c)^(1/2)-5/1024*b^2*c^6/d^(7/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/5*a*b*x^3*(d*x^2+c)^(7/2)/d-3/40*a*b*c/d^2*x*(d*x^2+c)^(7/2)+1/80*a*b*c^2/d^2*x*(d*x^2+c)^(5/2)+1/64*a*b*c^3/d^2*x*(d*x^2+c)^(3/2)+3/128*a*b*c^4/d^2*x*(d*x^2+c)^(1/2)+3/128*a*b*c^5/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/8*a^2*x*(d*x^2+c)^(7/2)/d-1/48*a^2*c/d*x*(d*x^2+c)^(5/2)-5/192*a^2*c^2/d*x*(d*x^2+c)^(3/2)-5/128*a^2*c^3/d*x*(d*x^2+c)^(1/2)-5/128*a^2*c^4/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
627,1,69,65,0.007000," ","int(x*(b*x^2+a)^2*(d*x^2+c)^(5/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} \left(63 b^{2} x^{4} d^{2}+154 a b \,d^{2} x^{2}-28 b^{2} c d \,x^{2}+99 a^{2} d^{2}-44 a b c d +8 b^{2} c^{2}\right)}{693 d^{3}}"," ",0,"1/693*(d*x^2+c)^(7/2)*(63*b^2*d^2*x^4+154*a*b*d^2*x^2-28*b^2*c*d*x^2+99*a^2*d^2-44*a*b*c*d+8*b^2*c^2)/d^3","A"
628,1,308,212,0.019000," ","int((b*x^2+a)^2*(d*x^2+c)^(5/2),x)","\frac{5 a^{2} c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{16 \sqrt{d}}-\frac{5 a b \,c^{4} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{64 d^{\frac{3}{2}}}+\frac{3 b^{2} c^{5} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{256 d^{\frac{5}{2}}}+\frac{5 \sqrt{d \,x^{2}+c}\, a^{2} c^{2} x}{16}-\frac{5 \sqrt{d \,x^{2}+c}\, a b \,c^{3} x}{64 d}+\frac{3 \sqrt{d \,x^{2}+c}\, b^{2} c^{4} x}{256 d^{2}}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c x}{24}-\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b \,c^{2} x}{96 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c^{3} x}{128 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2} x^{3}}{10 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} x}{6}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b c x}{24 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c^{2} x}{160 d^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a b x}{4 d}-\frac{3 \left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2} c x}{80 d^{2}}"," ",0,"1/10*b^2*x^3*(d*x^2+c)^(7/2)/d-3/80*b^2*c/d^2*x*(d*x^2+c)^(7/2)+1/160*b^2*c^2/d^2*x*(d*x^2+c)^(5/2)+1/128*b^2*c^3/d^2*x*(d*x^2+c)^(3/2)+3/256*b^2*c^4/d^2*x*(d*x^2+c)^(1/2)+3/256*b^2*c^5/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/4*a*b*x*(d*x^2+c)^(7/2)/d-1/24*a*b*c/d*x*(d*x^2+c)^(5/2)-5/96*a*b*c^2/d*x*(d*x^2+c)^(3/2)-5/64*a*b*c^3/d*x*(d*x^2+c)^(1/2)-5/64*a*b*c^4/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/6*a^2*x*(d*x^2+c)^(5/2)+5/24*a^2*c*x*(d*x^2+c)^(3/2)+5/16*a^2*c^2*x*(d*x^2+c)^(1/2)+5/16*a^2*c^3/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
629,1,132,108,0.013000," ","int((b*x^2+a)^2*(d*x^2+c)^(5/2)/x,x)","-a^{2} c^{\frac{5}{2}} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+\sqrt{d \,x^{2}+c}\, a^{2} c^{2}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c}{3}+\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2} x^{2}}{9 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2}}{5}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a b}{7 d}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2} c}{63 d^{2}}"," ",0,"1/9*b^2*x^2*(d*x^2+c)^(7/2)/d-2/63*b^2*c/d^2*(d*x^2+c)^(7/2)+2/7*a*b*(d*x^2+c)^(7/2)/d+1/5*a^2*(d*x^2+c)^(5/2)+1/3*a^2*c*(d*x^2+c)^(3/2)-a^2*c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+a^2*c^2*(d*x^2+c)^(1/2)","A"
630,1,278,191,0.012000," ","int((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^2,x)","\frac{15 a^{2} c^{2} \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8}+\frac{5 a b \,c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 \sqrt{d}}-\frac{5 b^{2} c^{4} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{128 d^{\frac{3}{2}}}+\frac{15 \sqrt{d \,x^{2}+c}\, a^{2} c d x}{8}+\frac{5 \sqrt{d \,x^{2}+c}\, a b \,c^{2} x}{8}-\frac{5 \sqrt{d \,x^{2}+c}\, b^{2} c^{3} x}{128 d}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d x}{4}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b c x}{12}-\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c^{2} x}{192 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d x}{c}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b x}{3}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} c x}{48 d}+\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2} x}{8 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2}}{c x}"," ",0,"1/8*b^2*x*(d*x^2+c)^(7/2)/d-1/48*b^2*c/d*x*(d*x^2+c)^(5/2)-5/192*b^2*c^2/d*x*(d*x^2+c)^(3/2)-5/128*b^2*c^3/d*x*(d*x^2+c)^(1/2)-5/128*b^2*c^4/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/3*a*b*x*(d*x^2+c)^(5/2)+5/12*a*b*c*x*(d*x^2+c)^(3/2)+5/8*a*b*c^2*x*(d*x^2+c)^(1/2)+5/8*a*b*c^3/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-a^2*(d*x^2+c)^(7/2)/c/x+a^2*d/c*x*(d*x^2+c)^(5/2)+5/4*a^2*d*x*(d*x^2+c)^(3/2)+15/8*a^2*d*c*x*(d*x^2+c)^(1/2)+15/8*a^2*d^(1/2)*c^2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
631,1,193,134,0.013000," ","int((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^3,x)","-\frac{5 a^{2} c^{\frac{3}{2}} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2}-2 a b \,c^{\frac{5}{2}} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+\frac{5 \sqrt{d \,x^{2}+c}\, a^{2} c d}{2}+2 \sqrt{d \,x^{2}+c}\, a b \,c^{2}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d}{6}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b c}{3}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d}{2 c}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a b}{5}+\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2}}{7 d}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2}}{2 c \,x^{2}}"," ",0,"1/7*b^2*(d*x^2+c)^(7/2)/d-1/2*a^2*(d*x^2+c)^(7/2)/c/x^2+1/2*a^2*d/c*(d*x^2+c)^(5/2)+5/6*a^2*d*(d*x^2+c)^(3/2)-5/2*a^2*d*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+5/2*a^2*d*c*(d*x^2+c)^(1/2)+2/5*a*b*(d*x^2+c)^(5/2)+2/3*a*b*c*(d*x^2+c)^(3/2)-2*a*b*c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+2*a*b*(d*x^2+c)^(1/2)*c^2","A"
632,1,298,195,0.016000," ","int((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^4,x)","\frac{5 a^{2} c \,d^{\frac{3}{2}} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2}+\frac{15 a b \,c^{2} \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{4}+\frac{5 b^{2} c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{16 \sqrt{d}}+\frac{5 \sqrt{d \,x^{2}+c}\, a^{2} d^{2} x}{2}+\frac{15 \sqrt{d \,x^{2}+c}\, a b c d x}{4}+\frac{5 \sqrt{d \,x^{2}+c}\, b^{2} c^{2} x}{16}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d^{2} x}{3 c}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b d x}{2}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c x}{24}+\frac{4 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d^{2} x}{3 c^{2}}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a b d x}{c}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} x}{6}-\frac{4 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2} d}{3 c^{2} x}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a b}{c x}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2}}{3 c \,x^{3}}"," ",0,"1/6*x*b^2*(d*x^2+c)^(5/2)+5/24*b^2*c*x*(d*x^2+c)^(3/2)+5/16*b^2*c^2*x*(d*x^2+c)^(1/2)+5/16*b^2*c^3/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2*a*b/c/x*(d*x^2+c)^(7/2)+2*a*b*d/c*x*(d*x^2+c)^(5/2)+5/2*a*b*d*x*(d*x^2+c)^(3/2)+15/4*a*b*d*c*x*(d*x^2+c)^(1/2)+15/4*a*b*d^(1/2)*c^2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/3*a^2*(d*x^2+c)^(7/2)/c/x^3-4/3*a^2*d/c^2/x*(d*x^2+c)^(7/2)+4/3*a^2*d^2/c^2*x*(d*x^2+c)^(5/2)+5/3*a^2*d^2/c*x*(d*x^2+c)^(3/2)+5/2*a^2*d^2*x*(d*x^2+c)^(1/2)+5/2*a^2*d^(3/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
633,1,305,194,0.016000," ","int((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^5,x)","-\frac{15 a^{2} \sqrt{c}\, d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{8}-5 a b \,c^{\frac{3}{2}} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)-b^{2} c^{\frac{5}{2}} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+\frac{15 \sqrt{d \,x^{2}+c}\, a^{2} d^{2}}{8}+5 \sqrt{d \,x^{2}+c}\, a b c d +\sqrt{d \,x^{2}+c}\, b^{2} c^{2}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d^{2}}{8 c}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b d}{3}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c}{3}+\frac{3 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d^{2}}{8 c^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a b d}{c}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2}}{5}-\frac{3 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2} d}{8 c^{2} x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a b}{c \,x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2}}{4 c \,x^{4}}"," ",0,"-1/4*a^2*(d*x^2+c)^(7/2)/c/x^4-3/8*a^2*d/c^2/x^2*(d*x^2+c)^(7/2)+3/8*a^2*d^2/c^2*(d*x^2+c)^(5/2)+5/8*a^2*d^2/c*(d*x^2+c)^(3/2)-15/8*a^2*d^2*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+15/8*a^2*d^2*(d*x^2+c)^(1/2)-a*b/c/x^2*(d*x^2+c)^(7/2)+a*b*d/c*(d*x^2+c)^(5/2)+5/3*a*b*d*(d*x^2+c)^(3/2)-5*a*b*d*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+5*a*b*d*c*(d*x^2+c)^(1/2)+1/5*b^2*(d*x^2+c)^(5/2)+1/3*b^2*c*(d*x^2+c)^(3/2)-b^2*c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+b^2*(d*x^2+c)^(1/2)*c^2","A"
634,1,369,200,0.016000," ","int((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^6,x)","a^{2} d^{\frac{5}{2}} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+5 a b c \,d^{\frac{3}{2}} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+\frac{15 b^{2} c^{2} \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8}+\frac{\sqrt{d \,x^{2}+c}\, a^{2} d^{3} x}{c}+5 \sqrt{d \,x^{2}+c}\, a b \,d^{2} x +\frac{15 \sqrt{d \,x^{2}+c}\, b^{2} c d x}{8}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d^{3} x}{3 c^{2}}+\frac{10 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b \,d^{2} x}{3 c}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} d x}{4}+\frac{8 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d^{3} x}{15 c^{3}}+\frac{8 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a b \,d^{2} x}{3 c^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} d x}{c}-\frac{8 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2} d^{2}}{15 c^{3} x}-\frac{8 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a b d}{3 c^{2} x}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2}}{c x}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2} d}{15 c^{2} x^{3}}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a b}{3 c \,x^{3}}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2}}{5 c \,x^{5}}"," ",0,"-1/5*a^2*(d*x^2+c)^(7/2)/c/x^5-2/15*a^2*d/c^2/x^3*(d*x^2+c)^(7/2)-8/15*a^2*d^2/c^3/x*(d*x^2+c)^(7/2)+8/15*a^2*d^3/c^3*x*(d*x^2+c)^(5/2)+2/3*a^2*d^3/c^2*x*(d*x^2+c)^(3/2)+a^2*d^3/c*x*(d*x^2+c)^(1/2)+a^2*d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-b^2/c/x*(d*x^2+c)^(7/2)+b^2*d/c*x*(d*x^2+c)^(5/2)+5/4*b^2*d*x*(d*x^2+c)^(3/2)+15/8*b^2*d*c*x*(d*x^2+c)^(1/2)+15/8*b^2*d^(1/2)*c^2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2/3*a*b/c/x^3*(d*x^2+c)^(7/2)-8/3*a*b*d/c^2/x*(d*x^2+c)^(7/2)+8/3*a*b*d^2/c^2*x*(d*x^2+c)^(5/2)+10/3*a*b*d^2/c*x*(d*x^2+c)^(3/2)+5*a*b*d^2*x*(d*x^2+c)^(1/2)+5*a*b*d^(3/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
635,1,387,194,0.018000," ","int((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^7,x)","-\frac{5 a^{2} d^{3} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{16 \sqrt{c}}-\frac{15 a b \sqrt{c}\, d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{4}-\frac{5 b^{2} c^{\frac{3}{2}} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2}+\frac{5 \sqrt{d \,x^{2}+c}\, a^{2} d^{3}}{16 c}+\frac{15 \sqrt{d \,x^{2}+c}\, a b \,d^{2}}{4}+\frac{5 \sqrt{d \,x^{2}+c}\, b^{2} c d}{2}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} d^{3}}{48 c^{2}}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a b \,d^{2}}{4 c}+\frac{5 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} d}{6}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} a^{2} d^{3}}{16 c^{3}}+\frac{3 \left(d \,x^{2}+c \right)^{\frac{5}{2}} a b \,d^{2}}{4 c^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b^{2} d}{2 c}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2} d^{2}}{16 c^{3} x^{2}}-\frac{3 \left(d \,x^{2}+c \right)^{\frac{7}{2}} a b d}{4 c^{2} x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} b^{2}}{2 c \,x^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2} d}{24 c^{2} x^{4}}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a b}{2 c \,x^{4}}-\frac{\left(d \,x^{2}+c \right)^{\frac{7}{2}} a^{2}}{6 c \,x^{6}}"," ",0,"-1/6*a^2*(d*x^2+c)^(7/2)/c/x^6-1/24*a^2*d/c^2/x^4*(d*x^2+c)^(7/2)-1/16*a^2*d^2/c^3/x^2*(d*x^2+c)^(7/2)+1/16*a^2*d^3/c^3*(d*x^2+c)^(5/2)+5/48*a^2*d^3/c^2*(d*x^2+c)^(3/2)-5/16*a^2*d^3/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+5/16*a^2*d^3/c*(d*x^2+c)^(1/2)-1/2*b^2/c/x^2*(d*x^2+c)^(7/2)+1/2*b^2*d/c*(d*x^2+c)^(5/2)+5/6*b^2*d*(d*x^2+c)^(3/2)-5/2*b^2*d*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+5/2*b^2*d*c*(d*x^2+c)^(1/2)-1/2*a*b/c/x^4*(d*x^2+c)^(7/2)-3/4*a*b*d/c^2/x^2*(d*x^2+c)^(7/2)+3/4*a*b*d^2/c^2*(d*x^2+c)^(5/2)+5/4*a*b*d^2/c*(d*x^2+c)^(3/2)-15/4*a*b*d^2*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+15/4*a*b*d^2*(d*x^2+c)^(1/2)","A"
636,1,265,170,0.018000," ","int(x^4*(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, b^{2} x^{7}}{8 d}+\frac{\sqrt{d \,x^{2}+c}\, a b \,x^{5}}{3 d}-\frac{7 \sqrt{d \,x^{2}+c}\, b^{2} c \,x^{5}}{48 d^{2}}+\frac{\sqrt{d \,x^{2}+c}\, a^{2} x^{3}}{4 d}-\frac{5 \sqrt{d \,x^{2}+c}\, a b c \,x^{3}}{12 d^{2}}+\frac{35 \sqrt{d \,x^{2}+c}\, b^{2} c^{2} x^{3}}{192 d^{3}}+\frac{3 a^{2} c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 d^{\frac{5}{2}}}-\frac{5 a b \,c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 d^{\frac{7}{2}}}+\frac{35 b^{2} c^{4} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{128 d^{\frac{9}{2}}}-\frac{3 \sqrt{d \,x^{2}+c}\, a^{2} c x}{8 d^{2}}+\frac{5 \sqrt{d \,x^{2}+c}\, a b \,c^{2} x}{8 d^{3}}-\frac{35 \sqrt{d \,x^{2}+c}\, b^{2} c^{3} x}{128 d^{4}}"," ",0,"1/8*b^2*x^7*(d*x^2+c)^(1/2)/d-7/48*b^2*c/d^2*x^5*(d*x^2+c)^(1/2)+35/192*b^2*c^2/d^3*x^3*(d*x^2+c)^(1/2)-35/128*b^2*c^3/d^4*x*(d*x^2+c)^(1/2)+35/128*b^2*c^4/d^(9/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/3*a*b*x^5/d*(d*x^2+c)^(1/2)-5/12*a*b*c/d^2*x^3*(d*x^2+c)^(1/2)+5/8*a*b*c^2/d^3*x*(d*x^2+c)^(1/2)-5/8*a*b*c^3/d^(7/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/4*a^2*x^3/d*(d*x^2+c)^(1/2)-3/8*a^2*c/d^2*x*(d*x^2+c)^(1/2)+3/8*a^2*c^2/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
637,1,108,98,0.010000," ","int(x^3*(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{d \,x^{2}+c}\, \left(-15 b^{2} x^{6} d^{3}-42 a b \,d^{3} x^{4}+18 b^{2} c \,d^{2} x^{4}-35 a^{2} d^{3} x^{2}+56 a b c \,d^{2} x^{2}-24 b^{2} c^{2} d \,x^{2}+70 a^{2} c \,d^{2}-112 a b \,c^{2} d +48 b^{2} c^{3}\right)}{105 d^{4}}"," ",0,"-1/105*(d*x^2+c)^(1/2)*(-15*b^2*d^3*x^6-42*a*b*d^3*x^4+18*b^2*c*d^2*x^4-35*a^2*d^3*x^2+56*a*b*c*d^2*x^2-24*b^2*c^2*d*x^2+70*a^2*c*d^2-112*a*b*c^2*d+48*b^2*c^3)/d^4","A"
638,1,197,126,0.011000," ","int(x^2*(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, b^{2} x^{5}}{6 d}+\frac{\sqrt{d \,x^{2}+c}\, a b \,x^{3}}{2 d}-\frac{5 \sqrt{d \,x^{2}+c}\, b^{2} c \,x^{3}}{24 d^{2}}-\frac{a^{2} c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 d^{\frac{3}{2}}}+\frac{3 a b \,c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{4 d^{\frac{5}{2}}}-\frac{5 b^{2} c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{16 d^{\frac{7}{2}}}+\frac{\sqrt{d \,x^{2}+c}\, a^{2} x}{2 d}-\frac{3 \sqrt{d \,x^{2}+c}\, a b c x}{4 d^{2}}+\frac{5 \sqrt{d \,x^{2}+c}\, b^{2} c^{2} x}{16 d^{3}}"," ",0,"1/6*b^2*x^5*(d*x^2+c)^(1/2)/d-5/24*b^2*c/d^2*x^3*(d*x^2+c)^(1/2)+5/16*b^2*c^2/d^3*x*(d*x^2+c)^(1/2)-5/16*b^2*c^3/d^(7/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/2*a*b*x^3/d*(d*x^2+c)^(1/2)-3/4*a*b*c/d^2*x*(d*x^2+c)^(1/2)+3/4*a*b*c^2/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/2*a^2*x/d*(d*x^2+c)^(1/2)-1/2*a^2*c/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
639,1,69,64,0.007000," ","int(x*(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \left(3 b^{2} x^{4} d^{2}+10 a b \,d^{2} x^{2}-4 b^{2} c d \,x^{2}+15 a^{2} d^{2}-20 a b c d +8 b^{2} c^{2}\right)}{15 d^{3}}"," ",0,"1/15*(d*x^2+c)^(1/2)*(3*b^2*d^2*x^4+10*a*b*d^2*x^2-4*b^2*c*d*x^2+15*a^2*d^2-20*a*b*c*d+8*b^2*c^2)/d^3","A"
640,1,131,91,0.009000," ","int((b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, b^{2} x^{3}}{4 d}+\frac{a^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{\sqrt{d}}-\frac{a b c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{d^{\frac{3}{2}}}+\frac{3 b^{2} c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 d^{\frac{5}{2}}}+\frac{\sqrt{d \,x^{2}+c}\, a b x}{d}-\frac{3 \sqrt{d \,x^{2}+c}\, b^{2} c x}{8 d^{2}}"," ",0,"1/4*b^2*x^3/d*(d*x^2+c)^(1/2)-3/8*b^2*c/d^2*x*(d*x^2+c)^(1/2)+3/8*b^2*c^2/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+a*b*x/d*(d*x^2+c)^(1/2)-a*b*c/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+a^2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))/d^(1/2)","A"
641,1,87,63,0.014000," ","int((b*x^2+a)^2/x/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, b^{2} x^{2}}{3 d}-\frac{a^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{\sqrt{c}}+\frac{2 \sqrt{d \,x^{2}+c}\, a b}{d}-\frac{2 \sqrt{d \,x^{2}+c}\, b^{2} c}{3 d^{2}}"," ",0,"1/3*b^2*x^2/d*(d*x^2+c)^(1/2)-2/3*b^2*c/d^2*(d*x^2+c)^(1/2)+2*a*b/d*(d*x^2+c)^(1/2)-a^2/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
642,1,88,68,0.012000," ","int((b*x^2+a)^2/x^2/(d*x^2+c)^(1/2),x)","\frac{2 a b \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{\sqrt{d}}-\frac{b^{2} c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 d^{\frac{3}{2}}}+\frac{\sqrt{d \,x^{2}+c}\, b^{2} x}{2 d}-\frac{\sqrt{d \,x^{2}+c}\, a^{2}}{c x}"," ",0,"1/2*b^2*x*(d*x^2+c)^(1/2)/d-1/2*b^2*c/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+2*a*b*ln(d^(1/2)*x+(d*x^2+c)^(1/2))/d^(1/2)-a^2*(d*x^2+c)^(1/2)/c/x","A"
643,1,100,66,0.018000," ","int((b*x^2+a)^2/x^3/(d*x^2+c)^(1/2),x)","\frac{a^{2} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 c^{\frac{3}{2}}}-\frac{2 a b \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{\sqrt{c}}+\frac{\sqrt{d \,x^{2}+c}\, b^{2}}{d}-\frac{\sqrt{d \,x^{2}+c}\, a^{2}}{2 c \,x^{2}}"," ",0,"b^2*(d*x^2+c)^(1/2)/d-1/2*a^2*(d*x^2+c)^(1/2)/c/x^2+1/2*a^2*d/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-2*a*b/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
644,1,85,70,0.013000," ","int((b*x^2+a)^2/x^4/(d*x^2+c)^(1/2),x)","\frac{b^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{\sqrt{d}}+\frac{2 \sqrt{d \,x^{2}+c}\, a^{2} d}{3 c^{2} x}-\frac{2 \sqrt{d \,x^{2}+c}\, a b}{c x}-\frac{\sqrt{d \,x^{2}+c}\, a^{2}}{3 c \,x^{3}}"," ",0,"b^2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))/d^(1/2)-2*a*b/c/x*(d*x^2+c)^(1/2)-1/3*a^2*(d*x^2+c)^(1/2)/c/x^3+2/3*a^2*d/c^2/x*(d*x^2+c)^(1/2)","A"
645,1,157,90,0.012000," ","int((b*x^2+a)^2/x^5/(d*x^2+c)^(1/2),x)","-\frac{3 a^{2} d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{8 c^{\frac{5}{2}}}+\frac{a b d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{c^{\frac{3}{2}}}-\frac{b^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{\sqrt{c}}+\frac{3 \sqrt{d \,x^{2}+c}\, a^{2} d}{8 c^{2} x^{2}}-\frac{\sqrt{d \,x^{2}+c}\, a b}{c \,x^{2}}-\frac{\sqrt{d \,x^{2}+c}\, a^{2}}{4 c \,x^{4}}"," ",0,"-1/4*a^2*(d*x^2+c)^(1/2)/c/x^4+3/8*a^2*d/c^2/x^2*(d*x^2+c)^(1/2)-3/8*a^2*d^2/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-a*b/c/x^2*(d*x^2+c)^(1/2)+a*b*d/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-b^2/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
646,1,78,87,0.007000," ","int((b*x^2+a)^2/x^6/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{d \,x^{2}+c}\, \left(8 a^{2} d^{2} x^{4}-20 a b c d \,x^{4}+15 b^{2} c^{2} x^{4}-4 a^{2} c d \,x^{2}+10 a b \,c^{2} x^{2}+3 a^{2} c^{2}\right)}{15 c^{3} x^{5}}"," ",0,"-1/15*(d*x^2+c)^(1/2)*(8*a^2*d^2*x^4-20*a*b*c*d*x^4+15*b^2*c^2*x^4-4*a^2*c*d*x^2+10*a*b*c^2*x^2+3*a^2*c^2)/x^5/c^3","A"
647,1,224,131,0.014000," ","int((b*x^2+a)^2/x^7/(d*x^2+c)^(1/2),x)","\frac{5 a^{2} d^{3} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{16 c^{\frac{7}{2}}}-\frac{3 a b \,d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{4 c^{\frac{5}{2}}}+\frac{b^{2} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 c^{\frac{3}{2}}}-\frac{5 \sqrt{d \,x^{2}+c}\, a^{2} d^{2}}{16 c^{3} x^{2}}+\frac{3 \sqrt{d \,x^{2}+c}\, a b d}{4 c^{2} x^{2}}-\frac{\sqrt{d \,x^{2}+c}\, b^{2}}{2 c \,x^{2}}+\frac{5 \sqrt{d \,x^{2}+c}\, a^{2} d}{24 c^{2} x^{4}}-\frac{\sqrt{d \,x^{2}+c}\, a b}{2 c \,x^{4}}-\frac{\sqrt{d \,x^{2}+c}\, a^{2}}{6 c \,x^{6}}"," ",0,"-1/6*a^2*(d*x^2+c)^(1/2)/c/x^6+5/24*a^2*d/c^2/x^4*(d*x^2+c)^(1/2)-5/16*a^2*d^2/c^3/x^2*(d*x^2+c)^(1/2)+5/16*a^2*d^3/c^(7/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/2*a*b/c/x^4*(d*x^2+c)^(1/2)+3/4*a*b*d/c^2/x^2*(d*x^2+c)^(1/2)-3/4*a*b*d^2/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/2*b^2/c/x^2*(d*x^2+c)^(1/2)+1/2*b^2*d/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
648,1,263,175,0.022000," ","int(x^4*(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{b^{2} x^{7}}{6 \sqrt{d \,x^{2}+c}\, d}+\frac{a b \,x^{5}}{2 \sqrt{d \,x^{2}+c}\, d}-\frac{7 b^{2} c \,x^{5}}{24 \sqrt{d \,x^{2}+c}\, d^{2}}+\frac{a^{2} x^{3}}{2 \sqrt{d \,x^{2}+c}\, d}-\frac{5 a b c \,x^{3}}{4 \sqrt{d \,x^{2}+c}\, d^{2}}+\frac{35 b^{2} c^{2} x^{3}}{48 \sqrt{d \,x^{2}+c}\, d^{3}}+\frac{3 a^{2} c x}{2 \sqrt{d \,x^{2}+c}\, d^{2}}-\frac{15 a b \,c^{2} x}{4 \sqrt{d \,x^{2}+c}\, d^{3}}+\frac{35 b^{2} c^{3} x}{16 \sqrt{d \,x^{2}+c}\, d^{4}}-\frac{3 a^{2} c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 d^{\frac{5}{2}}}+\frac{15 a b \,c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{4 d^{\frac{7}{2}}}-\frac{35 b^{2} c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{16 d^{\frac{9}{2}}}"," ",0,"1/6*b^2*x^7/d/(d*x^2+c)^(1/2)-7/24*b^2*c/d^2*x^5/(d*x^2+c)^(1/2)+35/48*b^2*c^2/d^3*x^3/(d*x^2+c)^(1/2)+35/16*b^2*c^3/d^4*x/(d*x^2+c)^(1/2)-35/16*b^2*c^3/d^(9/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/2*a*b*x^5/d/(d*x^2+c)^(1/2)-5/4*a*b*c/d^2*x^3/(d*x^2+c)^(1/2)-15/4*a*b*c^2/d^3*x/(d*x^2+c)^(1/2)+15/4*a*b*c^2/d^(7/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/2*a^2*x^3/d/(d*x^2+c)^(1/2)+3/2*a^2*c/d^2*x/(d*x^2+c)^(1/2)-3/2*a^2*c/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
649,1,108,96,0.007000," ","int(x^3*(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{3 b^{2} x^{6} d^{3}+10 a b \,d^{3} x^{4}-6 b^{2} c \,d^{2} x^{4}+15 a^{2} d^{3} x^{2}-40 a b c \,d^{2} x^{2}+24 b^{2} c^{2} d \,x^{2}+30 a^{2} c \,d^{2}-80 a b \,c^{2} d +48 b^{2} c^{3}}{15 \sqrt{d \,x^{2}+c}\, d^{4}}"," ",0,"1/15*(3*b^2*d^3*x^6+10*a*b*d^3*x^4-6*b^2*c*d^2*x^4+15*a^2*d^3*x^2-40*a*b*c*d^2*x^2+24*b^2*c^2*d*x^2+30*a^2*c*d^2-80*a*b*c^2*d+48*b^2*c^3)/(d*x^2+c)^(1/2)/d^4","A"
650,1,192,134,0.010000," ","int(x^2*(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{b^{2} x^{5}}{4 \sqrt{d \,x^{2}+c}\, d}+\frac{a b \,x^{3}}{\sqrt{d \,x^{2}+c}\, d}-\frac{5 b^{2} c \,x^{3}}{8 \sqrt{d \,x^{2}+c}\, d^{2}}-\frac{a^{2} x}{\sqrt{d \,x^{2}+c}\, d}+\frac{3 a b c x}{\sqrt{d \,x^{2}+c}\, d^{2}}-\frac{15 b^{2} c^{2} x}{8 \sqrt{d \,x^{2}+c}\, d^{3}}+\frac{a^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{d^{\frac{3}{2}}}-\frac{3 a b c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{d^{\frac{5}{2}}}+\frac{15 b^{2} c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 d^{\frac{7}{2}}}"," ",0,"1/4*b^2*x^5/d/(d*x^2+c)^(1/2)-5/8*b^2*c/d^2*x^3/(d*x^2+c)^(1/2)-15/8*b^2*c^2/d^3*x/(d*x^2+c)^(1/2)+15/8*b^2*c^2/d^(7/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+a*b*x^3/d/(d*x^2+c)^(1/2)+3*a*b*c/d^2*x/(d*x^2+c)^(1/2)-3*a*b*c/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-a^2*x/d/(d*x^2+c)^(1/2)+a^2/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
651,1,69,65,0.006000," ","int(x*(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","-\frac{-b^{2} x^{4} d^{2}-6 a b \,d^{2} x^{2}+4 b^{2} c d \,x^{2}+3 a^{2} d^{2}-12 a b c d +8 b^{2} c^{2}}{3 \sqrt{d \,x^{2}+c}\, d^{3}}"," ",0,"-1/3*(-b^2*d^2*x^4-6*a*b*d^2*x^2+4*b^2*c*d*x^2+3*a^2*d^2-12*a*b*c*d+8*b^2*c^2)/(d*x^2+c)^(1/2)/d^3","A"
652,1,123,92,0.009000," ","int((b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{b^{2} x^{3}}{2 \sqrt{d \,x^{2}+c}\, d}+\frac{a^{2} x}{\sqrt{d \,x^{2}+c}\, c}-\frac{2 a b x}{\sqrt{d \,x^{2}+c}\, d}+\frac{3 b^{2} c x}{2 \sqrt{d \,x^{2}+c}\, d^{2}}+\frac{2 a b \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{d^{\frac{3}{2}}}-\frac{3 b^{2} c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 d^{\frac{5}{2}}}"," ",0,"1/2*b^2*x^3/d/(d*x^2+c)^(1/2)+3/2*b^2*c/d^2*x/(d*x^2+c)^(1/2)-3/2*b^2*c/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2*a*b*x/d/(d*x^2+c)^(1/2)+2*a*b/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+a^2*x/c/(d*x^2+c)^(1/2)","A"
653,1,102,65,0.011000," ","int((b*x^2+a)^2/x/(d*x^2+c)^(3/2),x)","\frac{b^{2} x^{2}}{\sqrt{d \,x^{2}+c}\, d}-\frac{a^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{c^{\frac{3}{2}}}+\frac{a^{2}}{\sqrt{d \,x^{2}+c}\, c}-\frac{2 a b}{\sqrt{d \,x^{2}+c}\, d}+\frac{2 b^{2} c}{\sqrt{d \,x^{2}+c}\, d^{2}}"," ",0,"b^2*x^2/d/(d*x^2+c)^(1/2)+2*b^2*c/d^2/(d*x^2+c)^(1/2)-2*a*b/d/(d*x^2+c)^(1/2)+a^2/c/(d*x^2+c)^(1/2)-a^2/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
654,1,99,81,0.011000," ","int((b*x^2+a)^2/x^2/(d*x^2+c)^(3/2),x)","-\frac{2 a^{2} d x}{\sqrt{d \,x^{2}+c}\, c^{2}}+\frac{2 a b x}{\sqrt{d \,x^{2}+c}\, c}-\frac{b^{2} x}{\sqrt{d \,x^{2}+c}\, d}+\frac{b^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{d^{\frac{3}{2}}}-\frac{a^{2}}{\sqrt{d \,x^{2}+c}\, c x}"," ",0,"-b^2*x/d/(d*x^2+c)^(1/2)+b^2/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+2*a*b*x/c/(d*x^2+c)^(1/2)-a^2/c/x/(d*x^2+c)^(1/2)-2*a^2*d/c^2*x/(d*x^2+c)^(1/2)","A"
655,1,135,87,0.012000," ","int((b*x^2+a)^2/x^3/(d*x^2+c)^(3/2),x)","\frac{3 a^{2} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 c^{\frac{5}{2}}}-\frac{2 a b \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{c^{\frac{3}{2}}}-\frac{3 a^{2} d}{2 \sqrt{d \,x^{2}+c}\, c^{2}}+\frac{2 a b}{\sqrt{d \,x^{2}+c}\, c}-\frac{b^{2}}{\sqrt{d \,x^{2}+c}\, d}-\frac{a^{2}}{2 \sqrt{d \,x^{2}+c}\, c \,x^{2}}"," ",0,"-b^2/d/(d*x^2+c)^(1/2)-1/2*a^2/c/x^2/(d*x^2+c)^(1/2)-3/2*a^2*d/c^2/(d*x^2+c)^(1/2)+3/2*a^2*d/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+2*a*b/c/(d*x^2+c)^(1/2)-2*a*b/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
656,1,77,85,0.006000," ","int((b*x^2+a)^2/x^4/(d*x^2+c)^(3/2),x)","-\frac{-8 a^{2} d^{2} x^{4}+12 a b c d \,x^{4}-3 b^{2} c^{2} x^{4}-4 a^{2} c d \,x^{2}+6 a b \,c^{2} x^{2}+a^{2} c^{2}}{3 \sqrt{d \,x^{2}+c}\, c^{3} x^{3}}"," ",0,"-1/3*(-8*a^2*d^2*x^4+12*a*b*c*d*x^4-3*b^2*c^2*x^4-4*a^2*c*d*x^2+6*a*b*c^2*x^2+a^2*c^2)/(d*x^2+c)^(1/2)/x^3/c^3","A"
657,1,211,125,0.013000," ","int((b*x^2+a)^2/x^5/(d*x^2+c)^(3/2),x)","-\frac{15 a^{2} d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{8 c^{\frac{7}{2}}}+\frac{3 a b d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{c^{\frac{5}{2}}}-\frac{b^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{c^{\frac{3}{2}}}+\frac{15 a^{2} d^{2}}{8 \sqrt{d \,x^{2}+c}\, c^{3}}-\frac{3 a b d}{\sqrt{d \,x^{2}+c}\, c^{2}}+\frac{b^{2}}{\sqrt{d \,x^{2}+c}\, c}+\frac{5 a^{2} d}{8 \sqrt{d \,x^{2}+c}\, c^{2} x^{2}}-\frac{a b}{\sqrt{d \,x^{2}+c}\, c \,x^{2}}-\frac{a^{2}}{4 \sqrt{d \,x^{2}+c}\, c \,x^{4}}"," ",0,"-1/4*a^2/c/x^4/(d*x^2+c)^(1/2)+5/8*a^2*d/c^2/x^2/(d*x^2+c)^(1/2)+15/8*a^2*d^2/c^3/(d*x^2+c)^(1/2)-15/8*a^2*d^2/c^(7/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-a*b/c/x^2/(d*x^2+c)^(1/2)-3*a*b*d/c^2/(d*x^2+c)^(1/2)+3*a*b*d/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+b^2/c/(d*x^2+c)^(1/2)-b^2/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
658,1,117,125,0.009000," ","int((b*x^2+a)^2/x^6/(d*x^2+c)^(3/2),x)","-\frac{48 a^{2} d^{3} x^{6}-80 a b c \,d^{2} x^{6}+30 b^{2} c^{2} d \,x^{6}+24 a^{2} c \,d^{2} x^{4}-40 a b \,c^{2} d \,x^{4}+15 b^{2} c^{3} x^{4}-6 a^{2} c^{2} d \,x^{2}+10 a b \,c^{3} x^{2}+3 a^{2} c^{3}}{15 \sqrt{d \,x^{2}+c}\, c^{4} x^{5}}"," ",0,"-1/15*(48*a^2*d^3*x^6-80*a*b*c*d^2*x^6+30*b^2*c^2*d*x^6+24*a^2*c*d^2*x^4-40*a*b*c^2*d*x^4+15*b^2*c^3*x^4-6*a^2*c^2*d*x^2+10*a*b*c^3*x^2+3*a^2*c^3)/(d*x^2+c)^(1/2)/x^5/c^4","A"
659,1,281,166,0.016000," ","int((b*x^2+a)^2/x^7/(d*x^2+c)^(3/2),x)","\frac{35 a^{2} d^{3} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{16 c^{\frac{9}{2}}}-\frac{15 a b \,d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{4 c^{\frac{7}{2}}}+\frac{3 b^{2} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 c^{\frac{5}{2}}}-\frac{35 a^{2} d^{3}}{16 \sqrt{d \,x^{2}+c}\, c^{4}}+\frac{15 a b \,d^{2}}{4 \sqrt{d \,x^{2}+c}\, c^{3}}-\frac{3 b^{2} d}{2 \sqrt{d \,x^{2}+c}\, c^{2}}-\frac{35 a^{2} d^{2}}{48 \sqrt{d \,x^{2}+c}\, c^{3} x^{2}}+\frac{5 a b d}{4 \sqrt{d \,x^{2}+c}\, c^{2} x^{2}}-\frac{b^{2}}{2 \sqrt{d \,x^{2}+c}\, c \,x^{2}}+\frac{7 a^{2} d}{24 \sqrt{d \,x^{2}+c}\, c^{2} x^{4}}-\frac{a b}{2 \sqrt{d \,x^{2}+c}\, c \,x^{4}}-\frac{a^{2}}{6 \sqrt{d \,x^{2}+c}\, c \,x^{6}}"," ",0,"-1/6*a^2/c/x^6/(d*x^2+c)^(1/2)+7/24*a^2*d/c^2/x^4/(d*x^2+c)^(1/2)-35/48*a^2*d^2/c^3/x^2/(d*x^2+c)^(1/2)-35/16*a^2*d^3/c^4/(d*x^2+c)^(1/2)+35/16*a^2*d^3/c^(9/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/2*b^2/c/x^2/(d*x^2+c)^(1/2)-3/2*b^2*d/c^2/(d*x^2+c)^(1/2)+3/2*b^2*d/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/2*a*b/c/x^4/(d*x^2+c)^(1/2)+5/4*a*b*d/c^2/x^2/(d*x^2+c)^(1/2)+15/4*a*b*d^2/c^3/(d*x^2+c)^(1/2)-15/4*a*b*d^2/c^(7/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
660,1,255,178,0.022000," ","int(x^4*(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","\frac{b^{2} x^{7}}{4 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d}+\frac{a b \,x^{5}}{\left(d \,x^{2}+c \right)^{\frac{3}{2}} d}-\frac{7 b^{2} c \,x^{5}}{8 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d^{2}}-\frac{a^{2} x^{3}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d}+\frac{5 a b c \,x^{3}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d^{2}}-\frac{35 b^{2} c^{2} x^{3}}{24 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d^{3}}-\frac{a^{2} x}{\sqrt{d \,x^{2}+c}\, d^{2}}+\frac{5 a b c x}{\sqrt{d \,x^{2}+c}\, d^{3}}-\frac{35 b^{2} c^{2} x}{8 \sqrt{d \,x^{2}+c}\, d^{4}}+\frac{a^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{d^{\frac{5}{2}}}-\frac{5 a b c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{d^{\frac{7}{2}}}+\frac{35 b^{2} c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 d^{\frac{9}{2}}}"," ",0,"1/4*b^2*x^7/d/(d*x^2+c)^(3/2)-7/8*b^2*c/d^2*x^5/(d*x^2+c)^(3/2)-35/24*b^2*c^2/d^3*x^3/(d*x^2+c)^(3/2)-35/8*b^2*c^2/d^4*x/(d*x^2+c)^(1/2)+35/8*b^2*c^2/d^(9/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+a*b*x^5/d/(d*x^2+c)^(3/2)+5/3*a*b*c/d^2*x^3/(d*x^2+c)^(3/2)+5*a*b*c/d^3*x/(d*x^2+c)^(1/2)-5*a*b*c/d^(7/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/3*a^2*x^3/d/(d*x^2+c)^(3/2)-a^2/d^2*x/(d*x^2+c)^(1/2)+a^2/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","A"
661,1,108,98,0.008000," ","int(x^3*(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","-\frac{-b^{2} x^{6} d^{3}-6 a b \,d^{3} x^{4}+6 b^{2} c \,d^{2} x^{4}+3 a^{2} d^{3} x^{2}-24 a b c \,d^{2} x^{2}+24 b^{2} c^{2} d \,x^{2}+2 a^{2} c \,d^{2}-16 a b \,c^{2} d +16 b^{2} c^{3}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d^{4}}"," ",0,"-1/3*(-b^2*d^3*x^6-6*a*b*d^3*x^4+6*b^2*c*d^2*x^4+3*a^2*d^3*x^2-24*a*b*c*d^2*x^2+24*b^2*c^2*d*x^2+2*a^2*c*d^2-16*a*b*c^2*d+16*b^2*c^3)/(d*x^2+c)^(3/2)/d^4","A"
662,1,185,103,0.012000," ","int(x^2*(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","\frac{b^{2} x^{5}}{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d}-\frac{2 a b \,x^{3}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d}+\frac{5 b^{2} c \,x^{3}}{6 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d^{2}}-\frac{a^{2} x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d}+\frac{a^{2} x}{3 \sqrt{d \,x^{2}+c}\, c d}-\frac{2 a b x}{\sqrt{d \,x^{2}+c}\, d^{2}}+\frac{5 b^{2} c x}{2 \sqrt{d \,x^{2}+c}\, d^{3}}+\frac{2 a b \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{d^{\frac{5}{2}}}-\frac{5 b^{2} c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 d^{\frac{7}{2}}}"," ",0,"1/2*b^2*x^5/d/(d*x^2+c)^(3/2)+5/6*b^2*c/d^2*x^3/(d*x^2+c)^(3/2)+5/2*b^2*c/d^3*x/(d*x^2+c)^(1/2)-5/2*b^2*c/d^(7/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2/3*a*b*x^3/d/(d*x^2+c)^(3/2)-2*a*b/d^2*x/(d*x^2+c)^(1/2)+2*a*b/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/3*a^2/d*x/(d*x^2+c)^(3/2)+1/3*a^2/c/d*x/(d*x^2+c)^(1/2)","A"
663,1,68,64,0.006000," ","int(x*(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","-\frac{-3 b^{2} x^{4} d^{2}+6 a b \,d^{2} x^{2}-12 b^{2} c d \,x^{2}+a^{2} d^{2}+4 a b c d -8 b^{2} c^{2}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d^{3}}"," ",0,"-1/3*(-3*b^2*d^2*x^4+6*a*b*d^2*x^2-12*b^2*c*d*x^2+a^2*d^2+4*a*b*c*d-8*b^2*c^2)/(d*x^2+c)^(3/2)/d^3","A"
664,1,136,91,0.009000," ","int((b*x^2+a)^2/(d*x^2+c)^(5/2),x)","-\frac{b^{2} x^{3}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d}+\frac{a^{2} x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c}-\frac{2 a b x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d}+\frac{2 a^{2} x}{3 \sqrt{d \,x^{2}+c}\, c^{2}}+\frac{2 a b x}{3 \sqrt{d \,x^{2}+c}\, c d}-\frac{b^{2} x}{\sqrt{d \,x^{2}+c}\, d^{2}}+\frac{b^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{d^{\frac{5}{2}}}"," ",0,"-1/3*b^2*x^3/d/(d*x^2+c)^(3/2)-b^2/d^2*x/(d*x^2+c)^(1/2)+b^2/d^(5/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2/3*a*b/d*x/(d*x^2+c)^(3/2)+2/3*a*b/c/d*x/(d*x^2+c)^(1/2)+1/3*a^2*x/c/(d*x^2+c)^(3/2)+2/3*a^2/c^2*x/(d*x^2+c)^(1/2)","A"
665,1,120,76,0.013000," ","int((b*x^2+a)^2/x/(d*x^2+c)^(5/2),x)","-\frac{b^{2} x^{2}}{\left(d \,x^{2}+c \right)^{\frac{3}{2}} d}+\frac{a^{2}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c}-\frac{2 a b}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d}-\frac{2 b^{2} c}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d^{2}}-\frac{a^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{c^{\frac{5}{2}}}+\frac{a^{2}}{\sqrt{d \,x^{2}+c}\, c^{2}}"," ",0,"-b^2*x^2/d/(d*x^2+c)^(3/2)-2/3*b^2*c/d^2/(d*x^2+c)^(3/2)-2/3*a*b/d/(d*x^2+c)^(3/2)+1/3*a^2/c/(d*x^2+c)^(3/2)+a^2/c^2/(d*x^2+c)^(1/2)-a^2/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
666,1,78,80,0.008000," ","int((b*x^2+a)^2/x^2/(d*x^2+c)^(5/2),x)","-\frac{8 a^{2} d^{2} x^{4}-4 a b c d \,x^{4}-b^{2} c^{2} x^{4}+12 a^{2} c d \,x^{2}-6 a b \,c^{2} x^{2}+3 a^{2} c^{2}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{3} x}"," ",0,"-1/3*(8*a^2*d^2*x^4-4*a*b*c*d*x^4-b^2*c^2*x^4+12*a^2*c*d*x^2-6*a*b*c^2*x^2+3*a^2*c^2)/(d*x^2+c)^(3/2)/x/c^3","A"
667,1,169,111,0.017000," ","int((b*x^2+a)^2/x^3/(d*x^2+c)^(5/2),x)","-\frac{5 a^{2} d}{6 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2}}+\frac{2 a b}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c}-\frac{b^{2}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d}+\frac{5 a^{2} d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 c^{\frac{7}{2}}}-\frac{2 a b \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{c^{\frac{5}{2}}}-\frac{5 a^{2} d}{2 \sqrt{d \,x^{2}+c}\, c^{3}}+\frac{2 a b}{\sqrt{d \,x^{2}+c}\, c^{2}}-\frac{a^{2}}{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c \,x^{2}}"," ",0,"-1/3*b^2/d/(d*x^2+c)^(3/2)-1/2*a^2/c/x^2/(d*x^2+c)^(3/2)-5/6*a^2*d/c^2/(d*x^2+c)^(3/2)-5/2*a^2*d/c^3/(d*x^2+c)^(1/2)+5/2*a^2*d/c^(7/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+2/3*a*b/c/(d*x^2+c)^(3/2)+2*a*b/c^2/(d*x^2+c)^(1/2)-2*a*b/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
668,1,116,117,0.007000," ","int((b*x^2+a)^2/x^4/(d*x^2+c)^(5/2),x)","-\frac{-16 a^{2} d^{3} x^{6}+16 a b c \,d^{2} x^{6}-2 b^{2} c^{2} d \,x^{6}-24 a^{2} c \,d^{2} x^{4}+24 a b \,c^{2} d \,x^{4}-3 b^{2} c^{3} x^{4}-6 a^{2} c^{2} d \,x^{2}+6 a b \,c^{3} x^{2}+a^{2} c^{3}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{4} x^{3}}"," ",0,"-1/3*(-16*a^2*d^3*x^6+16*a*b*c*d^2*x^6-2*b^2*c^2*d*x^6-24*a^2*c*d^2*x^4+24*a*b*c^2*d*x^4-3*b^2*c^3*x^4-6*a^2*c^2*d*x^2+6*a*b*c^3*x^2+a^2*c^3)/(d*x^2+c)^(3/2)/x^3/c^4","A"
669,1,265,161,0.017000," ","int((b*x^2+a)^2/x^5/(d*x^2+c)^(5/2),x)","\frac{35 a^{2} d^{2}}{24 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{3}}-\frac{5 a b d}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2}}+\frac{b^{2}}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c}-\frac{35 a^{2} d^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{8 c^{\frac{9}{2}}}+\frac{5 a b d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{c^{\frac{7}{2}}}-\frac{b^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{c^{\frac{5}{2}}}+\frac{35 a^{2} d^{2}}{8 \sqrt{d \,x^{2}+c}\, c^{4}}-\frac{5 a b d}{\sqrt{d \,x^{2}+c}\, c^{3}}+\frac{b^{2}}{\sqrt{d \,x^{2}+c}\, c^{2}}+\frac{7 a^{2} d}{8 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2} x^{2}}-\frac{a b}{\left(d \,x^{2}+c \right)^{\frac{3}{2}} c \,x^{2}}-\frac{a^{2}}{4 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c \,x^{4}}"," ",0,"-a*b/c/x^2/(d*x^2+c)^(3/2)-5/3*a*b*d/c^2/(d*x^2+c)^(3/2)-5*a*b*d/c^3/(d*x^2+c)^(1/2)+5*a*b*d/c^(7/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/4*a^2/c/x^4/(d*x^2+c)^(3/2)+7/8*a^2*d/c^2/x^2/(d*x^2+c)^(3/2)+35/24*a^2*d^2/c^3/(d*x^2+c)^(3/2)+35/8*a^2*d^2/c^4/(d*x^2+c)^(1/2)-35/8*a^2*d^2/c^(9/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/3*b^2/c/(d*x^2+c)^(3/2)+b^2/c^2/(d*x^2+c)^(1/2)-b^2/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","A"
670,1,158,163,0.009000," ","int((b*x^2+a)^2/x^6/(d*x^2+c)^(5/2),x)","-\frac{128 a^{2} d^{4} x^{8}-160 a b c \,d^{3} x^{8}+40 b^{2} c^{2} d^{2} x^{8}+192 a^{2} c \,d^{3} x^{6}-240 a b \,c^{2} d^{2} x^{6}+60 b^{2} c^{3} d \,x^{6}+48 a^{2} c^{2} d^{2} x^{4}-60 a b \,c^{3} d \,x^{4}+15 b^{2} c^{4} x^{4}-8 a^{2} c^{3} d \,x^{2}+10 a b \,c^{4} x^{2}+3 a^{2} c^{4}}{15 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{5} x^{5}}"," ",0,"-1/15*(128*a^2*d^4*x^8-160*a*b*c*d^3*x^8+40*b^2*c^2*d^2*x^8+192*a^2*c*d^3*x^6-240*a*b*c^2*d^2*x^6+60*b^2*c^3*d*x^6+48*a^2*c^2*d^2*x^4-60*a*b*c^3*d*x^4+15*b^2*c^4*x^4-8*a^2*c^3*d*x^2+10*a*b*c^4*x^2+3*a^2*c^4)/(d*x^2+c)^(3/2)/x^5/c^5","A"
671,1,53,56,0.031000," ","int(x^5/(b*x^2+a)/(d*x^2)^(1/2),x)","\frac{\left(\sqrt{a b}\, b \,x^{3}+3 a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-3 \sqrt{a b}\, a x \right) x}{3 \sqrt{d \,x^{2}}\, \sqrt{a b}\, b^{2}}"," ",0,"1/3*x*((a*b)^(1/2)*x^3*b-3*(a*b)^(1/2)*x*a+3*a^2*arctan(1/(a*b)^(1/2)*b*x))/(d*x^2)^(1/2)/b^2/(a*b)^(1/2)","A"
672,1,38,40,0.006000," ","int(x^3/(b*x^2+a)/(d*x^2)^(1/2),x)","\frac{\left(-a \arctan \left(\frac{b x}{\sqrt{a b}}\right)+\sqrt{a b}\, x \right) x}{\sqrt{d \,x^{2}}\, \sqrt{a b}\, b}"," ",0,"x*(x*(a*b)^(1/2)-a*arctan(1/(a*b)^(1/2)*b*x))/(d*x^2)^(1/2)/b/(a*b)^(1/2)","A"
673,1,24,24,0.006000," ","int(x/(b*x^2+a)/(d*x^2)^(1/2),x)","\frac{x \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{d \,x^{2}}\, \sqrt{a b}}"," ",0,"1/(d*x^2)^(1/2)*x/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
674,1,36,38,0.010000," ","int(1/x/(b*x^2+a)/(d*x^2)^(1/2),x)","-\frac{b x \arctan \left(\frac{b x}{\sqrt{a b}}\right)+\sqrt{a b}}{\sqrt{d \,x^{2}}\, \sqrt{a b}\, a}"," ",0,"-(b*arctan(1/(a*b)^(1/2)*b*x)*x+(a*b)^(1/2))/(d*x^2)^(1/2)/a/(a*b)^(1/2)","A"
675,1,58,52,0.013000," ","int(1/x^3/(b*x^2+a)/(d*x^2)^(1/2),x)","\frac{3 b^{2} x^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3 \sqrt{a b}\, b \,x^{2}-\sqrt{a b}\, a}{3 \sqrt{d \,x^{2}}\, \sqrt{a b}\, a^{2} x^{2}}"," ",0,"1/3/x^2*(3*b^2*arctan(1/(a*b)^(1/2)*b*x)*x^3+3*b*(a*b)^(1/2)*x^2-a*(a*b)^(1/2))/(d*x^2)^(1/2)/a^2/(a*b)^(1/2)","A"
676,1,1088,131,0.073000," ","int(x^4*(d*x^2+c)^(1/2)/(b*x^2+a),x)","\frac{a^{3} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{3} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a^{2} c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a^{2} \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}+\frac{a^{2} \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}-\frac{a c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 b^{2} \sqrt{d}}-\frac{c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 b \,d^{\frac{3}{2}}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}{2 \sqrt{-a b}\, b^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}{2 \sqrt{-a b}\, b^{2}}-\frac{\sqrt{d \,x^{2}+c}\, a x}{2 b^{2}}-\frac{\sqrt{d \,x^{2}+c}\, c x}{8 b d}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} x}{4 b d}"," ",0,"1/4/b*x*(d*x^2+c)^(3/2)/d-1/8/b*c/d*x*(d*x^2+c)^(1/2)-1/8/b*c^2/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/2/b^2*a*x*(d*x^2+c)^(1/2)-1/2/b^2*a*c/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/2/b^2*a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*d*(-a*b)^(1/2)/b*(x+(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2)+1/2/b^3*a^2*d^(1/2)*ln((-d*(-a*b)^(1/2)/b+d*(x+(-a*b)^(1/2)/b))/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*d*(-a*b)^(1/2)/b*(x+(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))-1/2/b^3*a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b-2*d*(-a*b)^(1/2)/b*(x+(-a*b)^(1/2)/b)+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*d*(-a*b)^(1/2)/b*(x+(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d+1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b-2*d*(-a*b)^(1/2)/b*(x+(-a*b)^(1/2)/b)+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*d*(-a*b)^(1/2)/b*(x+(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/2/b^2*a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*d*(-a*b)^(1/2)/b*(x-(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2)+1/2/b^3*a^2*d^(1/2)*ln((d*(-a*b)^(1/2)/b+d*(x-(-a*b)^(1/2)/b))/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*d*(-a*b)^(1/2)/b*(x-(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))+1/2/b^3*a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b+2*d*(-a*b)^(1/2)/b*(x-(-a*b)^(1/2)/b)+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*d*(-a*b)^(1/2)/b*(x-(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d-1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b+2*d*(-a*b)^(1/2)/b*(x-(-a*b)^(1/2)/b)+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*d*(-a*b)^(1/2)/b*(x-(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
677,1,963,72,0.013000," ","int(x^3*(d*x^2+c)^(1/2)/(b*x^2+a),x)","-\frac{a^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{a c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{-a b}\, a \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}-\frac{\sqrt{-a b}\, a \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{2 b^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{2 b^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}{3 b d}"," ",0,"1/3*(d*x^2+c)^(3/2)/b/d-1/2*a/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*a/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/2*a/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*a/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
678,1,1010,90,0.013000," ","int(x^2*(d*x^2+c)^(1/2)/(b*x^2+a),x)","-\frac{a^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{2}}-\frac{a \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{2}}+\frac{c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 b \sqrt{d}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{2 \sqrt{-a b}\, b}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{2 \sqrt{-a b}\, b}+\frac{\sqrt{d \,x^{2}+c}\, x}{2 b}"," ",0,"1/2*x*(d*x^2+c)^(1/2)/b+1/2/b*c/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/2*a/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*a/b^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2*a^2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d-1/2*a/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/2*a/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*a/b^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2*a^2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d+1/2*a/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
679,1,936,53,0.011000," ","int(x*(d*x^2+c)^(1/2)/(b*x^2+a),x)","\frac{a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{2}}+\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 b}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 b}"," ",0,"1/2/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/b^2*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/2/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/b^2*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
680,1,948,65,0.009000," ","int((d*x^2+c)^(1/2)/(b*x^2+a),x)","\frac{a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{\sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b}+\frac{\sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 \sqrt{-a b}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 \sqrt{-a b}}"," ",0,"-1/2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*d^(1/2)/b*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d+1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*d^(1/2)/b*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d-1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
681,1,984,64,0.013000," ","int((d*x^2+c)^(1/2)/x/(b*x^2+a),x)","\frac{c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a}+\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a b}-\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 a}+\frac{\sqrt{d \,x^{2}+c}}{a}"," ",0,"-1/2/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/a*d^(1/2)*(-a*b)^(1/2)/b*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d+1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/2/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a*d^(1/2)*(-a*b)^(1/2)/b*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d+1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-1/a*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/a*(d*x^2+c)^(1/2)","B"
682,1,1017,58,0.020000," ","int((d*x^2+c)^(1/2)/x^2/(b*x^2+a),x)","\frac{b c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{\sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{a}-\frac{\sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a}-\frac{\sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{2 \sqrt{-a b}\, a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{2 \sqrt{-a b}\, a}+\frac{\sqrt{d \,x^{2}+c}\, d x}{a c}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}{a c x}"," ",0,"1/2*b/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d-1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/2*b/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d+1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-1/a/c/x*(d*x^2+c)^(3/2)+1/a*d/c*x*(d*x^2+c)^(1/2)+1/a*d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","B"
683,1,1054,91,0.014000," ","int((d*x^2+c)^(1/2)/x^3/(b*x^2+a),x)","\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 a \sqrt{c}}+\frac{b \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{2}}-\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a^{2}}+\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a^{2}}+\frac{\sqrt{d \,x^{2}+c}\, d}{2 a c}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{2 a^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{2 a^{2}}-\frac{\sqrt{d \,x^{2}+c}\, b}{a^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}{2 a c \,x^{2}}"," ",0,"1/2/a^2*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a^2*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d-1/2/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/2/a/c/x^2*(d*x^2+c)^(3/2)-1/2/a*d/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/2/a*d/c*(d*x^2+c)^(1/2)+1/2/a^2*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/a^2*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d-1/2/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+1/a^2*b*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/a^2*b*(d*x^2+c)^(1/2)","B"
684,1,1059,87,0.013000," ","int((d*x^2+c)^(1/2)/x^4/(b*x^2+a),x)","\frac{b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b^{2} c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{2} c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{a^{2}}+\frac{b \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a^{2}}+\frac{b \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{2 \sqrt{-a b}\, a^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{2 \sqrt{-a b}\, a^{2}}-\frac{\sqrt{d \,x^{2}+c}\, b d x}{a^{2} c}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b}{a^{2} c x}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}{3 a c \,x^{3}}"," ",0,"-1/2*b^2/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*b/a^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d+1/2*b^2/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/2*b^2/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*b/a^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d-1/2*b^2/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+1/a^2*b/c/x*(d*x^2+c)^(3/2)-1/a^2*b*d/c*x*(d*x^2+c)^(1/2)-1/a^2*b*d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/3/a/c/x^3*(d*x^2+c)^(3/2)","B"
685,1,2081,180,0.022000," ","int(x^4*(d*x^2+c)^(3/2)/(b*x^2+a),x)","-\frac{a^{4} d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{4}}+\frac{a^{4} d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{4}}+\frac{a^{3} c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{3} c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} c^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a^{2} c^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{a^{3} d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{4}}-\frac{a^{3} d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{4}}+\frac{3 a^{2} c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{3}}+\frac{3 a^{2} c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{3}}-\frac{3 a \,c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 b^{2} \sqrt{d}}-\frac{c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{16 b \,d^{\frac{3}{2}}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} d}{2 \sqrt{-a b}\, b^{3}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} d}{2 \sqrt{-a b}\, b^{3}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}{2 \sqrt{-a b}\, b^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}{2 \sqrt{-a b}\, b^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} d x}{4 b^{3}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} d x}{4 b^{3}}-\frac{3 \sqrt{d \,x^{2}+c}\, a c x}{8 b^{2}}-\frac{\sqrt{d \,x^{2}+c}\, c^{2} x}{16 b d}+\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}{6 \sqrt{-a b}\, b^{2}}-\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}{6 \sqrt{-a b}\, b^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a x}{4 b^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} c x}{24 b d}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} x}{6 b d}"," ",0,"1/b^3*a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c-1/b^3*a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c-1/2/b^4*a^4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2-1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+1/2/b^4*a^4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2+1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+1/6/b^2*a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/b^4*a^3*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/6/b^2*a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/b^4*a^3*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/6/b*x*(d*x^2+c)^(5/2)/d-1/16/b*c^3/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/4/b^2*a*x*(d*x^2+c)^(3/2)-1/2/b^3*a^3/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+1/2/b^2*a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/24/b*c/d*x*(d*x^2+c)^(3/2)-1/16/b*c^2/d*x*(d*x^2+c)^(1/2)-3/8/b^2*a*c*x*(d*x^2+c)^(1/2)-3/8/b^2*a*c^2/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/4/b^3*a^2*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/b^3*a^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2/b^3*a^3/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/2/b^2*a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/4/b^3*a^2*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/b^3*a^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c","B"
686,1,1897,95,0.015000," ","int(x^3*(d*x^2+c)^(3/2)/(b*x^2+a),x)","\frac{a^{3} d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{4}}+\frac{a^{3} d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{4}}-\frac{a^{2} c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{a \,c^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a \,c^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\sqrt{-a b}\, a^{2} d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{4}}+\frac{\sqrt{-a b}\, a^{2} d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{4}}+\frac{3 \sqrt{-a b}\, a c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{3}}-\frac{3 \sqrt{-a b}\, a c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{3}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} d}{2 b^{3}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} d}{2 b^{3}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}{2 b^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}{2 b^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d x}{4 b^{3}}-\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d x}{4 b^{3}}-\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}{6 b^{2}}-\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}{6 b^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}}}{5 b d}"," ",0,"1/5*(d*x^2+c)^(5/2)/b/d-1/6*a/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4*a/b^3*(-a*b)^(1/2)*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*a/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2*a^2/b^3*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/2*a/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/2*a^2/b^4*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2*a^3/b^4/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2-a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-1/6*a/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4*a/b^3*(-a*b)^(1/2)*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4*a/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2*a^2/b^3*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/2*a/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/2*a^2/b^4*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2*a^3/b^4/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2-a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2","B"
687,1,1973,132,0.012000," ","int(x^2*(d*x^2+c)^(3/2)/(b*x^2+a),x)","\frac{a^{3} d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{3} d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a^{2} c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a \,c^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a \,c^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{a^{2} d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}+\frac{a^{2} d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}-\frac{3 a c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}-\frac{3 a c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}+\frac{3 c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{8 b \sqrt{d}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} d}{2 \sqrt{-a b}\, b^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} d}{2 \sqrt{-a b}\, b^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}{2 \sqrt{-a b}\, b}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}{2 \sqrt{-a b}\, b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d x}{4 b^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d x}{4 b^{2}}+\frac{3 \sqrt{d \,x^{2}+c}\, c x}{8 b}+\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}{6 \sqrt{-a b}\, b}-\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}{6 \sqrt{-a b}\, b}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} x}{4 b}"," ",0,"1/4/b*x*(d*x^2+c)^(3/2)+3/8/b*c*x*(d*x^2+c)^(1/2)+3/8/b*c^2/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/6*a/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4*a/b^2*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4*a/b^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2*a^2/(-a*b)^(1/2)/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+1/2*a/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/2*a^2/b^3*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2*a^3/(-a*b)^(1/2)/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2+a^2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c-1/2*a/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-1/6*a/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4*a/b^2*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4*a/b^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2*a^2/(-a*b)^(1/2)/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/2*a/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/2*a^2/b^3*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2*a^3/(-a*b)^(1/2)/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2-a^2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c+1/2*a/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2","B"
688,1,1856,75,0.013000," ","int(x*(d*x^2+c)^(3/2)/(b*x^2+a),x)","-\frac{a^{2} d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{a c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{c^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{c^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\sqrt{-a b}\, a \,d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}-\frac{\sqrt{-a b}\, a \,d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}-\frac{3 \sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}+\frac{3 \sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d}{2 b^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d}{2 b^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}{2 b}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}{2 b}-\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 b^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 b^{2}}+\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{6 b}+\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{6 b}"," ",0,"1/6/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/b^2*(-a*b)^(1/2)*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/b^2*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d+1/2/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/2/b^3*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a-1/2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a^2*d^2+1/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d*c-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+1/6/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/b^2*(-a*b)^(1/2)*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/b^2*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d+1/2/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/2/b^3*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a-1/2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a^2*d^2+1/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d*c-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2","B"
689,1,1875,91,0.013000," ","int((d*x^2+c)^(3/2)/(b*x^2+a),x)","-\frac{a^{2} d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a^{2} d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{c^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{c^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}-\frac{a \,d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{2}}-\frac{a \,d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{2}}+\frac{3 c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b}+\frac{3 c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d}{2 \sqrt{-a b}\, b}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d}{2 \sqrt{-a b}\, b}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 b}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}{2 \sqrt{-a b}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}{2 \sqrt{-a b}}-\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{6 \sqrt{-a b}}+\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{6 \sqrt{-a b}}"," ",0,"-1/6/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/b*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/b*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d-1/2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/2/b^2*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a+1/2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a^2*d^2-1/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d*c+1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+1/6/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/b*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/b*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d+1/2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/2/b^2*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a-1/2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a^2*d^2+1/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d*c-1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2","B"
690,1,1919,78,0.011000," ","int((d*x^2+c)^(3/2)/x/(b*x^2+a),x)","\frac{a \,d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a \,d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{c^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{c^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, b}-\frac{c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, b}-\frac{c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a}+\frac{3 \sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a b}-\frac{3 \sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a b}-\frac{\sqrt{-a b}\, d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{2}}+\frac{\sqrt{-a b}\, d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 a b}-\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 a b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}{2 a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}{2 a}+\frac{\sqrt{d \,x^{2}+c}\, c}{a}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{2 b}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{2 b}-\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{6 a}-\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{6 a}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}{3 a}"," ",0,"-1/6/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/a*(-a*b)^(1/2)/b*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/a/b*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/2/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/2/b^2*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2-1/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c+1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-1/6/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/a*(-a*b)^(1/2)/b*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a/b*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/2/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/2/b^2*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2-1/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c+1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+1/3/a*(d*x^2+c)^(3/2)-1/a*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/a*(d*x^2+c)^(1/2)*c","B"
691,1,1956,84,0.015000," ","int((d*x^2+c)^(3/2)/x^2/(b*x^2+a),x)","\frac{a \,d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a \,d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{b \,c^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b \,c^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{3 c \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 a}-\frac{3 c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a}-\frac{3 c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a}+\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b}+\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}{2 \sqrt{-a b}\, a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}{2 \sqrt{-a b}\, a}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 a}+\frac{3 \sqrt{d \,x^{2}+c}\, d x}{2 a}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{2 \sqrt{-a b}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{2 \sqrt{-a b}}+\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}{6 \sqrt{-a b}\, a}-\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}{6 \sqrt{-a b}\, a}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} d x}{a c}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}}}{a c x}"," ",0,"1/6*b/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/a*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+1/2*b/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/2/b*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2/b*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2+1/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c-1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-1/6*b/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/a*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/2*b/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/2/b*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/b*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2-1/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c+1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-1/a/c/x*(d*x^2+c)^(5/2)+1/a*d/c*x*(d*x^2+c)^(3/2)+3/2/a*d*x*(d*x^2+c)^(1/2)+3/2/a*d^(1/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))","B"
692,1,2003,92,0.013000," ","int((d*x^2+c)^(3/2)/x^3/(b*x^2+a),x)","\frac{c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, a}+\frac{c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b \,c^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b \,c^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{3 \sqrt{c}\, d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 a}+\frac{b \,c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{2}}+\frac{\sqrt{-a b}\, d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a b}-\frac{\sqrt{-a b}\, d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a b}-\frac{3 \sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}+\frac{3 \sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{2 a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{2 a}+\frac{3 \sqrt{d \,x^{2}+c}\, d}{2 a}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}{2 a^{2}}-\frac{\sqrt{d \,x^{2}+c}\, b c}{a^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}{2 a^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 a^{2}}-\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 a^{2}}+\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} d}{2 a c}+\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}{6 a^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b}{3 a^{2}}+\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}{6 a^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}}}{2 a c \,x^{2}}"," ",0,"1/6/a^2*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/3/a^2*b*(d*x^2+c)^(3/2)+1/6/a^2*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+3/2/a*d*(d*x^2+c)^(1/2)+1/2/a^2*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2+1/a^2*b*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/a^2*b*(d*x^2+c)^(1/2)*c-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2-1/2/a/c/x^2*(d*x^2+c)^(5/2)+1/2/a*d/c*(d*x^2+c)^(3/2)-3/2/a*d*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/2/a^2*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/2/a/b*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c-1/2/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+3/4/a^2*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2/a/b*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c-1/2/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+1/4/a^2*(-a*b)^(1/2)*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/a^2*(-a*b)^(1/2)*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a^2*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c","B"
693,1,2089,84,0.013000," ","int((d*x^2+c)^(3/2)/x^4/(b*x^2+a),x)","\frac{b c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b^{2} c^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{2} c^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{d^{\frac{3}{2}} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{a}-\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a}-\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a}-\frac{3 b c \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 a^{2}}+\frac{3 b c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}+\frac{3 b c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d}{2 \sqrt{-a b}\, a}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d}{2 \sqrt{-a b}\, a}+\frac{\sqrt{d \,x^{2}+c}\, d^{2} x}{a c}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}{2 \sqrt{-a b}\, a^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}{2 \sqrt{-a b}\, a^{2}}-\frac{3 \sqrt{d \,x^{2}+c}\, b d x}{2 a^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d x}{4 a^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d x}{4 a^{2}}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d^{2} x}{3 a \,c^{2}}+\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}{6 \sqrt{-a b}\, a^{2}}-\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}{6 \sqrt{-a b}\, a^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} b d x}{a^{2} c}-\frac{2 \left(d \,x^{2}+c \right)^{\frac{5}{2}} d}{3 a \,c^{2} x}+\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}} b}{a^{2} c x}-\frac{\left(d \,x^{2}+c \right)^{\frac{5}{2}}}{3 a c \,x^{3}}"," ",0,"b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c-b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c-1/a^2*b*d/c*x*(d*x^2+c)^(3/2)+1/2*b^2/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-1/2*b^2/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-1/3/a/c/x^3*(d*x^2+c)^(5/2)+1/6*b^2/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2-1/6*b^2/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2-1/2*b/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+1/2*b^2/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/a^2*b/c/x*(d*x^2+c)^(5/2)-3/2/a^2*b*d*x*(d*x^2+c)^(1/2)-3/2/a^2*b*d^(1/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2/3/a*d/c^2/x*(d*x^2+c)^(5/2)+2/3/a*d^2/c^2*x*(d*x^2+c)^(3/2)+1/a*d^2/c*x*(d*x^2+c)^(1/2)+1/4*b/a^2*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*b/a^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2*b/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/2*b^2/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/4*b/a^2*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*b/a^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/a*d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/2/a*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2/a*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))","B"
694,1,3373,257,0.023000," ","int(x^4*(d*x^2+c)^(5/2)/(b*x^2+a),x)","\text{output too large to display}"," ",0,"-3/2/b^3*a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c^2-3/2/b^4*a^4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2*c+3/2/b^3*a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c^2+3/2/b^4*a^4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2*c+7/16/b^3*a^2*d*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/b^3*a^3/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c+1/2/b^5*a^5/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^3-1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3+7/16/b^3*a^2*d*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/b^3*a^3/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c-1/2/b^5*a^5/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^3+1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3+1/10/b^2*a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/2/b^5*a^4*d^(5/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/10/b^2*a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/2/b^5*a^4*d^(5/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-5/128/b*c^4/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/6/b^2*a*x*(d*x^2+c)^(5/2)+1/8/b*x*(d*x^2+c)^(7/2)/d-1/6/b^3*a^3/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d+1/6/b^2*a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/4/b^4*a^3*d^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4/b^4*a^3*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2/b^4*a^4/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2+1/2/b^2*a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-1/48/b*c/d*x*(d*x^2+c)^(5/2)-5/192/b*c^2/d*x*(d*x^2+c)^(3/2)-5/128/b*c^3/d*x*(d*x^2+c)^(1/2)-5/24/b^2*a*c*x*(d*x^2+c)^(3/2)+1/8/b^3*a^2*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/16/b^3*a^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/6/b^3*a^3/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d-1/6/b^2*a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/4/b^4*a^3*d^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4/b^4*a^3*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2/b^4*a^4/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2-1/2/b^2*a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-5/16/b^2*a*c^2*x*(d*x^2+c)^(1/2)-5/16/b^2*a*c^3/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/8/b^3*a^2*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/16/b^3*a^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2","B"
695,1,3127,120,0.013000," ","int(x^3*(d*x^2+c)^(5/2)/(b*x^2+a),x)","\text{output too large to display}"," ",0,"-1/6*a/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/2*a^3/b^4*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2-1/2*a/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-7/16*a/b^3*(-a*b)^(1/2)*d*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+7/16*a/b^3*(-a*b)^(1/2)*d*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/6*a^2/b^3*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d+1/6*a^2/b^3*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d-1/6*a/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/2*a^3/b^4*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2-1/2*a/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2+1/7*(d*x^2+c)^(7/2)/b/d+15/16*a/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+3/2*a^3/b^4/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2*c-3/2*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c^2-5/4*a^2/b^4*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/2*a^3/b^4/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2*c-3/2*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c^2-1/4*a^2/b^4*(-a*b)^(1/2)*d^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/8*a/b^3*(-a*b)^(1/2)*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/8*a/b^3*(-a*b)^(1/2)*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-15/16*a/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/4*a^2/b^4*(-a*b)^(1/2)*d^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4*a^2/b^4*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2*a^4/b^5/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^3+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3+a^2/b^3*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c+1/2*a^3/b^5*d^(5/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+a^2/b^3*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c-1/2*a^3/b^5*d^(5/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2*a^4/b^5/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^3+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3-1/10*a/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/10*a/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)","B"
696,1,3235,187,0.015000," ","int(x^2*(d*x^2+c)^(5/2)/(b*x^2+a),x)","\text{output too large to display}"," ",0,"1/6*a/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/8*a/b^2*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/16/b*c^3/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+5/24/b*c*x*(d*x^2+c)^(3/2)+5/16/b*c^2*x*(d*x^2+c)^(1/2)+1/10*a/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/2*a^3/b^4*d^(5/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2*a^3/b^4*d^(5/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/2*a^2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c^2-3/2*a^3/(-a*b)^(1/2)/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2*c+3/2*a^2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c^2+3/2*a^3/(-a*b)^(1/2)/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2*c-1/10*a/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/2*a/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3-7/16*a/b^2*d*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+a^2/(-a*b)^(1/2)/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c-1/2*a^4/(-a*b)^(1/2)/b^4/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^3+1/2*a^4/(-a*b)^(1/2)/b^4/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^3-1/2*a/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3-7/16*a/b^2*d*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-a^2/(-a*b)^(1/2)/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c-1/2*a/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2+1/4*a^2/b^3*d^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4*a^2/b^3*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2*a^3/(-a*b)^(1/2)/b^3*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2+1/6/b*x*(d*x^2+c)^(5/2)-1/8*a/b^2*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/6*a^2/(-a*b)^(1/2)/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d+1/4*a^2/b^3*d^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4*a^2/b^3*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2*a^3/(-a*b)^(1/2)/b^3*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2+1/2*a/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-15/16*a/b^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2-15/16*a/b^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/6*a^2/(-a*b)^(1/2)/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d-1/6*a/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c","B"
697,1,3078,99,0.012000," ","int(x*(d*x^2+c)^(5/2)/(b*x^2+a),x)","\text{output too large to display}"," ",0,"-1/8/b^2*(-a*b)^(1/2)*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-15/16/b^2*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/6/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c+1/2/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2+1/6/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c+1/2/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-1/4/b^3*(-a*b)^(1/2)*d^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x*a-5/4/b^3*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a*c-7/16/b^2*(-a*b)^(1/2)*d*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/b^3*(-a*b)^(1/2)*d^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x*a+5/4/b^3*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a*c-3/2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a^2*d^2*c+3/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d*c^2-3/2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a^2*d^2*c+3/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d*c^2+7/16/b^2*(-a*b)^(1/2)*d*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/6/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*a*d+1/2/b^3*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a^2*d^2-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3-1/6/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*a*d+1/2/b^3*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a^2*d^2-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3+1/10/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/10/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d*c-1/2/b^4*d^(5/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a^2+1/8/b^2*(-a*b)^(1/2)*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/16/b^2*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2-1/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d*c+1/2/b^4*d^(5/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a^2+1/2/b^4/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a^3*d^3+1/2/b^4/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a^3*d^3","B"
698,1,3101,130,0.013000," ","int((d*x^2+c)^(5/2)/(b*x^2+a),x)","\text{output too large to display}"," ",0,"7/16/b*d*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/6/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*a*d-3/2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a^2*d^2*c+3/2/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d*c^2+3/2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a^2*d^2*c-3/2/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d*c^2-1/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d*c+1/2/(-a*b)^(1/2)/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a^3*d^3+1/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d*c-1/2/(-a*b)^(1/2)/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a^3*d^3+1/8/b*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/16/b*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/2/b^3*d^(5/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a^2-1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3+1/2/b^3*d^(5/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a^2+1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3+1/8/b*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/16/b*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/10/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/10/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-1/6/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2+1/6/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/4/b^2*d^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x*a-5/4/b^2*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a*c+1/6/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*a*d-1/4/b^2*d^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x*a-5/4/b^2*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a*c-1/2/(-a*b)^(1/2)/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a^2*d^2+1/2/(-a*b)^(1/2)/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a^2*d^2+7/16/b*d*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x","B"
699,1,3148,102,0.016000," ","int((d*x^2+c)^(5/2)/x/(b*x^2+a),x)","\text{output too large to display}"," ",0,"1/3/a*c*(d*x^2+c)^(3/2)-1/a*c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/a*(d*x^2+c)^(1/2)*c^2+1/6/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d-1/6/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/2/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-1/2/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2+1/6/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d-1/6/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-7/16/a*(-a*b)^(1/2)/b*d*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+7/16/a*(-a*b)^(1/2)/b*d*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/8/a*(-a*b)^(1/2)/b*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/16/a/b*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+3/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2*c-1/8/a*(-a*b)^(1/2)/b*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-15/16/a/b*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+3/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2*c+1/5/a*(d*x^2+c)^(5/2)-1/10/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/10/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c-1/2*a/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2-1/2*a/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2+1/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c+1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3+1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3-1/2*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^3-3/2/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c^2+1/4/b^2*(-a*b)^(1/2)*d^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4/b^2*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2*a/b^3*d^(5/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^3-3/2/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c^2+1/2*a/b^3*d^(5/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/b^2*(-a*b)^(1/2)*d^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4/b^2*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c","B"
700,1,3191,121,0.015000," ","int((d*x^2+c)^(5/2)/x^2/(b*x^2+a),x)","\text{output too large to display}"," ",0,"3/2/b*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2*c-3/2/b*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2*c-1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^3+1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3+1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^3-1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3-1/6/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d+1/6/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d+1/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c-1/2/b^2*a*d^(5/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+5/4/b*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c-1/2/b^2*a*d^(5/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/10*b/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/8/a*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-15/16/a*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/4/b*d^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/a/c/x*(d*x^2+c)^(7/2)+5/4/a*d*x*(d*x^2+c)^(3/2)+15/8/a*d^(1/2)*c^2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/10*b/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/8/a*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-15/16/a*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/4/b*d^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4/b*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2/b*a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2-1/2*b/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-3/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c^2+1/a*d/c*x*(d*x^2+c)^(5/2)+15/8/a*d*c*x*(d*x^2+c)^(1/2)+1/2/b*a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2+1/2*b/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2+3/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c^2-7/16/a*d*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/6*b/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-7/16/a*d*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/6*b/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c","B"
701,1,3247,118,0.015000," ","int((d*x^2+c)^(5/2)/x^3/(b*x^2+a),x)","\text{output too large to display}"," ",0,"5/4/a/b*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+7/16/a^2*(-a*b)^(1/2)*d*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/a/b*(-a*b)^(1/2)*d^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4/a/b*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-7/16/a^2*(-a*b)^(1/2)*d*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/a/b*(-a*b)^(1/2)*d^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/5/a^2*b*(d*x^2+c)^(5/2)+1/10/a^2*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/6/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d+1/2/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2+1/6/a^2*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c+1/2/a^2*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2+1/2/b^2*d^(5/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/3/a^2*b*c*(d*x^2+c)^(3/2)+1/a^2*b*c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/a^2*b*(d*x^2+c)^(1/2)*c^2+1/2/a*d/c*(d*x^2+c)^(5/2)-5/2/a*d*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+5/2/a*d*c*(d*x^2+c)^(1/2)-1/2/a/c/x^2*(d*x^2+c)^(7/2)+1/6/a^2*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c+1/2/a^2*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-1/2/b^2*d^(5/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/8/a^2*(-a*b)^(1/2)*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-15/16/a^2*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^3-3/2/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2*c+3/2/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c^2-1/2/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3+1/8/a^2*(-a*b)^(1/2)*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/16/a^2*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^3-3/2/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2*c+3/2/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c^2-1/2/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3+5/6/a*d*(d*x^2+c)^(3/2)+1/10/a^2*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/6/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d+1/2/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2","B"
702,1,3346,108,0.017000," ","int((d*x^2+c)^(5/2)/x^4/(b*x^2+a),x)","\text{output too large to display}"," ",0,"3/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c^2-3/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c^2+1/2*b^2/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3+7/16*b/a^2*d*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-15/8/a^2*b*d*c*x*(d*x^2+c)^(1/2)-1/2*b^2/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3-1/a^2*b*d/c*x*(d*x^2+c)^(5/2)+7/16*b/a^2*d*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+b/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c-1/2/b*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^3-b/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*c+1/2/b*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^3-5/4/a*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4/a*d^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/10*b^2/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/3/a/c/x^3*(d*x^2+c)^(7/2)+5/2/a*d^2*x*(d*x^2+c)^(1/2)+5/2/a*d^(3/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/10*b^2/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/4/a*d^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4/a*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-15/8/a^2*b*d^(1/2)*c^2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-4/3/a*d/c^2/x*(d*x^2+c)^(7/2)+4/3/a*d^2/c^2*x*(d*x^2+c)^(5/2)+5/3/a*d^2/c*x*(d*x^2+c)^(3/2)+3/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2*c+1/8*b/a^2*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/16*b/a^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2-1/6*b/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d+1/6*b^2/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c+1/2*b^2/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-3/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2*c+1/8*b/a^2*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/16*b/a^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+1/6*b/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*d-1/6*b^2/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-1/2*b^2/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2+1/a^2*b/c/x*(d*x^2+c)^(7/2)-5/4/a^2*b*d*x*(d*x^2+c)^(3/2)-1/2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2+1/2/b*d^(5/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d^2+1/2/b*d^(5/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))","B"
703,1,362,84,0.022000," ","int(x^5/(b*x^2+a)/(d*x^2+c)^(1/2),x)","-\frac{a^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{\sqrt{d \,x^{2}+c}\, x^{2}}{3 b d}-\frac{\sqrt{d \,x^{2}+c}\, a}{b^{2} d}-\frac{2 \sqrt{d \,x^{2}+c}\, c}{3 b \,d^{2}}"," ",0,"1/3/b*x^2/d*(d*x^2+c)^(1/2)-2/3/b*c/d^2*(d*x^2+c)^(1/2)-1/b^2*a/d*(d*x^2+c)^(1/2)-1/2/b^3*a^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/b^3*a^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
704,1,318,56,0.014000," ","int(x^3/(b*x^2+a)/(d*x^2+c)^(1/2),x)","\frac{a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{d \,x^{2}+c}}{b d}"," ",0,"(d*x^2+c)^(1/2)/b/d+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
705,1,300,39,0.010000," ","int(x/(b*x^2+a)/(d*x^2+c)^(1/2),x)","-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b}"," ",0,"-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
706,1,331,64,0.013000," ","int(1/x/(b*x^2+a)/(d*x^2+c)^(1/2),x)","\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{\ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a \sqrt{c}}"," ",0,"1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/a/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
707,1,385,93,0.015000," ","int(1/x^3/(b*x^2+a)/(d*x^2+c)^(1/2),x)","-\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 a \,c^{\frac{3}{2}}}+\frac{b \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{2} \sqrt{c}}-\frac{\sqrt{d \,x^{2}+c}}{2 a c \,x^{2}}"," ",0,"-1/2*b/a^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2*(d*x^2+c)^(1/2)/a/c/x^2+1/2/a*d/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/2*b/a^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/a^2*b/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
708,1,386,92,0.014000," ","int(x^4/(b*x^2+a)/(d*x^2+c)^(1/2),x)","-\frac{a^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{a \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{b^{2} \sqrt{d}}-\frac{c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 b \,d^{\frac{3}{2}}}+\frac{\sqrt{d \,x^{2}+c}\, x}{2 b d}"," ",0,"1/2*x*(d*x^2+c)^(1/2)/b/d-1/2/b*c/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/b^2*a*ln(d^(1/2)*x+(d*x^2+c)^(1/2))/d^(1/2)+1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/b^2*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
709,1,337,66,0.013000," ","int(x^2/(b*x^2+a)/(d*x^2+c)^(1/2),x)","\frac{a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{b \sqrt{d}}"," ",0,"1/b*ln(d^(1/2)*x+(d*x^2+c)^(1/2))/d^(1/2)-1/2*a/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2*a/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
710,1,306,39,0.013000," ","int(1/(b*x^2+a)/(d*x^2+c)^(1/2),x)","-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}"," ",0,"1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
711,1,334,62,0.015000," ","int(1/x^2/(b*x^2+a)/(d*x^2+c)^(1/2),x)","\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{\sqrt{d \,x^{2}+c}}{a c x}"," ",0,"-1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2*b/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-(d*x^2+c)^(1/2)/a/c/x","B"
712,1,379,92,0.015000," ","int(1/x^4/(b*x^2+a)/(d*x^2+c)^(1/2),x)","-\frac{b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{2 \sqrt{d \,x^{2}+c}\, d}{3 a \,c^{2} x}+\frac{\sqrt{d \,x^{2}+c}\, b}{a^{2} c x}-\frac{\sqrt{d \,x^{2}+c}}{3 a c \,x^{3}}"," ",0,"1/2*b^2/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2*b^2/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/a^2*b/c/x*(d*x^2+c)^(1/2)-1/3*(d*x^2+c)^(1/2)/a/c/x^3+2/3/a*d/c^2/x*(d*x^2+c)^(1/2)","B"
713,1,720,91,0.020000," ","int(x^4/(b*x^2+a)/(d*x^2+c)^(3/2),x)","\frac{a^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{a^{2}}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}-\frac{a^{2}}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}+\frac{a^{2} d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}+\frac{a^{2} d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}-\frac{a x}{\sqrt{d \,x^{2}+c}\, b^{2} c}-\frac{x}{\sqrt{d \,x^{2}+c}\, b d}+\frac{\ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{b \,d^{\frac{3}{2}}}"," ",0,"-1/b*x/d/(d*x^2+c)^(1/2)+1/b/d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/b^2*a*x/c/(d*x^2+c)^(1/2)+1/2/b*a^2/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/b^2*a^2/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/b*a^2/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/b*a^2/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/b^2*a^2/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/b*a^2/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
714,1,653,65,0.013000," ","int(x^3/(b*x^2+a)/(d*x^2+c)^(3/2),x)","-\frac{a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{a}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}+\frac{a}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}+\frac{\sqrt{-a b}\, a d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}-\frac{\sqrt{-a b}\, a d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}-\frac{1}{\sqrt{d \,x^{2}+c}\, b d}"," ",0,"-1/b/d/(d*x^2+c)^(1/2)+1/2*a/b/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*a/b^2*(-a*b)^(1/2)/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*a/b/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2*a/b/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*a/b^2*(-a*b)^(1/2)/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*a/b/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
715,1,653,62,0.017000," ","int(x^2/(b*x^2+a)/(d*x^2+c)^(3/2),x)","-\frac{a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}+\frac{a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}-\frac{a d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{a d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{a}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{a}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{x}{\sqrt{d \,x^{2}+c}\, b c}"," ",0,"1/b*x/c/(d*x^2+c)^(1/2)-1/2*a/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*a/b/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*a/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2*a/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*a/b/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*a/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
716,1,618,60,0.013000," ","int(x/(b*x^2+a)/(d*x^2+c)^(3/2),x)","\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}-\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}+\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{1}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{1}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}"," ",0,"-1/2/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/b*(-a*b)^(1/2)/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/b*(-a*b)^(1/2)/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
717,1,628,67,0.010000," ","int(1/(b*x^2+a)/(d*x^2+c)^(3/2),x)","\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}+\frac{b}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{b}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}"," ",0,"1/2/(-a*b)^(1/2)/(a*d-b*c)*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/(-a*b)^(1/2)/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/(-a*b)^(1/2)/(a*d-b*c)*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/(-a*b)^(1/2)/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
718,1,681,89,0.015000," ","int(1/x/(b*x^2+a)/(d*x^2+c)^(3/2),x)","-\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{b}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}+\frac{b}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}+\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{\ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a \,c^{\frac{3}{2}}}+\frac{1}{\sqrt{d \,x^{2}+c}\, a c}"," ",0,"1/2/a/(a*d-b*c)*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/a*(-a*b)^(1/2)/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/a/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2/a/(a*d-b*c)*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a*(-a*b)^(1/2)/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/a/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/a/c/(d*x^2+c)^(1/2)-1/a/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
719,1,695,110,0.017000," ","int(1/x^2/(b*x^2+a)/(d*x^2+c)^(3/2),x)","-\frac{b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{b^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b^{2}}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}+\frac{b^{2}}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{b d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{b d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{2 d x}{\sqrt{d \,x^{2}+c}\, a \,c^{2}}-\frac{1}{\sqrt{d \,x^{2}+c}\, a c x}"," ",0,"-1/2*b^2/a/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*b/a/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*b^2/a/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2*b^2/a/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*b/a/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*b^2/a/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/a/c/x/(d*x^2+c)^(1/2)-2/a*d/c^2*x/(d*x^2+c)^(1/2)","B"
720,1,763,130,0.018000," ","int(1/x^3/(b*x^2+a)/(d*x^2+c)^(3/2),x)","\frac{b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{2}}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{2}}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{\sqrt{-a b}\, b d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{\sqrt{-a b}\, b d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{3 d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 a \,c^{\frac{5}{2}}}+\frac{b \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{2} c^{\frac{3}{2}}}-\frac{3 d}{2 \sqrt{d \,x^{2}+c}\, a \,c^{2}}-\frac{b}{\sqrt{d \,x^{2}+c}\, a^{2} c}-\frac{1}{2 \sqrt{d \,x^{2}+c}\, a c \,x^{2}}"," ",0,"-1/2/a^2*b^2/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a^2*b*(-a*b)^(1/2)/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/a^2*b^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/a/c/x^2/(d*x^2+c)^(1/2)-3/2/a*d/c^2/(d*x^2+c)^(1/2)+3/2/a*d/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/2/a^2*b^2/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/a^2*b*(-a*b)^(1/2)/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/a^2*b^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/a^2*b/c/(d*x^2+c)^(1/2)+1/a^2*b/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
721,1,762,156,0.018000," ","int(1/x^4/(b*x^2+a)/(d*x^2+c)^(3/2),x)","\frac{b^{3} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{3} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{3}}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{3}}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{2} d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{b^{2} d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{8 d^{2} x}{3 \sqrt{d \,x^{2}+c}\, a \,c^{3}}+\frac{2 b d x}{\sqrt{d \,x^{2}+c}\, a^{2} c^{2}}+\frac{4 d}{3 \sqrt{d \,x^{2}+c}\, a \,c^{2} x}+\frac{b}{\sqrt{d \,x^{2}+c}\, a^{2} c x}-\frac{1}{3 \sqrt{d \,x^{2}+c}\, a c \,x^{3}}"," ",0,"1/2*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*b^2/a^2/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*b^2/a^2/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/a^2*b/c/x/(d*x^2+c)^(1/2)+2/a^2*b*d/c^2*x/(d*x^2+c)^(1/2)-1/3/a/c/x^3/(d*x^2+c)^(1/2)+4/3/a*d/c^2/x/(d*x^2+c)^(1/2)+8/3/a*d^2/c^3*x/(d*x^2+c)^(1/2)","B"
722,1,1207,99,0.029000," ","int(x^4/(b*x^2+a)/(d*x^2+c)^(5/2),x)","-\frac{a^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{a^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}-\frac{a^{2} d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{a^{2} d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{a^{2}}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{a^{2}}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{a^{2}}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}-\frac{a^{2}}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}+\frac{a^{2} d x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}+\frac{a^{2} d x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}+\frac{a^{2} d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}+\frac{a^{2} d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}-\frac{a x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c}-\frac{x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b d}-\frac{2 a x}{3 \sqrt{d \,x^{2}+c}\, b^{2} c^{2}}+\frac{x}{3 \sqrt{d \,x^{2}+c}\, b c d}"," ",0,"-1/3/b/d*x/(d*x^2+c)^(3/2)+1/3/b/c/d*x/(d*x^2+c)^(1/2)-1/3/b^2*a*x/c/(d*x^2+c)^(3/2)-2/3/b^2*a/c^2*x/(d*x^2+c)^(1/2)+1/6/b*a^2/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6/b^2*a^2*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3/b^2*a^2*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2*a^2/(-a*b)^(1/2)/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/b*a^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*a^2/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/6/b*a^2/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6/b^2*a^2*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3/b^2*a^2*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2*a^2/(-a*b)^(1/2)/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/b*a^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*a^2/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
723,1,1123,87,0.018000," ","int(x^3/(b*x^2+a)/(d*x^2+c)^(5/2),x)","\frac{a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}-\frac{\sqrt{-a b}\, a d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}+\frac{\sqrt{-a b}\, a d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{a}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{a}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{a}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}+\frac{a}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}+\frac{\sqrt{-a b}\, a d x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}-\frac{\sqrt{-a b}\, a d x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}+\frac{\sqrt{-a b}\, a d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}-\frac{\sqrt{-a b}\, a d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}-\frac{1}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b d}"," ",0,"-1/3/b/d/(d*x^2+c)^(3/2)+1/6*a/b/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2*a/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*a/b/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*a/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/6*a/b/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/6*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/3*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2*a/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*a/b/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*a/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
724,1,1134,97,0.015000," ","int(x^2/(b*x^2+a)/(d*x^2+c)^(5/2),x)","\frac{a b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}-\frac{a b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{a b}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{a b}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{a d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{a d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}-\frac{a d x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}-\frac{a d x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}-\frac{a}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}+\frac{a}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}-\frac{a d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}-\frac{a d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}+\frac{x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b c}+\frac{2 x}{3 \sqrt{d \,x^{2}+c}\, b \,c^{2}}"," ",0,"1/3/b*x/c/(d*x^2+c)^(3/2)+2/3/b/c^2*x/(d*x^2+c)^(1/2)-1/6*a/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/6*a/b*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/3*a/b*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2*a/(-a*b)^(1/2)*b/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*a/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*a/(-a*b)^(1/2)*b/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/6*a/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/6*a/b*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/3*a/b*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2*a/(-a*b)^(1/2)*b/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*a/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*a/(-a*b)^(1/2)*b/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
725,1,1086,82,0.013000," ","int(x/(b*x^2+a)/(d*x^2+c)^(5/2),x)","-\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{b}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{b}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}-\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}-\frac{\sqrt{-a b}\, d x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}+\frac{\sqrt{-a b}\, d x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}-\frac{\sqrt{-a b}\, d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}+\frac{\sqrt{-a b}\, d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}-\frac{1}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}-\frac{1}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}"," ",0,"-1/6/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/6/b*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/3/b*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2*b/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*b/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/6/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6/b*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3/b*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2*b/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*b/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
726,1,1086,104,0.013000," ","int(1/(b*x^2+a)/(d*x^2+c)^(5/2),x)","-\frac{b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{b^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}-\frac{b^{2}}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{b^{2}}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{b d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}-\frac{b d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{b}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}-\frac{b}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}+\frac{d x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} c}+\frac{d x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} c}+\frac{d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c^{2}}+\frac{d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c^{2}}"," ",0,"1/6/(-a*b)^(1/2)/(a*d-b*c)*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2/(-a*b)^(1/2)*b^2/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*b/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/(-a*b)^(1/2)*b^2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/6/(-a*b)^(1/2)/(a*d-b*c)*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2/(-a*b)^(1/2)*b^2/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*b/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/(-a*b)^(1/2)*b^2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
727,1,1186,123,0.016000," ","int(1/x/(b*x^2+a)/(d*x^2+c)^(5/2),x)","\frac{b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{b^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b^{2}}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{b^{2}}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{\sqrt{-a b}\, b d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}+\frac{\sqrt{-a b}\, b d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}+\frac{b}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}+\frac{b}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}+\frac{\sqrt{-a b}\, d x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a c}-\frac{\sqrt{-a b}\, d x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a c}+\frac{\sqrt{-a b}\, d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a \,c^{2}}-\frac{\sqrt{-a b}\, d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a \,c^{2}}+\frac{1}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a c}-\frac{\ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a \,c^{\frac{5}{2}}}+\frac{1}{\sqrt{d \,x^{2}+c}\, a \,c^{2}}"," ",0,"1/6/a/(a*d-b*c)*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6/a*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3/a*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2/a*b^2/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a*b/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/a*b^2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/6/a/(a*d-b*c)*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/6/a*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/3/a*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2/a*b^2/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/a*b/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/a*b^2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/3/a/c/(d*x^2+c)^(3/2)+1/a/c^2/(d*x^2+c)^(1/2)-1/a/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
728,1,1192,156,0.017000," ","int(1/x^2/(b*x^2+a)/(d*x^2+c)^(5/2),x)","\frac{b^{3} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b^{3} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{b^{3}}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{b^{3}}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}+\frac{b^{2} d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}+\frac{b^{2} d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{b^{2}}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}+\frac{b^{2}}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}-\frac{b d x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a c}-\frac{b d x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a c}-\frac{b d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a \,c^{2}}-\frac{b d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a \,c^{2}}-\frac{4 d x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \,c^{2}}-\frac{8 d x}{3 \sqrt{d \,x^{2}+c}\, a \,c^{3}}-\frac{1}{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a c x}"," ",0,"-1/6*b^2/a/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/6*b/a*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/3*b/a*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2*b^3/a/(-a*b)^(1/2)/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*b^2/a/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*b^3/a/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/6*b^2/a/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/6*b/a*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/3*b/a*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2*b^3/a/(-a*b)^(1/2)/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2*b^2/a/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*b^3/a/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/a/c/x/(d*x^2+c)^(3/2)-4/3/a*d/c^2*x/(d*x^2+c)^(3/2)-8/3/a*d/c^3*x/(d*x^2+c)^(1/2)","B"
729,1,1289,181,0.016000," ","int(1/x^3/(b*x^2+a)/(d*x^2+c)^(5/2),x)","-\frac{b^{3} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{3} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{3}}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{3}}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{\sqrt{-a b}\, b^{2} d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}-\frac{\sqrt{-a b}\, b^{2} d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}-\frac{b^{2}}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{2}}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}-\frac{\sqrt{-a b}\, b d x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2} c}+\frac{\sqrt{-a b}\, b d x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2} c}-\frac{\sqrt{-a b}\, b d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c^{2}}+\frac{\sqrt{-a b}\, b d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c^{2}}-\frac{5 d}{6 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \,c^{2}}-\frac{b}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c}+\frac{5 d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 a \,c^{\frac{7}{2}}}+\frac{b \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{2} c^{\frac{5}{2}}}-\frac{5 d}{2 \sqrt{d \,x^{2}+c}\, a \,c^{3}}-\frac{b}{\sqrt{d \,x^{2}+c}\, a^{2} c^{2}}-\frac{1}{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a c \,x^{2}}"," ",0,"-1/6/a^2*b^2/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/6/a^2*b*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/3/a^2*b*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2/a^2*b^3/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/a^2*b^2/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/a^2*b^3/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/a/c/x^2/(d*x^2+c)^(3/2)-5/6/a*d/c^2/(d*x^2+c)^(3/2)-5/2/a*d/c^3/(d*x^2+c)^(1/2)+5/2/a*d/c^(7/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/6/a^2*b^2/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6/a^2*b*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3/a^2*b*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2/a^2*b^3/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a^2*b^2/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/a^2*b^3/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/3/a^2*b/c/(d*x^2+c)^(3/2)-1/a^2*b/c^2/(d*x^2+c)^(1/2)+1/a^2*b/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
730,1,1285,221,0.020000," ","int(1/x^4/(b*x^2+a)/(d*x^2+c)^(5/2),x)","-\frac{b^{4} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{4} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{4}}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{4}}{2 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{3} d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}-\frac{b^{3} d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{b^{3}}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{3}}{6 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}+\frac{b^{2} d x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2} c}+\frac{b^{2} d x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2} c}+\frac{b^{2} d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c^{2}}+\frac{b^{2} d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c^{2}}+\frac{8 d^{2} x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \,c^{3}}+\frac{4 b d x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c^{2}}+\frac{16 d^{2} x}{3 \sqrt{d \,x^{2}+c}\, a \,c^{4}}+\frac{8 b d x}{3 \sqrt{d \,x^{2}+c}\, a^{2} c^{3}}+\frac{2 d}{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a \,c^{2} x}+\frac{b}{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c x}-\frac{1}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a c \,x^{3}}"," ",0,"1/6*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6*b^2/a^2*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3*b^2/a^2*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2*b^4/a^2/(-a*b)^(1/2)/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*b^3/a^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*b^4/a^2/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/6*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6*b^2/a^2*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3*b^2/a^2*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2*b^4/a^2/(-a*b)^(1/2)/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2*b^3/a^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2*b^4/a^2/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/a^2*b/c/x/(d*x^2+c)^(3/2)+4/3/a^2*b*d/c^2*x/(d*x^2+c)^(3/2)+8/3/a^2*b*d/c^3*x/(d*x^2+c)^(1/2)-1/3/a/c/x^3/(d*x^2+c)^(3/2)+2/a*d/c^2/x/(d*x^2+c)^(3/2)+8/3/a*d^2/c^3*x/(d*x^2+c)^(3/2)+16/3/a*d^2/c^4*x/(d*x^2+c)^(1/2)","B"
731,1,2615,124,0.026000," ","int(x^4*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x)","-\frac{a^{2} d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{3}}-\frac{a^{2} d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{3}}+\frac{a c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{2}}+\frac{a c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{2}}-\frac{3 a^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{3 a^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{\sqrt{-a b}\, a^{2} d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{4}}-\frac{\sqrt{-a b}\, a^{2} d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{4}}+\frac{3 a c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{3 a c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d x}{4 \left(a d -b c \right) b^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d x}{4 \left(a d -b c \right) b^{2}}-\frac{\sqrt{-a b}\, a c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{\sqrt{-a b}\, a c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{3 a \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{3}}-\frac{3 a \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{3}}+\frac{c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 b^{2} \sqrt{d}}-\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) b^{2}}+\frac{3 \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{4 \sqrt{-a b}\, b^{2}}-\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) b^{2}}-\frac{3 \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{4 \sqrt{-a b}\, b^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d}{4 \left(a d -b c \right) b^{3}}-\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d}{4 \left(a d -b c \right) b^{3}}+\frac{\sqrt{d \,x^{2}+c}\, x}{2 b^{2}}"," ",0,"1/2*x*(d*x^2+c)^(1/2)/b^2+1/2/b^2*c/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/4*a/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*a^2/b^3*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4*a^2/b^4*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+1/4*a/b^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4*a/b^2*d^(1/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4/b^2*a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/b^3*a*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/4/b^3*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d-3/4/b^2*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/4*a/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*a^2/b^3*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*a^2/b^4*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/4*a/b^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4*a/b^2*d^(1/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-3/4/b^2*a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/b^3*a*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4/b^3*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d+3/4/b^2*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
732,1,2543,116,0.014000," ","int(x^3*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x)","\frac{a^{2} d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{a^{2} d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{a c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\sqrt{-a b}\, a \,d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{3}}+\frac{\sqrt{-a b}\, a \,d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{3}}+\frac{\sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{2}}-\frac{\sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d}{4 \left(a d -b c \right) b^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a d}{4 \left(a d -b c \right) b^{2}}+\frac{a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 \left(a d -b c \right) b^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 \left(a d -b c \right) b^{2}}-\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}+\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 b^{3}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 b^{2}}+\frac{\sqrt{-a b}\, \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) b^{2}}-\frac{\sqrt{-a b}\, \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) b^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 b^{2}}"," ",0,"1/2/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d-1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4*a/b^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4*(-a*b)^(1/2)/b^3*a*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4*a^2/b^3*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4*a/b^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-1/4*(-a*b)^(1/2)/b^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4*(-a*b)^(1/2)/b^2*d^(1/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4*a/b^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*(-a*b)^(1/2)/b^3*a*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4*a^2/b^3*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*a/b^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/4*(-a*b)^(1/2)/b^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4*(-a*b)^(1/2)/b^2*d^(1/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/2/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d-1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
733,1,2547,98,0.013000," ","int(x^2*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x)","\frac{a \,d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{2}}+\frac{a \,d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{2}}-\frac{c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b}-\frac{c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b}+\frac{a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\sqrt{-a b}\, a \,d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{\sqrt{-a b}\, a \,d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 \left(a d -b c \right) b}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 \left(a d -b c \right) b}+\frac{\sqrt{-a b}\, c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\sqrt{-a b}\, c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}+\frac{\sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \sqrt{-a b}\, b}+\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) b}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \sqrt{-a b}\, b}+\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) b}+\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) b^{2}}-\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) b^{2}}"," ",0,"-1/4/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d+1/4/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/4/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b^2*a*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/b^3*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a-1/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/4/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/b*d^(1/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d-1/4/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+1/4/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b^2*a*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/b^3*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a+1/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-1/4/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/b*d^(1/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c","B"
734,1,1617,64,0.013000," ","int(x*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x)","-\frac{a \,d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{a \,d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{\sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a b}+\frac{\sqrt{-a b}\, c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a b}+\frac{\sqrt{-a b}\, d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{2}}-\frac{\sqrt{-a b}\, d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b^{2}}-\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 \left(a d -b c \right) a b}+\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 \left(a d -b c \right) a b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) b}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) b}+\frac{\sqrt{-a b}\, \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a b}-\frac{\sqrt{-a b}\, \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a b}"," ",0,"1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4*(-a*b)^(1/2)/b^2*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*a/b^2*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/4*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4*(-a*b)^(1/2)/a/b*d^(1/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*(-a*b)^(1/2)/b^2*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*a/b^2*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/4/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+1/4*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4*(-a*b)^(1/2)/a/b*d^(1/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c","B"
735,1,2559,66,0.012000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)^2,x)","\frac{c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a}+\frac{c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a}-\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b}-\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) b}-\frac{\sqrt{-a b}\, c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a b}+\frac{\sqrt{-a b}\, c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a b}-\frac{c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 \left(a d -b c \right) a}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d x}{4 \left(a d -b c \right) a}+\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\sqrt{-a b}\, d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\sqrt{-a b}\, d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a b}+\frac{\sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a b}+\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) a b}-\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) a b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \sqrt{-a b}\, a}-\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a}-\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \sqrt{-a b}\, a}"," ",0,"-1/4/(-a*b)^(1/2)/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a*d^(1/2)/b*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d+1/4/(-a*b)^(1/2)/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/4/a/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/b*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/b^2*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+1/4/a*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/a*d^(1/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4/a/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/b*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/b^2*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/4/a*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/a*d^(1/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4/(-a*b)^(1/2)/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a*d^(1/2)/b*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d-1/4/(-a*b)^(1/2)/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
736,1,2585,97,0.014000," ","int((d*x^2+c)^(1/2)/x/(b*x^2+a)^2,x)","-\frac{b c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) a}+\frac{b c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) a}+\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)}-\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d x}{4 \sqrt{-a b}\, \left(a d -b c \right) a}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d x}{4 \sqrt{-a b}\, \left(a d -b c \right) a}-\frac{c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a}-\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a}-\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a b}-\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a b}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) a}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) a}+\frac{c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{2}}+\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a^{2} b}-\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{2 a^{2} b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 a^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{2 a^{2}}+\frac{\sqrt{d \,x^{2}+c}}{a^{2}}"," ",0,"-1/2/a^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/a^2*d^(1/2)*(-a*b)^(1/2)/b*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2/a/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d+1/2/a^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/4/(-a*b)^(1/2)/a/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/a*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/(-a*b)^(1/2)*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4*d^2/(a*d-b*c)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/4/(-a*b)^(1/2)/a*d/(a*d-b*c)*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/(-a*b)^(1/2)/a*d^(1/2)/(a*d-b*c)*b*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4/(-a*b)^(1/2)/a/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/a*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/(-a*b)^(1/2)*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4*d^2/(a*d-b*c)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/a*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+1/4/(-a*b)^(1/2)/a*d/(a*d-b*c)*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/(-a*b)^(1/2)/a*d^(1/2)/(a*d-b*c)*b*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/2/a^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a^2*d^(1/2)*(-a*b)^(1/2)/b*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/2/a/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d+1/2/a^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-1/a^2*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/a^2*(d*x^2+c)^(1/2)","B"
737,1,2618,93,0.020000," ","int((d*x^2+c)^(1/2)/x^2/(b*x^2+a)^2,x)","\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a}+\frac{d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a}-\frac{b c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a^{2}}-\frac{b c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a^{2}}-\frac{\sqrt{-a b}\, d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a b}+\frac{\sqrt{-a b}\, d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a b}-\frac{3 d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{3 d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{3 b c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{3 b c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d x}{4 \left(a d -b c \right) a^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d x}{4 \left(a d -b c \right) a^{2}}+\frac{\sqrt{-a b}\, c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\sqrt{-a b}\, c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{\sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{a^{2}}-\frac{3 \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}-\frac{3 \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}-\frac{3 \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 \sqrt{-a b}\, a^{2}}+\frac{3 \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 \sqrt{-a b}\, a^{2}}+\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a^{2}}+\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a^{2}}+\frac{\sqrt{d \,x^{2}+c}\, d x}{a^{2} c}-\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) a^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, d}{4 \left(a d -b c \right) a^{2}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}{a^{2} c x}"," ",0,"1/4/a*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4*b/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/a^2/c/x*(d*x^2+c)^(3/2)+1/4/a*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/4*b/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a^2*d^(1/2)/(a*d-b*c)*b*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4/a^2*d/(a*d-b*c)*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/a^2*d^(1/2)/(a*d-b*c)*b*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-3/4*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/4/a^2*d/(a*d-b*c)*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/a^2*d/c*x*(d*x^2+c)^(1/2)+1/4/a^2/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-1/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d+1/4/a^2/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d-3/4/a^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4/a^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/a^2*d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/4/a*(-a*b)^(1/2)*d^2/(a*d-b*c)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/4/a*(-a*b)^(1/2)*d^2/(a*d-b*c)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
738,1,2669,133,0.022000," ","int((d*x^2+c)^(1/2)/x^3/(b*x^2+a)^2,x)","-\frac{b \,d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) a}+\frac{b \,d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) a}+\frac{b^{2} c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) a^{2}}-\frac{b^{2} c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) a^{2}}-\frac{d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} d x}{4 \sqrt{-a b}\, \left(a d -b c \right) a^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} d x}{4 \sqrt{-a b}\, \left(a d -b c \right) a^{2}}+\frac{b c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{b c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a^{2}}+\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d}{4 \left(a d -b c \right) a^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d}{4 \left(a d -b c \right) a^{2}}+\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{b c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 a^{2} \sqrt{c}}+\frac{2 b \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{3}}-\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{a^{3}}+\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{a^{3}}+\frac{\sqrt{d \,x^{2}+c}\, d}{2 a^{2} c}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{a^{3}}-\frac{2 \sqrt{d \,x^{2}+c}\, b}{a^{3}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{a^{3}}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}{2 a^{2} c \,x^{2}}"," ",0,"-1/4*b/a/(-a*b)^(1/2)*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4*b/a/(-a*b)^(1/2)*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/a^2/c/x^2*(d*x^2+c)^(3/2)-1/2/a^2*d/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/2/a^2*d/c*(d*x^2+c)^(1/2)+1/a^3*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/a^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d+2*b/a^3*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/a^3*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/a^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d-b/a^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-1/4*b/a^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-b/a^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+b/a^3*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-2*b/a^3*(d*x^2+c)^(1/2)+b/a^3*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4*b/a^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+1/4*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4*b^2/a^2/(-a*b)^(1/2)*d^(1/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4*b^2/a^2/(-a*b)^(1/2)*d^(1/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4*b/a^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-1/4*b/a^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))","B"
739,1,2667,123,0.019000," ","int((d*x^2+c)^(1/2)/x^4/(b*x^2+a)^2,x)","-\frac{b \,d^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a^{2}}-\frac{b \,d^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a^{2}}+\frac{b^{2} c \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a^{3}}+\frac{b^{2} c \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 \left(a d -b c \right) a^{3}}+\frac{5 b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{5 b d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{\sqrt{-a b}\, d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\sqrt{-a b}\, d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{5 b^{2} c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{5 b^{2} c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} d x}{4 \left(a d -b c \right) a^{3}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} d x}{4 \left(a d -b c \right) a^{3}}-\frac{\sqrt{-a b}\, b c d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{\sqrt{-a b}\, b c d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{2 b \sqrt{d}\, \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{a^{3}}+\frac{5 b \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{3}}+\frac{5 b \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{3}}+\frac{5 \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{4 \sqrt{-a b}\, a^{3}}-\frac{5 \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{4 \sqrt{-a b}\, a^{3}}-\frac{\left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a^{3}}-\frac{\left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a^{3}}-\frac{2 \sqrt{d \,x^{2}+c}\, b d x}{a^{3} c}+\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d}{4 \left(a d -b c \right) a^{3}}-\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b d}{4 \left(a d -b c \right) a^{3}}+\frac{2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b}{a^{3} c x}-\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}{3 a^{2} c \,x^{3}}"," ",0,"5/4*b/a^3*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/3/a^2/c/x^3*(d*x^2+c)^(3/2)+5/4*b^2/a^3/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+5/4*b/a^3*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-5/4*b^2/a^3/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-2*b/a^3*d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+5/4*b^2/a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-5/4*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d+1/4*b^2/a^3*d^(1/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a^2*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/4*b^2/a^3*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4*b^2/a^3*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4*b^2/a^3*d^(1/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+5/4*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d-5/4*b^2/a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-2*b/a^3*d/c*x*(d*x^2+c)^(1/2)-1/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a^2*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*b^2/a^3/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4*b/a^2*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+2*b/a^3/c/x*(d*x^2+c)^(3/2)-1/4*b^2/a^3/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4*b/a^2*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+1/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c","B"
740,1,4795,165,0.026000," ","int(x^4*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"-9/8*a^2/b^3*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4*a^2/b^4*(-a*b)^(1/2)*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4*a/b^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+3/8*a/b^2*d^(1/2)/(a*d-b*c)*c^2*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4/b^4*a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2-3/4/b^2*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+3/8*a/b^2*d^(1/2)/(a*d-b*c)*c^2*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/4/b^4*a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2+3/4/b^2*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+1/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/8*a^2/b^3*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8*a^2/b^3*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-3/4*a^2/b^4*(-a*b)^(1/2)*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4*a/b^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-3/8*a^2/b^3*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/b^2*a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/4/b^4*a^2*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/8/b^2*c*x*(d*x^2+c)^(1/2)+3/8/b^2*c^2/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/4/b^2*a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/4/b^4*a^2*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/4*a^3/b^5*(-a*b)^(1/2)*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/8*a/b^2*d/(a*d-b*c)*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-3/4*a^3/b^5*(-a*b)^(1/2)*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+3/8*a/b^2*d/(a*d-b*c)*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/2/b^3*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c+3/2/b^3*a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c-3/8/b^3*a*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8/b^3*a*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4/b^3*a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-3/4/b^2*a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/4*a/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+3/4*a^3/b^4*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/8/b^3*a*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8/b^3*a*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-3/4/b^3*a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+3/4/b^2*a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/4*a/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+3/4*a^3/b^4*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/2*a^2/b^4*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-3/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-3/2*a^2/b^4*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+3/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+1/4/b^2*x*(d*x^2+c)^(3/2)","B"
741,1,4673,139,0.017000," ","int(x^3*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/4/b^3*(-a*b)^(1/2)*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4*(-a*b)^(1/2)/b^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d*c-3/4*a^3/b^4*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4*(-a*b)^(1/2)/b^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-3/8*(-a*b)^(1/2)/b^2*d^(1/2)/(a*d-b*c)*c^2*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4*(-a*b)^(1/2)/b^4*a^2*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/4*a/b^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/8*(-a*b)^(1/2)/b^2*d^(1/2)/(a*d-b*c)*c^2*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d*c+3/4*a/b^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/4*(-a*b)^(1/2)/b^4*a^2*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4*a^3/b^4*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-1/2/b^3*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d-1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-1/2/b^3*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d+1/6/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/6/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/b^4*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a-1/2/b^4/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a^2*d^2+1/2/b^4*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a-1/2/b^4/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a^2*d^2-1/4/b^3*(-a*b)^(1/2)*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/b^3*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/4*a/b^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4*a^2/b^3*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/4*a/b^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4*a^2/b^3*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/2*a^2/b^3*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-3/4*a/b^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+3/8*(-a*b)^(1/2)/b^2*d/(a*d-b*c)*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8*(-a*b)^(1/2)/b^3*a*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-3/8*(-a*b)^(1/2)/b^2*d/(a*d-b*c)*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+9/8*(-a*b)^(1/2)/b^3*a*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/8*(-a*b)^(1/2)/b^3*a*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/8*(-a*b)^(1/2)/b^3*a*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/2*a^2/b^3*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-3/4*a/b^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+1/2/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/2/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c","B"
742,1,4685,123,0.015000," ","int(x^2*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"-3/8/b*d/(a*d-b*c)*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/8/b^2*a*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+9/8/b^2*a*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-3/4/b^3*(-a*b)^(1/2)*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a+3/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+1/4/(-a*b)^(1/2)/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a^2*d^2+3/4/b^3*(-a*b)^(1/2)*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a-3/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-3/8/b*d/(a*d-b*c)*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/(-a*b)^(1/2)/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a^2*d^2+3/8/b^2*a*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+9/8/b^2*a*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/8/b^2*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/8/b^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/4/b^3*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a+1/4/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/4/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/8/b^2*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/8/b^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/4/b^3*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*a-1/4/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-3/8/b*d^(1/2)/(a*d-b*c)*c^2*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*d*c+3/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-3/2/b^3*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a*c+3/2/b^3*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*c-1/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4/b^3*a^2*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4/b^3*a^2*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/(-a*b)^(1/2)/b^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d-1/4/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+1/4/(-a*b)^(1/2)/b^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*a*d+1/4/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-1/4/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-3/8/b*d^(1/2)/(a*d-b*c)*c^2*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/12/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/12/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4/b^4*(-a*b)^(1/2)*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a^2-3/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-1/2/(-a*b)^(1/2)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*a*d*c+3/4/b^4*(-a*b)^(1/2)*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*a^2","B"
743,1,2821,79,0.013000," ","int(x*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"-3/2*a/b^2*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-3/8*(-a*b)^(1/2)/a/b*d^(1/2)/(a*d-b*c)*c^2*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/2*a/b^2*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/4*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+9/8*(-a*b)^(1/2)/b^2*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-3/4*(-a*b)^(1/2)*a/b^3*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/4*a^2/b^3*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/4/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+3/8*(-a*b)^(1/2)/b^2*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+3/4*a^2/b^3*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-3/8*(-a*b)^(1/2)/b^2*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8*(-a*b)^(1/2)/b^2*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4*(-a*b)^(1/2)*a/b^3*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/4/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/4*a/b^2*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*a/b^2*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/8*(-a*b)^(1/2)/a/b*d^(1/2)/(a*d-b*c)*c^2*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-3/4/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/8*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/8*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x","B"
744,1,4689,109,0.015000," ","int((d*x^2+c)^(3/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"3/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/2/b^2*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+3/4*a/b^3*(-a*b)^(1/2)*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-3/2/b^2*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-3/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/4/b^2*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/12/(-a*b)^(1/2)/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/b^2*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/12/(-a*b)^(1/2)/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/8/a*d/(a*d-b*c)*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/(-a*b)^(1/2)*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2-1/2/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c+1/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/8/a*d/(a*d-b*c)*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/(-a*b)^(1/2)*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2+1/2/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c+1/4/(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-1/4/(-a*b)^(1/2)/a*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/4/a/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/4/(-a*b)^(1/2)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+1/4/(-a*b)^(1/2)/a*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/4/a/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/8/a/b*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/8/a/b*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/4/(-a*b)^(1/2)/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+3/8/a/b*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4/(-a*b)^(1/2)/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-3/8/b*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4*a/b^3*(-a*b)^(1/2)*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-9/8/b*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-3/4/b^2*(-a*b)^(1/2)*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*a/b^2*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/a*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+3/8/a*d^(1/2)/(a*d-b*c)*c^2*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-9/8/b*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4/b^2*(-a*b)^(1/2)*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*a/b^2*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/a*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+3/8/a*d^(1/2)/(a*d-b*c)*c^2*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/8/a/b*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/8/b*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+3/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2","B"
745,1,4718,107,0.016000," ","int((d*x^2+c)^(3/2)/x/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"-1/4/a^2*(-a*b)^(1/2)/b*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a^2/b*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/a/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c-3/4/(-a*b)^(1/2)*a/b*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4*a*d^3/(a*d-b*c)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/2*d^2/(a*d-b*c)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-3/4/a*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+1/4/(-a*b)^(1/2)/a/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/4/(-a*b)^(1/2)/a/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+3/4/(-a*b)^(1/2)*a/b*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4*a*d^3/(a*d-b*c)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+3/2*d^2/(a*d-b*c)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-3/4/a*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-1/a/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c+3/4/a^2/b*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4/a^2*(-a*b)^(1/2)/b*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2/a/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2+1/2/a^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+1/2/a/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2+1/2/a^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+1/4/a*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4*d^2/(a*d-b*c)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4*d^2/(a*d-b*c)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/3/a^2*(d*x^2+c)^(3/2)-1/6/a^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/6/a^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/8/(-a*b)^(1/2)/a*d^(1/2)/(a*d-b*c)*b*c^2*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/(-a*b)^(1/2)/a*d/(a*d-b*c)*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/2/a/b^2*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/2/a/b^2*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/8/(-a*b)^(1/2)*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8/(-a*b)^(1/2)*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4/a*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/8/(-a*b)^(1/2)*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+9/8/(-a*b)^(1/2)*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4/a*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/8/(-a*b)^(1/2)/a*d^(1/2)/(a*d-b*c)*b*c^2*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/(-a*b)^(1/2)/a*d/(a*d-b*c)*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+3/8/(-a*b)^(1/2)/a*d/(a*d-b*c)*b*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/8/(-a*b)^(1/2)/a*d/(a*d-b*c)*b*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2/a^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/2/a^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-1/a^2*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/a^2*(d*x^2+c)^(1/2)*c","B"
746,1,4764,108,0.019000," ","int((d*x^2+c)^(3/2)/x^2/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"-3/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/4*(-a*b)^(1/2)*d^3/(a*d-b*c)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/a^2*d/(a*d-b*c)*b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-3/8/a^2*d^(1/2)/(a*d-b*c)*b*c^2*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/4/a*(-a*b)^(1/2)*d^2/(a*d-b*c)/b*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/2/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c+3/4*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-3/8/a^2*d^(1/2)/(a*d-b*c)*b*c^2*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-3/4*(-a*b)^(1/2)*d^3/(a*d-b*c)/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a^2*d/(a*d-b*c)*b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-3/4/a*(-a*b)^(1/2)*d^2/(a*d-b*c)/b*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+3/2/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c-3/8/a^2*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8/a^2*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-3/4/a/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+3/4/b/a*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4/b*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/a^2/c/x*(d*x^2+c)^(5/2)+3/2/a^2*d*x*(d*x^2+c)^(1/2)+3/2/a^2*d^(1/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-1/4*b/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/8/a^2*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8/a^2*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4/a/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+3/4/b/a*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-3/4/b*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4*b/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/a^2/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/4/b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2+1/a^2*d/c*x*(d*x^2+c)^(3/2)+3/4*b/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-3/4/b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2+3/8/a*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+9/8/a*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4/a^2/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+1/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/8/a*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+9/8/a*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-3/4*b/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/2/a*(-a*b)^(1/2)*d^2/(a*d-b*c)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-3/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-3/8/a^2*d/(a*d-b*c)*b*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-3/8/a^2*d/(a*d-b*c)*b*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/2/a*(-a*b)^(1/2)*d^2/(a*d-b*c)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
747,1,4820,142,0.016000," ","int((d*x^2+c)^(3/2)/x^3/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-3/4*b/a^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-3/2/a*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-3/4*b/a^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-3/2/a*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+b/a^3*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/4/(-a*b)^(1/2)*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/4/a*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/2/a^2*d*c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/2/a^2*d/c*(d*x^2+c)^(3/2)-1/2/a^2/c/x^2*(d*x^2+c)^(5/2)-2*b/a^3*(d*x^2+c)^(1/2)*c+3/4/a*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/(-a*b)^(1/2)*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+b/a^3*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+2*b/a^3*c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-3/8*b^2/a^2/(-a*b)^(1/2)*d^(1/2)/(a*d-b*c)*c^2*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/8*b/a/(-a*b)^(1/2)*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+9/8*b/a/(-a*b)^(1/2)*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4*b/a^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-b/a^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+1/2/a^3*(-a*b)^(1/2)*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/2/a^3*d^(1/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-1/b/a^2*d^(3/2)*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/b/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2+2/a^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c-1/4*b/a^2*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/4/b*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/a^3*(-a*b)^(1/2)*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/2/a^3*d^(1/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/b/a^2*d^(3/2)*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/b/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2+2/a^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c-b/a^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-9/8*b/a/(-a*b)^(1/2)*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+3/4*b/a^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2+1/4*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+3/8*b^2/a^2/(-a*b)^(1/2)*d^(1/2)/(a*d-b*c)*c^2*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-3/8*b/a/(-a*b)^(1/2)*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4*b/a^2*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/4/b*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+3/8*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/8*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/3*b/a^3*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/a^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-2/3*b/a^3*(d*x^2+c)^(3/2)+1/3*b/a^3*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/a^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+3/2/a^2*d*(d*x^2+c)^(1/2)","B"
748,1,4908,142,0.017000," ","int((d*x^2+c)^(3/2)/x^4/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/a^2*d^(3/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-5/4/a^2*d^(3/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-5/4/a^2*d^(3/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/8*b/a^2*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8*b/a^2*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4*b^2/a^3*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+3/8*b^2/a^3*d^(1/2)/(a*d-b*c)*c^2*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-5/4*b^2/a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-2*b/a^3*d/c*x*(d*x^2+c)^(3/2)+1/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/8*b/a^2*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-9/8*b/a^2*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4*b^2/a^3*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+3/8*b^2/a^3*d^(1/2)/(a*d-b*c)*c^2*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+5/4*b^2/a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-3/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+3/4/b/a*(-a*b)^(1/2)*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-3/2/a^2*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c+3/8*b^2/a^3*d/(a*d-b*c)*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/2*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d*c+3/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-3/4/b/a*(-a*b)^(1/2)*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+3/2/a^2*(-a*b)^(1/2)*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c+5/12*b^2/a^3/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/4/a*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+3/4/a*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-5/12*b^2/a^3/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/3/a^2/c/x^3*(d*x^2+c)^(5/2)+15/8*b/a^3*d^(1/2)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+5/4*b/a^2/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d-5/4*b^2/a^3/(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+5/4/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d^2+5/8*b/a^3*d*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4*b^2/a^3/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-3/4/a^2*(-a*b)^(1/2)*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*b^2/a^3/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+3/4/a^2*(-a*b)^(1/2)*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+5/8*b/a^3*d*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+15/8*b/a^3*d^(1/2)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c-5/4*b/a^2/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d+5/4*b^2/a^3/(-a*b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-5/4/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*d^2+2*b/a^3/c/x*(d*x^2+c)^(5/2)-3*b/a^3*d*x*(d*x^2+c)^(1/2)-3*b/a^3*d^(1/2)*c*ln(d^(1/2)*x+(d*x^2+c)^(1/2))-2/3/a^2*d/c^2/x*(d*x^2+c)^(5/2)+2/3/a^2*d^2/c^2*x*(d*x^2+c)^(3/2)+1/a^2*d^2/c*x*(d*x^2+c)^(1/2)+3/8*b^2/a^3*d/(a*d-b*c)*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/2*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*d*c-3/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2+3/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2","B"
749,1,7611,222,0.029000," ","int(x^4*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
750,1,7443,170,0.016000," ","int(x^3*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
751,1,7459,163,0.019000," ","int(x^2*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
752,1,4363,102,0.014000," ","int(x*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"5/2*a/b^2*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c-5/4*(-a*b)^(1/2)*a^2/b^4*d^(7/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-5/4*a^3/b^4*d^4/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+5/4/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^3-1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(7/2)-5/16*(-a*b)^(1/2)/b^2*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-75/32*(-a*b)^(1/2)/b^2*d^(3/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2-5/4*a^3/b^4*d^4/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+5/4/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^3+1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(7/2)+5/16*(-a*b)^(1/2)/b^2*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+75/32*(-a*b)^(1/2)/b^2*d^(3/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c^2+5/2*a/b^2*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c+5/4*(-a*b)^(1/2)*a^2/b^4*d^(7/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)-1/4/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)+5/12*a/b^2*d^2/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/12/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-5/4*a^2/b^3*d^3/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-5/4/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2-5/12/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*c-5/4*a^2/b^3*d^3/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-5/4/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*c^2+5/12*a/b^2*d^2/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/16*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-15/32*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*c^2*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/16*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+15/32*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*c^2*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/8*(-a*b)^(1/2)*a/b^3*d^3/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+35/32*(-a*b)^(1/2)/b^2*d^2/(a*d-b*c)*c*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-35/32*(-a*b)^(1/2)/b^2*d^2/(a*d-b*c)*c*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/8*(-a*b)^(1/2)*a/b^3*d^3/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+25/8*(-a*b)^(1/2)*a/b^3*d^(5/2)/(a*d-b*c)*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+1/4*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)*x+15/32*(-a*b)^(1/2)/a/b*d^(1/2)/(a*d-b*c)*c^3*ln(((x-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+15/4*a^2/b^3*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c-15/4*a/b^2*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c^2-25/8*(-a*b)^(1/2)*a/b^3*d^(5/2)/(a*d-b*c)*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))*c+15/4*a^2/b^3*d^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-15/4*a/b^2*d^2/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c^2-1/4*(-a*b)^(1/2)/a/b*d/(a*d-b*c)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(5/2)*x-15/32*(-a*b)^(1/2)/a/b*d^(1/2)/(a*d-b*c)*c^3*ln(((x+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))","B"
753,1,7451,146,0.016000," ","int((d*x^2+c)^(5/2)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
754,1,7477,134,0.018000," ","int((d*x^2+c)^(5/2)/x/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
755,1,7529,142,0.018000," ","int((d*x^2+c)^(5/2)/x^2/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
756,1,7590,152,0.020000," ","int((d*x^2+c)^(5/2)/x^3/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
757,1,7705,152,0.020000," ","int((d*x^2+c)^(5/2)/x^4/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
758,1,846,110,0.021000," ","int(x^4/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{3 a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{3 a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{-a b}\, a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{\sqrt{-a b}\, a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) b^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) b^{2}}+\frac{\ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{b^{2} \sqrt{d}}"," ",0,"1/b^2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))/d^(1/2)-1/4*a/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-3/4/b^2*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*a/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*a/b^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/4/b^2*a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
759,1,807,83,0.015000," ","int(x^3/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) b^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) b^{2}}"," ",0,"-1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4*a/b^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4*a/b^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
760,1,817,73,0.017000," ","int(x^2/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{\sqrt{-a b}\, d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{-a b}\, d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) b}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) b}"," ",0,"1/4/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/(-a*b)^(1/2)/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/4/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
761,1,513,71,0.012000," ","int(x/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","-\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\sqrt{-a b}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a b}-\frac{\sqrt{-a b}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a b}"," ",0,"1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
762,1,823,84,0.013000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{\sqrt{-a b}\, d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a b}-\frac{\sqrt{-a b}\, d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a b}-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a}"," ",0,"1/4/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/a/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a/b*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
763,1,838,108,0.016000," ","int(1/x/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a}+\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{2} \sqrt{c}}"," ",0,"1/2/a^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4/a/(-a*b)^(1/2)/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2/a^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/a/(-a*b)^(1/2)/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/a^2/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
764,1,841,127,0.014000," ","int(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{3 b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{3 b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\sqrt{-a b}\, d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{\sqrt{-a b}\, d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a^{2}}-\frac{\sqrt{d \,x^{2}+c}}{a^{2} c x}"," ",0,"1/4/a^2/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-3/4*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4/a^2/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/4*b/a^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/a^2/c/x*(d*x^2+c)^(1/2)","B"
765,1,899,157,0.016000," ","int(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","-\frac{b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a^{2}}-\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 a^{2} c^{\frac{3}{2}}}+\frac{2 b \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{3} \sqrt{c}}-\frac{\sqrt{d \,x^{2}+c}}{2 a^{2} c \,x^{2}}"," ",0,"-1/a^3*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*b/a^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/a^2/c/x^2*(d*x^2+c)^(1/2)+1/2/a^2*d/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/a^3*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*b/a^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+2*b/a^3/c^(1/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
766,1,893,182,0.020000," ","int(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","-\frac{5 b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{5 b^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{\sqrt{-a b}\, b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{\sqrt{-a b}\, b d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a^{3}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a^{3}}+\frac{2 \sqrt{d \,x^{2}+c}\, d}{3 a^{2} c^{2} x}+\frac{2 \sqrt{d \,x^{2}+c}\, b}{a^{3} c x}-\frac{\sqrt{d \,x^{2}+c}}{3 a^{2} c \,x^{3}}"," ",0,"5/4*b^2/a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*b^2/a^3/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-5/4*b^2/a^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4*b^2/a^3/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+2*b/a^3/c/x*(d*x^2+c)^(1/2)-1/3/a^2/c/x^3*(d*x^2+c)^(1/2)+2/3/a^2*d/c^2/x*(d*x^2+c)^(1/2)","B"
767,1,1498,110,0.027000," ","int(x^4/(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{3 a^{2} d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}+\frac{3 a^{2} d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}-\frac{3 a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{3 a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{3 \sqrt{-a b}\, a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{3 \sqrt{-a b}\, a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{3 a}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}+\frac{3 a}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}-\frac{5 a d x}{4 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}-\frac{5 a d x}{4 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}+\frac{3 \sqrt{-a b}\, a d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}-\frac{3 \sqrt{-a b}\, a d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}-\frac{a}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}-\frac{a}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}+\frac{x}{\sqrt{d \,x^{2}+c}\, b^{2} c}"," ",0,"1/b^2*x/c/(d*x^2+c)^(1/2)-1/4*a/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*a^2/b^2*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-5/4*a/b^2/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-3/4/b*a/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-5/4/b^2*a/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+3/4/b*a/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*a/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*a^2/b^2*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/4/b*a/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/b*a/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
768,1,1456,114,0.015000," ","int(x^3/(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","-\frac{3 a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{3 a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{3 a d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}+\frac{3 a d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}-\frac{3 \sqrt{-a b}\, a \,d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}+\frac{3 \sqrt{-a b}\, a \,d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}+\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{1}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}-\frac{1}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}-\frac{\sqrt{-a b}\, d x}{\left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}+\frac{\sqrt{-a b}\, d x}{\left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c}+\frac{\sqrt{-a b}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}-\frac{\sqrt{-a b}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}"," ",0,"-1/2/b/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/b^2*(-a*b)^(1/2)/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/b/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*a/b*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*(-a*b)^(1/2)/b^2*a*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4*a/b*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+(-a*b)^(1/2)/b^2/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*a/b*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*(-a*b)^(1/2)/b^2*a*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4*a/b*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/b/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/b/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
769,1,1453,103,0.017000," ","int(x^2/(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","-\frac{3 a \,d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{3 a \,d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}+\frac{3 \sqrt{-a b}\, d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{3 \sqrt{-a b}\, d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}-\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}+\frac{3 d x}{4 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}+\frac{3 d x}{4 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}+\frac{3 \sqrt{-a b}\, d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}-\frac{3 \sqrt{-a b}\, d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}+\frac{1}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}+\frac{1}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}+\frac{1}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{1}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}"," ",0,"1/4/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4/b/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/4/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4/b*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/b*a*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/b*(-a*b)^(1/2)*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4/b/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/4/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/4/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/b*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/b*a*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/b*(-a*b)^(1/2)*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
770,1,989,93,0.012000," ","int(x/(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{3 d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{3 d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{3 \sqrt{-a b}\, d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{3 \sqrt{-a b}\, d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{3 d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{3 d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a b c}+\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a b c}-\frac{\sqrt{-a b}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a b}+\frac{\sqrt{-a b}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a b}"," ",0,"-1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*(-a*b)^(1/2)/b*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/2*(-a*b)^(1/2)/a/b/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*(-a*b)^(1/2)/b*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2*(-a*b)^(1/2)/a/b/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x","B"
771,1,1461,122,0.014000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{3 d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{3 d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{3 \sqrt{-a b}\, d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{3 \sqrt{-a b}\, d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{b}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{b}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{d x}{4 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{d x}{4 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}+\frac{3 \sqrt{-a b}\, d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{3 \sqrt{-a b}\, d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{1}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{1}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}"," ",0,"-1/4/a/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4/a*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a*(-a*b)^(1/2)*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/a/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/4/a/(-a*b)^(1/2)/(a*d-b*c)*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/4/a/(-a*b)^(1/2)/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/a*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/a*(-a*b)^(1/2)*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a/(-a*b)^(1/2)/(a*d-b*c)*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a/(-a*b)^(1/2)/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
772,1,1672,144,0.016000," ","int(1/x/(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","-\frac{3 b \,d^{2} x}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{3 b \,d^{2} x}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}-\frac{3 b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{3 b d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{b d x}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{b d x}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}+\frac{3 b d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}+\frac{3 b d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}+\frac{b}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{b}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{b}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{b}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}-\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}-\frac{\ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{2} c^{\frac{3}{2}}}+\frac{1}{\sqrt{d \,x^{2}+c}\, a^{2} c}"," ",0,"1/2/a^2/(a*d-b*c)*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/a^2*(-a*b)^(1/2)/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/a^2/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4/(-a*b)^(1/2)/a/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4/a*d/(a*d-b*c)^2*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/(-a*b)^(1/2)*b*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a*d/(a*d-b*c)^2*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/2/(-a*b)^(1/2)/a/(a*d-b*c)*b/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/a^2/(a*d-b*c)*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/2/a^2*(-a*b)^(1/2)/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/a^2/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/(-a*b)^(1/2)/a/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4/a*d/(a*d-b*c)^2*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4/(-a*b)^(1/2)*b*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a*d/(a*d-b*c)^2*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/2/(-a*b)^(1/2)/a/(a*d-b*c)*b/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/a^2/c/(d*x^2+c)^(1/2)-1/a^2/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
773,1,1524,181,0.021000," ","int(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","-\frac{3 b \,d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{3 b \,d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{3 b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{3 b^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{3 \sqrt{-a b}\, b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{3 \sqrt{-a b}\, b d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{3 b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{3 b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{b d x}{4 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}-\frac{b d x}{4 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}-\frac{3 \sqrt{-a b}\, b d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{3 \sqrt{-a b}\, b d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{b}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{b}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{2 d x}{\sqrt{d \,x^{2}+c}\, a^{2} c^{2}}-\frac{1}{\sqrt{d \,x^{2}+c}\, a^{2} c x}"," ",0,"1/4/a^2/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^2*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/a*b*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^2*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/a^2/(a*d-b*c)*b/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-3/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*b/a^2/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+3/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4/a^2/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^2*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4/a*b*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^2*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/a^2/c/x/(d*x^2+c)^(1/2)-2/a^2*d/c^2*x/(d*x^2+c)^(1/2)","B"
774,1,1778,209,0.018000," ","int(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{3 b^{2} d^{2} x}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{3 b^{2} d^{2} x}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}+\frac{3 b^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{3 b^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{2} d x}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{b^{2} d x}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}-\frac{3 b^{2} d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{3 b^{2} d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{\left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{b^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{\left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{b^{2}}{\left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}-\frac{b^{2}}{\left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}-\frac{\sqrt{-a b}\, b d x}{\left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} c}+\frac{\sqrt{-a b}\, b d x}{\left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} c}+\frac{3 d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{2 a^{2} c^{\frac{5}{2}}}+\frac{2 b \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)}{a^{3} c^{\frac{3}{2}}}-\frac{3 d}{2 \sqrt{d \,x^{2}+c}\, a^{2} c^{2}}-\frac{2 b}{\sqrt{d \,x^{2}+c}\, a^{3} c}-\frac{1}{2 \sqrt{d \,x^{2}+c}\, a^{2} c \,x^{2}}"," ",0,"-b^2/a^3/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-b/a^3*(-a*b)^(1/2)/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+b^2/a^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*b^2/a^2*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*b^2/a/(-a*b)^(1/2)*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*b^2/a^2*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/2/a^2/c/x^2/(d*x^2+c)^(1/2)-3/2/a^2*d/c^2/(d*x^2+c)^(1/2)+3/2/a^2*d/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-b^2/a^3/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+b/a^3*(-a*b)^(1/2)/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+b^2/a^3/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*b^2/a^2*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*b^2/a/(-a*b)^(1/2)*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*b^2/a^2*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/2*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-2*b/a^3/c/(d*x^2+c)^(1/2)+2*b/a^3/c^(3/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)","B"
775,1,1608,249,0.020000," ","int(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{3 b^{2} d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{3 b^{2} d^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{5 b^{3} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{5 b^{3} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{3 \sqrt{-a b}\, b^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{3 \sqrt{-a b}\, b^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{5 b^{3}}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}-\frac{5 b^{3}}{4 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}+\frac{3 b^{2} d x}{4 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} c}+\frac{3 b^{2} d x}{4 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} c}-\frac{3 \sqrt{-a b}\, b^{2} d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}+\frac{3 \sqrt{-a b}\, b^{2} d}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}-\frac{b^{2}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}-\frac{b^{2}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}+\frac{8 d^{2} x}{3 \sqrt{d \,x^{2}+c}\, a^{2} c^{3}}+\frac{4 b d x}{\sqrt{d \,x^{2}+c}\, a^{3} c^{2}}+\frac{4 d}{3 \sqrt{d \,x^{2}+c}\, a^{2} c^{2} x}+\frac{2 b}{\sqrt{d \,x^{2}+c}\, a^{3} c x}-\frac{1}{3 \sqrt{d \,x^{2}+c}\, a^{2} c \,x^{3}}"," ",0,"5/4*b^3/a^3/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*b^2/a^3/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-5/4*b^3/a^3/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*b^2/a^3/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*b^2/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*b^2/a^2*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*b^2/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-5/4*b^3/a^3/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*b^2/a^3/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+5/4*b^3/a^3/(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4*b^2/a^3/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*b^2/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*b^2/a^2*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-3/4*b^2/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+2*b/a^3/c/x/(d*x^2+c)^(1/2)+4*b/a^3*d/c^2*x/(d*x^2+c)^(1/2)-1/3/a^2/c/x^3/(d*x^2+c)^(1/2)+4/3/a^2*d/c^2/x/(d*x^2+c)^(1/2)+8/3/a^2*d^2/c^3*x/(d*x^2+c)^(1/2)","B"
776,1,2463,150,0.027000," ","int(x^4/(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","-\frac{5 a^{2} d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{5 a^{2} d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}+\frac{5 a^{2} d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}+\frac{5 a^{2} d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}+\frac{5 \sqrt{-a b}\, a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{5 \sqrt{-a b}\, a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{3 a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}-\frac{3 a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{5 a^{2} d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}+\frac{5 a^{2} d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}+\frac{3 a d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}+\frac{3 a d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}+\frac{5 \sqrt{-a b}\, a d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}-\frac{5 \sqrt{-a b}\, a d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}-\frac{3 a}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{3 a}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{a}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}+\frac{a}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}-\frac{7 a d x}{12 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}-\frac{7 a d x}{12 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}-\frac{5 \sqrt{-a b}\, a d}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}+\frac{5 \sqrt{-a b}\, a d}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}-\frac{7 a d x}{6 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}-\frac{7 a d x}{6 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}-\frac{a}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}-\frac{a}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}+\frac{x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b^{2} c}+\frac{2 x}{3 \sqrt{d \,x^{2}+c}\, b^{2} c^{2}}"," ",0,"-3/4*a/(-a*b)^(1/2)/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+3/4*a/(-a*b)^(1/2)/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/3/b^2*x/c/(d*x^2+c)^(3/2)+2/3/b^2/c^2*x/(d*x^2+c)^(1/2)-5/12*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4*a/b*(-a*b)^(1/2)*d/(a*d-b*c)^3/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+5/12*a/b^2*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/4*a/b*(-a*b)^(1/2)*d/(a*d-b*c)^3/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*a/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/b*a/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4*a/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4*a/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/b*a/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/4*a/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+5/4*a/b*(-a*b)^(1/2)*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-7/12*a/b^2*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-7/6*a/b^2*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/12*a^2/b^2*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/6*a^2/b^2*d^2/(a*d-b*c)^2/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*a^2/b*d^2/(a*d-b*c)^3/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*a/b*(-a*b)^(1/2)*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/4/b*a/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-7/12/b^2*a*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-7/6/b^2*a*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4/b*a/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+5/12*a^2/b^2*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/6*a^2/b^2*d^2/(a*d-b*c)^2/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*a^2/b*d^2/(a*d-b*c)^3/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x","B"
777,1,2400,146,0.020000," ","int(x^3/(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","\frac{5 a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}}+\frac{5 a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}}+\frac{5 \sqrt{-a b}\, a \,d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{5 \sqrt{-a b}\, a \,d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{5 a d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{5 a d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{5 a d}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}+\frac{5 a d}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}+\frac{5 \sqrt{-a b}\, a \,d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}-\frac{5 \sqrt{-a b}\, a \,d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}-\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{5 \sqrt{-a b}\, a \,d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}-\frac{5 \sqrt{-a b}\, a \,d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}+\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b c}-\frac{1}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}-\frac{1}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}-\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}+\frac{\sqrt{-a b}\, d x}{2 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2} c}-\frac{\sqrt{-a b}\, d x}{\left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}+\frac{\sqrt{-a b}\, d x}{\left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2} c^{2}}+\frac{\sqrt{-a b}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}-\frac{\sqrt{-a b}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b^{2}}+\frac{1}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{1}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}"," ",0,"5/12*a/b*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4*a*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-5/4*a*d/(a*d-b*c)^3/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-5/4*a*d/(a*d-b*c)^3/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+5/4*(-a*b)^(1/2)/b*a*d^2/(a*d-b*c)^3/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/12*(-a*b)^(1/2)/b^2*a*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/6*(-a*b)^(1/2)/b^2*a*d^2/(a*d-b*c)^2/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*(-a*b)^(1/2)/b*a*d^2/(a*d-b*c)^3/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/12*(-a*b)^(1/2)/b^2*a*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-5/6*(-a*b)^(1/2)/b^2*a*d^2/(a*d-b*c)^2/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4*a*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/6/b/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/6/b/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/b^2*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2/b/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2*(-a*b)^(1/2)/b^2*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+(-a*b)^(1/2)/b^2*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2/b/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4*(-a*b)^(1/2)/b^2/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/12*a/b*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)","B"
778,1,2369,139,0.019000," ","int(x^2/(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","\frac{5 a \,d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{5 a \,d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}-\frac{5 a \,d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}-\frac{5 a \,d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}-\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}+\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}}-\frac{5 \sqrt{-a b}\, d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}}+\frac{5 \sqrt{-a b}\, d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}}-\frac{5 a \,d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}-\frac{5 a \,d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}+\frac{b}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{b}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}-\frac{d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{5 \sqrt{-a b}\, d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{5 \sqrt{-a b}\, d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{5 d x}{12 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}+\frac{5 d x}{12 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}+\frac{5 \sqrt{-a b}\, d}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}-\frac{5 \sqrt{-a b}\, d}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}+\frac{5 d x}{6 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}+\frac{5 d x}{6 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}+\frac{1}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}+\frac{1}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b}+\frac{1}{12 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}-\frac{1}{12 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}"," ",0,"-1/4/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/4/(-a*b)^(1/2)*b/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+5/4*a*d^2/(a*d-b*c)^3/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/12/b*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/6/b*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4*a*d^2/(a*d-b*c)^3/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/12/b*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/6/b*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/(-a*b)^(1/2)*b/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4*(-a*b)^(1/2)*d/(a*d-b*c)^3/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/4*(-a*b)^(1/2)*d/(a*d-b*c)^3/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/(-a*b)^(1/2)*b/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-5/4*(-a*b)^(1/2)*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/4/(-a*b)^(1/2)*b/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+5/4*(-a*b)^(1/2)*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+5/12/b*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/12/b*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/6/b*a*d^2/(a*d-b*c)^2/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/12/b*a*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-5/12/b*a*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-5/6/b*a*d^2/(a*d-b*c)^2/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/12/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/12/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)","B"
779,1,1639,116,0.016000," ","int(x/(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","-\frac{5 b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}}-\frac{5 b d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}}+\frac{5 b d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{5 b d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{5 \sqrt{-a b}\, d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{5 \sqrt{-a b}\, d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{5 \sqrt{-a b}\, d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}-\frac{5 \sqrt{-a b}\, d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} b c}-\frac{5 d}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}-\frac{5 d}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}}}+\frac{5 \sqrt{-a b}\, d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}-\frac{5 \sqrt{-a b}\, d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b \,c^{2}}-\frac{\sqrt{-a b}\, d x}{3 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a b c}+\frac{\sqrt{-a b}\, d x}{3 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a b c}-\frac{2 \sqrt{-a b}\, d x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a b \,c^{2}}+\frac{2 \sqrt{-a b}\, d x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a b \,c^{2}}-\frac{\sqrt{-a b}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a b}+\frac{\sqrt{-a b}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a b}"," ",0,"-1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/12*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/12*(-a*b)^(1/2)/b*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/6*(-a*b)^(1/2)/b*d^2/(a*d-b*c)^2/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4*b*d/(a*d-b*c)^3/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-5/4*(-a*b)^(1/2)*d^2/(a*d-b*c)^3/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*b*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/3*(-a*b)^(1/2)/a/b*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-2/3*(-a*b)^(1/2)/a/b*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/12*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/12*(-a*b)^(1/2)/b*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-5/6*(-a*b)^(1/2)/b*d^2/(a*d-b*c)^2/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4*b*d/(a*d-b*c)^3/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+5/4*(-a*b)^(1/2)*d^2/(a*d-b*c)^3/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*b*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/3*(-a*b)^(1/2)/a/b*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+2/3*(-a*b)^(1/2)/a/b*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x","B"
780,1,2405,177,0.017000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","-\frac{5 b \,d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}-\frac{5 b \,d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}-\frac{b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{b^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{5 \sqrt{-a b}\, b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{5 \sqrt{-a b}\, b d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{5 d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} c}+\frac{5 d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} c}-\frac{b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}+\frac{b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{b d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{b d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}+\frac{5 \sqrt{-a b}\, b d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}-\frac{5 \sqrt{-a b}\, b d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}+\frac{5 d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c^{2}}+\frac{5 d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c^{2}}+\frac{b}{12 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}-\frac{b}{12 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}-\frac{d x}{4 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a c}-\frac{d x}{4 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a c}-\frac{5 \sqrt{-a b}\, d}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}+\frac{5 \sqrt{-a b}\, d}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}-\frac{d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a \,c^{2}}-\frac{d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a \,c^{2}}-\frac{1}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}-\frac{1}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a}"," ",0,"-5/4*b*d^2/(a*d-b*c)^3/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/a*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/2/a*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4/a*b*(-a*b)^(1/2)*d/(a*d-b*c)^3/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-5/4*b*d^2/(a*d-b*c)^3/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4/a*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/2/a*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/(-a*b)^(1/2)/a*b^2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/(-a*b)^(1/2)/a*b^2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-5/4/a*b*(-a*b)^(1/2)*d/(a*d-b*c)^3/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/a/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4/(-a*b)^(1/2)/a*b^2/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/12/(-a*b)^(1/2)/a/(a*d-b*c)*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/12/(-a*b)^(1/2)/a/(a*d-b*c)*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/12/a*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/6*d^2/(a*d-b*c)^2/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/12*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-5/4/a*b*(-a*b)^(1/2)*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a*b/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+5/4/a*b*(-a*b)^(1/2)*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/a*b/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+5/12/a*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/12*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/6*d^2/(a*d-b*c)^2/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/4/(-a*b)^(1/2)/a*b^2/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)","B"
781,1,2837,195,0.019000," ","int(1/x/(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"1/4/(-a*b)^(1/2)/a/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4/a*d/(a*d-b*c)^3*b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/(-a*b)^(1/2)/a/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4/a*d/(a*d-b*c)^3*b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/6/a^2/(a*d-b*c)*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/a^2*b^2/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/6/a^2/(a*d-b*c)*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/2/a^2*b^2/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/3/(-a*b)^(1/2)/a*d/(a*d-b*c)*b/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+2/3/(-a*b)^(1/2)/a*d/(a*d-b*c)*b/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/2/a^2*b/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-1/3/(-a*b)^(1/2)/a*d/(a*d-b*c)*b/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-2/3/(-a*b)^(1/2)/a*d/(a*d-b*c)*b/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/2/a^2*b/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/2/a^2*b^2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+5/12/a*d/(a*d-b*c)^2*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/4/a*d/(a*d-b*c)^3*b^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/2/a^2*b^2/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/6/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-1/3/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/12/(-a*b)^(1/2)*b*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-5/6/(-a*b)^(1/2)*b*d^2/(a*d-b*c)^2/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4/(-a*b)^(1/2)*b^2*d^2/(a*d-b*c)^3/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4/(-a*b)^(1/2)*b^2*d^2/(a*d-b*c)^3/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/12/a*d/(a*d-b*c)^2*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/4/a*d/(a*d-b*c)^3*b^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+5/12/(-a*b)^(1/2)*b*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/6/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/3/a^2*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/6/(-a*b)^(1/2)*b*d^2/(a*d-b*c)^2/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/a^2/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)+1/3/a^2/c/(d*x^2+c)^(3/2)+1/a^2/c^2/(d*x^2+c)^(1/2)","B"
782,1,2513,251,0.023000," ","int(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","\frac{5 b^{2} d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}+\frac{5 b^{2} d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a c}-\frac{5 b \,d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a c}-\frac{5 b \,d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a c}+\frac{3 b^{3} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{3 b^{3} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{5 \sqrt{-a b}\, b^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{5 \sqrt{-a b}\, b^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{5 b \,d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a \,c^{2}}-\frac{5 b \,d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a \,c^{2}}+\frac{3 b^{3}}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{3 b^{3}}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}+\frac{3 b^{2} d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{3 b^{2} d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{5 \sqrt{-a b}\, b^{2} d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{5 \sqrt{-a b}\, b^{2} d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}-\frac{b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}+\frac{b^{2}}{4 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}+\frac{b d x}{12 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2} c}+\frac{b d x}{12 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2} c}-\frac{5 \sqrt{-a b}\, b d}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}+\frac{5 \sqrt{-a b}\, b d}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}+\frac{b d x}{6 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c^{2}}+\frac{b d x}{6 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c^{2}}+\frac{b}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}+\frac{b}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2}}-\frac{4 d x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c^{2}}-\frac{8 d x}{3 \sqrt{d \,x^{2}+c}\, a^{2} c^{3}}-\frac{1}{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c x}"," ",0,"-5/12/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^2*b/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^3*b^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+5/12/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^2*b/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^3*b^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-3/4*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/4*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/a^2/c/x/(d*x^2+c)^(3/2)-1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+3/4*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a^2/(a*d-b*c)*b/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4/a^2/(a*d-b*c)*b/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-3/4*b^3/a^2/(-a*b)^(1/2)/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-4/3/a^2*d/c^2*x/(d*x^2+c)^(3/2)-8/3/a^2*d/c^3*x/(d*x^2+c)^(1/2)-5/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^3*b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+5/4/a*b^2*d^2/(a*d-b*c)^3/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*b^2/a^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-5/12/a*b*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-5/6/a*b*d^2/(a*d-b*c)^2/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4/a*b^2*d^2/(a*d-b*c)^3/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4/a^2*(-a*b)^(1/2)*d/(a*d-b*c)^3*b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/12*b/a^2*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/6*b/a^2*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/12/a*b*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-5/6/a*b*d^2/(a*d-b*c)^2/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/12/a^2*d/(a*d-b*c)*b/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/6/a^2*d/(a*d-b*c)*b/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+3/4*b^2/a^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x","B"
783,1,2980,268,0.020000," ","int(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"-5/4*b^3/a^2*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-5/4*b^3/a^2*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-1/4*b^2/a^2/(-a*b)^(1/2)/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-2*b/a^3/c^2/(d*x^2+c)^(1/2)+2*b/a^3/c^(5/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/2/a^2/c/x^2/(d*x^2+c)^(3/2)-5/6/a^2*d/c^2/(d*x^2+c)^(3/2)-5/2/a^2*d/c^3/(d*x^2+c)^(1/2)+5/2/a^2*d/c^(7/2)*ln((2*c+2*(d*x^2+c)^(1/2)*c^(1/2))/x)-1/3*b^2/a^3/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+b^3/a^3/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/3*b^2/a^3/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+b^3/a^3/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-2/3*b/a^3/c/(d*x^2+c)^(3/2)-b^2/a^3/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x-5/12*b^2/a^2*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4*b^3/a^2*d/(a*d-b*c)^3/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-b^3/a^3/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-5/12*b^2/a^2*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4*b^3/a^2*d/(a*d-b*c)^3/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-b^3/a^3/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-5/12*b^2/a/(-a*b)^(1/2)*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-5/6*b^2/a/(-a*b)^(1/2)*d^2/(a*d-b*c)^2/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/4*b^3/a/(-a*b)^(1/2)*d^2/(a*d-b*c)^3/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/3*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+2/3*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/3*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-2/3*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+b^2/a^3/(a*d-b*c)^2*(-a*b)^(1/2)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+5/12*b^2/a/(-a*b)^(1/2)*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/6*b^2/a/(-a*b)^(1/2)*d^2/(a*d-b*c)^2/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*b^3/a/(-a*b)^(1/2)*d^2/(a*d-b*c)^3/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/3*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x-2/3*b^2/a^2/(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+1/3*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+2/3*b/a^3*(-a*b)^(1/2)*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x","B"
784,1,2623,330,0.024000," ","int(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","-\frac{5 b^{3} d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}-\frac{5 b^{3} d^{2} x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c}+\frac{5 b^{2} d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2} c}+\frac{5 b^{2} d^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{2} c}-\frac{5 b^{4} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{5 b^{4} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{5 \sqrt{-a b}\, b^{3} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{5 \sqrt{-a b}\, b^{3} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{5 b^{2} d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c^{2}}+\frac{5 b^{2} d^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2} c^{2}}-\frac{5 b^{4}}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}+\frac{5 b^{4}}{4 \sqrt{-a b}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}-\frac{5 b^{3} d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} c}-\frac{5 b^{3} d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} c}+\frac{5 \sqrt{-a b}\, b^{3} d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}-\frac{5 \sqrt{-a b}\, b^{3} d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3}}+\frac{5 b^{3}}{12 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{3}}-\frac{5 b^{3}}{12 \sqrt{-a b}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{3}}+\frac{b^{2} d x}{12 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{3} c}+\frac{b^{2} d x}{12 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{3} c}-\frac{5 \sqrt{-a b}\, b^{2} d}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{3}}+\frac{5 \sqrt{-a b}\, b^{2} d}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{3}}+\frac{b^{2} d x}{6 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} c^{2}}+\frac{b^{2} d x}{6 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{3} c^{2}}-\frac{b^{2}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) \left(\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{3}}-\frac{b^{2}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) \left(\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}\right)^{\frac{3}{2}} a^{3}}+\frac{8 d^{2} x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c^{3}}+\frac{8 b d x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{3} c^{2}}+\frac{16 d^{2} x}{3 \sqrt{d \,x^{2}+c}\, a^{2} c^{4}}+\frac{16 b d x}{3 \sqrt{d \,x^{2}+c}\, a^{3} c^{3}}+\frac{2 d}{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c^{2} x}+\frac{2 b}{\left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{3} c x}-\frac{1}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a^{2} c \,x^{3}}"," ",0,"5/4*b^4/a^3/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+8/3*b/a^3*d/c^2*x/(d*x^2+c)^(3/2)+16/3*b/a^3*d/c^3*x/(d*x^2+c)^(1/2)-5/12*b^2/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4*b^3/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^3/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+5/12*b^2/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/4*b^3/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^3/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-5/4*b^4/a^3/(-a*b)^(1/2)/(a*d-b*c)^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/3/a^2/c/x^3/(d*x^2+c)^(3/2)-5/4*b^3/a^3/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+5/12*b^2/a^2*d^2/(a*d-b*c)^2/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/6*b^2/a^2*d^2/(a*d-b*c)^2/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*b^3/a^2*d^2/(a*d-b*c)^3/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x+5/6*b^2/a^2*d^2/(a*d-b*c)^2/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*b^3/a^2*d^2/(a*d-b*c)^3/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*b^3/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/12*b^2/a^3*d/(a*d-b*c)/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/6*b^2/a^3*d/(a*d-b*c)/c^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-5/4*b^3/a^3/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*d*x+1/12*b^2/a^3*d/(a*d-b*c)/c/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+1/6*b^2/a^3*d/(a*d-b*c)/c^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)*x-1/4*b^2/a^3/(a*d-b*c)/(x+(-a*b)^(1/2)/b)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/12*b^3/a^3/(-a*b)^(1/2)/(a*d-b*c)/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/4*b^4/a^3/(-a*b)^(1/2)/(a*d-b*c)^2/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*b^2/a^3/(a*d-b*c)/(x-(-a*b)^(1/2)/b)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)-5/12*b^3/a^3/(-a*b)^(1/2)/(a*d-b*c)/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)+5/4*b^4/a^3/(-a*b)^(1/2)/(a*d-b*c)^2/((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+2*b/a^3/c/x/(d*x^2+c)^(3/2)+2/a^2*d/c^2/x/(d*x^2+c)^(3/2)+8/3/a^2*d^2/c^3*x/(d*x^2+c)^(3/2)+16/3/a^2*d^2/c^4*x/(d*x^2+c)^(1/2)+5/12*b^2/a^2*d^2/(a*d-b*c)^2/c/((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(3/2)*x+5/4*b^3/a^3*(-a*b)^(1/2)*d/(a*d-b*c)^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
785,1,276,213,0.132000," ","int((e*x)^(3/2)*(B*x^2+A)*(b*x^2+a)^(1/2),x)","-\frac{2 \sqrt{e x}\, \left(-21 B \,b^{4} x^{7}-33 A \,b^{4} x^{5}-27 B a \,b^{3} x^{5}-55 A a \,b^{3} x^{3}+4 B \,a^{2} b^{2} x^{3}-22 A \,a^{2} b^{2} x +10 B \,a^{3} b x +11 \sqrt{2}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A \,a^{2} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) e}{231 \sqrt{b \,x^{2}+a}\, b^{3} x}"," ",0,"-2/231*e/x*(e*x)^(1/2)/(b*x^2+a)^(1/2)*(-21*B*x^7*b^4+11*A*2^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-x/(-a*b)^(1/2)*b)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^2*b-33*A*x^5*b^4-5*B*2^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-x/(-a*b)^(1/2)*b)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^3-27*B*x^5*a*b^3-55*A*x^3*a*b^3+4*B*x^3*a^2*b^2-22*A*x*a^2*b^2+10*B*x*a^3*b)/b^3","A"
786,1,414,351,0.043000," ","int((B*x^2+A)*(e*x)^(1/2)*(b*x^2+a)^(1/2),x)","\frac{2 \sqrt{e x}\, \left(5 B \,b^{3} x^{6}+9 A \,b^{3} x^{4}+7 B a \,b^{2} x^{4}+9 A a \,b^{2} x^{2}+2 B \,a^{2} b \,x^{2}+18 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-9 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right)}{45 \sqrt{b \,x^{2}+a}\, b^{2} x}"," ",0,"2/45*(e*x)^(1/2)/(b*x^2+a)^(1/2)/b^2*(5*B*x^6*b^3+18*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-9*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3+3*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3+9*A*b^3*x^4+7*B*a*b^2*x^4+9*A*a*b^2*x^2+2*B*a^2*b*x^2)/x","A"
787,1,246,183,0.035000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(1/2),x)","\frac{\frac{2 B \,b^{3} x^{5}}{7}+\frac{2 A \,b^{3} x^{3}}{3}+\frac{10 B a \,b^{2} x^{3}}{21}+\frac{2 A a \,b^{2} x}{3}+\frac{4 B \,a^{2} b x}{21}+\frac{2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3}-\frac{2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{21}}{\sqrt{b \,x^{2}+a}\, \sqrt{e x}\, b^{2}}"," ",0,"2/21/(b*x^2+a)^(1/2)*(7*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a*b-B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^2+3*B*x^5*b^3+7*A*x^3*b^3+5*B*x^3*a*b^2+7*A*x*a*b^2+2*B*x*a^2*b)/(e*x)^(1/2)/b^2","A"
788,1,391,349,0.051000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(3/2),x)","\frac{\frac{2 B \,b^{2} x^{4}}{5}-2 A \,b^{2} x^{2}+\frac{2 B a b \,x^{2}}{5}+4 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+\frac{4 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}-2 A a b}{\sqrt{b \,x^{2}+a}\, \sqrt{e x}\, b e}"," ",0,"2/5*(10*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-5*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b+2*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2-B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2+B*b^2*x^4-5*A*b^2*x^2+B*a*b*x^2-5*A*a*b)/(b*x^2+a)^(1/2)/b/e/(e*x)^(1/2)","A"
789,1,234,179,0.049000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(5/2),x)","\frac{\frac{2 B \,b^{2} x^{4}}{3}-\frac{2 A \,b^{2} x^{2}}{3}+\frac{2 B a b \,x^{2}}{3}+\frac{2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A b x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3}+\frac{2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B a x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3}-\frac{2 A a b}{3}}{\sqrt{b \,x^{2}+a}\, \sqrt{e x}\, b \,e^{2} x}"," ",0,"2/3/(b*x^2+a)^(1/2)/x*(A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*b+B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*a+B*b^2*x^4-A*b^2*x^2+B*a*b*x^2-A*a*b)/e^2/(e*x)^(1/2)/b","A"
790,1,417,352,0.047000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(7/2),x)","\frac{-\frac{4 A \,b^{2} x^{4}}{5}-2 B a b \,x^{4}+\frac{4 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \,x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}+4 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-\frac{6 A a b \,x^{2}}{5}-2 B \,a^{2} x^{2}-\frac{2 A \,a^{2}}{5}}{\sqrt{b \,x^{2}+a}\, \sqrt{e x}\, a \,e^{3} x^{2}}"," ",0,"2/5/x^2*(2*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b-A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b+10*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2-5*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2-2*A*b^2*x^4-5*B*x^4*a*b-3*A*a*b*x^2-5*B*a^2*x^2-A*a^2)/(b*x^2+a)^(1/2)/e^3/(e*x)^(1/2)/a","A"
791,1,242,153,0.051000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^(9/2),x)","-\frac{2 \left(2 A \,b^{2} x^{4}+7 B a b \,x^{4}+\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A b \,x^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-7 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B a \,x^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+5 A a b \,x^{2}+7 B \,a^{2} x^{2}+3 A \,a^{2}\right)}{21 \sqrt{b \,x^{2}+a}\, a \,x^{\frac{7}{2}}}"," ",0,"-2/21/(b*x^2+a)^(1/2)*(A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x^3*b-7*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x^3*a+2*A*b^2*x^4+7*B*a*b*x^4+5*A*a*b*x^2+7*B*a^2*x^2+3*A*a^2)/x^(7/2)/a","A"
792,1,439,327,0.069000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^(11/2),x)","-\frac{2 \left(-6 A \,b^{3} x^{6}+18 B a \,b^{2} x^{6}+6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a \,b^{2} x^{4} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a \,b^{2} x^{4} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-18 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} b \,x^{4} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+9 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} b \,x^{4} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-4 A a \,b^{2} x^{4}+27 B \,a^{2} b \,x^{4}+7 A \,a^{2} b \,x^{2}+9 B \,a^{3} x^{2}+5 A \,a^{3}\right)}{45 \sqrt{b \,x^{2}+a}\, a^{2} x^{\frac{9}{2}}}"," ",0,"-2/45*(6*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a*b^2-3*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a*b^2-18*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^2*b+9*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^2*b-6*A*x^6*b^3+18*B*a*b^2*x^6-4*A*x^4*a*b^2+27*B*x^4*a^2*b+7*A*x^2*a^2*b+9*B*x^2*a^3+5*A*a^3)/(b*x^2+a)^(1/2)/x^(9/2)/a^2","A"
793,1,270,182,0.042000," ","int((B*x^2+A)*(b*x^2+a)^(1/2)/x^(13/2),x)","\frac{\frac{20 A \,b^{3} x^{6}}{231}-\frac{4 B a \,b^{2} x^{6}}{21}+\frac{10 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A \,b^{2} x^{5} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{231}-\frac{2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B a b \,x^{5} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{21}+\frac{8 A a \,b^{2} x^{4}}{231}-\frac{10 B \,a^{2} b \,x^{4}}{21}-\frac{18 A \,a^{2} b \,x^{2}}{77}-\frac{2 B \,a^{3} x^{2}}{7}-\frac{2 A \,a^{3}}{11}}{\sqrt{b \,x^{2}+a}\, a^{2} x^{\frac{11}{2}}}"," ",0,"2/231/(b*x^2+a)^(1/2)*(5*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x^5*b^2-11*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x^5*a*b+10*A*b^3*x^6-22*B*a*b^2*x^6+4*A*a*b^2*x^4-55*B*a^2*b*x^4-27*A*a^2*b*x^2-33*B*a^3*x^2-21*A*a^3)/x^(11/2)/a^2","A"
794,1,300,247,0.036000," ","int((e*x)^(3/2)*(b*x^2+a)^(3/2)*(B*x^2+A),x)","-\frac{2 \sqrt{e x}\, \left(-77 B \,b^{5} x^{9}-105 A \,b^{5} x^{7}-196 B a \,b^{4} x^{7}-300 A a \,b^{4} x^{5}-131 B \,a^{2} b^{3} x^{5}-255 A \,a^{2} b^{3} x^{3}+8 B \,a^{3} b^{2} x^{3}-60 A \,a^{3} b^{2} x +20 B \,a^{4} b x +30 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A \,a^{3} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{4} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) e}{1155 \sqrt{b \,x^{2}+a}\, b^{3} x}"," ",0,"-2/1155*e/x*(e*x)^(1/2)/(b*x^2+a)^(1/2)*(-77*B*b^5*x^9-105*A*x^7*b^5-196*B*x^7*a*b^4+30*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^3*b-300*A*x^5*a*b^4-10*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^4-131*B*x^5*a^2*b^3-255*A*x^3*a^2*b^3+8*B*x^3*a^3*b^2-60*A*x*a^3*b^2+20*B*x*a^4*b)/b^3","A"
795,1,438,385,0.032000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)*(e*x)^(1/2),x)","\frac{2 \sqrt{e x}\, \left(45 B \,b^{4} x^{8}+65 A \,b^{4} x^{6}+120 B a \,b^{3} x^{6}+208 A a \,b^{3} x^{4}+87 B \,a^{2} b^{2} x^{4}+143 A \,a^{2} b^{2} x^{2}+12 B \,a^{3} b \,x^{2}+156 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{3} b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-78 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{3} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-36 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{4} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+18 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{4} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right)}{585 \sqrt{b \,x^{2}+a}\, b^{2} x}"," ",0,"2/585/(b*x^2+a)^(1/2)*(e*x)^(1/2)/b^2*(45*x^8*B*b^4+65*A*x^6*b^4+120*B*x^6*a*b^3+156*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b-78*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b-36*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^4+18*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^4+208*A*x^4*a*b^3+87*B*x^4*a^2*b^2+143*A*x^2*a^2*b^2+12*B*x^2*a^3*b)/x","A"
796,1,272,215,0.017000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(1/2),x)","\frac{\frac{2 B \,b^{4} x^{7}}{11}+\frac{2 A \,b^{4} x^{5}}{7}+\frac{40 B a \,b^{3} x^{5}}{77}+\frac{8 A a \,b^{3} x^{3}}{7}+\frac{34 B \,a^{2} b^{2} x^{3}}{77}+\frac{6 A \,a^{2} b^{2} x}{7}+\frac{8 B \,a^{3} b x}{77}+\frac{4 \sqrt{2}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A \,a^{2} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{7}-\frac{4 \sqrt{2}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{77}}{\sqrt{b \,x^{2}+a}\, \sqrt{e x}\, b^{2}}"," ",0,"2/77/(b*x^2+a)^(1/2)*(7*B*b^4*x^7+22*A*2^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^2*b+11*A*b^4*x^5-2*B*2^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^3+20*B*a*b^3*x^5+44*A*a*b^3*x^3+17*B*a^2*b^2*x^3+33*A*a^2*b^2*x+4*B*a^3*b*x)/b^2/(e*x)^(1/2)","A"
797,1,421,377,0.023000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(3/2),x)","\frac{\frac{2 B \,b^{3} x^{6}}{9}+\frac{2 A \,b^{3} x^{4}}{5}+\frac{32 B a \,b^{2} x^{4}}{45}-\frac{8 A a \,b^{2} x^{2}}{5}+\frac{22 B \,a^{2} b \,x^{2}}{45}+\frac{24 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{12 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{8 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{15}-\frac{4 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{15}-2 A \,a^{2} b}{\sqrt{b \,x^{2}+a}\, \sqrt{e x}\, b e}"," ",0,"2/45*(5*B*b^3*x^6+108*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-54*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b+12*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3-6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3+9*A*b^3*x^4+16*B*a*b^2*x^4-36*A*a*b^2*x^2+11*B*a^2*b*x^2-45*A*a^2*b)/(b*x^2+a)^(1/2)/b/e/(e*x)^(1/2)","A"
798,1,255,211,0.020000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(5/2),x)","\frac{\frac{2 B \,b^{3} x^{6}}{7}+\frac{2 A \,b^{3} x^{4}}{3}+\frac{8 B a \,b^{2} x^{4}}{7}+\frac{6 B \,a^{2} b \,x^{2}}{7}+\frac{4 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A a b x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3}+\frac{4 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{2} x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{7}-\frac{2 A \,a^{2} b}{3}}{\sqrt{b \,x^{2}+a}\, \sqrt{e x}\, b \,e^{2} x}"," ",0,"2/21/(b*x^2+a)^(1/2)/x*(14*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*a*b+6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*a^2+3*B*b^3*x^6+7*A*b^3*x^4+12*B*a*b^2*x^4+9*B*a^2*b*x^2-7*A*a^2*b)/b/e^2/(e*x)^(1/2)","A"
799,1,422,375,0.023000," ","int((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(7/2),x)","\frac{\frac{2 B \,b^{2} x^{6}}{5}-\frac{14 A \,b^{2} x^{4}}{5}-\frac{8 B a b \,x^{4}}{5}+\frac{24 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \,x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{12 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{24 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{12 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{16 A a b \,x^{2}}{5}-2 B \,a^{2} x^{2}-\frac{2 A \,a^{2}}{5}}{\sqrt{b \,x^{2}+a}\, \sqrt{e x}\, e^{3} x^{2}}"," ",0,"2/5/x^2*(12*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b-6*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b+12*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2-6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2+B*x^6*b^2-7*A*b^2*x^4-4*B*a*b*x^4-8*A*a*b*x^2-5*B*a^2*x^2-A*a^2)/(b*x^2+a)^(1/2)/e^3/(e*x)^(1/2)","A"
800,1,417,352,0.037000," ","int((e*x)^(5/2)*(B*x^2+A)/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{e x}\, \left(-10 B \,b^{3} x^{6}-18 A \,b^{3} x^{4}+4 B a \,b^{2} x^{4}-18 A a \,b^{2} x^{2}+14 B \,a^{2} b \,x^{2}+54 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-27 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) e^{2}}{45 \sqrt{b \,x^{2}+a}\, b^{3} x}"," ",0,"-1/45*e^2/x*(e*x)^(1/2)/(b*x^2+a)^(1/2)/b^3*(-10*B*b^3*x^6+54*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-27*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-42*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3+21*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3-18*A*b^3*x^4+4*B*a*b^2*x^4-18*A*a*b^2*x^2+14*B*a^2*b*x^2)","A"
801,1,250,181,0.036000," ","int((e*x)^(3/2)*(B*x^2+A)/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{e x}\, \left(-6 B \,b^{3} x^{5}-14 A \,b^{3} x^{3}+4 B a \,b^{2} x^{3}-14 A a \,b^{2} x +10 B \,a^{2} b x +7 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) e}{21 \sqrt{b \,x^{2}+a}\, b^{3} x}"," ",0,"-1/21*e/x*(e*x)^(1/2)/(b*x^2+a)^(1/2)*(7*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a*b-5*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^2-6*B*b^3*x^5-14*A*b^3*x^3+4*B*a*b^2*x^3-14*A*a*b^2*x+10*B*a^2*b*x)/b^3","A"
802,1,379,319,0.018000," ","int((B*x^2+A)*(e*x)^(1/2)/(b*x^2+a)^(1/2),x)","\frac{\sqrt{e x}\, \left(2 B \,b^{2} x^{4}+2 B a b \,x^{2}+10 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right)}{5 \sqrt{b \,x^{2}+a}\, b^{2} x}"," ",0,"1/5*(e*x)^(1/2)/(b*x^2+a)^(1/2)/b^2*(10*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-5*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2+3*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2+2*B*b^2*x^4+2*B*a*b*x^2)/x","A"
803,1,214,152,0.017000," ","int((B*x^2+A)/(e*x)^(1/2)/(b*x^2+a)^(1/2),x)","\frac{2 B \,b^{2} x^{3}+2 B a b x +3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B a \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{b \,x^{2}+a}\, \sqrt{e x}\, b^{2}}"," ",0,"1/3/(b*x^2+a)^(1/2)*(3*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*b-B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a+2*B*b^2*x^3+2*B*x*a*b)/(e*x)^(1/2)/b^2","A"
804,1,378,318,0.023000," ","int((B*x^2+A)/(e*x)^(3/2)/(b*x^2+a)^(1/2),x)","\frac{-2 A \,b^{2} x^{2}+2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-2 A a b}{\sqrt{b \,x^{2}+a}\, \sqrt{e x}\, a b e}"," ",0,"(2*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b+2*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2-B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2-2*A*b^2*x^2-2*A*a*b)/(b*x^2+a)^(1/2)/b/e/(e*x)^(1/2)/a","A"
805,1,223,151,0.020000," ","int((B*x^2+A)/(e*x)^(5/2)/(b*x^2+a)^(1/2),x)","-\frac{2 A \,b^{2} x^{2}+\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A b x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B a x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+2 A a b}{3 \sqrt{b \,x^{2}+a}\, \sqrt{e x}\, a b \,e^{2} x}"," ",0,"-1/3/(b*x^2+a)^(1/2)/x*(A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*b-3*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*a+2*A*b^2*x^2+2*A*a*b)/b/a/e^2/(e*x)^(1/2)","A"
806,1,417,356,0.023000," ","int((B*x^2+A)/(e*x)^(7/2)/(b*x^2+a)^(1/2),x)","-\frac{-6 A \,b^{2} x^{4}+10 B a b \,x^{4}+6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \,x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-4 A a b \,x^{2}+10 B \,a^{2} x^{2}+2 A \,a^{2}}{5 \sqrt{b \,x^{2}+a}\, \sqrt{e x}\, a^{2} e^{3} x^{2}}"," ",0,"-1/5/x^2*(6*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b-3*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b-10*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2+5*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2-6*A*b^2*x^4+10*B*a*b*x^4-4*A*a*b*x^2+10*B*a^2*x^2+2*A*a^2)/(b*x^2+a)^(1/2)/e^3/(e*x)^(1/2)/a^2","A"
807,1,252,212,0.048000," ","int((e*x)^(7/2)*(B*x^2+A)/(b*x^2+a)^(3/2),x)","-\frac{\sqrt{e x}\, \left(-12 B \,b^{3} x^{5}-28 A \,b^{3} x^{3}+36 B a \,b^{2} x^{3}-70 A a \,b^{2} x +90 B \,a^{2} b x +35 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-45 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) e^{3}}{42 \sqrt{b \,x^{2}+a}\, b^{4} x}"," ",0,"-1/42*e^3/x*(e*x)^(1/2)*(35*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a*b-45*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^2-12*B*b^3*x^5-28*A*b^3*x^3+36*B*a*b^2*x^3-70*A*a*b^2*x+90*B*a^2*b*x)/(b*x^2+a)^(1/2)/b^4","A"
808,1,391,351,0.049000," ","int((e*x)^(5/2)*(B*x^2+A)/(b*x^2+a)^(3/2),x)","\frac{\sqrt{e x}\, \left(4 B \,b^{2} x^{4}-10 A \,b^{2} x^{2}+14 B a b \,x^{2}+30 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) e^{2}}{10 \sqrt{b \,x^{2}+a}\, b^{3} x}"," ",0,"1/10*e^2/x*(e*x)^(1/2)*(30*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-15*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-42*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2+21*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2+4*B*b^2*x^4-10*A*b^2*x^2+14*B*a*b*x^2)/(b*x^2+a)^(1/2)/b^3","A"
809,1,225,181,0.023000," ","int((e*x)^(3/2)*(B*x^2+A)/(b*x^2+a)^(3/2),x)","\frac{\sqrt{e x}\, \left(4 B \,b^{2} x^{3}-6 A \,b^{2} x +10 B a b x +3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B a \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) e}{6 \sqrt{b \,x^{2}+a}\, b^{3} x}"," ",0,"1/6*e/x*(e*x)^(1/2)*(3*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*b-5*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a+4*B*b^2*x^3-6*A*x*b^2+10*B*a*b*x)/(b*x^2+a)^(1/2)/b^3","A"
810,1,382,327,0.020000," ","int((B*x^2+A)*(e*x)^(1/2)/(b*x^2+a)^(3/2),x)","-\frac{\sqrt{e x}\, \left(-2 A \,b^{2} x^{2}+2 B a b \,x^{2}+2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right)}{2 \sqrt{b \,x^{2}+a}\, a \,b^{2} x}"," ",0,"-1/2*(e*x)^(1/2)*(2*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2+3*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2-2*A*b^2*x^2+2*B*a*b*x^2)/(b*x^2+a)^(1/2)/b^2/x/a","A"
811,1,213,159,0.022000," ","int((B*x^2+A)/(b*x^2+a)^(3/2)/(e*x)^(1/2),x)","\frac{2 A \,b^{2} x -2 B a b x +\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B a \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{b \,x^{2}+a}\, \sqrt{e x}\, a \,b^{2}}"," ",0,"1/2*(A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*b+B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a+2*A*b^2*x-2*B*a*b*x)/(b*x^2+a)^(1/2)/a/(e*x)^(1/2)/b^2","A"
812,1,386,355,0.023000," ","int((B*x^2+A)/(e*x)^(3/2)/(b*x^2+a)^(3/2),x)","\frac{-6 A \,b^{2} x^{2}+2 B a b \,x^{2}+6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-4 A a b}{2 \sqrt{b \,x^{2}+a}\, \sqrt{e x}\, a^{2} b e}"," ",0,"1/2*(6*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-3*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a*b-2*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2+B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2-6*A*b^2*x^2+2*B*a*b*x^2-4*A*a*b)/(b*x^2+a)^(1/2)/b/e/(e*x)^(1/2)/a^2","A"
813,1,232,183,0.024000," ","int((B*x^2+A)/(e*x)^(5/2)/(b*x^2+a)^(3/2),x)","-\frac{10 A \,b^{2} x^{2}-6 B a b \,x^{2}+5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A b x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B a x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+4 A a b}{6 \sqrt{b \,x^{2}+a}\, \sqrt{e x}\, a^{2} b \,e^{2} x}"," ",0,"-1/6/x*(5*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*b-3*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*a+10*A*b^2*x^2-6*B*a*b*x^2+4*A*a*b)/(b*x^2+a)^(1/2)/b/a^2/e^2/(e*x)^(1/2)","A"
814,1,417,387,0.026000," ","int((B*x^2+A)/(e*x)^(7/2)/(b*x^2+a)^(3/2),x)","-\frac{-42 A \,b^{2} x^{4}+30 B a b \,x^{4}+42 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \,x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-30 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-28 A a b \,x^{2}+20 B \,a^{2} x^{2}+4 A \,a^{2}}{10 \sqrt{b \,x^{2}+a}\, \sqrt{e x}\, a^{3} e^{3} x^{2}}"," ",0,"-1/10/x^2*(42*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b-21*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b-30*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2+15*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2-42*A*b^2*x^4+30*B*a*b*x^4-28*A*a*b*x^2+20*B*a^2*x^2+4*A*a^2)/(b*x^2+a)^(1/2)/e^3/(e*x)^(1/2)/a^3","A"
815,1,439,209,0.054000," ","int((e*x)^(7/2)*(B*x^2+A)/(b*x^2+a)^(5/2),x)","\frac{\left(8 B \,b^{3} x^{5}-14 A \,b^{3} x^{3}+42 B a \,b^{2} x^{3}+5 \sqrt{-a b}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,b^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{-a b}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B a b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-10 A a \,b^{2} x +30 B \,a^{2} b x +5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{e x}\, e^{3}}{12 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{4} x}"," ",0,"1/12*(5*A*(-a*b)^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2-15*B*(-a*b)^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b+5*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a*b-15*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^2+8*B*b^3*x^5-14*A*b^3*x^3+42*B*a*b^2*x^3-10*A*a*b^2*x+30*B*a^2*b*x)*e^3/x*(e*x)^(1/2)/b^4/(b*x^2+a)^(3/2)","B"
816,1,767,363,0.053000," ","int((e*x)^(5/2)*(B*x^2+A)/(b*x^2+a)^(5/2),x)","-\frac{\left(-6 A \,b^{3} x^{4}+18 B a \,b^{2} x^{4}+6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a \,b^{2} x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a \,b^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} b \,x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-2 A a \,b^{2} x^{2}+14 B \,a^{2} b \,x^{2}+6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{e x}\, e^{2}}{12 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,b^{3} x}"," ",0,"-1/12*(6*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2-3*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2-42*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b+21*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b+6*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-3*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-42*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3+21*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3-6*A*b^3*x^4+18*B*a*b^2*x^4-2*A*a*b^2*x^2+14*B*a^2*b*x^2)*e^2/x*(e*x)^(1/2)/b^3/a/(b*x^2+a)^(3/2)","B"
817,1,429,192,0.021000," ","int((e*x)^(3/2)*(B*x^2+A)/(b*x^2+a)^(5/2),x)","\frac{\left(2 A \,b^{3} x^{3}-14 B a \,b^{2} x^{3}+\sqrt{-a b}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,b^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{-a b}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B a b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-2 A a \,b^{2} x -10 B \,a^{2} b x +\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{e x}\, e}{12 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,b^{3} x}"," ",0,"1/12*(A*(-a*b)^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2+5*B*(-a*b)^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b+A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a*b+5*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^2+2*A*b^3*x^3-14*B*a*b^2*x^3-2*A*a*b^2*x-10*B*a^2*b*x)*e/x*(e*x)^(1/2)/a/b^3/(b*x^2+a)^(3/2)","B"
818,1,764,358,0.024000," ","int((B*x^2+A)*(e*x)^(1/2)/(b*x^2+a)^(5/2),x)","-\frac{\left(-6 A \,b^{3} x^{4}-6 B a \,b^{2} x^{4}+6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a \,b^{2} x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a \,b^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} b \,x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-10 A a \,b^{2} x^{2}-2 B \,a^{2} b \,x^{2}+6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{e x}}{12 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} b^{2} x}"," ",0,"-1/12*(6*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2-3*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2+6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b-3*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b+6*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-3*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b+6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3-3*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3-6*A*b^3*x^4-6*B*a*b^2*x^4-10*A*a*b^2*x^2-2*B*a^2*b*x^2)*(e*x)^(1/2)/b^2/a^2/x/(b*x^2+a)^(3/2)","B"
819,1,425,194,0.026000," ","int((B*x^2+A)/(b*x^2+a)^(5/2)/(e*x)^(1/2),x)","\frac{10 A \,b^{3} x^{3}+2 B a \,b^{2} x^{3}+5 \sqrt{-a b}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,b^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{-a b}\, \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B a b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+14 A a \,b^{2} x -2 B \,a^{2} b x +5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A a b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{12 \sqrt{e x}\, \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} b^{2}}"," ",0,"1/12*(5*A*(-a*b)^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2+B*(-a*b)^(1/2)*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b+5*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a*b+B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*a^2+10*A*b^3*x^3+2*B*a*b^2*x^3+14*A*a*b^2*x-2*B*a^2*b*x)/(e*x)^(1/2)/a^2/b^2/(b*x^2+a)^(3/2)","B"
820,1,771,387,0.028000," ","int((B*x^2+A)/(e*x)^(3/2)/(b*x^2+a)^(5/2),x)","\frac{-42 A \,b^{3} x^{4}+6 B a \,b^{2} x^{4}+42 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a \,b^{2} x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A a \,b^{2} x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} b \,x^{2} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{2} b \,x^{2} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-70 A a \,b^{2} x^{2}+10 B \,a^{2} b \,x^{2}+42 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, A \,a^{2} b \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticE \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, B \,a^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-24 A \,a^{2} b}{12 \sqrt{e x}\, \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{3} b e}"," ",0,"1/12*(42*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2-21*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2-6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b+3*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b+42*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-21*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b-6*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticE(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3+3*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*a^3-42*A*b^3*x^4+6*B*a*b^2*x^4-70*A*a*b^2*x^2+10*B*a^2*b*x^2-24*A*a^2*b)/b/a^3/e/(e*x)^(1/2)/(b*x^2+a)^(3/2)","A"
821,1,446,214,0.028000," ","int((B*x^2+A)/(e*x)^(5/2)/(b*x^2+a)^(5/2),x)","-\frac{30 A \,b^{3} x^{4}-10 B a \,b^{2} x^{4}+15 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A \,b^{2} x^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B a b \,x^{3} \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+42 A a \,b^{2} x^{2}-14 B \,a^{2} b \,x^{2}+15 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, A a b x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-b x +\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \sqrt{-a b}\, B \,a^{2} x \EllipticF \left(\sqrt{\frac{b x +\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+8 A \,a^{2} b}{12 \sqrt{e x}\, \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{3} b \,e^{2} x}"," ",0,"-1/12*(15*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x^3*b^2-5*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x^3*a*b+15*A*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*a*b-5*B*((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)*EllipticF(((b*x+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*x*a^2+30*A*b^3*x^4-10*B*a*b^2*x^4+42*A*a*b^2*x^2-14*B*a^2*b*x^2+8*A*a^2*b)/x/e^2/(e*x)^(1/2)/a^3/b/(b*x^2+a)^(3/2)","B"
822,1,448,283,0.079000," ","int((e*x)^(3/2)*(b*x^2+a)^2*(d*x^2+c)^(1/2),x)","-\frac{2 \sqrt{e x}\, \left(-77 b^{2} d^{5} x^{9}-210 a b \,d^{5} x^{7}-91 b^{2} c \,d^{4} x^{7}-165 a^{2} d^{5} x^{5}-270 a b c \,d^{4} x^{5}+4 b^{2} c^{2} d^{3} x^{5}-275 a^{2} c \,d^{4} x^{3}+40 a b \,c^{2} d^{3} x^{3}-12 b^{2} c^{3} d^{2} x^{3}-110 a^{2} c^{2} d^{3} x +100 a b \,c^{3} d^{2} x -30 b^{2} c^{4} d x +55 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-50 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) e}{1155 \sqrt{d \,x^{2}+c}\, d^{4} x}"," ",0,"-2/1155*e/x*(e*x)^(1/2)/(d*x^2+c)^(1/2)*(-77*x^9*b^2*d^5-210*x^7*a*b*d^5-91*x^7*b^2*c*d^4+55*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-x*d/(-c*d)^(1/2))^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2-50*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-x*d/(-c*d)^(1/2))^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d+15*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-x*d/(-c*d)^(1/2))^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-165*x^5*a^2*d^5-270*x^5*a*b*c*d^4+4*x^5*b^2*c^2*d^3-275*x^3*a^2*c*d^4+40*x^3*a*b*c^2*d^3-12*x^3*b^2*c^3*d^2-110*x*a^2*c^2*d^3+100*x*a*b*c^3*d^2-30*x*b^2*c^4*d)/d^4","A"
823,1,658,433,0.056000," ","int((b*x^2+a)^2*(e*x)^(1/2)*(d*x^2+c)^(1/2),x)","\frac{2 \sqrt{e x}\, \left(45 b^{2} d^{4} x^{8}+130 a b \,d^{4} x^{6}+55 b^{2} c \,d^{3} x^{6}+117 a^{2} d^{4} x^{4}+182 a b c \,d^{3} x^{4}-4 b^{2} c^{2} d^{2} x^{4}+117 a^{2} c \,d^{3} x^{2}+52 a b \,c^{2} d^{2} x^{2}-14 b^{2} c^{3} d \,x^{2}+234 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-117 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-156 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+78 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+42 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right)}{585 \sqrt{d \,x^{2}+c}\, d^{3} x}"," ",0,"2/585*(e*x)^(1/2)/(d*x^2+c)^(1/2)/d^3*(45*x^8*b^2*d^4+130*x^6*a*b*d^4+55*x^6*b^2*c*d^3+234*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2-156*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d+42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-117*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2+78*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d-21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4+117*x^4*a^2*d^4+182*x^4*a*b*c*d^3-4*x^4*b^2*c^2*d^2+117*x^2*a^2*c*d^3+52*x^2*a*b*c^2*d^2-14*x^2*b^2*c^3*d)/x","A"
824,1,401,245,0.036000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(1/2),x)","\frac{\frac{2 b^{2} d^{4} x^{7}}{11}+\frac{4 a b \,d^{4} x^{5}}{7}+\frac{18 b^{2} c \,d^{3} x^{5}}{77}+\frac{2 a^{2} d^{4} x^{3}}{3}+\frac{20 a b c \,d^{3} x^{3}}{21}-\frac{8 b^{2} c^{2} d^{2} x^{3}}{231}+\frac{2 a^{2} c \,d^{3} x}{3}+\frac{8 a b \,c^{2} d^{2} x}{21}-\frac{20 b^{2} c^{3} d x}{231}+\frac{2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{3}-\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{21}+\frac{10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{231}}{\sqrt{d \,x^{2}+c}\, \sqrt{e x}\, d^{3}}"," ",0,"2/231/(d*x^2+c)^(1/2)*(21*x^7*b^2*d^4+77*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a^2*c*d^2-22*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a*b*c^2*d+5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*b^2*c^3+66*x^5*a*b*d^4+27*x^5*b^2*c*d^3+77*x^3*a^2*d^4+110*x^3*a*b*c*d^3-4*x^3*b^2*c^2*d^2+77*x*a^2*c*d^3+44*x*a*b*c^2*d^2-10*x*b^2*c^3*d)/(e*x)^(1/2)/d^3","A"
825,1,624,431,0.046000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(3/2),x)","\frac{\frac{2 b^{2} d^{3} x^{6}}{9}+\frac{4 a b \,d^{3} x^{4}}{5}+\frac{14 b^{2} c \,d^{2} x^{4}}{45}-2 a^{2} d^{3} x^{2}+\frac{4 a b c \,d^{2} x^{2}}{5}+\frac{4 b^{2} c^{2} d \,x^{2}}{45}+4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+\frac{8 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{15}+\frac{2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{15}-2 a^{2} c \,d^{2}}{\sqrt{d \,x^{2}+c}\, \sqrt{e x}\, d^{2} e}"," ",0,"2/45*(5*x^6*b^2*d^3+90*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2+36*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d-6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-45*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2-18*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d+3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3+18*x^4*a*b*d^3+7*x^4*b^2*c*d^2-45*a^2*d^3*x^2+18*a*b*c*d^2*x^2+2*x^2*b^2*c^2*d-45*a^2*c*d^2)/(d*x^2+c)^(1/2)/d^2/e/(e*x)^(1/2)","A"
826,1,383,235,0.041000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(5/2),x)","\frac{\frac{2 b^{2} d^{3} x^{6}}{7}+\frac{4 a b \,d^{3} x^{4}}{3}+\frac{10 b^{2} c \,d^{2} x^{4}}{21}-\frac{2 a^{2} d^{3} x^{2}}{3}+\frac{4 a b c \,d^{2} x^{2}}{3}+\frac{4 b^{2} c^{2} d \,x^{2}}{21}+\frac{2 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} d^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{3}+\frac{4 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b c d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{3}-\frac{2 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{21}-\frac{2 a^{2} c \,d^{2}}{3}}{\sqrt{d \,x^{2}+c}\, \sqrt{e x}\, d^{2} e^{2} x}"," ",0,"2/21/(d*x^2+c)^(1/2)/x*(7*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a^2*d^2+14*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a*b*c*d-(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*b^2*c^2+3*b^2*d^3*x^6+14*a*b*d^3*x^4+5*b^2*c*d^2*x^4-7*a^2*d^3*x^2+14*a*b*c*d^2*x^2+2*b^2*c^2*d*x^2-7*a^2*c*d^2)/e^2/(e*x)^(1/2)/d^2","A"
827,1,648,429,0.048000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(7/2),x)","\frac{\frac{2 b^{2} c \,d^{2} x^{6}}{5}-\frac{4 a^{2} d^{3} x^{4}}{5}-4 a b c \,d^{2} x^{4}+\frac{2 b^{2} c^{2} d \,x^{4}}{5}+\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}+8 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{6 a^{2} c \,d^{2} x^{2}}{5}-4 a b \,c^{2} d \,x^{2}-\frac{2 a^{2} c^{2} d}{5}}{\sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c d \,e^{3} x^{2}}"," ",0,"2/5/x^2*(2*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2+20*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d+2*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3-((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2-10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d-((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3+x^6*b^2*c*d^2-2*x^4*a^2*d^3-10*x^4*a*b*c*d^2+x^4*b^2*c^2*d-3*x^2*a^2*c*d^2-10*x^2*a*b*c^2*d-a^2*c^2*d)/(d*x^2+c)^(1/2)/d/e^3/(e*x)^(1/2)/c","A"
828,1,385,208,0.073000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(9/2),x)","-\frac{2 \left(-7 b^{2} c \,d^{2} x^{6}+2 a^{2} d^{3} x^{4}+14 a b c \,d^{2} x^{4}-7 b^{2} c^{2} d \,x^{4}+\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{2} x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-14 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c d \,x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-7 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+5 a^{2} c \,d^{2} x^{2}+14 a b \,c^{2} d \,x^{2}+3 a^{2} c^{2} d \right)}{21 \sqrt{d \,x^{2}+c}\, c d \,x^{\frac{7}{2}}}"," ",0,"-2/21/(d*x^2+c)^(1/2)*(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^3*a^2*d^2-14*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^3*a*b*c*d-7*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^3*b^2*c^2-7*b^2*c*d^2*x^6+2*a^2*d^3*x^4+14*a*b*c*d^2*x^4-7*b^2*c^2*d*x^4+5*a^2*c*d^2*x^2+14*a*b*c^2*d*x^2+3*a^2*c^2*d)/x^(7/2)/c/d","A"
829,1,659,382,0.103000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(11/2),x)","-\frac{2 \left(-6 a^{2} d^{3} x^{6}+36 a b c \,d^{2} x^{6}+45 b^{2} c^{2} d \,x^{6}+6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-36 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+18 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-90 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+45 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-4 a^{2} c \,d^{2} x^{4}+54 a b \,c^{2} d \,x^{4}+45 b^{2} c^{3} x^{4}+7 a^{2} c^{2} d \,x^{2}+18 a b \,c^{3} x^{2}+5 a^{2} c^{3}\right)}{45 \sqrt{d \,x^{2}+c}\, c^{2} x^{\frac{9}{2}}}"," ",0,"-2/45*(6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^2*c*d^2-36*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a*b*c^2*d-90*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b^2*c^3-3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^2*c*d^2+18*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a*b*c^2*d+45*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b^2*c^3-6*x^6*a^2*d^3+36*x^6*a*b*c*d^2+45*x^6*b^2*c^2*d-4*x^4*a^2*c*d^2+54*a*b*c^2*d*x^4+45*x^4*b^2*c^3+7*x^2*a^2*c^2*d+18*x^2*a*b*c^3+5*a^2*c^3)/(d*x^2+c)^(1/2)/x^(9/2)/c^2","A"
830,1,403,212,0.055000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(13/2),x)","\frac{\frac{20 a^{2} d^{3} x^{6}}{231}-\frac{8 a b c \,d^{2} x^{6}}{21}-\frac{2 b^{2} c^{2} d \,x^{6}}{3}+\frac{10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{2} x^{5} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{231}-\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c d \,x^{5} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{21}+\frac{2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} x^{5} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{3}+\frac{8 a^{2} c \,d^{2} x^{4}}{231}-\frac{20 a b \,c^{2} d \,x^{4}}{21}-\frac{2 b^{2} c^{3} x^{4}}{3}-\frac{18 a^{2} c^{2} d \,x^{2}}{77}-\frac{4 a b \,c^{3} x^{2}}{7}-\frac{2 a^{2} c^{3}}{11}}{\sqrt{d \,x^{2}+c}\, c^{2} x^{\frac{11}{2}}}"," ",0,"2/231/(d*x^2+c)^(1/2)*(5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^5*a^2*d^2-22*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^5*a*b*c*d+77*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^5*b^2*c^2+10*a^2*d^3*x^6-44*a*b*c*d^2*x^6-77*b^2*c^2*d*x^6+4*a^2*c*d^2*x^4-110*a*b*c^2*d*x^4-77*b^2*c^3*x^4-27*a^2*c^2*d*x^2-66*a*b*c^3*x^2-21*a^2*c^3)/x^(11/2)/c^2","A"
831,1,706,431,0.056000," ","int((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(15/2),x)","\frac{-\frac{28 a^{2} d^{4} x^{8}}{195}+\frac{8 a b c \,d^{3} x^{8}}{15}-\frac{4 b^{2} c^{2} d^{2} x^{8}}{5}+\frac{28 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{6} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{195}-\frac{14 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{6} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{195}-\frac{8 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{6} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{15}+\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{6} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{15}+\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{6} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{6} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{56 a^{2} c \,d^{3} x^{6}}{585}+\frac{16 a b \,c^{2} d^{2} x^{6}}{45}-\frac{6 b^{2} c^{3} d \,x^{6}}{5}+\frac{8 a^{2} c^{2} d^{2} x^{4}}{585}-\frac{28 a b \,c^{3} d \,x^{4}}{45}-\frac{2 b^{2} c^{4} x^{4}}{5}-\frac{22 a^{2} c^{3} d \,x^{2}}{117}-\frac{4 a b \,c^{4} x^{2}}{9}-\frac{2 a^{2} c^{4}}{13}}{\sqrt{d \,x^{2}+c}\, c^{3} x^{\frac{13}{2}}}"," ",0,"2/585*(42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^6*a^2*c*d^3-156*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^6*a*b*c^2*d^2+234*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^6*b^2*c^3*d-21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^6*a^2*c*d^3+78*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^6*a*b*c^2*d^2-117*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^6*b^2*c^3*d-42*x^8*a^2*d^4+156*x^8*a*b*c*d^3-234*x^8*b^2*c^2*d^2-28*x^6*a^2*c*d^3+104*x^6*a*b*c^2*d^2-351*x^6*b^2*c^3*d+4*x^4*a^2*c^2*d^2-182*x^4*a*b*c^3*d-117*x^4*b^2*c^4-55*a^2*c^3*d*x^2-130*x^2*a*b*c^4-45*a^2*c^4)/(d*x^2+c)^(1/2)/x^(13/2)/c^3","A"
832,1,743,526,0.051000," ","int((e*x)^(5/2)*(b*x^2+a)^2*(d*x^2+c)^(3/2),x)","-\frac{2 \sqrt{e x}\, \left(-3315 b^{2} d^{6} x^{12}-8190 a b \,d^{6} x^{10}-7800 b^{2} c \,d^{5} x^{10}-5355 a^{2} d^{6} x^{8}-20160 a b c \,d^{5} x^{8}-4665 b^{2} c^{2} d^{4} x^{8}-14280 a^{2} c \,d^{5} x^{6}-12810 a b \,c^{2} d^{4} x^{6}+40 b^{2} c^{3} d^{3} x^{6}-10353 a^{2} c^{2} d^{4} x^{4}+336 a b \,c^{3} d^{3} x^{4}-88 b^{2} c^{4} d^{2} x^{4}-1428 a^{2} c^{3} d^{3} x^{2}+1176 a b \,c^{4} d^{2} x^{2}-308 b^{2} c^{5} d \,x^{2}+4284 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{4} d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-2142 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{4} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-3528 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{5} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+1764 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{5} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+924 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{6} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-462 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{6} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) e^{2}}{69615 \sqrt{d \,x^{2}+c}\, d^{4} x}"," ",0,"-2/69615*e^2/x*(e*x)^(1/2)/(d*x^2+c)^(1/2)/d^4*(-3315*x^12*b^2*d^6-8190*x^10*a*b*d^6-7800*x^10*b^2*c*d^5-5355*x^8*a^2*d^6-20160*x^8*a*b*c*d^5-4665*x^8*b^2*c^2*d^4-14280*x^6*a^2*c*d^5-12810*x^6*a*b*c^2*d^4+40*x^6*b^2*c^3*d^3+4284*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^4*d^2-3528*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^5*d+924*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^6-2142*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^4*d^2+1764*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^5*d-462*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^6-10353*x^4*a^2*c^2*d^4+336*x^4*a*b*c^3*d^3-88*x^4*b^2*c^4*d^2-1428*x^2*a^2*c^3*d^3+1176*x^2*a*b*c^4*d^2-308*x^2*b^2*c^5*d)","A"
833,1,489,329,0.040000," ","int((e*x)^(3/2)*(b*x^2+a)^2*(d*x^2+c)^(3/2),x)","-\frac{2 \sqrt{e x}\, \left(-1155 b^{2} d^{6} x^{11}-2926 a b \,d^{6} x^{9}-2772 b^{2} c \,d^{5} x^{9}-1995 a^{2} d^{6} x^{7}-7448 a b c \,d^{5} x^{7}-1701 b^{2} c^{2} d^{4} x^{7}-5700 a^{2} c \,d^{5} x^{5}-4978 a b \,c^{2} d^{4} x^{5}+24 b^{2} c^{3} d^{3} x^{5}-4845 a^{2} c^{2} d^{4} x^{3}+304 a b \,c^{3} d^{3} x^{3}-72 b^{2} c^{4} d^{2} x^{3}-1140 a^{2} c^{3} d^{3} x +760 a b \,c^{4} d^{2} x -180 b^{2} c^{5} d x +570 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{3} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-380 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{4} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+90 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{5} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) e}{21945 \sqrt{d \,x^{2}+c}\, d^{4} x}"," ",0,"-2/21945*e/x*(e*x)^(1/2)/(d*x^2+c)^(1/2)*(-1155*x^11*b^2*d^6-2926*x^9*a*b*d^6-2772*x^9*b^2*c*d^5-1995*x^7*a^2*d^6-7448*x^7*a*b*c*d^5-1701*x^7*b^2*c^2*d^4+570*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^3*d^2-380*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^4*d+90*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^5-5700*x^5*a^2*c*d^5-4978*x^5*a*b*c^2*d^4+24*x^5*b^2*c^3*d^3-4845*x^3*a^2*c^2*d^4+304*x^3*a*b*c^3*d^3-72*x^3*b^2*c^4*d^2-1140*x*a^2*c^3*d^3+760*x*a*b*c^4*d^2-180*x*b^2*c^5*d)/d^4","A"
834,1,699,484,0.024000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)*(e*x)^(1/2),x)","\frac{2 \sqrt{e x}\, \left(585 b^{2} d^{5} x^{10}+1530 a b \,d^{5} x^{8}+1440 b^{2} c \,d^{4} x^{8}+1105 a^{2} d^{5} x^{6}+4080 a b c \,d^{4} x^{6}+915 b^{2} c^{2} d^{3} x^{6}+3536 a^{2} c \,d^{4} x^{4}+2958 a b \,c^{2} d^{3} x^{4}-24 b^{2} c^{3} d^{2} x^{4}+2431 a^{2} c^{2} d^{3} x^{2}+408 a b \,c^{3} d^{2} x^{2}-84 b^{2} c^{4} d \,x^{2}+2652 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{3} d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-1326 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{3} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-1224 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{4} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+612 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{4} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+252 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{5} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-126 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{5} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right)}{9945 \sqrt{d \,x^{2}+c}\, d^{3} x}"," ",0,"2/9945/(d*x^2+c)^(1/2)*(e*x)^(1/2)/d^3*(585*x^10*b^2*d^5+1530*x^8*a*b*d^5+1440*x^8*b^2*c*d^4+1105*x^6*a^2*d^5+4080*x^6*a*b*c*d^4+915*x^6*b^2*c^2*d^3+2652*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^3*d^2-1224*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^4*d+252*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^5-1326*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^3*d^2+612*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^4*d-126*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^5+3536*x^4*a^2*c*d^4+2958*x^4*a*b*c^2*d^3-24*x^4*b^2*c^3*d^2+2431*x^2*a^2*c^2*d^3+408*x^2*a*b*c^3*d^2-84*x^2*b^2*c^4*d)/x","A"
835,1,444,281,0.022000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(1/2),x)","\frac{\frac{2 b^{2} d^{5} x^{9}}{15}+\frac{4 a b \,d^{5} x^{7}}{11}+\frac{56 b^{2} c \,d^{4} x^{7}}{165}+\frac{2 a^{2} d^{5} x^{5}}{7}+\frac{80 a b c \,d^{4} x^{5}}{77}+\frac{262 b^{2} c^{2} d^{3} x^{5}}{1155}+\frac{8 a^{2} c \,d^{4} x^{3}}{7}+\frac{68 a b \,c^{2} d^{3} x^{3}}{77}-\frac{16 b^{2} c^{3} d^{2} x^{3}}{1155}+\frac{6 a^{2} c^{2} d^{3} x}{7}+\frac{16 a b \,c^{3} d^{2} x}{77}-\frac{8 b^{2} c^{4} d x}{231}+\frac{4 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{7}-\frac{8 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{77}+\frac{4 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{231}}{\sqrt{d \,x^{2}+c}\, \sqrt{e x}\, d^{3}}"," ",0,"2/1155/(d*x^2+c)^(1/2)*(77*b^2*d^5*x^9+210*a*b*d^5*x^7+196*b^2*c*d^4*x^7+330*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2-60*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d+10*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4+165*a^2*d^5*x^5+600*a*b*c*d^4*x^5+131*b^2*c^2*d^3*x^5+660*a^2*c*d^4*x^3+510*a*b*c^2*d^3*x^3-8*b^2*c^3*d^2*x^3+495*a^2*c^2*d^3*x+120*a*b*c^3*d^2*x-20*b^2*c^4*d*x)/d^3/(e*x)^(1/2)","A"
836,1,669,480,0.028000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(3/2),x)","\frac{\frac{2 b^{2} d^{4} x^{8}}{13}+\frac{4 a b \,d^{4} x^{6}}{9}+\frac{16 b^{2} c \,d^{3} x^{6}}{39}+\frac{2 a^{2} d^{4} x^{4}}{5}+\frac{64 a b c \,d^{3} x^{4}}{45}+\frac{58 b^{2} c^{2} d^{2} x^{4}}{195}-\frac{8 a^{2} c \,d^{3} x^{2}}{5}+\frac{44 a b \,c^{2} d^{2} x^{2}}{45}+\frac{8 b^{2} c^{3} d \,x^{2}}{195}+\frac{24 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{12 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{16 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{15}-\frac{8 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{15}-\frac{8 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{65}+\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{65}-2 a^{2} c^{2} d^{2}}{\sqrt{d \,x^{2}+c}\, \sqrt{e x}\, d^{2} e}"," ",0,"2/585*(45*b^2*d^4*x^8+130*a*b*d^4*x^6+120*b^2*c*d^3*x^6+1404*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2+312*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d-36*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-702*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2-156*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d+18*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4+117*a^2*d^4*x^4+416*a*b*c*d^3*x^4+87*b^2*c^2*d^2*x^4-468*a^2*c*d^3*x^2+286*a*b*c^2*d^2*x^2+12*b^2*c^3*d*x^2-585*a^2*c^2*d^2)/(d*x^2+c)^(1/2)/d^2/e/(e*x)^(1/2)","A"
837,1,415,283,0.025000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(5/2),x)","\frac{\frac{2 b^{2} d^{4} x^{8}}{11}+\frac{4 a b \,d^{4} x^{6}}{7}+\frac{40 b^{2} c \,d^{3} x^{6}}{77}+\frac{2 a^{2} d^{4} x^{4}}{3}+\frac{16 a b c \,d^{3} x^{4}}{7}+\frac{34 b^{2} c^{2} d^{2} x^{4}}{77}+\frac{12 a b \,c^{2} d^{2} x^{2}}{7}+\frac{8 b^{2} c^{3} d \,x^{2}}{77}+\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} c \,d^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{3}+\frac{8 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b \,c^{2} d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{7}-\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{3} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{77}-\frac{2 a^{2} c^{2} d^{2}}{3}}{\sqrt{d \,x^{2}+c}\, \sqrt{e x}\, d^{2} e^{2} x}"," ",0,"2/231/(d*x^2+c)^(1/2)/x*(21*b^2*d^4*x^8+154*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x*a^2*c*d^2+132*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x*a*b*c^2*d-6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x*b^2*c^3+66*a*b*d^4*x^6+60*b^2*c*d^3*x^6+77*a^2*d^4*x^4+264*a*b*c*d^3*x^4+51*b^2*c^2*d^2*x^4+198*a*b*c^2*d^2*x^2+12*b^2*c^3*d*x^2-77*a^2*c^2*d^2)/d^2/e^2/(e*x)^(1/2)","A"
838,1,668,472,0.026000," ","int((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(7/2),x)","\frac{\frac{2 b^{2} d^{3} x^{8}}{9}+\frac{4 a b \,d^{3} x^{6}}{5}+\frac{32 b^{2} c \,d^{2} x^{6}}{45}-\frac{14 a^{2} d^{3} x^{4}}{5}-\frac{16 a b c \,d^{2} x^{4}}{5}+\frac{22 b^{2} c^{2} d \,x^{4}}{45}+\frac{24 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{12 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{48 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{24 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{8 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{15}-\frac{4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{15}-\frac{16 a^{2} c \,d^{2} x^{2}}{5}-4 a b \,c^{2} d \,x^{2}-\frac{2 a^{2} c^{2} d}{5}}{\sqrt{d \,x^{2}+c}\, \sqrt{e x}\, d \,e^{3} x^{2}}"," ",0,"2/45/x^2*(5*b^2*d^3*x^8+108*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2+216*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d+12*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3-54*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2-108*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d-6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3+18*x^6*a*b*d^3+16*b^2*c*d^2*x^6-63*a^2*d^3*x^4-72*a*b*c*d^2*x^4+11*b^2*c^2*d*x^4-72*a^2*c*d^2*x^2-90*a*b*c^2*d*x^2-9*a^2*c^2*d)/(d*x^2+c)^(1/2)/d/e^3/(e*x)^(1/2)","A"
839,1,661,438,0.039000," ","int((e*x)^(5/2)*(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{e x}\, \left(-90 b^{2} d^{4} x^{8}-260 a b \,d^{4} x^{6}+20 b^{2} c \,d^{3} x^{6}-234 a^{2} d^{4} x^{4}+104 a b c \,d^{3} x^{4}-44 b^{2} c^{2} d^{2} x^{4}-234 a^{2} c \,d^{3} x^{2}+364 a b \,c^{2} d^{2} x^{2}-154 b^{2} c^{3} d \,x^{2}+702 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-351 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-1092 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+546 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+462 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-231 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) e^{2}}{585 \sqrt{d \,x^{2}+c}\, d^{4} x}"," ",0,"-1/585*e^2/x*(e*x)^(1/2)/(d*x^2+c)^(1/2)/d^4*(-90*b^2*d^4*x^8-260*a*b*d^4*x^6+20*b^2*c*d^3*x^6+702*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2-1092*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d+462*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-351*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2+546*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d-231*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-234*a^2*d^4*x^4+104*a*b*c*d^3*x^4-44*b^2*c^2*d^2*x^4-234*a^2*c*d^3*x^2+364*a*b*c^2*d^2*x^2-154*b^2*c^3*d*x^2)","A"
840,1,405,241,0.052000," ","int((e*x)^(3/2)*(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{e x}\, \left(-42 b^{2} d^{4} x^{7}-132 a b \,d^{4} x^{5}+12 b^{2} c \,d^{3} x^{5}-154 a^{2} d^{4} x^{3}+88 a b c \,d^{3} x^{3}-36 b^{2} c^{2} d^{2} x^{3}-154 a^{2} c \,d^{3} x +220 a b \,c^{2} d^{2} x -90 b^{2} c^{3} d x +77 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-110 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+45 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) e}{231 \sqrt{d \,x^{2}+c}\, d^{4} x}"," ",0,"-1/231*e/x*(e*x)^(1/2)/(d*x^2+c)^(1/2)*(-42*b^2*d^4*x^7+77*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a^2*c*d^2-110*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a*b*c^2*d+45*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*b^2*c^3-132*a*b*d^4*x^5+12*b^2*c*d^3*x^5-154*a^2*d^4*x^3+88*a*b*c*d^3*x^3-36*b^2*c^2*d^2*x^3-154*a^2*c*d^3*x+220*a*b*c^2*d^2*x-90*b^2*c^3*d*x)/d^4","A"
841,1,604,389,0.022000," ","int((b*x^2+a)^2*(e*x)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{e x}\, \left(10 b^{2} d^{3} x^{6}+36 a b \,d^{3} x^{4}-4 b^{2} c \,d^{2} x^{4}+36 a b c \,d^{2} x^{2}-14 b^{2} c^{2} d \,x^{2}+90 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-45 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-108 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+54 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+42 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right)}{45 \sqrt{d \,x^{2}+c}\, d^{3} x}"," ",0,"1/45*(e*x)^(1/2)/(d*x^2+c)^(1/2)/d^3*(10*b^2*d^3*x^6+90*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2-108*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d+42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-45*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2+54*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d-21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3+36*a*b*d^3*x^4-4*b^2*c*d^2*x^4+36*a*b*c*d^2*x^2-14*b^2*c^2*d*x^2)/x","A"
842,1,350,200,0.020000," ","int((b*x^2+a)^2/(e*x)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{6 b^{2} d^{3} x^{5}+28 a b \,d^{3} x^{3}-4 b^{2} c \,d^{2} x^{3}+28 a b c \,d^{2} x -10 b^{2} c^{2} d x +21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-14 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{21 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, d^{3}}"," ",0,"1/21/(d*x^2+c)^(1/2)*(21*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*(-c*d)^(1/2)*a^2*d^2-14*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*(-c*d)^(1/2)*a*b*c*d+5*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*(-c*d)^(1/2)*b^2*c^2+6*x^5*b^2*d^3+28*x^3*a*b*d^3-4*x^3*b^2*c*d^2+28*x*a*b*c*d^2-10*x*b^2*c^2*d)/(e*x)^(1/2)/d^3","A"
843,1,595,388,0.027000," ","int((b*x^2+a)^2/(e*x)^(3/2)/(d*x^2+c)^(1/2),x)","\frac{2 b^{2} c \,d^{2} x^{4}-10 a^{2} d^{3} x^{2}+2 b^{2} c^{2} d \,x^{2}+10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+20 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-10 a^{2} c \,d^{2}}{5 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c \,d^{2} e}"," ",0,"1/5*(10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2+20*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d-6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2-10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d+3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3+2*b^2*c*d^2*x^4-10*a^2*d^3*x^2+2*b^2*c^2*d*x^2-10*a^2*c*d^2)/(d*x^2+c)^(1/2)/d^2/e/(e*x)^(1/2)/c","A"
844,1,352,191,0.021000," ","int((b*x^2+a)^2/(e*x)^(5/2)/(d*x^2+c)^(1/2),x)","-\frac{-2 b^{2} c \,d^{2} x^{4}+2 a^{2} d^{3} x^{2}-2 b^{2} c^{2} d \,x^{2}+\sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} d^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b c d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+2 a^{2} c \,d^{2}}{3 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c \,d^{2} e^{2} x}"," ",0,"-1/3/(d*x^2+c)^(1/2)/x*((-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a^2*d^2-6*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a*b*c*d+(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*b^2*c^2-2*b^2*c*d^2*x^4+2*a^2*d^3*x^2-2*b^2*c^2*d*x^2+2*a^2*c*d^2)/c/e^2/(e*x)^(1/2)/d^2","A"
845,1,626,401,0.026000," ","int((b*x^2+a)^2/(e*x)^(7/2)/(d*x^2+c)^(1/2),x)","-\frac{-6 a^{2} d^{3} x^{4}+20 a b c \,d^{2} x^{4}+6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-20 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-4 a^{2} c \,d^{2} x^{2}+20 a b \,c^{2} d \,x^{2}+2 a^{2} c^{2} d}{5 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c^{2} d \,e^{3} x^{2}}"," ",0,"-1/5/x^2*(6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2-20*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d-10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3-3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2+10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d+5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3-6*a^2*d^3*x^4+20*a*b*c*d^2*x^4-4*a^2*c*d^2*x^2+20*a*b*c^2*d*x^2+2*a^2*c^2*d)/(d*x^2+c)^(1/2)/d/e^3/(e*x)^(1/2)/c^2","A"
846,1,370,200,0.046000," ","int((b*x^2+a)^2/(e*x)^(9/2)/(d*x^2+c)^(1/2),x)","\frac{10 a^{2} d^{3} x^{4}-28 a b c \,d^{2} x^{4}+5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{2} x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-14 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c d \,x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+4 a^{2} c \,d^{2} x^{2}-28 a b \,c^{2} d \,x^{2}-6 a^{2} c^{2} d}{21 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c^{2} d \,e^{4} x^{3}}"," ",0,"1/21/(d*x^2+c)^(1/2)/x^3*(5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^3*a^2*d^2-14*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^3*a*b*c*d+21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^3*b^2*c^2+10*a^2*d^3*x^4-28*a*b*c*d^2*x^4+4*a^2*c*d^2*x^2-28*a*b*c^2*d*x^2-6*a^2*c^2*d)/d/c^2/e^4/(e*x)^(1/2)","A"
847,1,667,446,0.052000," ","int((b*x^2+a)^2/(e*x)^(11/2)/(d*x^2+c)^(1/2),x)","\frac{-42 a^{2} d^{3} x^{6}+108 a b c \,d^{2} x^{6}-90 b^{2} c^{2} d \,x^{6}+42 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-108 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+54 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+90 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-45 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-28 a^{2} c \,d^{2} x^{4}+72 a b \,c^{2} d \,x^{4}-90 b^{2} c^{3} x^{4}+4 a^{2} c^{2} d \,x^{2}-36 a b \,c^{3} x^{2}-10 a^{2} c^{3}}{45 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c^{3} e^{5} x^{4}}"," ",0,"1/45/x^4*(42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^2*c*d^2-108*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a*b*c^2*d+90*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b^2*c^3-21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^2*c*d^2+54*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a*b*c^2*d-45*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b^2*c^3-42*a^2*d^3*x^6+108*a*b*c*d^2*x^6-90*b^2*c^2*d*x^6-28*a^2*c*d^2*x^4+72*a*b*c^2*d*x^4-90*b^2*c^3*x^4+4*a^2*c^2*d*x^2-36*a*b*c^3*x^2-10*a^2*c^3)/(d*x^2+c)^(1/2)/e^5/(e*x)^(1/2)/c^3","A"
848,1,411,243,0.049000," ","int((b*x^2+a)^2/(e*x)^(13/2)/(d*x^2+c)^(1/2),x)","-\frac{90 a^{2} d^{3} x^{6}-220 a b c \,d^{2} x^{6}+154 b^{2} c^{2} d \,x^{6}+45 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{2} x^{5} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-110 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c d \,x^{5} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+77 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} x^{5} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+36 a^{2} c \,d^{2} x^{4}-88 a b \,c^{2} d \,x^{4}+154 b^{2} c^{3} x^{4}-12 a^{2} c^{2} d \,x^{2}+132 a b \,c^{3} x^{2}+42 a^{2} c^{3}}{231 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c^{3} e^{6} x^{5}}"," ",0,"-1/231/(d*x^2+c)^(1/2)/x^5*(45*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^5*a^2*d^2-110*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^5*a*b*c*d+77*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^5*b^2*c^2+90*a^2*d^3*x^6-220*a*b*c*d^2*x^6+154*b^2*c^2*d*x^6+36*a^2*c*d^2*x^4-88*a*b*c^2*d*x^4+154*b^2*c^3*x^4-12*a^2*c^2*d*x^2+132*a*b*c^3*x^2+42*a^2*c^3)/c^3/e^6/(e*x)^(1/2)","A"
849,1,407,293,0.061000," ","int((e*x)^(7/2)*(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","-\frac{\sqrt{e x}\, \left(-84 b^{2} d^{4} x^{7}-264 a b \,d^{4} x^{5}+156 b^{2} c \,d^{3} x^{5}-308 a^{2} d^{4} x^{3}+792 a b c \,d^{3} x^{3}-468 b^{2} c^{2} d^{2} x^{3}-770 a^{2} c \,d^{3} x +1980 a b \,c^{2} d^{2} x -1170 b^{2} c^{3} d x +385 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-990 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+585 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) e^{3}}{462 \sqrt{d \,x^{2}+c}\, d^{5} x}"," ",0,"-1/462*e^3/x*(e*x)^(1/2)*(-84*b^2*d^4*x^7+385*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a^2*c*d^2-990*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a*b*c^2*d+585*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*b^2*c^3-264*a*b*d^4*x^5+156*b^2*c*d^3*x^5-308*a^2*d^4*x^3+792*a*b*c*d^3*x^3-468*b^2*c^2*d^2*x^3-770*a^2*c*d^3*x+1980*a*b*c^2*d^2*x-1170*b^2*c^3*d*x)/(d*x^2+c)^(1/2)/d^5","A"
850,1,618,446,0.061000," ","int((e*x)^(5/2)*(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{\sqrt{e x}\, \left(20 b^{2} d^{3} x^{6}+72 a b \,d^{3} x^{4}-44 b^{2} c \,d^{2} x^{4}-90 a^{2} d^{3} x^{2}+252 a b c \,d^{2} x^{2}-154 b^{2} c^{2} d \,x^{2}+270 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-135 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-756 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+378 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+462 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-231 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) e^{2}}{90 \sqrt{d \,x^{2}+c}\, d^{4} x}"," ",0,"1/90*e^2/x*(e*x)^(1/2)*(20*b^2*d^3*x^6+270*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2-756*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d+462*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-135*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2+378*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d-231*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3+72*a*b*d^3*x^4-44*b^2*c*d^2*x^4-90*a^2*d^3*x^2+252*a*b*c*d^2*x^2-154*b^2*c^2*d*x^2)/(d*x^2+c)^(1/2)/d^4","A"
851,1,363,248,0.027000," ","int((e*x)^(3/2)*(b*x^2+a)^2/(d*x^2+c)^(3/2),x)","\frac{\sqrt{e x}\, \left(12 b^{2} d^{3} x^{5}+56 a b \,d^{3} x^{3}-36 b^{2} c \,d^{2} x^{3}-42 a^{2} d^{3} x +140 a b c \,d^{2} x -90 b^{2} c^{2} d x +21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-70 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+45 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) e}{42 \sqrt{d \,x^{2}+c}\, d^{4} x}"," ",0,"1/42*e/x*(e*x)^(1/2)*(21*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*(-c*d)^(1/2)*a^2*d^2-70*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*(-c*d)^(1/2)*a*b*c*d+45*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*(-c*d)^(1/2)*b^2*c^2+12*b^2*d^3*x^5+56*a*b*d^3*x^3-36*b^2*c*d^2*x^3-42*x*a^2*d^3+140*a*b*c*d^2*x-90*b^2*c^2*d*x)/(d*x^2+c)^(1/2)/d^4","A"
852,1,597,400,0.027000," ","int((b*x^2+a)^2*(e*x)^(1/2)/(d*x^2+c)^(3/2),x)","-\frac{\sqrt{e x}\, \left(-4 b^{2} c \,d^{2} x^{4}-10 a^{2} d^{3} x^{2}+20 a b c \,d^{2} x^{2}-14 b^{2} c^{2} d \,x^{2}+10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-60 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+30 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+42 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right)}{10 \sqrt{d \,x^{2}+c}\, c \,d^{3} x}"," ",0,"-1/10*(e*x)^(1/2)*(10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2-60*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d+42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2+30*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d-21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-4*b^2*c*d^2*x^4-10*a^2*d^3*x^2+20*a*b*c*d^2*x^2-14*b^2*c^2*d*x^2)/(d*x^2+c)^(1/2)/d^3/x/c","A"
853,1,341,202,0.030000," ","int((b*x^2+a)^2/(d*x^2+c)^(3/2)/(e*x)^(1/2),x)","\frac{4 b^{2} c \,d^{2} x^{3}+6 a^{2} d^{3} x -12 a b c \,d^{2} x +10 b^{2} c^{2} d x +3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{6 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c \,d^{3}}"," ",0,"1/6*(3*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*(-c*d)^(1/2)*a^2*d^2+6*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*(-c*d)^(1/2)*a*b*c*d-5*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*(-c*d)^(1/2)*b^2*c^2+4*b^2*c*d^2*x^3+6*a^2*d^3*x-12*a*b*c*d^2*x+10*b^2*c^2*d*x)/(d*x^2+c)^(1/2)/c/(e*x)^(1/2)/d^3","A"
854,1,594,415,0.031000," ","int((b*x^2+a)^2/(e*x)^(3/2)/(d*x^2+c)^(3/2),x)","\frac{-6 a^{2} d^{3} x^{2}+4 a b c \,d^{2} x^{2}-2 b^{2} c^{2} d \,x^{2}+6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-4 a^{2} c \,d^{2}}{2 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c^{2} d^{2} e}"," ",0,"1/2*(6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2-4*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d+6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2+2*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d-3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-6*a^2*d^3*x^2+4*a*b*c*d^2*x^2-2*b^2*c^2*d*x^2-4*a^2*c*d^2)/(d*x^2+c)^(1/2)/d^2/e/(e*x)^(1/2)/c^2","A"
855,1,353,214,0.028000," ","int((b*x^2+a)^2/(e*x)^(5/2)/(d*x^2+c)^(3/2),x)","-\frac{10 a^{2} d^{3} x^{2}-12 a b c \,d^{2} x^{2}+6 b^{2} c^{2} d \,x^{2}+5 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} d^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b c d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-c d}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+4 a^{2} c \,d^{2}}{6 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c^{2} d^{2} e^{2} x}"," ",0,"-1/6/x*(5*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a^2*d^2-6*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a*b*c*d-3*(-c*d)^(1/2)*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*b^2*c^2+10*a^2*d^3*x^2-12*a*b*c*d^2*x^2+6*b^2*c^2*d*x^2+4*a^2*c*d^2)/(d*x^2+c)^(1/2)/c^2/e^2/(e*x)^(1/2)/d^2","A"
856,1,638,442,0.029000," ","int((b*x^2+a)^2/(e*x)^(7/2)/(d*x^2+c)^(3/2),x)","-\frac{-42 a^{2} d^{3} x^{4}+60 a b c \,d^{2} x^{4}-10 b^{2} c^{2} d \,x^{4}+42 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-60 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+30 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-28 a^{2} c \,d^{2} x^{2}+40 a b \,c^{2} d \,x^{2}+4 a^{2} c^{2} d}{10 \sqrt{d \,x^{2}+c}\, \sqrt{e x}\, c^{3} d \,e^{3} x^{2}}"," ",0,"-1/10/x^2*(42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2-60*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d+10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3-21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2+30*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d-5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3-42*a^2*d^3*x^4+60*a*b*c*d^2*x^4-10*b^2*c^2*d*x^4-28*a^2*c*d^2*x^2+40*a*b*c^2*d*x^2+4*a^2*c^2*d)/(d*x^2+c)^(1/2)/d/e^3/(e*x)^(1/2)/c^3","A"
857,1,696,297,0.057000," ","int((e*x)^(7/2)*(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","\frac{\left(24 b^{2} d^{4} x^{7}+112 a b \,d^{4} x^{5}-104 b^{2} c \,d^{3} x^{5}-98 a^{2} d^{4} x^{3}+588 a b c \,d^{3} x^{3}-546 b^{2} c^{2} d^{2} x^{3}+35 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-210 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+195 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-70 a^{2} c \,d^{3} x +420 a b \,c^{2} d^{2} x -390 b^{2} c^{3} d x +35 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-210 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+195 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{e x}\, e^{3}}{84 \left(d \,x^{2}+c \right)^{\frac{3}{2}} d^{5} x}"," ",0,"1/84*(35*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^2*a^2*d^3-210*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^2*a*b*c*d^2+195*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^2*b^2*c^2*d+24*b^2*d^4*x^7+35*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a^2*c*d^2-210*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a*b*c^2*d+195*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*b^2*c^3+112*a*b*d^4*x^5-104*b^2*c*d^3*x^5-98*a^2*d^4*x^3+588*a*b*c*d^3*x^3-546*b^2*c^2*d^2*x^3-70*a^2*c*d^3*x+420*a*b*c^2*d^2*x-390*b^2*c^3*d*x)*e^3/x*(e*x)^(1/2)/d^5/(d*x^2+c)^(3/2)","B"
858,1,1191,450,0.073000," ","int((e*x)^(5/2)*(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","-\frac{\left(-24 b^{2} c \,d^{3} x^{6}-30 a^{2} d^{4} x^{4}+180 a b c \,d^{3} x^{4}-198 b^{2} c^{2} d^{2} x^{4}+30 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-420 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+210 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+462 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-231 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-10 a^{2} c \,d^{3} x^{2}+140 a b \,c^{2} d^{2} x^{2}-154 b^{2} c^{3} d \,x^{2}+30 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-420 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+210 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+462 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-231 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{e x}\, e^{2}}{60 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c \,d^{4} x}"," ",0,"-1/60*(30*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^3-420*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d^2+462*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3*d-15*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^3+210*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d^2-231*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3*d-24*b^2*c*d^3*x^6+30*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2-420*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d+462*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-15*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2+210*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d-231*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-30*a^2*d^4*x^4+180*a*b*c*d^3*x^4-198*b^2*c^2*d^2*x^4-10*a^2*c*d^3*x^2+140*a*b*c^2*d^2*x^2-154*b^2*c^3*d*x^2)*e^2/x*(e*x)^(1/2)/d^4/c/(d*x^2+c)^(3/2)","B"
859,1,674,249,0.027000," ","int((e*x)^(3/2)*(b*x^2+a)^2/(d*x^2+c)^(5/2),x)","\frac{\left(8 b^{2} c \,d^{3} x^{5}+2 a^{2} d^{4} x^{3}-28 a b c \,d^{3} x^{3}+42 b^{2} c^{2} d^{2} x^{3}+\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-2 a^{2} c \,d^{3} x -20 a b \,c^{2} d^{2} x +30 b^{2} c^{3} d x +\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{e x}\, e}{12 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c \,d^{4} x}"," ",0,"1/12*(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^2*a^2*d^3+10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^2*a*b*c*d^2-15*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^2*b^2*c^2*d+((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a^2*c*d^2+10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a*b*c^2*d-15*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*b^2*c^3+8*b^2*c*d^3*x^5+2*a^2*d^4*x^3-28*a*b*c*d^3*x^3+42*b^2*c^2*d^2*x^3-2*a^2*c*d^3*x-20*a*b*c^2*d^2*x+30*b^2*c^3*d*x)*e/x*(e*x)^(1/2)/c/d^4/(d*x^2+c)^(3/2)","B"
860,1,1176,417,0.030000," ","int((b*x^2+a)^2*(e*x)^(1/2)/(d*x^2+c)^(5/2),x)","-\frac{\left(-6 a^{2} d^{4} x^{4}-12 a b c \,d^{3} x^{4}+18 b^{2} c^{2} d^{2} x^{4}+6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+12 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-10 a^{2} c \,d^{3} x^{2}-4 a b \,c^{2} d^{2} x^{2}+14 b^{2} c^{3} d \,x^{2}+6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+12 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{e x}}{12 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2} d^{3} x}"," ",0,"-1/12*(6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^3+12*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d^2-42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3*d-3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^3-6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d^2+21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3*d+6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2+12*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d-42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2-6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d+21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-6*a^2*d^4*x^4-12*a*b*c*d^3*x^4+18*b^2*c^2*d^2*x^4-10*a^2*c*d^3*x^2-4*a*b*c^2*d^2*x^2+14*b^2*c^3*d*x^2)*(e*x)^(1/2)/d^3/c^2/x/(d*x^2+c)^(3/2)","B"
861,1,660,220,0.031000," ","int((b*x^2+a)^2/(d*x^2+c)^(5/2)/(e*x)^(1/2),x)","\frac{10 a^{2} d^{4} x^{3}+4 a b c \,d^{3} x^{3}-14 b^{2} c^{2} d^{2} x^{3}+5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} d^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+14 a^{2} c \,d^{3} x -4 a b \,c^{2} d^{2} x -10 b^{2} c^{3} d x +5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)}{12 \sqrt{e x}\, \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2} d^{3}}"," ",0,"1/12*(5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^2*a^2*d^3+2*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^2*a*b*c*d^2+5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x^2*b^2*c^2*d+5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a^2*c*d^2+2*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*a*b*c^2*d+5*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*b^2*c^3+10*a^2*d^4*x^3+4*a*b*c*d^3*x^3-14*b^2*c^2*d^2*x^3+14*a^2*c*d^3*x-4*a*b*c^2*d^2*x-10*b^2*c^3*d*x)/(e*x)^(1/2)/c^2/d^3/(d*x^2+c)^(3/2)","B"
862,1,1187,452,0.051000," ","int((b*x^2+a)^2/(e*x)^(3/2)/(d*x^2+c)^(5/2),x)","\frac{-42 a^{2} d^{4} x^{4}+12 a b c \,d^{3} x^{4}+6 b^{2} c^{2} d^{2} x^{4}+42 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-70 a^{2} c \,d^{3} x^{2}+20 a b \,c^{2} d^{2} x^{2}+2 b^{2} c^{3} d \,x^{2}+42 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-24 a^{2} c^{2} d^{2}}{12 \sqrt{e x}\, \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{3} d^{2} e}"," ",0,"1/12*(42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^3-12*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d^2-6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3*d-21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^3+6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d^2+3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3*d+42*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2-12*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d-6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-21*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c^2*d^2+6*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^3*d+3*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^4-42*a^2*d^4*x^4+12*a*b*c*d^3*x^4+6*b^2*c^2*d^2*x^4-70*a^2*c*d^3*x^2+20*a*b*c^2*d^2*x^2+2*b^2*c^3*d*x^2-24*a^2*c^2*d^2)/d^2/c^3/e/(e*x)^(1/2)/(d*x^2+c)^(3/2)","B"
863,1,686,259,0.034000," ","int((b*x^2+a)^2/(e*x)^(5/2)/(d*x^2+c)^(5/2),x)","-\frac{30 a^{2} d^{4} x^{4}-20 a b c \,d^{3} x^{4}-2 b^{2} c^{2} d^{2} x^{4}+15 \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{-c d}\, a^{2} d^{3} x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{-c d}\, a b c \,d^{2} x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{-c d}\, b^{2} c^{2} d \,x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+42 a^{2} c \,d^{3} x^{2}-28 a b \,c^{2} d^{2} x^{2}+2 b^{2} c^{3} d \,x^{2}+15 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a^{2} c \,d^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, a b \,c^{2} d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, \sqrt{-c d}\, b^{2} c^{3} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+8 a^{2} c^{2} d^{2}}{12 \sqrt{e x}\, \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{3} d^{2} e^{2} x}"," ",0,"-1/12*(15*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*(-c*d)^(1/2)*x^3*a^2*d^3-10*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*(-c*d)^(1/2)*x^3*a*b*c*d^2-((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*(-c*d)^(1/2)*x^3*b^2*c^2*d+15*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x*a^2*c*d^2-10*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x*a*b*c^2*d-((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*(-c*d)^(1/2)*x*b^2*c^3+30*a^2*d^4*x^4-20*a*b*c*d^3*x^4-2*b^2*c^2*d^2*x^4+42*a^2*c*d^3*x^2-28*a*b*c^2*d^2*x^2+2*b^2*c^3*d*x^2+8*a^2*c^2*d^2)/x/e^2/(e*x)^(1/2)/c^3/d^2/(d*x^2+c)^(3/2)","B"
864,1,1231,491,0.040000," ","int((b*x^2+a)^2/(e*x)^(7/2)/(d*x^2+c)^(5/2),x)","-\frac{-462 a^{2} d^{4} x^{6}+420 a b c \,d^{3} x^{6}-30 b^{2} c^{2} d^{2} x^{6}+462 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-231 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c \,d^{3} x^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-420 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+210 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{2} d^{2} x^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+30 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{3} d \,x^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-770 a^{2} c \,d^{3} x^{4}+700 a b \,c^{2} d^{2} x^{4}-50 b^{2} c^{3} d \,x^{4}+462 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-231 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a^{2} c^{2} d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-420 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+210 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, a b \,c^{3} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)+30 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{-c d}}{\sqrt{-c d}}}\, \sqrt{-\frac{d x}{\sqrt{-c d}}}\, b^{2} c^{4} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{-c d}}{\sqrt{-c d}}}, \frac{\sqrt{2}}{2}\right)-264 a^{2} c^{2} d^{2} x^{2}+240 a b \,c^{3} d \,x^{2}+24 a^{2} c^{3} d}{60 \sqrt{e x}\, \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{4} d \,e^{3} x^{2}}"," ",0,"-1/60*(462*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^2*c*d^3-420*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a*b*c^2*d^2+30*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b^2*c^3*d-231*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^2*c*d^3+210*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a*b*c^2*d^2-15*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b^2*c^3*d+462*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c^2*d^2-420*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^3*d+30*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^4-231*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c^2*d^2+210*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^3*d-15*((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2)*(-1/(-c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(-c*d)^(1/2))/(-c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^4-462*x^6*a^2*d^4+420*x^6*a*b*c*d^3-30*x^6*b^2*c^2*d^2-770*x^4*a^2*c*d^3+700*x^4*a*b*c^2*d^2-50*x^4*b^2*c^3*d-264*x^2*a^2*c^2*d^2+240*x^2*a*b*c^3*d+24*a^2*c^3*d)/x^2/d/c^4/e^3/(e*x)^(1/2)/(d*x^2+c)^(3/2)","B"
865,1,1479,288,0.129000," ","int((e*x)^(7/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x)","\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \left(12 \sqrt{a b}\, a \,b^{2} d^{4} x^{5}-12 \sqrt{a b}\, b^{3} c \,d^{3} x^{5}+28 \sqrt{a b}\, a^{2} b \,d^{4} x^{3}-48 \sqrt{a b}\, a \,b^{2} c \,d^{3} x^{3}+20 \sqrt{a b}\, b^{3} c^{2} d^{2} x^{3}-21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} b c \,d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} b c \,d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-28 \sqrt{a b}\, a^{2} b c \,d^{3} x +36 \sqrt{a b}\, a \,b^{2} c^{2} d^{2} x -8 \sqrt{a b}\, b^{3} c^{3} d x +42 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} d^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-70 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+24 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) e^{3}}{42 \left(d \,x^{2}-c \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b^{2} d x}"," ",0,"1/42*e^3*(e*x)^(1/2)*(-d*x^2+c)^(1/2)/b^2/d*(42*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-70*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+24*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*d*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+4*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b+(a*b)^(1/2)*d),1/2*2^(1/2))*a^3*b*c*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b+(a*b)^(1/2)*d),1/2*2^(1/2))*a^3*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b+(a*b)^(1/2)*d),1/2*2^(1/2))*a^2*b^2*c^2*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b+(a*b)^(1/2)*d),1/2*2^(1/2))*a^2*b*c*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b-(a*b)^(1/2)*d),1/2*2^(1/2))*a^3*b*c*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b-(a*b)^(1/2)*d),1/2*2^(1/2))*a^3*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b-(a*b)^(1/2)*d),1/2*2^(1/2))*a^2*b^2*c^2*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b-(a*b)^(1/2)*d),1/2*2^(1/2))*a^2*b*c*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+12*x^5*a*b^2*d^4*(a*b)^(1/2)-12*x^5*b^3*c*d^3*(a*b)^(1/2)+28*x^3*a^2*b*d^4*(a*b)^(1/2)-48*x^3*a*b^2*c*d^3*(a*b)^(1/2)+20*x^3*b^3*c^2*d^2*(a*b)^(1/2)-28*x*a^2*b*c*d^3*(a*b)^(1/2)+36*x*a*b^2*c^2*d^2*(a*b)^(1/2)-8*x*b^3*c^3*d*(a*b)^(1/2))/x/(d*x^2-c)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
866,1,1491,308,0.070000," ","int((e*x)^(5/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x)","-\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \left(-4 a \,b^{2} d^{3} x^{4}+4 b^{3} c \,d^{2} x^{4}+4 a \,b^{2} c \,d^{2} x^{2}-4 b^{3} c^{2} d \,x^{2}+20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-28 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+14 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+8 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) e^{2}}{10 \left(d \,x^{2}-c \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b^{2} x}"," ",0,"-1/10*e^2*(e*x)^(1/2)*(-d*x^2+c)^(1/2)*(20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2-28*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*d+8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2+14*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*d-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d-4*x^4*a*b^2*d^3+4*x^4*b^3*c*d^2+4*x^2*a*b^2*c*d^2-4*x^2*b^3*c^2*d)/x/b^2/(d*x^2-c)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
867,1,1286,237,0.024000," ","int((e*x)^(3/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x)","\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \left(4 \sqrt{a b}\, a b \,d^{3} x^{3}-4 \sqrt{a b}\, b^{2} c \,d^{2} x^{3}-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a b c \,d^{2} x +4 \sqrt{a b}\, b^{2} c^{2} d x +6 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) e}{6 \left(d \,x^{2}-c \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b x}"," ",0,"1/6*e*(e*x)^(1/2)*(-d*x^2+c)^(1/2)/b*(6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-10*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+4*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d+4*x^3*a*b*d^3*(a*b)^(1/2)-4*x^3*b^2*c*d^2*(a*b)^(1/2)-4*x*a*b*c*d^2*(a*b)^(1/2)+4*x*b^2*c^2*d*(a*b)^(1/2))/x/(d*x^2-c)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
868,1,701,269,0.018000," ","int((e*x)^(1/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x)","-\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \left(4 a b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{a b}\, \sqrt{c d}\, b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, \sqrt{c d}\, b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d}{2 \left(d \,x^{2}-c \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b x}"," ",0,"-1/2*(e*x)^(1/2)*(-d*x^2+c)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*d*(4*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d-4*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2-2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d+2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2+(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d-(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b*c-(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d+(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b*c-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d+EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c^2-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d+EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c^2)/b/x/(d*x^2-c)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
869,1,651,213,0.063000," ","int((-d*x^2+c)^(1/2)/(-b*x^2+a)/(e*x)^(1/2),x)","\frac{\sqrt{-d \,x^{2}+c}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \left(-\sqrt{c d}\, a b d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{c d}\, a b d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{a b}\, a \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, a \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, a \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{c d}\, b^{2} c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{c d}\, b^{2} c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{a b}\, b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{a b}\, b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{a b}\, b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right)}{2 \sqrt{e x}\, \left(d \,x^{2}-c \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right)}"," ",0,"1/2*(-d*x^2+c)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*d*(c*d)^(1/2)-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*d^2*(a*b)^(1/2)-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c*(c*d)^(1/2)+EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b*c*d*(a*b)^(1/2)-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*d*(c*d)^(1/2)-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*d^2*(a*b)^(1/2)+EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c*(c*d)^(1/2)+EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b*c*d*(a*b)^(1/2)+2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*d^2*(a*b)^(1/2)-2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b*c*d*(a*b)^(1/2))/(e*x)^(1/2)/(d*x^2-c)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
870,1,1274,292,0.063000," ","int((-d*x^2+c)^(1/2)/(e*x)^(3/2)/(-b*x^2+a),x)","\frac{\sqrt{-d \,x^{2}+c}\, \left(4 a b \,d^{2} x^{2}-4 b^{2} c d \,x^{2}+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a b c d +4 b^{2} c^{2}+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d}{2 \sqrt{e x}\, \left(d \,x^{2}-c \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a e}"," ",0,"1/2*(-d*x^2+c)^(1/2)*d*(4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b*c+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b*c+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c^2+4*x^2*a*b*d^2-4*x^2*b^2*c*d-4*a*b*c*d+4*b^2*c^2)/e/(e*x)^(1/2)/(d*x^2-c)/a/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
871,1,1167,230,0.050000," ","int((-d*x^2+c)^(1/2)/(e*x)^(5/2)/(-b*x^2+a),x)","\frac{\sqrt{-d \,x^{2}+c}\, \left(-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a \,d^{2} x^{2}-4 \sqrt{a b}\, b c d \,x^{2}+2 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, a d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, a d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, a d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b c x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b c x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b c x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a c d +4 \sqrt{a b}\, b \,c^{2}\right) b d}{6 \sqrt{e x}\, \left(d \,x^{2}-c \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a \,e^{2} x}"," ",0,"1/6*(-d*x^2+c)^(1/2)*b*d*(2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*b*c*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b*c*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b*c*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+4*x^2*a*d^2*(a*b)^(1/2)-4*x^2*b*c*d*(a*b)^(1/2)-4*a*c*d*(a*b)^(1/2)+4*b*c^2*(a*b)^(1/2))/x/a/e^2/(e*x)^(1/2)/(d*x^2-c)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
872,1,1553,345,0.057000," ","int((-d*x^2+c)^(1/2)/(e*x)^(7/2)/(-b*x^2+a),x)","\frac{\sqrt{-d \,x^{2}+c}\, \left(-8 a^{2} d^{3} x^{4}+28 a b c \,d^{2} x^{4}-20 b^{2} c^{2} d \,x^{4}-8 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+28 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b \,c^{2} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-14 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b \,c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b \,c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b \,c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+12 a^{2} c \,d^{2} x^{2}-32 a b \,c^{2} d \,x^{2}+20 b^{2} c^{3} x^{2}+5 \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, a c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, a c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b \,c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b \,c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a^{2} c^{2} d +4 a b \,c^{3}\right) b d}{10 \sqrt{e x}\, \left(d \,x^{2}-c \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a^{2} c \,e^{3} x^{2}}"," ",0,"1/10*(-d*x^2+c)^(1/2)*d*b*(5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b*c^2*d-5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^2*c^3+5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b*c^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b*c^2*d+5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^2*c^3-5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b*c^2-8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2+28*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2-14*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3-8*a^2*d^3*x^4+28*a*b*c*d^2*x^4-20*b^2*c^2*d*x^4+12*a^2*c*d^2*x^2-32*a*b*c^2*d*x^2+20*x^2*b^2*c^3-4*a^2*c^2*d+4*a*b*c^3)/x^2/e^3/(e*x)^(1/2)/(d*x^2-c)/a^2/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/c","B"
873,1,2183,373,0.054000," ","int((e*x)^(5/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a),x)","-\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \left(20 a \,b^{3} d^{4} x^{6}-20 b^{4} c \,d^{3} x^{6}+36 a^{2} b^{2} d^{4} x^{4}-100 a \,b^{3} c \,d^{3} x^{4}+64 b^{4} c^{2} d^{2} x^{4}-36 a^{2} b^{2} c \,d^{3} x^{2}+80 a \,b^{3} c^{2} d^{2} x^{2}-44 b^{4} c^{3} d \,x^{2}-180 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+90 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+45 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} b c \,d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+45 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} b c \,d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+432 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-216 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-90 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-90 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-300 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+150 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+45 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+45 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+48 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{4} c^{4} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-24 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{4} c^{4} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+45 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-45 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-90 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+90 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+45 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-45 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) e^{2}}{90 \left(d \,x^{2}-c \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b^{3} x}"," ",0,"-1/90*e^2*(e*x)^(1/2)*(-d*x^2+c)^(1/2)*(20*x^6*a*b^3*d^4-20*x^6*b^4*c*d^3+36*x^4*a^2*b^2*d^4+64*x^4*b^4*c^2*d^2-44*x^2*b^4*c^3*d+90*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-90*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-100*x^4*a*b^3*c*d^3-216*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d^2+150*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3*d+45*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3*d+45*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3*d-180*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^3+432*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d^2-300*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3*d+90*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^3-36*x^2*a^2*b^2*c*d^3+80*x^2*a*b^3*c^2*d^2-45*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2*d+45*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2*d-24*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^4*c^4+48*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^4*c^4+45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-90*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-90*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2))/x/b^3/(d*x^2-c)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
874,1,1920,288,0.030000," ","int((e*x)^(3/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a),x)","\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \left(-12 \sqrt{a b}\, a \,b^{2} d^{4} x^{5}+12 \sqrt{a b}\, b^{3} c \,d^{3} x^{5}-28 \sqrt{a b}\, a^{2} b \,d^{4} x^{3}+76 \sqrt{a b}\, a \,b^{2} c \,d^{3} x^{3}-48 \sqrt{a b}\, b^{3} c^{2} d^{2} x^{3}+21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} b c \,d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} b c \,d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+42 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+28 \sqrt{a b}\, a^{2} b c \,d^{3} x -64 \sqrt{a b}\, a \,b^{2} c^{2} d^{2} x +36 \sqrt{a b}\, b^{3} c^{3} d x -42 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} d^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{3} d^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+112 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-94 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+24 \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) e}{42 \left(d \,x^{2}-c \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b^{2} x}"," ",0,"1/42*e*(e*x)^(1/2)*(-d*x^2+c)^(1/2)/b^2*(21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-42*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-42*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+21*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3*d+21*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2*d-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+42*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-42*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-21*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3*d+21*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2*d-42*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*d^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+112*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-94*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*d*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+24*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-12*(a*b)^(1/2)*a*b^2*d^4*x^5+12*(a*b)^(1/2)*b^3*c*d^3*x^5-28*(a*b)^(1/2)*a^2*b*d^4*x^3+76*(a*b)^(1/2)*a*b^2*c*d^3*x^3-48*(a*b)^(1/2)*b^3*c^2*d^2*x^3+28*(a*b)^(1/2)*a^2*b*c*d^3*x-64*(a*b)^(1/2)*a*b^2*c^2*d^2*x+36*(a*b)^(1/2)*b^3*c^3*d*x)/x/(d*x^2-c)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
875,1,1927,315,0.027000," ","int((-d*x^2+c)^(3/2)*(e*x)^(1/2)/(-b*x^2+a),x)","\frac{\sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, \left(-4 a \,b^{2} d^{3} x^{4}+4 b^{3} c \,d^{2} x^{4}+4 a \,b^{2} c \,d^{2} x^{2}-4 b^{3} c^{2} d \,x^{2}+20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-48 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+24 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+28 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-14 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d}{10 \left(d \,x^{2}-c \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b^{2} x}"," ",0,"1/10*(-d*x^2+c)^(1/2)*(e*x)^(1/2)*d*(20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2-48*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*d+28*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2+24*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*d-14*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b^2*c^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b^2*c^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^3*c^3-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^3*c^3-4*a*b^2*d^3*x^4+4*b^3*c*d^2*x^4+4*a*b^2*c*d^2*x^2-4*b^3*c^2*d*x^2)/b^2/x/(d*x^2-c)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
876,1,1721,250,0.030000," ","int((-d*x^2+c)^(3/2)/(-b*x^2+a)/(e*x)^(1/2),x)","-\frac{\sqrt{-d \,x^{2}+c}\, \left(4 \sqrt{a b}\, a b \,d^{3} x^{3}-4 \sqrt{a b}\, b^{2} c \,d^{2} x^{3}-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a b c \,d^{2} x +4 \sqrt{a b}\, b^{2} c^{2} d x +6 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-16 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d}{6 \sqrt{e x}\, \left(d \,x^{2}-c \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b}"," ",0,"-1/6*(-d*x^2+c)^(1/2)/b*d*(6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-16*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+10*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2-6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d+6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^3*c^3-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2+6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d+6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^3*c^3-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b^2*c^2+4*(a*b)^(1/2)*a*b*d^3*x^3-4*(a*b)^(1/2)*b^2*c*d^2*x^3-4*(a*b)^(1/2)*a*b*c*d^2*x+4*(a*b)^(1/2)*b^2*c^2*d*x)/(e*x)^(1/2)/(d*x^2-c)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
877,1,1758,317,0.033000," ","int((-d*x^2+c)^(3/2)/(e*x)^(3/2)/(-b*x^2+a),x)","\frac{\sqrt{-d \,x^{2}+c}\, \left(4 a \,b^{2} c \,d^{2} x^{2}-4 b^{3} c^{2} d \,x^{2}+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a \,b^{2} c^{2} d +4 b^{3} c^{3}-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d}{2 \sqrt{e x}\, \left(d \,x^{2}-c \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a b e}"," ",0,"1/2*(-d*x^2+c)^(1/2)*d*(4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b^2*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b^2*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^3*c^3-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^3*c^3+4*a*b^2*c*d^2*x^2-4*b^3*c^2*d*x^2-4*a*c^2*d*b^2+4*c^3*b^3)/b/e/(e*x)^(1/2)/(d*x^2-c)/a/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
878,1,1740,252,0.036000," ","int((-d*x^2+c)^(3/2)/(e*x)^(5/2)/(-b*x^2+a),x)","-\frac{\sqrt{-d \,x^{2}+c}\, \left(-3 \sqrt{2}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} b c \,d^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{2}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a \,b^{2} c^{2} d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{2}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a \,b^{2} c^{2} d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{3} c^{3} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{3} c^{3} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a b c \,d^{2} x^{2}+4 \sqrt{a b}\, b^{2} c^{2} d \,x^{2}+6 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-8 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a b \,c^{2} d -4 \sqrt{a b}\, b^{2} c^{3}\right) d}{6 \sqrt{e x}\, \left(d \,x^{2}-c \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a \,e^{2} x}"," ",0,"-1/6*(-d*x^2+c)^(1/2)*d*(6*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a^2*d^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-8*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a*b*c*d*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a^2*b*c*d^2*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a^2*d^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-6*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b^2*c^2*d*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+6*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b*c*d*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^3*c^3*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a^2*b*c*d^2*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a^2*d^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+6*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b^2*c^2*d*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+6*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b*c*d*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^3*c^3*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-4*x^2*a*b*c*d^2*(a*b)^(1/2)+4*x^2*b^2*c^2*d*(a*b)^(1/2)+4*a*b*c^2*d*(a*b)^(1/2)-4*b^2*c^3*(a*b)^(1/2))/x/a/e^2/(e*x)^(1/2)/(d*x^2-c)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
879,1,2028,347,0.033000," ","int((-d*x^2+c)^(3/2)/(e*x)^(7/2)/(-b*x^2+a),x)","-\frac{\sqrt{-d \,x^{2}+c}\, \left(28 a^{2} b \,d^{3} x^{4}-48 a \,b^{2} c \,d^{2} x^{4}+20 b^{3} c^{2} d \,x^{4}+28 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-14 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-48 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+24 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-32 a^{2} b c \,d^{2} x^{2}+52 a \,b^{2} c^{2} d \,x^{2}-20 b^{3} c^{3} x^{2}+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 a^{2} b \,c^{2} d -4 a \,b^{2} c^{3}\right) d}{10 \sqrt{e x}\, \left(d \,x^{2}-c \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a^{2} e^{3} x^{2}}"," ",0,"-1/10*(-d*x^2+c)^(1/2)*d*(28*x^4*a^2*b*d^3+20*x^4*b^3*c^2*d+4*a^2*b*c^2*d-48*x^4*a*b^2*c*d^2+28*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*c*d^2-48*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c^2*d-14*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*c*d^2+24*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c^2*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a^2*d^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a^2*d^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*c*d^2-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*c*d^2-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d-20*x^2*b^3*c^3+52*x^2*a*b^2*c^2*d-32*x^2*a^2*b*c*d^2+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^3+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*c*d-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*c*d-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^3+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3-4*a*b^2*c^3)/x^2/e^3/(e*x)^(1/2)/(d*x^2-c)/a^2/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
880,1,853,227,0.047000," ","int((e*x)^(7/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x)","-\frac{\left(4 \sqrt{a b}\, a b \,d^{3} x^{3}-4 \sqrt{a b}\, b^{2} c \,d^{2} x^{3}-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a b c \,d^{2} x +4 \sqrt{a b}\, b^{2} c^{2} d x +6 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, e^{3}}{6 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(d \,x^{2}-c \right) b d x}"," ",0,"-1/6/b/d*(6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-4*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2+4*(a*b)^(1/2)*a*b*d^3*x^3-4*(a*b)^(1/2)*b^2*c*d^2*x^3-4*(a*b)^(1/2)*a*b*c*d^2*x+4*(a*b)^(1/2)*b^2*c^2*d*x)*(-d*x^2+c)^(1/2)*e^3*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(d*x^2-c)","B"
881,1,470,253,0.042000," ","int((e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x)","-\frac{\left(-4 a b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, e^{2}}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(d \,x^{2}-c \right) b x}"," ",0,"-1/2*(EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d-(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d+EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d+(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d-4*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d+4*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2+2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d-2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-d*x^2+c)^(1/2)*e^2*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(d*x^2-c)/b","A"
882,1,417,191,0.026000," ","int((e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x)","-\frac{\left(-\sqrt{c d}\, a b \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{c d}\, a b \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{a b}\, a d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{a b}\, b c \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, e}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(d \,x^{2}-c \right) x}"," ",0,"-1/2*(2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*d*(a*b)^(1/2)-2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b*c*(a*b)^(1/2)+EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*(c*d)^(1/2)-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*d*(a*b)^(1/2)-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*(c*d)^(1/2)-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*d*(a*b)^(1/2))*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-d*x^2+c)^(1/2)*e*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(d*x^2-c)","B"
883,1,337,143,0.024000," ","int((e*x)^(1/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x)","-\frac{\left(b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{a b}\, \sqrt{c d}\, \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, \sqrt{c d}\, \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, d}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(d \,x^{2}-c \right) x}"," ",0,"-1/2*(EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b*c-(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)+EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b*c+(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2))*d*(-1/(c*d)^(1/2)*d*x)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-d*x^2+c)^(1/2)*(e*x)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/x/(d*x^2-c)","B"
884,1,346,136,0.029000," ","int(1/(-b*x^2+a)/(e*x)^(1/2)/(-d*x^2+c)^(1/2),x)","-\frac{\left(-\sqrt{c d}\, b \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{c d}\, b \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{a b}\, d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-d \,x^{2}+c}\, b}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(d \,x^{2}-c \right) \sqrt{e x}}"," ",0,"-1/2*(EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b-(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*d-EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b-(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*d)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*b*(-d*x^2+c)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(d*x^2-c)/(e*x)^(1/2)","B"
885,1,837,279,0.036000," ","int(1/(e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x)","\frac{\left(4 a \,d^{2} x^{2}-4 b c d \,x^{2}+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b \,c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b \,c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b \,c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b \,c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a c d +4 b \,c^{2}-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, b d}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(d \,x^{2}-c \right) \sqrt{e x}\, a c e}"," ",0,"1/2*(4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*c*d-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b*c^2-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*c*d+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b*c^2+4*x^2*a*d^2-4*x^2*b*c*d-4*a*c*d+4*b*c^2)*d*b*(-d*x^2+c)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/a/c/(d*x^2-c)/e/(e*x)^(1/2)","B"
886,1,740,219,0.032000," ","int(1/(e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x)","\frac{\left(3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a \,d^{2} x^{2}-4 \sqrt{a b}\, b c d \,x^{2}+2 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, a d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b c x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b c x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b c x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a c d +4 \sqrt{a b}\, b \,c^{2}\right) \sqrt{-d \,x^{2}+c}\, b d}{6 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(d \,x^{2}-c \right) \sqrt{e x}\, a c \,e^{2} x}"," ",0,"1/6*b*d*(2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*b*c*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b*c*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b*c*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+4*(a*b)^(1/2)*a*d^2*x^2-4*(a*b)^(1/2)*b*c*d*x^2-4*(a*b)^(1/2)*a*c*d+4*(a*b)^(1/2)*b*c^2)*(-d*x^2+c)^(1/2)/x/c/a/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(d*x^2-c)/e^2/(e*x)^(1/2)","B"
887,1,1109,332,0.037000," ","int(1/(e*x)^(7/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x)","\frac{\left(12 a^{2} d^{3} x^{4}+8 a b c \,d^{2} x^{4}-20 b^{2} c^{2} d \,x^{4}+12 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} c \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+8 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b \,c^{2} d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b \,c^{2} d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-8 a^{2} c \,d^{2} x^{2}-12 a b \,c^{2} d \,x^{2}+20 b^{2} c^{3} x^{2}-5 \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b \,c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, b \,c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a^{2} c^{2} d +4 a b \,c^{3}\right) \sqrt{-d \,x^{2}+c}\, b d}{10 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(d \,x^{2}-c \right) \sqrt{e x}\, a^{2} c^{2} e^{3} x^{2}}"," ",0,"1/10*(12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2+8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3-6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*c*d^2-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*c^2*d+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c^3+5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b*c^2-5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b*c^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^2*c^3-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^2*c^3+12*a^2*d^3*x^4+8*a*b*c*d^2*x^4-20*b^2*c^2*d*x^4-8*a^2*c*d^2*x^2-12*a*b*c^2*d*x^2+20*b^2*c^3*x^2-4*a^2*c^2*d+4*a*b*c^3)*b*d*(-d*x^2+c)^(1/2)/x^2/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/a^2/c^2/(d*x^2-c)/e^3/(e*x)^(1/2)","B"
888,1,1041,344,0.054000," ","int((e*x)^(9/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x)","-\frac{\left(-2 a \,b^{2} c \,d^{2} x^{2}+2 b^{3} c^{2} d \,x^{2}+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, e^{4}}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) b d x}"," ",0,"-1/2*(4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*d+6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^3*c^3+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-2*a*b^2*c*d^2*x^2+2*b^3*c^2*d*x^2)*(-d*x^2+c)^(1/2)*e^4*(e*x)^(1/2)/x/d/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*d-b*c)/(d*x^2-c)/b","B"
889,1,826,264,0.056000," ","int((e*x)^(7/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x)","\frac{\left(-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{a b}\, a b c \,d^{2} x -2 \sqrt{a b}\, b^{2} c^{2} d x +2 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, e^{3}}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(a d -b c \right) \left(d \,x^{2}-c \right) d x}"," ",0,"1/2/d*(2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d^2+2*(a*b)^(1/2)*a*b*c*d^2*x-2*(a*b)^(1/2)*b^2*c^2*d*x)*(-d*x^2+c)^(1/2)*e^3*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(a*d-b*c)/(d*x^2-c)","B"
890,1,841,314,0.032000," ","int((e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x)","-\frac{\left(-2 a b \,d^{2} x^{2}+2 b^{2} c d \,x^{2}-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, e^{2}}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) x}"," ",0,"-1/2*(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*d+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^2-2*a*b*d^2*x^2+2*b^2*c*d*x^2)*(-d*x^2+c)^(1/2)*e^2*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*d-b*c)/(d*x^2-c)","B"
891,1,704,240,0.035000," ","int((e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x)","\frac{\left(-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{a b}\, a \,d^{2} x -2 \sqrt{a b}\, b c d x +\sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b c \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, b e}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(a d -b c \right) \left(d \,x^{2}-c \right) x}"," ",0,"1/2*b*(2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*d*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b*c*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*d+2*x*a*d^2*(a*b)^(1/2)-2*x*b*c*d*(a*b)^(1/2))*(-d*x^2+c)^(1/2)*e*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(a*d-b*c)/(d*x^2-c)","B"
892,1,830,320,0.035000," ","int((e*x)^(1/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x)","\frac{\left(2 a \,d^{2} x^{2}-2 b c d \,x^{2}+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b \,c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b \,c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b \,c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b \,c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, b d}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) c x}"," ",0,"1/2*(2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*c*d-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*c+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*c+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b*c^2+2*a*d^2*x^2-2*b*c*d*x^2)*d*b*(-d*x^2+c)^(1/2)*(e*x)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/c/(a*d-b*c)/(d*x^2-c)/x","B"
893,1,708,254,0.037000," ","int(1/(-b*x^2+a)/(-d*x^2+c)^(3/2)/(e*x)^(1/2),x)","\frac{\left(-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{a b}\, a \,d^{2} x -2 \sqrt{a b}\, b c d x +\sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b c \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, b d}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(a d -b c \right) \left(d \,x^{2}-c \right) \sqrt{e x}\, c}"," ",0,"1/2*b*d*(2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*d*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b*c*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b*c+2*(a*b)^(1/2)*a*d^2*x-2*(a*b)^(1/2)*b*c*d*x)*(-d*x^2+c)^(1/2)/c/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(a*d-b*c)/(d*x^2-c)/(e*x)^(1/2)","B"
894,1,1058,389,0.036000," ","int(1/(e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x)","\frac{\left(6 a^{2} d^{3} x^{2}-10 a b c \,d^{2} x^{2}+4 b^{2} c^{2} d \,x^{2}+6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b \,c^{2} d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b \,c^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a^{2} c \,d^{2}+8 a b \,c^{2} d -4 b^{2} c^{3}+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b \,c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b \,c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, b d}{2 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) \sqrt{e x}\, a \,c^{2} e}"," ",0,"1/2*(6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*c*d^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c^2*d-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*b^2*c^3-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*b*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c^3+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*b^2*c^3+6*a^2*d^3*x^2-10*a*b*c*d^2*x^2+4*b^2*c^2*d*x^2-4*a^2*c*d^2+8*a*b*c^2*d-4*b^2*c^3)*b*d*(-d*x^2+c)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/a/(a*d-b*c)/c^2/(d*x^2-c)/e/(e*x)^(1/2)","B"
895,1,896,315,0.036000," ","int(1/(e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x)","\frac{\left(-3 \sqrt{2}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{3} c^{3} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{3} c^{3} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{a b}\, a^{2} d^{3} x^{2}-14 \sqrt{a b}\, a b c \,d^{2} x^{2}+4 \sqrt{a b}\, b^{2} c^{2} d \,x^{2}+5 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-7 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{a b}\, \sqrt{c d}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a^{2} c \,d^{2}+8 \sqrt{a b}\, a b \,c^{2} d -4 \sqrt{a b}\, b^{2} c^{3}\right) \sqrt{-d \,x^{2}+c}\, b d}{6 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(a d -b c \right) \left(d \,x^{2}-c \right) \sqrt{e x}\, a \,c^{2} e^{2} x}"," ",0,"1/6*b*d*(5*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a^2*d^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-7*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a*b*c*d*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^3*c^3*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^3*c^3*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*b^2*c^2*(a*b)^(1/2)*(c*d)^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+10*x^2*a^2*d^3*(a*b)^(1/2)-14*(a*b)^(1/2)*a*b*c*d^2*x^2+4*(a*b)^(1/2)*b^2*c^2*d*x^2-4*a^2*c*d^2*(a*b)^(1/2)+8*(a*b)^(1/2)*a*b*c^2*d-4*(a*b)^(1/2)*b^2*c^3)*(-d*x^2+c)^(1/2)/x/c^2/a/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(a*d-b*c)/(d*x^2-c)/e^2/(e*x)^(1/2)","B"
896,1,2561,274,0.061000," ","int((e*x)^(7/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x)","-\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \left(16 \sqrt{a b}\, a \,b^{2} d^{3} x^{5}-16 \sqrt{a b}\, b^{3} c \,d^{2} x^{5}-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-28 \sqrt{a b}\, a^{2} b \,d^{3} x^{3}+12 \sqrt{a b}\, a \,b^{2} c \,d^{2} x^{3}+16 \sqrt{a b}\, b^{3} c^{2} d \,x^{3}+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+42 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-58 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+16 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+28 \sqrt{a b}\, a^{2} b c \,d^{2} x -28 \sqrt{a b}\, a \,b^{2} c^{2} d x -42 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+58 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-16 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) e^{3}}{24 \left(d \,x^{2}-c \right) \left(b \,x^{2}-a \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b^{2} x}"," ",0,"-1/24*e^3*(e*x)^(1/2)*(-d*x^2+c)^(1/2)/b^2*(15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-58*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+28*x*a^2*b*c*d^2*(a*b)^(1/2)-28*x*a*b^2*c^2*d*(a*b)^(1/2)+12*x^3*a*b^2*c*d^2*(a*b)^(1/2)+16*x^5*a*b^2*d^3*(a*b)^(1/2)-42*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+16*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-16*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-16*x^5*b^3*c*d^2*(a*b)^(1/2)-28*x^3*a^2*b*d^3*(a*b)^(1/2)+16*x^3*b^3*c^2*d*(a*b)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+42*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+58*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))/x/(d*x^2-c)/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
897,1,2542,303,0.060000," ","int((e*x)^(5/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x)","\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \left(4 a \,b^{2} d^{2} x^{4}-4 b^{3} c d \,x^{4}+20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a \,b^{2} c d \,x^{2}+4 b^{3} c^{2} x^{2}-20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d \,e^{2}}{8 \left(d \,x^{2}-c \right) \left(b \,x^{2}-a \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b^{2} x}"," ",0,"1/8*e^2*(e*x)^(1/2)*(-d*x^2+c)^(1/2)*d*(4*x^4*a*b^2*d^2-4*x^4*b^3*c*d-4*x^2*a*b^2*c*d+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+4*x^2*b^3*c^2)/x/b^2/(d*x^2-c)/(b*x^2-a)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
898,1,2255,246,0.024000," ","int((e*x)^(3/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x)","-\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \left(-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a b \,d^{2} x^{3}+4 \sqrt{a b}\, b^{2} c d \,x^{3}+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a b c d x -4 \sqrt{a b}\, b^{2} c^{2} x -6 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d e}{8 \left(d \,x^{2}-c \right) \left(b \,x^{2}-a \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) b x}"," ",0,"-1/8*e*(e*x)^(1/2)*(-d*x^2+c)^(1/2)/b*d*(6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c-4*x^3*a*b*d^2*(a*b)^(1/2)+4*x^3*b^2*c*d*(a*b)^(1/2)+4*x*a*b*c*d*(a*b)^(1/2)-4*x*b^2*c^2*(a*b)^(1/2))/x/(d*x^2-c)/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
899,1,2534,307,0.024000," ","int((e*x)^(1/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x)","\frac{\sqrt{e x}\, \sqrt{-d \,x^{2}+c}\, \left(4 a \,b^{2} d^{2} x^{4}-4 b^{3} c d \,x^{4}+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a \,b^{2} c d \,x^{2}+4 b^{3} c^{2} x^{2}-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d}{8 \left(d \,x^{2}-c \right) \left(b \,x^{2}-a \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a b x}"," ",0,"1/8*(e*x)^(1/2)*(-d*x^2+c)^(1/2)*d*(4*a*b^2*d^2*x^4-4*b^3*c*d*x^4-4*a*b^2*c*d*x^2+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+4*b^3*c^2*x^2)/b/x/(d*x^2-c)/a/(b*x^2-a)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
900,1,2251,253,0.036000," ","int((-d*x^2+c)^(1/2)/(e*x)^(1/2)/(-b*x^2+a)^2,x)","\frac{\sqrt{-d \,x^{2}+c}\, \left(-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a b \,d^{2} x^{3}-4 \sqrt{a b}\, b^{2} c d \,x^{3}+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a b c d x +4 \sqrt{a b}\, b^{2} c^{2} x -2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d}{8 \sqrt{e x}\, \left(d \,x^{2}-c \right) \left(b \,x^{2}-a \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a}"," ",0,"1/8*(-d*x^2+c)^(1/2)*d*(2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+4*(a*b)^(1/2)*a*b*d^2*x^3-4*(a*b)^(1/2)*b^2*c*d*x^3-4*(a*b)^(1/2)*a*b*c*d*x+4*(a*b)^(1/2)*b^2*c^2*x)/a/(e*x)^(1/2)/(d*x^2-c)/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
901,1,2568,328,0.034000," ","int((-d*x^2+c)^(1/2)/(e*x)^(3/2)/(-b*x^2+a)^2,x)","\frac{\sqrt{-d \,x^{2}+c}\, \left(20 a \,b^{2} d^{2} x^{4}-20 b^{3} c d \,x^{4}+20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-16 a^{2} b \,d^{2} x^{2}-4 a \,b^{2} c d \,x^{2}+20 b^{3} c^{2} x^{2}-20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+20 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-10 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+16 a^{2} b c d -16 a \,b^{2} c^{2}-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d}{8 \sqrt{e x}\, \left(d \,x^{2}-c \right) \left(b \,x^{2}-a \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a^{2} e}"," ",0,"1/8*(-d*x^2+c)^(1/2)*d*(20*a*b^2*d^2*x^4-20*b^3*c*d*x^4-16*x^2*a^2*b*d^2+16*a^2*b*c*d-4*a*b^2*c*d*x^2+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2-16*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+20*b^3*c^2*x^2)/e/(e*x)^(1/2)/(d*x^2-c)/a^2/(b*x^2-a)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
902,1,2316,267,0.033000," ","int((-d*x^2+c)^(1/2)/(e*x)^(5/2)/(-b*x^2+a)^2,x)","\frac{\sqrt{-d \,x^{2}+c}\, \left(-15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+28 \sqrt{a b}\, a b \,d^{2} x^{4}-28 \sqrt{a b}\, b^{2} c d \,x^{4}+15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+14 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b d \,x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b d \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b d \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-14 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c \,x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{2} c \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-16 \sqrt{a b}\, a^{2} d^{2} x^{2}-12 \sqrt{a b}\, a b c d \,x^{2}+28 \sqrt{a b}\, b^{2} c^{2} x^{2}-14 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+14 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{c d}\, \sqrt{a b}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a b c x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+16 \sqrt{a b}\, a^{2} c d -16 \sqrt{a b}\, a b \,c^{2}\right) b d}{24 \sqrt{e x}\, \left(d \,x^{2}-c \right) \left(b \,x^{2}-a \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a^{2} e^{2} x}"," ",0,"1/24*(-d*x^2+c)^(1/2)*b*d*(16*a^2*c*d*(a*b)^(1/2)-16*a*b*c^2*(a*b)^(1/2)+28*x^2*b^2*c^2*(a*b)^(1/2)-16*x^2*a^2*d^2*(a*b)^(1/2)-12*x^2*a*b*c*d*(a*b)^(1/2)+28*x^4*a*b*d^2*(a*b)^(1/2)+14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^3*a*b*d*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b*d*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b*d*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a*b*c*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b*c*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b*c*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^3*b^2*c*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^2*c*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^2*c*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a^2*d*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*d*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+15*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*d*(c*d)^(1/2)*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-28*x^4*b^2*c*d*(a*b)^(1/2))/x/a^2/e^2/(e*x)^(1/2)/(d*x^2-c)/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
903,1,3790,335,0.039000," ","int((e*x)^(7/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/168*e^3*(e*x)^(1/2)*(-d*x^2+c)^(1/2)/b^3*(-536*x*a^2*b^2*c^2*d^2*(a*b)^(1/2)+228*x*a*b^3*c^3*d*(a*b)^(1/2)-368*x^5*a*b^3*c*d^3*(a*b)^(1/2)+360*x^3*a^2*b^2*c*d^3*(a*b)^(1/2)+92*x^3*a*b^3*c^2*d^2*(a*b)^(1/2)+308*x*a^3*b*c*d^3*(a*b)^(1/2)-462*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^4*d^3*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-231*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^4*b*c*d^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+231*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^4*d^3*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+336*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b^2*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-105*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^3*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+231*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^4*b*c*d^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+231*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^4*d^3*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-336*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b^2*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+105*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^3*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-308*x^3*a^3*b*d^4*(a*b)^(1/2)-980*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+614*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+336*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-105*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+336*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-105*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-96*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+231*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^3*b^2*c*d^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-336*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^3*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+105*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^4*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-231*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^3*b^2*c*d^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+336*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^3*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-105*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^4*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+96*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+48*x^7*a*b^3*d^4*(a*b)^(1/2)-48*x^7*b^4*c*d^3*(a*b)^(1/2)+176*x^5*a^2*b^2*d^4*(a*b)^(1/2)+192*x^5*b^4*c^2*d^2*(a*b)^(1/2)-144*x^3*b^4*c^3*d*(a*b)^(1/2)-614*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-336*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+105*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-336*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+105*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+462*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^3*b*d^3*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-231*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^3*b*d^3*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-231*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^3*b*d^3*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+980*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2*(a*b)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))/x/(d*x^2-c)/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
904,1,3886,369,0.036000," ","int((e*x)^(5/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/40*e^2*(e*x)^(1/2)*(-d*x^2+c)^(1/2)*d*(60*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-60*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-36*x^4*a^2*b^2*d^3-4*x^4*b^4*c^2*d+16*x^6*a*b^3*d^3-16*x^6*b^4*c*d^2+40*x^4*a*b^3*c*d^2+45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-60*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-60*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-132*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3+66*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3+132*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3-66*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-180*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2+312*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d+90*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2-156*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2-45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-60*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+60*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+180*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2-312*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d-90*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2+156*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d+36*x^2*a^2*b^2*c*d^2-56*x^2*a*b^3*c^2*d+20*x^2*b^4*c^3-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+60*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-45*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+60*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))/x/b^3/(d*x^2-c)/(b*x^2-a)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
905,1,3466,293,0.034000," ","int((e*x)^(3/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/24*e*(e*x)^(1/2)*(-d*x^2+c)^(1/2)/b^2*d*(24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-76*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+28*(a*b)^(1/2)*a^2*b*c*d^2*x-40*(a*b)^(1/2)*a*b^2*c^2*d*x+12*x*b^3*c^3*(a*b)^(1/2)+24*(a*b)^(1/2)*a*b^2*c*d^2*x^3+16*(a*b)^(1/2)*a*b^2*d^3*x^5-42*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+34*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-34*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2-16*(a*b)^(1/2)*b^3*c*d^2*x^5-28*(a*b)^(1/2)*a^2*b*d^3*x^3+4*(a*b)^(1/2)*b^3*c^2*d*x^3-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+42*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+76*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))/x/(d*x^2-c)/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
906,1,3858,364,0.034000," ","int((e*x)^(1/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/8*(e*x)^(1/2)*(-d*x^2+c)^(1/2)*d*(4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*x^4*a^2*b^2*d^3-4*x^4*b^4*c^2*d+8*x^4*a*b^3*c*d^2+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2+24*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2-12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2-24*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2+12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d+4*x^2*a^2*b^2*c*d^2-8*x^2*a*b^3*c^2*d+4*x^2*b^4*c^3+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))/b^2/x/(d*x^2-c)/a/(b*x^2-a)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
907,1,2531,284,0.035000," ","int((-d*x^2+c)^(3/2)/(e*x)^(1/2)/(-b*x^2+a)^2,x)","\frac{\sqrt{-d \,x^{2}+c}\, \left(-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{4} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{4} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a^{2} b \,d^{3} x^{3}+8 \sqrt{a b}\, a \,b^{2} c \,d^{2} x^{3}-4 \sqrt{a b}\, b^{3} c^{2} d \,x^{3}+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a^{2} b c \,d^{2} x -8 \sqrt{a b}\, a \,b^{2} c^{2} d x +4 \sqrt{a b}\, b^{3} c^{3} x -6 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) d}{8 \sqrt{e x}\, \left(d \,x^{2}-c \right) \left(b \,x^{2}-a \right) \sqrt{a b}\, \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) a b}"," ",0,"1/8*(-d*x^2+c)^(1/2)/b*d*(-4*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*(a*b)^(1/2)*a^2*b*c*d^2*x-8*(a*b)^(1/2)*a*b^2*c^2*d*x+4*x*b^3*c^3*(a*b)^(1/2)+8*(a*b)^(1/2)*a*b^2*c*d^2*x^3-6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2-4*(a*b)^(1/2)*a^2*b*d^3*x^3-4*(a*b)^(1/2)*b^3*c^2*d*x^3-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2))/a/(e*x)^(1/2)/(d*x^2-c)/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
908,1,3879,403,0.046000," ","int((-d*x^2+c)^(3/2)/(e*x)^(3/2)/(-b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/8*(-d*x^2+c)^(1/2)*d*(-4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*x^4*a^2*b^2*d^3-20*x^4*b^4*c^2*d+16*a^2*b^2*c^2*d-16*a*b^3*c^3+24*x^4*a*b^3*c*d^2+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2+24*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2-12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2-24*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2+12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d-12*x^2*a^2*b^2*c*d^2-8*x^2*a*b^3*c^2*d+20*x^2*b^4*c^3+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))/b/e/(e*x)^(1/2)/(d*x^2-c)/a^2/(b*x^2-a)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
909,1,3484,324,0.041000," ","int((-d*x^2+c)^(3/2)/(e*x)^(5/2)/(-b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"-1/24*(-d*x^2+c)^(1/2)*d*(-40*x^4*a*b^2*c*d^2*(a*b)^(1/2)+4*x^2*a^2*b*c*d^2*(a*b)^(1/2)-28*x^2*b^3*c^3*(a*b)^(1/2)+16*a*b^2*c^3*(a*b)^(1/2)+24*x^2*a*b^2*c^2*d*(a*b)^(1/2)-14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^3*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+12*x^4*a^2*b*d^3*(a*b)^(1/2)+28*x^4*b^3*c^2*d*(a*b)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^3*c^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^3*c^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-16*a^2*b*c^2*d*(a*b)^(1/2)-24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-20*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^3*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+20*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^4*c^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^4*c^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^3*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+24*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))/x/a^2/e^2/(e*x)^(1/2)/(d*x^2-c)/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)","B"
910,1,2956,374,0.037000," ","int((e*x)^(9/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x)","\text{output too large to display}"," ",0,"1/8*(7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*x^4*a^2*b^2*d^3+4*x^4*a*b^3*c*d^2+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-16*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3+8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3+16*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3-8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2+36*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2-18*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2-36*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2+18*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d+4*x^2*a^2*b^2*c*d^2-4*x^2*a*b^3*c^2*d-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))*(-d*x^2+c)^(1/2)*e^4*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(b*x^2-a)/(a*d-b*c)/(d*x^2-c)/b^2","B"
911,1,2520,294,0.033000," ","int((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x)","\frac{\left(-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a^{2} b \,d^{3} x^{3}+4 \sqrt{a b}\, a \,b^{2} c \,d^{2} x^{3}+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-14 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+8 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a^{2} b c \,d^{2} x -4 \sqrt{a b}\, a \,b^{2} c^{2} d x -6 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+14 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-8 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, e^{3}}{8 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(b \,x^{2}-a \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) b x}"," ",0,"1/8/b*(5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*(a*b)^(1/2)*a^2*b*c*d^2*x-4*(a*b)^(1/2)*a*b^2*c^2*d*x+4*(a*b)^(1/2)*a*b^2*c*d^2*x^3-6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+8*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-8*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*(a*b)^(1/2)*a^2*b*d^3*x^3-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))*(-d*x^2+c)^(1/2)*e^3*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(b*x^2-a)/(a*d-b*c)/(d*x^2-c)","B"
912,1,2548,350,0.036000," ","int((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x)","-\frac{\left(4 a \,b^{2} d^{2} x^{4}-4 b^{3} c d \,x^{4}+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a \,b^{2} c d \,x^{2}+4 b^{3} c^{2} x^{2}-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, d \,e^{2}}{8 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(b \,x^{2}-a \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) b x}"," ",0,"-1/8*(4*a*b^2*d^2*x^4-4*b^3*c*d*x^4-4*a*b^2*c*d*x^2+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+4*b^3*c^2*x^2)*d*(-d*x^2+c)^(1/2)*e^2*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(b*x^2-a)/(a*d-b*c)/(d*x^2-c)/b","B"
913,1,2258,281,0.035000," ","int((e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x)","-\frac{\left(-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a b \,d^{2} x^{3}-4 \sqrt{a b}\, b^{2} c d \,x^{3}+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a b c d x +4 \sqrt{a b}\, b^{2} c^{2} x -2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, d e}{8 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(b \,x^{2}-a \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) x}"," ",0,"-1/8*d*(2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+4*(a*b)^(1/2)*a*b*d^2*x^3-4*(a*b)^(1/2)*b^2*c*d*x^3-4*(a*b)^(1/2)*a*b*c*d*x+4*(a*b)^(1/2)*b^2*c^2*x)*(-d*x^2+c)^(1/2)*e*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(b*x^2-a)/(a*d-b*c)/(d*x^2-c)","B"
914,1,2545,354,0.038000," ","int((e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x)","-\frac{\left(4 a \,b^{2} d^{2} x^{4}-4 b^{3} c d \,x^{4}+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 a \,b^{2} c d \,x^{2}+4 b^{3} c^{2} x^{2}-4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, d}{8 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(b \,x^{2}-a \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) a x}"," ",0,"-1/8*(4*a*b^2*d^2*x^4-4*b^3*c*d*x^4-4*a*b^2*c*d*x^2+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+4*b^3*c^2*x^2)*d*(-d*x^2+c)^(1/2)*(e*x)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(b*x^2-a)/a/(a*d-b*c)/x/(d*x^2-c)","B"
915,1,2266,285,0.050000," ","int(1/(e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x)","-\frac{\left(-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a b \,d^{2} x^{3}-4 \sqrt{a b}\, b^{2} c d \,x^{3}+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{a b}\, a b c d x +4 \sqrt{a b}\, b^{2} c^{2} x -2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, b d}{8 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(b \,x^{2}-a \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) \sqrt{e x}\, a}"," ",0,"-1/8*b*d*(2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+4*(a*b)^(1/2)*a*b*d^2*x^3-4*(a*b)^(1/2)*b^2*c*d*x^3-4*(a*b)^(1/2)*a*b*c*d*x+4*(a*b)^(1/2)*b^2*c^2*x)*(-d*x^2+c)^(1/2)/a/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(b*x^2-a)/(a*d-b*c)/(d*x^2-c)/(e*x)^(1/2)","B"
916,1,2982,419,0.046000," ","int(1/(e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x)","\text{output too large to display}"," ",0,"-1/8*(-36*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c^2*d+18*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c^2*d-7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d-7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d-16*a^2*b*d^3*x^4-20*b^3*c^2*d*x^4+32*a^2*b*c^2*d+16*x^2*a^3*d^3+36*a*b^2*c*d^2*x^4-16*a^3*c*d^2-16*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*c*d^2+36*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c^2*d+8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*c*d^2-18*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c^2*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c^2-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c^2+7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d+7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c^2-7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*c*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c^2+7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*c*d+20*b^3*c^3*x^2+16*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*c*d^2-20*a*b^2*c^2*d*x^2-16*a^2*b*c*d^2*x^2-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^3-7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*c*d+7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*c*d+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^3-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^3-8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*c*d^2-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^3+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^3+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^3-16*a*b^2*c^3)*b*d*(-d*x^2+c)^(1/2)/c/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(b*x^2-a)/(a*d-b*c)/a^2/(d*x^2-c)/e/(e*x)^(1/2)","B"
917,1,2622,341,0.041000," ","int(1/(e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x)","\frac{\left(27 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-27 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{4} c^{3} x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{4} c^{3} x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+16 \sqrt{a b}\, a^{2} b \,d^{3} x^{4}-44 \sqrt{a b}\, a \,b^{2} c \,d^{2} x^{4}+28 \sqrt{a b}\, b^{3} c^{2} d \,x^{4}-27 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+27 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+8 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-22 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+27 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+27 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+14 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, b^{3} c^{2} x^{3} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, b^{3} c^{2} x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, b^{3} c^{2} x^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-16 \sqrt{a b}\, a^{3} d^{3} x^{2}+16 \sqrt{a b}\, a^{2} b c \,d^{2} x^{2}+28 \sqrt{a b}\, a \,b^{2} c^{2} d \,x^{2}-28 \sqrt{a b}\, b^{3} c^{3} x^{2}-8 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+22 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-27 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-27 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-14 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c^{2} x \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c^{2} x \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+16 \sqrt{a b}\, a^{3} c \,d^{2}-32 \sqrt{a b}\, a^{2} b \,c^{2} d +16 \sqrt{a b}\, a \,b^{2} c^{3}\right) \sqrt{-d \,x^{2}+c}\, b d}{24 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(b \,x^{2}-a \right) \left(a d -b c \right) \left(d \,x^{2}-c \right) \sqrt{e x}\, a^{2} c \,e^{2} x}"," ",0,"1/24*b*d*(-44*x^4*a*b^2*c*d^2*(a*b)^(1/2)+16*x^2*a^2*b*c*d^2*(a*b)^(1/2)-16*x^2*a^3*d^3*(a*b)^(1/2)+16*a^3*c*d^2*(a*b)^(1/2)-28*x^2*b^3*c^3*(a*b)^(1/2)+16*a*b^2*c^3*(a*b)^(1/2)+28*x^2*a*b^2*c^2*d*(a*b)^(1/2)-14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+8*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^3*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+16*x^4*a^2*b*d^3*(a*b)^(1/2)+28*x^4*b^3*c^2*d*(a*b)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^3*c^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a*b^3*c^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-32*a^2*b*c^2*d*(a*b)^(1/2)-27*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-27*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-22*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^3*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+27*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+27*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+22*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^4*c^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^4*c^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-27*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+14*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^3*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-27*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+27*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^3*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-8*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+27*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))*(-d*x^2+c)^(1/2)/x/c/a^2/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(b*x^2-a)/(a*d-b*c)/(d*x^2-c)/e^2/(e*x)^(1/2)","B"
918,1,2964,413,0.039000," ","int((e*x)^(9/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x)","\text{output too large to display}"," ",0,"-1/8*(7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-4*x^4*a^2*b^2*d^3+8*x^4*b^4*c^2*d-4*x^4*a*b^3*c*d^2+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^3-8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^3-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c*d^2+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^2*d-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c*d^2-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^2*d+12*x^2*a^2*b^2*c*d^2-12*x^2*a*b^3*c^2*d-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+7*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))*(-d*x^2+c)^(1/2)*e^4*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(b*x^2-a)/(a*d-b*c)^2/(d*x^2-c)/b","B"
919,1,2530,332,0.040000," ","int((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x)","\frac{\left(-\sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{a b}\, a^{2} b \,d^{3} x^{3}+4 \sqrt{a b}\, a \,b^{2} c \,d^{2} x^{3}-8 \sqrt{a b}\, b^{3} c^{2} d \,x^{3}+\sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{3} b c \,d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{a b}\, a^{2} b c \,d^{2} x +12 \sqrt{a b}\, a \,b^{2} c^{2} d x -2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, e^{3}}{8 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(b \,x^{2}-a \right) \left(a d -b c \right)^{2} \left(d \,x^{2}-c \right) x}"," ",0,"1/8*(-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-12*(a*b)^(1/2)*a^2*b*c*d^2*x+12*(a*b)^(1/2)*a*b^2*c^2*d*x+4*(a*b)^(1/2)*a*b^2*c*d^2*x^3-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-4*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+4*(a*b)^(1/2)*a^2*b*d^3*x^3-8*(a*b)^(1/2)*b^3*c^2*d*x^3-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))*(-d*x^2+c)^(1/2)*e^3*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(b*x^2-a)/(a*d-b*c)^2/(d*x^2-c)","B"
920,1,2561,369,0.045000," ","int((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x)","\frac{\left(12 a \,b^{2} d^{2} x^{4}-12 b^{3} c d \,x^{4}+12 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-8 a^{2} b \,d^{2} x^{2}+4 a \,b^{2} c d \,x^{2}+4 b^{3} c^{2} x^{2}-12 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+12 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticE \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, d \,e^{2}}{8 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \left(b \,x^{2}-a \right) \left(a d -b c \right)^{2} \left(d \,x^{2}-c \right) x}"," ",0,"1/8*(12*a*b^2*d^2*x^4-12*b^3*c*d*x^4-8*a^2*b*d^2*x^2+4*a*b^2*c*d*x^2+12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d-6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d+6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d+12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2-6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+6*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c+4*b^3*c^2*x^2)*d*(-d*x^2+c)^(1/2)*e^2*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(b*x^2-a)/(a*d-b*c)^2/(d*x^2-c)","B"
921,1,2277,303,0.037000," ","int((e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x)","-\frac{\left(5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{a b}\, a b \,d^{2} x^{3}+12 \sqrt{a b}\, b^{2} c d \,x^{3}-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, b^{2} c \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{2} c \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+8 \sqrt{a b}\, a^{2} d^{2} x -4 \sqrt{a b}\, a b c d x -4 \sqrt{a b}\, b^{2} c^{2} x +6 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a^{2} d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{2}\, \sqrt{a b}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, a b c \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a b c \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{e x}\, b d e}{8 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(b \,x^{2}-a \right) \left(a d -b c \right)^{2} \left(d \,x^{2}-c \right) x}"," ",0,"-1/8*b*d*(8*x*a^2*d^2*(a*b)^(1/2)-4*(a*b)^(1/2)*b^2*c^2*x-4*(a*b)^(1/2)*a*b*c*d*x-12*(a*b)^(1/2)*a*b*d^2*x^3+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d-6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^2+6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^2*c*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^2-6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b*d*(a*b)^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)+12*(a*b)^(1/2)*b^2*c*d*x^3+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*d+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c)*(-d*x^2+c)^(1/2)*e*(e*x)^(1/2)/x/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(b*x^2-a)/(a*d-b*c)^2/(d*x^2-c)","B"
922,1,2950,415,0.043000," ","int((e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x)","\text{output too large to display}"," ",0,"-1/8*(-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c^2*d+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c^2*d+7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d+7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d-8*a^2*b*d^3*x^4+4*b^3*c^2*d*x^4+8*x^2*a^3*d^3+4*a*b^2*c*d^2*x^4-8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*c*d^2+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c^2*d+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*c*d^2-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c^2*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c^2+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^2*c^2-7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d-7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c^2+7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*c*d-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b*c^2-7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^2*c*d-4*b^3*c^3*x^2+8*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*c*d^2+4*a*b^2*c^2*d*x^2-8*a^2*b*c*d^2*x^2+4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^3+7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*c*d-7*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a*b*c*d-2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^3+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3+((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^3-4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*c*d^2+2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^3-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^3-((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^3)*d*b*(-d*x^2+c)^(1/2)*(e*x)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(b*x^2-a)/a/c/(a*d-b*c)^2/x/(d*x^2-c)","B"
923,1,2554,338,0.045000," ","int(1/(e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x)","\frac{\left(-9 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+9 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{4} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, b^{4} c^{3} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+8 \sqrt{a b}\, a^{2} b \,d^{3} x^{3}-4 \sqrt{a b}\, a \,b^{2} c \,d^{2} x^{3}-4 \sqrt{a b}\, b^{3} c^{2} d \,x^{3}+9 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-9 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a^{2} b^{2} c^{2} d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b \,d^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, a \,b^{3} c^{3} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-9 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-9 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c d \,x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, b^{3} c^{2} x^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-8 \sqrt{a b}\, a^{3} d^{3} x +8 \sqrt{a b}\, a^{2} b c \,d^{2} x -4 \sqrt{a b}\, a \,b^{2} c^{2} d x +4 \sqrt{a b}\, b^{3} c^{3} x -4 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{3} d^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)+9 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+9 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a^{2} b c d \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{c d}\, \sqrt{a b}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b -\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{2}\, \sqrt{\frac{-d x +\sqrt{c d}}{\sqrt{c d}}}\, \sqrt{-\frac{d x}{\sqrt{c d}}}\, \sqrt{a b}\, \sqrt{c d}\, a \,b^{2} c^{2} \EllipticPi \left(\sqrt{\frac{d x +\sqrt{c d}}{\sqrt{c d}}}, \frac{\sqrt{c d}\, b}{\sqrt{c d}\, b +\sqrt{a b}\, d}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-d \,x^{2}+c}\, b d}{8 \left(\sqrt{c d}\, b -\sqrt{a b}\, d \right) \left(\sqrt{c d}\, b +\sqrt{a b}\, d \right) \sqrt{a b}\, \left(b \,x^{2}-a \right) \left(a d -b c \right)^{2} \left(d \,x^{2}-c \right) \sqrt{e x}\, a c}"," ",0,"1/8*b*d*(-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^2*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+8*(a*b)^(1/2)*a^2*b*c*d^2*x-4*(a*b)^(1/2)*a*b^2*c^2*d*x-8*x*a^3*d^3*(a*b)^(1/2)+4*(a*b)^(1/2)*b^3*c^3*x-4*(a*b)^(1/2)*a*b^2*c*d^2*x^3-4*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^3*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^2*c^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^3+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*b^3*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a*b^2*c^2+8*(a*b)^(1/2)*a^2*b*d^3*x^3-4*(a*b)^(1/2)*b^3*c^2*d*x^3+4*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+2*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b*c*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^3-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))*(-d*x^2+c)^(1/2)/c/a/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(b*x^2-a)/(a*d-b*c)^2/(d*x^2-c)/(e*x)^(1/2)","B"
924,1,3385,506,0.053000," ","int(1/(e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x)","\text{output too large to display}"," ",0,"1/8*(-20*x^4*b^4*c^3*d+24*x^4*a^3*b*d^4-48*a^3*b*c^2*d^2+48*a^2*b^2*c^3*d+10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^4-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^4-5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^4-24*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^4*c*d^3+20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^4+12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^4*c*d^3-10*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^4+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^4+5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^4-24*x^2*a^4*d^4+20*x^2*b^4*c^4+40*x^2*a^3*b*c*d^3-11*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d+11*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d-36*x^2*a*b^3*c^3*d-56*x^4*a^2*b^2*c*d^3+52*x^4*a*b^3*c^2*d^2+5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^3-20*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^4+11*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d-11*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d+16*a^4*c*d^3-16*a*b^3*c^4+5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3-5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3+24*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^3*b*c*d^3-56*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c^2*d^2+52*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^3*d-12*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^3*b*c*d^3+28*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c^2*d^2-26*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^3*d+11*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^3*d+11*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^3*d-5*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^3+56*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c^2*d^2-52*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticE(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^3*d-28*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c^2*d^2+26*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^3*d-11*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^3*d-11*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^3*d)*d*b*(-d*x^2+c)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(b*x^2-a)/a^2/(a*d-b*c)^2/c^2/(d*x^2-c)/e/(e*x)^(1/2)","B"
925,1,2871,418,0.069000," ","int(1/(e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x)","\text{output too large to display}"," ",0,"1/24*b*d*(60*x^4*a*b^3*c^2*d^2*(a*b)^(1/2)+56*x^2*a^3*b*c*d^3*(a*b)^(1/2)-44*x^2*a*b^3*c^3*d*(a*b)^(1/2)-16*a*b^3*c^4*(a*b)^(1/2)+16*a^4*c*d^3*(a*b)^(1/2)-40*x^2*a^4*d^4*(a*b)^(1/2)+28*x^2*b^4*c^4*(a*b)^(1/2)-72*x^4*a^2*b^2*c*d^3*(a*b)^(1/2)+21*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b^4*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+40*x^4*a^3*b*d^4*(a*b)^(1/2)-21*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x^3*b^5*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-21*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b^4*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-14*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^3*b^4*c^3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-39*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a^2*b^3*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+39*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a^2*b^3*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-20*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a^4*d^3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+39*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x^3*a*b^4*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x^3*b^4*c^3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-39*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x^3*a*b^4*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+21*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x^3*b^4*c^3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-48*a^3*b*c^2*d^2*(a*b)^(1/2)+48*a^2*b^2*c^3*d*(a*b)^(1/2)-28*x^4*b^4*c^3*d*(a*b)^(1/2)+20*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^3*a^3*b*d^3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-21*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b^3*c^3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-21*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a*b^3*c^3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+14*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a*b^3*c^3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-39*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x^3*a*b^3*c^2*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-39*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x^3*a*b^3*c^2*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-36*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^3*a^2*b^2*c*d^2*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+30*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^3*a*b^3*c^2*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+39*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a^2*b^2*c^2*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+39*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x*a^2*b^2*c^2*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+36*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a^3*b*c*d^2*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)-30*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x*a^2*b^2*c^2*d*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)+21*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*2^(1/2)*x^3*b^5*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2))*(-d*x^2+c)^(1/2)/x/c^2/a^2/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/(a*b)^(1/2)/(b*x^2-a)/(a*d-b*c)^2/(d*x^2-c)/e^2/(e*x)^(1/2)","B"
926,1,5126,446,0.099000," ","int((e*x)^(9/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
927,1,4403,360,0.076000," ","int((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"1/24*e^3*(e*x)^(1/2)*(-d*x^2+c)^(1/2)*b*(-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a^2*b^2*c*d^3-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a*b^3*c^2*d^2+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a^2*b^2*c*d^3+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a*b^3*c^2*d^2+36*x^3*a^2*b*c*d^3*(a*b)^(1/2)-36*x^3*a*b^2*c^2*d^2*(a*b)^(1/2)-20*x*a^2*b*c^2*d^2*(a*b)^(1/2)+40*x*a*b^2*c^3*d*(a*b)^(1/2)+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^4*a^2*b*d^3+10*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*a^2*b*c^2*d*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+28*x^3*a^3*d^4*(a*b)^(1/2)+20*x^5*a*b^2*c*d^3*(a*b)^(1/2)-40*x^5*a^2*b*d^4*(a*b)^(1/2)+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^4*a^2*b*d^3-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a^3*d^3-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a^3*d^3+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^3*b*c*d^3+30*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c^2*d^2-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^3*b*c*d^3-30*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c^2*d^2+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^3*c*d^2+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*a^3*c*d^2-15*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d-15*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^4*a*b^2*c*d^2+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^4*a*b^2*c*d^2-30*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a^2*b*c*d^2-30*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a^2*b*c*d^2+20*x^5*b^3*c^2*d^2*(a*b)^(1/2)-28*x^3*b^3*c^3*d*(a*b)^(1/2)-20*x*a^3*c*d^3*(a*b)^(1/2)+15*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d+15*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d-20*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^4*a^2*b*d^3*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+10*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^4*b^3*c^2*d*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^3*d-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^3*d-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^3*d+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^3*d-15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c^2*d^2+15*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^3*b*c^2*d^2-20*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*a^3*c*d^2*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+10*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*a*b^2*c^3*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+20*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^2*a^3*d^3*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)-10*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^2*b^3*c^3*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+10*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^4*a*b^2*c*d^2*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+10*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^2*a^2*b*c*d^2*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)-20*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^2*a*b^2*c^2*d*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2))/x/(a*d-b*c)^3/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/(d*x^2-c)^2","B"
928,1,5078,429,0.070000," ","int((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
929,1,4403,353,0.049000," ","int((e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"-1/24*e*(e*x)^(1/2)*(-d*x^2+c)^(1/2)*b*d*(27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a*b^3*c^2*d^2-27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a*b^3*c^2*d^2-36*x^3*a^2*b*c*d^3*(a*b)^(1/2)-36*x^3*a*b^2*c^2*d^2*(a*b)^(1/2)+56*x*a^2*b*c^2*d^2*(a*b)^(1/2)-40*x*a*b^2*c^3*d*(a*b)^(1/2)+26*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*a^2*b*c^2*d*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)-4*x^3*a^3*d^4*(a*b)^(1/2)-12*x*b^3*c^4*(a*b)^(1/2)+52*x^5*a*b^2*c*d^3*(a*b)^(1/2)-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^4+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^4+3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^4-3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^4+4*x^5*a^2*b*d^4*(a*b)^(1/2)+3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*b^4*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*b^4*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c^2*d^2+27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c^2*d^2+30*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d+30*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^2*c^2*d-27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^4*a*b^2*c*d^2-27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^4*a*b^2*c*d^2+27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a^2*b*c*d^2+27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*(c*d)^(1/2)*x^2*a^2*b*c*d^2-3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^3-56*x^5*b^3*c^2*d^2*(a*b)^(1/2)+76*x^3*b^3*c^3*d*(a*b)^(1/2)-4*x*a^3*c*d^3*(a*b)^(1/2)-27*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d-27*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b*c^2*d-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-3*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*b^3*c^2*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^4*a^2*b*d^3*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)-28*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^4*b^3*c^2*d*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3+3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^3*c^3-30*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^3*d+30*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^3*d-3*(c*d)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(a*b)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^2*c^3+27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^3*d-27*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*2^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^3*d+2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*a^3*c*d^2*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)-28*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*a*b^2*c^3*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)-2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^2*a^3*d^3*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+28*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^2*b^3*c^3*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+26*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^4*a*b^2*c*d^2*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)-28*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^2*a^2*b*c*d^2*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)+2*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^2*a*b^2*c^2*d*(a*b)^(1/2)*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2))/x/(a*d-b*c)^3/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/(d*x^2-c)^2/c","B"
930,1,5689,503,0.054000," ","int((e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
931,1,4776,420,0.068000," ","int(1/(e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"1/24*(-d*x^2+c)^(1/2)*b*d*(56*x^5*a*b^3*c^2*d^3*(a*b)^(1/2)+60*x^3*a^3*b*c*d^4*(a*b)^(1/2)+36*x^3*a^2*b^2*c^2*d^3*(a*b)^(1/2)-52*x^3*a*b^3*c^3*d^2*(a*b)^(1/2)-104*x*a^3*b*c^2*d^3*(a*b)^(1/2)+76*x*a^2*b^2*c^3*d^2*(a*b)^(1/2)-12*x*a*b^3*c^4*d*(a*b)^(1/2)-20*x^3*a^4*d^5*(a*b)^(1/2)+12*x*b^4*c^5*(a*b)^(1/2)-88*x^5*a^2*b^2*c*d^4*(a*b)^(1/2)-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^5*c^5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^4*c^5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^4*c^5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^5*c^5*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+20*x^5*a^3*b*d^5*(a*b)^(1/2)-30*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^4*c^4*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^3*c^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a*b^4*c^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+30*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^4*c^4*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*b^4*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-10*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^4*d^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*b^4*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a*b^3*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+10*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^4*c*d^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a*b^3*c^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a*b^4*c^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^3*c^3*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+12*x^5*b^4*c^3*d^2*(a*b)^(1/2)-24*x^3*b^4*c^4*d*(a*b)^(1/2)+28*x*a^4*c*d^4*(a*b)^(1/2)-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*b^4*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*b^4*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+10*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^3*b*d^4*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+6*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b^4*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^2*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-44*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^3*b*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+28*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*a^2*b^2*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*b^5*c^4*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+9*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*b^5*c^4*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^3*c^4*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)-39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*a^2*b^3*c^4*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)+39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a*b^3*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^4*a*b^3*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-44*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a^2*b^2*c*d^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+28*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^4*a*b^3*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-30*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-39*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a^2*b^2*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-30*2^(1/2)*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)*b,1/2*2^(1/2))*x^2*a*b^3*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+34*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^3*b*c*d^3*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+16*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a^2*b^2*c^2*d^2*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)-34*2^(1/2)*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*x^2*a*b^3*c^3*d*((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-1/(c*d)^(1/2)*d*x)^(1/2)*(c*d)^(1/2)*(a*b)^(1/2))/(e*x)^(1/2)/(a*d-b*c)^3/(b*x^2-a)/(a*b)^(1/2)/((c*d)^(1/2)*b+(a*b)^(1/2)*d)/((c*d)^(1/2)*b-(a*b)^(1/2)*d)/(d*x^2-c)^2/a/c^2","B"
932,1,6334,607,0.102000," ","int(1/(e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
933,1,5248,506,0.114000," ","int(1/(e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
934,1,532,177,0.084000," ","int(x^5*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(16 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} d^{2} x^{4}+3 a^{3} d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 a^{2} b c \,d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+9 a \,b^{2} c^{2} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-15 b^{3} c^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+4 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\, a b \,d^{2} x^{2}-20 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c d \,x^{2}-6 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} d^{2}-8 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\, a b c d +30 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c^{2}\right)}{96 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} d^{3}}"," ",0,"1/96*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(16*x^4*b^2*d^2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*a*b*d^2*(b*d)^(1/2)-20*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*c*b^2*d*(b*d)^(1/2)+3*d^3*ln(1/2*(2*x^2*b*d+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+a*d+b*c)/(b*d)^(1/2))*a^3+3*ln(1/2*(2*x^2*b*d+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+a*d+b*c)/(b*d)^(1/2))*a^2*c*b*d^2+9*ln(1/2*(2*x^2*b*d+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+a*d+b*c)/(b*d)^(1/2))*a*c^2*b^2*d-15*b^3*ln(1/2*(2*x^2*b*d+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+a*d+b*c)/(b*d)^(1/2))*c^3-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a^2*d^2*(b*d)^(1/2)-8*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a*c*b*d*(b*d)^(1/2)+30*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*c^2*b^2*(b*d)^(1/2))/d^3/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/b^2/(b*d)^(1/2)","B"
935,1,339,111,0.017000," ","int(x^3*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(a^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 a b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-3 b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-4 \sqrt{b d}\, \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, b d \,x^{2}-2 \sqrt{b d}\, \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, a d +6 \sqrt{b d}\, \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, b c \right)}{16 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\, b \,d^{2}}"," ",0,"-1/16*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-4*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*b*d+d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2+2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*c*b*d-3*b^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*c^2-2*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a*d+6*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b*c)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/d^2/b/(b*d)^(1/2)","B"
936,1,198,66,0.014000," ","int(x*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(a d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-b c \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\right)}{4 \sqrt{x^{4} b d +x^{2} a d +b c \,x^{2}+a c}\, \sqrt{b d}\, d}"," ",0,"1/4*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(a*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*d-b*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/d/(b*d)^(1/2)","B"
937,1,177,68,0.033000," ","int((b*x^2+a)^(1/2)/x/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-\sqrt{b d}\, a \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+\sqrt{a c}\, b \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)\right)}{2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}}"," ",0,"1/2*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(b*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)-a*ln((x^2*a*d+b*c*x^2+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)+2*a*c)/x^2)*(b*d)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/(b*d)^(1/2)/(a*c)^(1/2)","B"
938,1,207,69,0.034000," ","int((b*x^2+a)^(1/2)/x^3/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(a d \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-b c \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\right)}{4 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, c \,x^{2}}"," ",0,"1/4*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/c*(ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a*d-ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*b*c-2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/x^2/(a*c)^(1/2)","B"
939,1,355,117,0.030000," ","int((b*x^2+a)^(1/2)/x^5/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(3 a^{2} d^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-2 a b c d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-b^{2} c^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-6 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a d \,x^{2}+2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b c \,x^{2}+4 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a c \right)}{16 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,c^{2} x^{4}}"," ",0,"-1/16*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/a/c^2*(3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^2*d^2-2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a*b*c*d-ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*b^2*c^2-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*d*a*x^2*(a*c)^(1/2)+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b*c*x^2*(a*c)^(1/2)+4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a*c*(a*c)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/x^4/(a*c)^(1/2)","B"
940,1,526,371,0.054000," ","int(x^4*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(3 \sqrt{-\frac{b}{a}}\, b^{2} d^{3} x^{7}+4 \sqrt{-\frac{b}{a}}\, a b \,d^{3} x^{5}-\sqrt{-\frac{b}{a}}\, b^{2} c \,d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}-4 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}+\sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{-\frac{b}{a}}\, a b \,c^{2} d x -3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+7 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{15 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, b \,d^{3}}"," ",0,"1/15*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(3*(-b/a)^(1/2)*x^7*b^2*d^3+4*(-b/a)^(1/2)*x^5*a*b*d^3-(-b/a)^(1/2)*x^5*b^2*c*d^2+(-b/a)^(1/2)*x^3*a^2*d^3-4*(-b/a)^(1/2)*x^3*b^2*c^2*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-b/a)^(1/2),(a*d/b/c)^(1/2))*a^2*c*d^2+7*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-b/a)^(1/2),(a*d/b/c)^(1/2))*a*b*c^2*d-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-b/a)^(1/2),(a*d/b/c)^(1/2))*b^2*c^3-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-b/a)^(1/2),(a*d/b/c)^(1/2))*a^2*c*d^2-3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-b/a)^(1/2),(a*d/b/c)^(1/2))*a*b*c^2*d+8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-b/a)^(1/2),(a*d/b/c)^(1/2))*b^2*c^3+(-b/a)^(1/2)*x*a^2*c*d^2-4*(-b/a)^(1/2)*x*a*b*c^2*d)/d^3/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/b/(-b/a)^(1/2)","A"
941,1,335,293,0.020000," ","int(x^2*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-\sqrt{-\frac{b}{a}}\, b \,d^{2} x^{5}-\sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}-\sqrt{-\frac{b}{a}}\, b c d \,x^{3}-\sqrt{-\frac{b}{a}}\, a c d x -\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{3 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d^{2}}"," ",0,"-1/3*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-(-1/a*b)^(1/2)*x^5*b*d^2-(-1/a*b)^(1/2)*x^3*a*d^2-(-1/a*b)^(1/2)*x^3*b*c*d+2*a*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2-(-1/a*b)^(1/2)*x*a*c*d)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/d^2/(-1/a*b)^(1/2)","A"
942,1,168,274,0.027000," ","int((b*x^2+a)^(1/2)/x^2/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-\sqrt{-\frac{b}{a}}\, b d \,x^{4}-\sqrt{-\frac{b}{a}}\, a d \,x^{2}-\sqrt{-\frac{b}{a}}\, b c \,x^{2}+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{-\frac{b}{a}}\, a c \right)}{\left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, c x}"," ",0,"(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-(-1/a*b)^(1/2)*x^4*b*d+b*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*x*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))-(-1/a*b)^(1/2)*x^2*a*d-(-1/a*b)^(1/2)*x^2*b*c-(-1/a*b)^(1/2)*a*c)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/c/(-1/a*b)^(1/2)/x","A"
943,1,418,335,0.031000," ","int((b*x^2+a)^(1/2)/x^4/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(2 \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{6}-\sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{6}+2 \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{4}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{4}+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a^{2} c d \,x^{2}-2 \sqrt{-\frac{b}{a}}\, a b \,c^{2} x^{2}-\sqrt{-\frac{b}{a}}\, a^{2} c^{2}\right)}{3 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, a \,c^{2} x^{3}}"," ",0,"1/3*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(2*(-1/a*b)^(1/2)*x^6*a*b*d^2-(-1/a*b)^(1/2)*x^6*b^2*c*d+b*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*c-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b*c*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2+2*(-1/a*b)^(1/2)*x^4*a^2*d^2-(-1/a*b)^(1/2)*x^4*b^2*c^2+(-1/a*b)^(1/2)*x^2*a^2*c*d-2*(-1/a*b)^(1/2)*x^2*a*b*c^2-(-1/a*b)^(1/2)*a^2*c^2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/c^2/x^3/a/(-1/a*b)^(1/2)","A"
944,1,770,238,0.038000," ","int(x^5*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(96 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} d^{3} x^{6}+144 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{2} d^{3} x^{4}-112 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} c \,d^{2} x^{4}+9 a^{4} d^{4} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+12 a^{3} b c \,d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+54 a^{2} b^{2} c^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-180 a \,b^{3} c^{3} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+105 b^{4} c^{4} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+12 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} b \,d^{3} x^{2}-184 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{2} c \,d^{2} x^{2}+140 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} c^{2} d \,x^{2}-18 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{3} d^{3}-30 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} b c \,d^{2}+290 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{2} c^{2} d -210 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} c^{3}\right)}{768 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} d^{4}}"," ",0,"1/768*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(96*x^6*b^3*d^3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+144*x^4*a*b^2*d^3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)-112*x^4*b^3*c*d^2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*a^2*b*d^3*(b*d)^(1/2)-184*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*a*c*b^2*d^2*(b*d)^(1/2)+140*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*c^2*b^3*d*(b*d)^(1/2)+9*d^4*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^4+12*a^3*c*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*b*d^3+54*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2*c^2*b^2*d^2-180*a*c^3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*b^3*d+105*b^4*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*c^4-18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a^3*d^3*(b*d)^(1/2)-30*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a^2*c*b*d^2*(b*d)^(1/2)+290*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a*c^2*b^2*d*(b*d)^(1/2)-210*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*c^3*b^3*(b*d)^(1/2))/b^2/d^4/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/(b*d)^(1/2)","B"
945,1,532,155,0.022000," ","int(x^3*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-16 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} d^{2} x^{4}+3 a^{3} d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+9 a^{2} b c \,d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-27 a \,b^{2} c^{2} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+15 b^{3} c^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-28 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b \,d^{2} x^{2}+20 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c d \,x^{2}-6 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} d^{2}+44 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b c d -30 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c^{2}\right)}{96 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b \,d^{3}}"," ",0,"-1/96*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^2*d^2*x^4-28*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b*d^2*x^2+20*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^2*c*d*x^2+3*a^3*d^3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+9*a^2*b*c*d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-27*a*b^2*c^2*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+15*b^3*c^3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^2*d^2+44*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b*c*d-30*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^2*c^2)/b/d^3/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/(b*d)^(1/2)","B"
946,1,337,99,0.016000," ","int(x*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(3 a^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-6 a b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+4 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b d \,x^{2}+10 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a d -6 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b c \right)}{16 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, d^{2}}"," ",0,"1/16*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(4*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b*d*x^2+3*a^2*d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-6*a*b*c*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+3*b^2*c^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+10*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a*d-6*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b*c)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/d^2/(b*d)^(1/2)","B"
947,1,287,101,0.019000," ","int((b*x^2+a)^(3/2)/x/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-2 \sqrt{b d}\, a^{2} d \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+3 \sqrt{a c}\, a b d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-\sqrt{a c}\, b^{2} c \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 \sqrt{b d}\, \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b \right)}{4 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}\, d}"," ",0,"1/4*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)*a*b*d-ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)*b^2*c-2*(b*d)^(1/2)*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*a^2*d+2*(b*d)^(1/2)*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/d/(b*d)^(1/2)/(a*c)^(1/2)","B"
948,1,298,104,0.021000," ","int((b*x^2+a)^(3/2)/x^3/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{b d}\, a^{2} d \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-3 \sqrt{b d}\, a b c \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+2 \sqrt{a c}\, b^{2} c \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}\, a \right)}{4 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}\, c \,x^{2}}"," ",0,"1/4*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/c*(2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^2*c*(a*c)^(1/2)+ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a^2*d*(b*d)^(1/2)-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a*b*c*(b*d)^(1/2)-2*a*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*(a*c)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/x^2/(b*d)^(1/2)/(a*c)^(1/2)","B"
949,1,352,105,0.020000," ","int((b*x^2+a)^(3/2)/x^5/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(3 a^{2} d^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-6 a b c d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+3 b^{2} c^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-6 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a d \,x^{2}+10 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b c \,x^{2}+4 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a c \right)}{16 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, c^{2} x^{4}}"," ",0,"-1/16*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/c^2*(3*a^2*d^2*x^4*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)-6*a*b*c*d*x^4*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)+3*b^2*c^2*x^4*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*a*d*x^2+10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*b*c*x^2+4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*a*c)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/x^4/(a*c)^(1/2)","B"
950,1,782,451,0.028000," ","int(x^4*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(5 \sqrt{-\frac{b}{a}}\, b^{3} d^{4} x^{9}+13 \sqrt{-\frac{b}{a}}\, a \,b^{2} d^{4} x^{7}-\sqrt{-\frac{b}{a}}\, b^{3} c \,d^{3} x^{7}+9 \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{4} x^{5}-4 \sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{3} x^{5}+2 \sqrt{-\frac{b}{a}}\, b^{3} c^{2} d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a^{3} d^{4} x^{3}-2 \sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{3} x^{3}-9 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} d^{2} x^{3}+8 \sqrt{-\frac{b}{a}}\, b^{3} c^{3} d \,x^{3}+\sqrt{-\frac{b}{a}}\, a^{3} c \,d^{3} x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} c \,d^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} c \,d^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-11 \sqrt{-\frac{b}{a}}\, a^{2} b \,c^{2} d^{2} x -4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+15 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{3} d x +24 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{3} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-32 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{3} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-16 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+16 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{35 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, b \,d^{4}}"," ",0,"1/35*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(5*(-1/a*b)^(1/2)*x^9*b^3*d^4+13*(-1/a*b)^(1/2)*x^7*a*b^2*d^4-(-1/a*b)^(1/2)*x^7*b^3*c*d^3+9*(-1/a*b)^(1/2)*x^5*a^2*b*d^4-4*(-1/a*b)^(1/2)*x^5*a*b^2*c*d^3+2*(-1/a*b)^(1/2)*x^5*b^3*c^2*d^2+(-1/a*b)^(1/2)*x^3*a^3*d^4-2*(-1/a*b)^(1/2)*x^3*a^2*b*c*d^3-9*(-1/a*b)^(1/2)*x^3*a*b^2*c^2*d^2+8*(-1/a*b)^(1/2)*x^3*b^3*c^3*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*c*d^3+15*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c^2*d^2-32*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^3*d+16*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^4-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*c*d^3-4*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c^2*d^2+24*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^3*d-16*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^4+(-1/a*b)^(1/2)*x*a^3*c*d^3-11*(-1/a*b)^(1/2)*x*a^2*b*c^2*d^2+8*(-1/a*b)^(1/2)*x*a*b^2*c^3*d)/b/d^4/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)","A"
951,1,544,363,0.023000," ","int(x^2*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-3 \sqrt{-\frac{b}{a}}\, b^{2} d^{3} x^{7}-9 \sqrt{-\frac{b}{a}}\, a b \,d^{3} x^{5}+\sqrt{-\frac{b}{a}}\, b^{2} c \,d^{2} x^{5}-6 \sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}-5 \sqrt{-\frac{b}{a}}\, a b c \,d^{2} x^{3}+4 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}-6 \sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x -3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+9 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{-\frac{b}{a}}\, a b \,c^{2} d x +13 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-17 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{15 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d^{3}}"," ",0,"-1/15*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-3*(-1/a*b)^(1/2)*b^2*d^3*x^7-9*(-1/a*b)^(1/2)*a*b*d^3*x^5+(-1/a*b)^(1/2)*b^2*c*d^2*x^5-6*(-1/a*b)^(1/2)*a^2*d^3*x^3-5*(-1/a*b)^(1/2)*x^3*a*b*c*d^2+4*(-1/a*b)^(1/2)*b^2*c^2*d*x^3+9*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2-17*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d+8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3-3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2+13*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3-6*(-1/a*b)^(1/2)*a^2*c*d^2*x+4*(-1/a*b)^(1/2)*a*b*c^2*d*x)/d^3/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)","A"
952,1,352,286,0.021000," ","int((b*x^2+a)^(3/2)/x^2/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-\sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{4}-\sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{2}-\sqrt{-\frac{b}{a}}\, a b c d \,x^{2}+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{-\frac{b}{a}}\, a^{2} c d \right)}{\left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, c d x}"," ",0,"(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-(-1/a*b)^(1/2)*x^4*a*b*d^2+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a*b*c*d-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*b^2*c^2+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a*b*c*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*b^2*c^2-(-1/a*b)^(1/2)*x^2*a^2*d^2-(-1/a*b)^(1/2)*x^2*a*b*c*d-(-1/a*b)^(1/2)*a^2*c*d)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/c/(-1/a*b)^(1/2)/d/x","A"
953,1,433,339,0.021000," ","int((b*x^2+a)^(3/2)/x^4/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(2 \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{6}-4 \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{6}+2 \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{4}-3 \sqrt{-\frac{b}{a}}\, a b c d \,x^{4}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{4}+4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a^{2} c d \,x^{2}-5 \sqrt{-\frac{b}{a}}\, a b \,c^{2} x^{2}-\sqrt{-\frac{b}{a}}\, a^{2} c^{2}\right)}{3 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, c^{2} x^{3}}"," ",0,"1/3*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(2*(-1/a*b)^(1/2)*a*b*d^2*x^6-4*(-1/a*b)^(1/2)*b^2*c*d*x^6+b*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*c-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b*c*d+4*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2+2*(-1/a*b)^(1/2)*a^2*d^2*x^4-3*(-1/a*b)^(1/2)*x^4*a*b*c*d-4*(-1/a*b)^(1/2)*b^2*c^2*x^4+(-1/a*b)^(1/2)*a^2*c*d*x^2-5*(-1/a*b)^(1/2)*a*b*c^2*x^2-(-1/a*b)^(1/2)*a^2*c^2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/c^2/x^3/(-1/a*b)^(1/2)","A"
954,1,1054,296,0.044000," ","int(x^5*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(768 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b^{4} d^{4} x^{8}+2016 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a \,b^{3} d^{4} x^{6}-864 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b^{4} c \,d^{3} x^{6}+1488 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a^{2} b^{2} d^{4} x^{4}-2368 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a \,b^{3} c \,d^{3} x^{4}+1008 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b^{4} c^{2} d^{2} x^{4}+45 a^{5} d^{5} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+75 a^{4} b c \,d^{4} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+450 a^{3} b^{2} c^{2} d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2250 a^{2} b^{3} c^{3} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2625 a \,b^{4} c^{4} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-945 b^{5} c^{5} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+60 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{3} b \,d^{4} x^{2}-1924 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} b^{2} c \,d^{3} x^{2}+2996 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{3} c^{2} d^{2} x^{2}-1260 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{4} c^{3} d \,x^{2}-90 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{4} d^{4}-180 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{3} b c \,d^{3}+3128 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} b^{2} c^{2} d^{2}-4620 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{3} c^{3} d +1890 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{4} c^{4}\right)}{7680 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} d^{5}}"," ",0,"1/7680*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(768*x^8*b^4*d^4*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)+2016*x^6*a*b^3*d^4*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)-864*x^6*b^4*c*d^3*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)+1488*x^4*a^2*b^2*d^4*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)-2368*x^4*a*b^3*c*d^3*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)+1008*x^4*b^4*c^2*d^2*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)+60*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*a^3*b*d^4*(b*d)^(1/2)-1924*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*a^2*c*b^2*d^3*(b*d)^(1/2)+2996*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*a*c^2*b^3*d^2*(b*d)^(1/2)-1260*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*c^3*b^4*d*(b*d)^(1/2)+45*d^5*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^5+75*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^4*c*b*d^4+450*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^3*c^2*b^2*d^3-2250*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2*c^3*b^3*d^2+2625*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*c^4*a*b^4*d-945*b^5*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*c^5-90*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a^4*d^4*(b*d)^(1/2)-180*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a^3*c*b*d^3*(b*d)^(1/2)+3128*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a^2*c^2*b^2*d^2*(b*d)^(1/2)-4620*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a*c^3*b^3*d*(b*d)^(1/2)+1890*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*c^4*b^4*(b*d)^(1/2))/b^2/d^5/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/(b*d)^(1/2)","B"
955,1,770,199,0.023000," ","int(x^3*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-96 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} d^{3} x^{6}-272 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{2} d^{3} x^{4}+112 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} c \,d^{2} x^{4}+15 a^{4} d^{4} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+60 a^{3} b c \,d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-270 a^{2} b^{2} c^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+300 a \,b^{3} c^{3} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-105 b^{4} c^{4} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-236 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} b \,d^{3} x^{2}+344 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{2} c \,d^{2} x^{2}-140 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} c^{2} d \,x^{2}-30 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{3} d^{3}+382 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} b c \,d^{2}-530 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{2} c^{2} d +210 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} c^{3}\right)}{768 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b \,d^{4}}"," ",0,"-1/768*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-96*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^3*d^3*x^6-272*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b^2*d^3*x^4+112*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^3*c*d^2*x^4-236*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^2*b*d^3*x^2+344*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b^2*c*d^2*x^2-140*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^3*c^2*d*x^2+15*a^4*d^4*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+60*a^3*b*c*d^3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-270*a^2*b^2*c^2*d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+300*a*b^3*c^3*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-105*b^4*c^4*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-30*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^3*d^3+382*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^2*b*c*d^2-530*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b^2*c^2*d+210*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^3*c^3)/b/d^4/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/(b*d)^(1/2)","B"
956,1,529,132,0.019000," ","int(x*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(16 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} d^{2} x^{4}+15 a^{3} d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-45 a^{2} b c \,d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+45 a \,b^{2} c^{2} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-15 b^{3} c^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+52 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b \,d^{2} x^{2}-20 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c d \,x^{2}+66 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} d^{2}-80 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b c d +30 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c^{2}\right)}{96 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, d^{3}}"," ",0,"1/96*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^2*d^2*x^4+52*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b*d^2*x^2-20*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^2*c*d*x^2+15*a^3*d^3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-45*a^2*b*c*d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+45*a*b^2*c^2*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-15*b^3*c^3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+66*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^2*d^2-80*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b*c*d+30*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^2*c^2)/d^3/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/(b*d)^(1/2)","B"
957,1,446,149,0.021000," ","int((b*x^2+a)^(5/2)/x/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-8 \sqrt{b d}\, a^{3} d^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+15 \sqrt{a c}\, a^{2} b \,d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-10 \sqrt{a c}\, a \,b^{2} c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 \sqrt{a c}\, b^{3} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+4 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}\, b^{2} d \,x^{2}+18 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}\, a b d -6 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}\, b^{2} c \right)}{16 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}\, d^{2}}"," ",0,"1/16*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*(a*c)^(1/2)*x^2*b^2*d+15*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)*a^2*b*d^2-10*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)*a*b^2*c*d+3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)*b^3*c^2-8*(b*d)^(1/2)*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*a^3*d^2+18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*(a*c)^(1/2)*a*b*d-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*(a*c)^(1/2)*b^2*c)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/d^2/(b*d)^(1/2)/(a*c)^(1/2)","B"
958,1,423,147,0.021000," ","int((b*x^2+a)^(5/2)/x^3/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{b d}\, a^{3} d^{2} x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-5 \sqrt{b d}\, a^{2} b c d \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+5 \sqrt{a c}\, a \,b^{2} c d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-\sqrt{a c}\, b^{3} c^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c \,x^{2}-2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} d \right)}{4 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}\, c d \,x^{2}}"," ",0,"1/4*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/c*(5*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b^2*c*d*(a*c)^(1/2)-ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^3*c^2*(a*c)^(1/2)+ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a^3*d^2*(b*d)^(1/2)-5*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a^2*b*c*d*(b*d)^(1/2)+2*x^2*b^2*c*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)-2*a^2*d*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/x^2/(b*d)^(1/2)/(a*c)^(1/2)/d","B"
959,1,464,154,0.022000," ","int((b*x^2+a)^(5/2)/x^5/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-3 \sqrt{b d}\, a^{3} d^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+10 \sqrt{b d}\, a^{2} b c d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-15 \sqrt{b d}\, a \,b^{2} c^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+8 \sqrt{a c}\, b^{3} c^{2} x^{4} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+6 \sqrt{b d}\, \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a^{2} d \,x^{2}-18 \sqrt{b d}\, \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a b c \,x^{2}-4 \sqrt{b d}\, \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a^{2} c \right)}{16 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, \sqrt{a c}\, c^{2} x^{4}}"," ",0,"1/16*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/c^2*(8*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^4*b^3*c^2*(a*c)^(1/2)-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^3*d^2*(b*d)^(1/2)+10*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^2*b*c*d*(b*d)^(1/2)-15*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a*b^2*c^2*(b*d)^(1/2)+6*x^2*a^2*d*(b*d)^(1/2)*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)-18*x^2*a*b*c*(b*d)^(1/2)*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)-4*a^2*c*(b*d)^(1/2)*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/x^4/(b*d)^(1/2)/(a*c)^(1/2)","B"
960,1,1047,569,0.033000," ","int(x^4*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(35 \sqrt{-\frac{b}{a}}\, b^{4} d^{5} x^{11}+130 \sqrt{-\frac{b}{a}}\, a \,b^{3} d^{5} x^{9}-5 \sqrt{-\frac{b}{a}}\, b^{4} c \,d^{4} x^{9}+170 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} d^{5} x^{7}-25 \sqrt{-\frac{b}{a}}\, a \,b^{3} c \,d^{4} x^{7}+8 \sqrt{-\frac{b}{a}}\, b^{4} c^{2} d^{3} x^{7}+80 \sqrt{-\frac{b}{a}}\, a^{3} b \,d^{5} x^{5}-50 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c \,d^{4} x^{5}+49 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{2} d^{3} x^{5}-16 \sqrt{-\frac{b}{a}}\, b^{4} c^{3} d^{2} x^{5}+5 \sqrt{-\frac{b}{a}}\, a^{4} d^{5} x^{3}-25 \sqrt{-\frac{b}{a}}\, a^{3} b c \,d^{4} x^{3}-64 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c^{2} d^{3} x^{3}+140 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{3} d^{2} x^{3}-64 \sqrt{-\frac{b}{a}}\, b^{4} c^{4} d \,x^{3}+5 \sqrt{-\frac{b}{a}}\, a^{4} c \,d^{4} x -10 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} c \,d^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+5 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} c \,d^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-105 \sqrt{-\frac{b}{a}}\, a^{3} b \,c^{2} d^{3} x -25 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b \,c^{2} d^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+130 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b \,c^{2} d^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+156 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c^{3} d^{2} x +243 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{3} d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-399 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{3} d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-64 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{4} d x -328 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{4} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+392 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{4} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+128 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{5} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-128 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{5} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{315 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, b \,d^{5}}"," ",0,"1/315*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-105*(-1/a*b)^(1/2)*x*a^3*b*c^2*d^3+156*(-1/a*b)^(1/2)*x*a^2*b^2*c^3*d^2-64*(-1/a*b)^(1/2)*x*a*b^3*c^4*d+5*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^4*c*d^4-10*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^4*c*d^4-50*(-1/a*b)^(1/2)*x^5*a^2*b^2*c*d^4+49*(-1/a*b)^(1/2)*x^5*a*b^3*c^2*d^3-25*(-1/a*b)^(1/2)*x^3*a^3*b*c*d^4-64*(-1/a*b)^(1/2)*x^3*a^2*b^2*c^2*d^3+140*(-1/a*b)^(1/2)*x^3*a*b^3*c^3*d^2+35*(-1/a*b)^(1/2)*x^11*b^4*d^5+5*(-1/a*b)^(1/2)*x^3*a^4*d^5-25*(-1/a*b)^(1/2)*x^7*a*b^3*c*d^4+130*(-1/a*b)^(1/2)*x^9*a*b^3*d^5-5*(-1/a*b)^(1/2)*x^9*b^4*c*d^4+130*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c^2*d^3-399*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^3*d^2+392*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^3*c^4*d-25*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c^2*d^3+243*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^3*d^2-328*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^3*c^4*d+5*(-1/a*b)^(1/2)*x*a^4*c*d^4+170*(-1/a*b)^(1/2)*x^7*a^2*b^2*d^5+8*(-1/a*b)^(1/2)*x^7*b^4*c^2*d^3+80*(-1/a*b)^(1/2)*x^5*a^3*b*d^5-16*(-1/a*b)^(1/2)*x^5*b^4*c^3*d^2-64*(-1/a*b)^(1/2)*x^3*b^4*c^4*d-128*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^4*c^5+128*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^4*c^5)/b/d^5/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)","A"
961,1,782,458,0.024000," ","int(x^2*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(-15 \sqrt{-\frac{b}{a}}\, b^{3} d^{4} x^{9}-60 \sqrt{-\frac{b}{a}}\, a \,b^{2} d^{4} x^{7}+3 \sqrt{-\frac{b}{a}}\, b^{3} c \,d^{3} x^{7}-90 \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{4} x^{5}+19 \sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{3} x^{5}-6 \sqrt{-\frac{b}{a}}\, b^{3} c^{2} d^{2} x^{5}-45 \sqrt{-\frac{b}{a}}\, a^{3} d^{4} x^{3}-29 \sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{3} x^{3}+55 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} d^{2} x^{3}-24 \sqrt{-\frac{b}{a}}\, b^{3} c^{3} d \,x^{3}-45 \sqrt{-\frac{b}{a}}\, a^{3} c \,d^{3} x -15 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} c \,d^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+60 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} c \,d^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+61 \sqrt{-\frac{b}{a}}\, a^{2} b \,c^{2} d^{2} x +103 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-164 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-24 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{3} d x -128 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{3} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+152 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{3} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+48 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-48 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{105 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d^{4}}"," ",0,"-1/105*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-15*(-1/a*b)^(1/2)*b^3*d^4*x^9-60*(-1/a*b)^(1/2)*a*b^2*d^4*x^7+3*(-1/a*b)^(1/2)*b^3*c*d^3*x^7-90*(-1/a*b)^(1/2)*a^2*b*d^4*x^5+19*(-1/a*b)^(1/2)*a*b^2*c*d^3*x^5-6*(-1/a*b)^(1/2)*b^3*c^2*d^2*x^5-45*(-1/a*b)^(1/2)*a^3*d^4*x^3-29*(-1/a*b)^(1/2)*a^2*b*c*d^3*x^3+55*(-1/a*b)^(1/2)*a*b^2*c^2*d^2*x^3-24*(-1/a*b)^(1/2)*b^3*c^3*d*x^3+60*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*c*d^3-164*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c^2*d^2+152*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^3*d-48*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^4-15*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*c*d^3+103*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c^2*d^2-128*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^3*d+48*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^4-45*(-1/a*b)^(1/2)*a^3*c*d^3*x+61*(-1/a*b)^(1/2)*a^2*b*c^2*d^2*x-24*(-1/a*b)^(1/2)*a*b^2*c^3*d*x)/d^4/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)","A"
962,1,568,360,0.022000," ","int((b*x^2+a)^(5/2)/x^2/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{-\frac{b}{a}}\, b^{3} c \,d^{2} x^{6}-3 \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{3} x^{4}+\sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{2} x^{4}+\sqrt{-\frac{b}{a}}\, b^{3} c^{2} d \,x^{4}-3 \sqrt{-\frac{b}{a}}\, a^{3} d^{3} x^{2}-3 \sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{2} x^{2}+3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+6 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} d \,x^{2}+7 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-3 \sqrt{-\frac{b}{a}}\, a^{3} c \,d^{2}\right)}{3 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, c \,d^{2} x}"," ",0,"1/3*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*((-1/a*b)^(1/2)*x^6*b^3*c*d^2-3*(-1/a*b)^(1/2)*x^4*a^2*b*d^3+(-1/a*b)^(1/2)*x^4*a*b^2*c*d^2+(-1/a*b)^(1/2)*x^4*b^3*c^2*d+6*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a^2*b*c*d^2-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a*b^2*c^2*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*b^3*c^3+3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a^2*b*c*d^2+7*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a*b^2*c^2*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*b^3*c^3-3*(-1/a*b)^(1/2)*x^2*a^3*d^3-3*(-1/a*b)^(1/2)*x^2*a^2*b*c*d^2+(-1/a*b)^(1/2)*x^2*a*b^2*c^2*d-3*(-1/a*b)^(1/2)*a^3*c*d^2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/d^2/(-1/a*b)^(1/2)/c/x","A"
963,1,583,364,0.023000," ","int((b*x^2+a)^(5/2)/x^4/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(2 \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{3} x^{6}-7 \sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{2} x^{6}+2 \sqrt{-\frac{b}{a}}\, a^{3} d^{3} x^{4}-6 \sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{2} x^{4}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-7 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} d \,x^{4}+7 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \,x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \,x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a^{3} c \,d^{2} x^{2}-8 \sqrt{-\frac{b}{a}}\, a^{2} b \,c^{2} d \,x^{2}-\sqrt{-\frac{b}{a}}\, a^{3} c^{2} d \right)}{3 \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, c^{2} d \,x^{3}}"," ",0,"1/3*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(2*(-1/a*b)^(1/2)*x^6*a^2*b*d^3-7*(-1/a*b)^(1/2)*x^6*a*b^2*c*d^2+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a^2*b*c*d^2+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b^2*c^2*d-3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^3*c^3-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a^2*b*c*d^2+7*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b^2*c^2*d+3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^3*c^3+2*(-1/a*b)^(1/2)*x^4*a^3*d^3-6*(-1/a*b)^(1/2)*x^4*a^2*b*c*d^2-7*(-1/a*b)^(1/2)*x^4*a*b^2*c^2*d+(-1/a*b)^(1/2)*x^2*a^3*c*d^2-8*(-1/a*b)^(1/2)*x^2*a^2*b*c^2*d-(-1/a*b)^(1/2)*a^3*c^2*d)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/c^2/x^3/(-1/a*b)^(1/2)/d","A"
964,1,135,101,0.197000," ","int(x^4*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x)","-\frac{\sqrt{3 x^{2}-1}\, \sqrt{2}\, \sqrt{-6 x^{2}+4}\, \left(243 x^{7}-54 x^{5}-135 x^{3}+42 x -12 \sqrt{3}\, \sqrt{2}\, \sqrt{-6 x^{2}+4}\, \sqrt{-3 x^{2}+1}\, \EllipticE \left(\frac{\sqrt{3}\, \sqrt{2}\, x}{2}, \sqrt{2}\right)+5 \sqrt{3}\, \sqrt{2}\, \sqrt{-6 x^{2}+4}\, \sqrt{-3 x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{810 \left(9 x^{4}-9 x^{2}+2\right)}"," ",0,"-1/810*(3*x^2-1)^(1/2)*2^(1/2)*(-6*x^2+4)^(1/2)*(243*x^7-54*x^5+5*3^(1/2)*2^(1/2)*(-6*x^2+4)^(1/2)*(-3*x^2+1)^(1/2)*EllipticF(1/2*3^(1/2)*2^(1/2)*x,2^(1/2))-12*3^(1/2)*2^(1/2)*(-6*x^2+4)^(1/2)*(-3*x^2+1)^(1/2)*EllipticE(1/2*3^(1/2)*2^(1/2)*x,2^(1/2))-135*x^3+42*x)/(9*x^4-9*x^2+2)","A"
965,1,81,51,0.029000," ","int(x^3*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x)","\frac{\sqrt{3 x^{2}-1}\, \sqrt{-3 x^{2}+2}\, \left(-12 \sqrt{-9 x^{4}+9 x^{2}-2}\, x^{2}+7 \arcsin \left(6 x^{2}-3\right)-10 \sqrt{-9 x^{4}+9 x^{2}-2}\right)}{144 \sqrt{-9 x^{4}+9 x^{2}-2}}"," ",0,"1/144*(3*x^2-1)^(1/2)*(-3*x^2+2)^(1/2)*(-12*x^2*(-9*x^4+9*x^2-2)^(1/2)+7*arcsin(6*x^2-3)-10*(-9*x^4+9*x^2-2)^(1/2))/(-9*x^4+9*x^2-2)^(1/2)","A"
966,1,129,78,0.015000," ","int(x^2*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x)","-\frac{\sqrt{3 x^{2}-1}\, \sqrt{2}\, \sqrt{-6 x^{2}+4}\, \left(54 x^{5}-54 x^{3}+12 x -3 \sqrt{3}\, \sqrt{2}\, \sqrt{-6 x^{2}+4}\, \sqrt{-3 x^{2}+1}\, \EllipticE \left(\frac{\sqrt{3}\, \sqrt{2}\, x}{2}, \sqrt{2}\right)+\sqrt{3}\, \sqrt{2}\, \sqrt{-6 x^{2}+4}\, \sqrt{-3 x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{108 \left(9 x^{4}-9 x^{2}+2\right)}"," ",0,"-1/108*(3*x^2-1)^(1/2)*2^(1/2)*(-6*x^2+4)^(1/2)*(54*x^5+3^(1/2)*2^(1/2)*(-6*x^2+4)^(1/2)*(-3*x^2+1)^(1/2)*EllipticF(1/2*3^(1/2)*2^(1/2)*x,2^(1/2))-3*3^(1/2)*2^(1/2)*(-6*x^2+4)^(1/2)*(-3*x^2+1)^(1/2)*EllipticE(1/2*3^(1/2)*2^(1/2)*x,2^(1/2))-54*x^3+12*x)/(9*x^4-9*x^2+2)","A"
967,1,60,31,0.013000," ","int(x*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x)","\frac{\sqrt{3 x^{2}-1}\, \sqrt{-3 x^{2}+2}\, \left(\arcsin \left(6 x^{2}-3\right)-2 \sqrt{-9 x^{4}+9 x^{2}-2}\right)}{12 \sqrt{-9 x^{4}+9 x^{2}-2}}"," ",0,"1/12*(3*x^2-1)^(1/2)*(-3*x^2+2)^(1/2)*(arcsin(6*x^2-3)-2*(-9*x^4+9*x^2-2)^(1/2))/(-9*x^4+9*x^2-2)^(1/2)","A"
968,1,306,265,0.046000," ","int(x^2*(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x)","\frac{\sqrt{b \,x^{2}+2}\, \sqrt{d \,x^{2}+3}\, \left(\sqrt{-d}\, b^{2} d \,x^{5}+3 \sqrt{-d}\, b^{2} x^{3}+2 \sqrt{-d}\, b d \,x^{3}+6 \sqrt{-d}\, b x -6 \sqrt{2}\, \sqrt{d \,x^{2}+3}\, \sqrt{b \,x^{2}+2}\, b \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{b}{d}}}{2}\right)+3 \sqrt{2}\, \sqrt{d \,x^{2}+3}\, \sqrt{b \,x^{2}+2}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{b}{d}}}{2}\right)+2 \sqrt{2}\, \sqrt{d \,x^{2}+3}\, \sqrt{b \,x^{2}+2}\, d \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{b}{d}}}{2}\right)-2 \sqrt{2}\, \sqrt{d \,x^{2}+3}\, \sqrt{b \,x^{2}+2}\, d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{b}{d}}}{2}\right)\right)}{3 \left(x^{4} b d +3 b \,x^{2}+2 d \,x^{2}+6\right) \sqrt{-d}\, b d}"," ",0,"1/3*(b*x^2+2)^(1/2)*(d*x^2+3)^(1/2)*(x^5*b^2*d*(-d)^(1/2)+3*x^3*b^2*(-d)^(1/2)+2*x^3*b*d*(-d)^(1/2)+3*2^(1/2)*EllipticF(1/3*x*3^(1/2)*(-d)^(1/2),1/2*3^(1/2)*2^(1/2)*(b/d)^(1/2))*b*(d*x^2+3)^(1/2)*(b*x^2+2)^(1/2)-2*2^(1/2)*EllipticF(1/3*x*3^(1/2)*(-d)^(1/2),1/2*3^(1/2)*2^(1/2)*(b/d)^(1/2))*d*(d*x^2+3)^(1/2)*(b*x^2+2)^(1/2)-6*2^(1/2)*EllipticE(1/3*x*3^(1/2)*(-d)^(1/2),1/2*3^(1/2)*2^(1/2)*(b/d)^(1/2))*b*(d*x^2+3)^(1/2)*(b*x^2+2)^(1/2)+2*2^(1/2)*EllipticE(1/3*x*3^(1/2)*(-d)^(1/2),1/2*3^(1/2)*2^(1/2)*(b/d)^(1/2))*d*(d*x^2+3)^(1/2)*(b*x^2+2)^(1/2)+6*x*b*(-d)^(1/2))/(b*d*x^4+3*b*x^2+2*d*x^2+6)/d/(-d)^(1/2)/b","A"
969,1,340,115,0.035000," ","int(x^5/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\left(3 a^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 a b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+4 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b d \,x^{2}-6 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a d -6 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b c \right) \sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}}{16 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b^{2} d^{2}}"," ",0,"1/16*(4*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b*d*x^2+3*a^2*d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+2*a*b*c*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+3*b^2*c^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-6*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a*d-6*(b*d)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b*c)*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(b*d)^(1/2)/d^2/b^2/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","B"
970,1,200,68,0.021000," ","int(x^3/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","-\frac{\left(a d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+b c \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\right) \sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}}{4 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, b d}"," ",0,"-1/4*(a*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+b*c*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/d/(b*d)^(1/2)/b/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","B"
971,1,103,33,0.019000," ","int(x/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)}{2 \sqrt{b d}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}"," ",0,"1/2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(b*d)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","B"
972,1,103,34,0.025000," ","int(1/x/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}\, \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)}{2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}"," ",0,"-1/2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)/(a*c)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","B"
973,1,209,71,0.024000," ","int(1/x^3/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\left(a d \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+b c \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\right) \sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}}{4 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a c \,x^{2}}"," ",0,"1/4/a/c*(a*d*x^2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)+b*c*x^2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)-2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)/(a*c)^(1/2)/x^2/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","B"
974,1,355,123,0.029000," ","int(1/x^5/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","-\frac{\left(3 a^{2} d^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+2 a b c d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+3 b^{2} c^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-6 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a d \,x^{2}-6 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b c \,x^{2}+4 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a c \right) \sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}}{16 \sqrt{a c}\, \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, a^{2} c^{2} x^{4}}"," ",0,"-1/16/a^2/c^2*(3*a^2*d^2*x^4*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)+2*a*b*c*d*x^4*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)+3*b^2*c^2*x^4*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*a*d*x^2-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*b*c*x^2+4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*a*c)*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)/(a*c)^(1/2)/x^4/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","B"
975,1,546,370,0.037000," ","int(x^6/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","-\frac{\left(-3 \sqrt{-\frac{b}{a}}\, b^{2} d^{3} x^{7}+\sqrt{-\frac{b}{a}}\, a b \,d^{3} x^{5}+\sqrt{-\frac{b}{a}}\, b^{2} c \,d^{2} x^{5}+4 \sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}+5 \sqrt{-\frac{b}{a}}\, a b c \,d^{2} x^{3}+4 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}+4 \sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x -8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{-\frac{b}{a}}\, a b \,c^{2} d x -7 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}}{15 \sqrt{-\frac{b}{a}}\, \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) b^{2} d^{3}}"," ",0,"-1/15*(-3*(-1/a*b)^(1/2)*b^2*d^3*x^7+(-1/a*b)^(1/2)*a*b*d^3*x^5+(-1/a*b)^(1/2)*b^2*c*d^2*x^5+4*(-1/a*b)^(1/2)*a^2*d^3*x^3+5*(-1/a*b)^(1/2)*a*b*c*d^2*x^3+4*(-1/a*b)^(1/2)*b^2*c^2*d*x^3+4*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2+3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d+8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2-7*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3+4*(-1/a*b)^(1/2)*a^2*c*d^2*x+4*(-1/a*b)^(1/2)*a*b*c^2*d*x)*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/d^3/b^2/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
976,1,333,295,0.027000," ","int(x^4/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\left(\sqrt{-\frac{b}{a}}\, b \,d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b c d \,x^{3}+\sqrt{-\frac{b}{a}}\, a c d x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}}{3 \sqrt{-\frac{b}{a}}\, \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) b \,d^{2}}"," ",0,"1/3*((-1/a*b)^(1/2)*b*d^2*x^5+(-1/a*b)^(1/2)*a*d^2*x^3+(-1/a*b)^(1/2)*b*c*d*x^3+a*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+(-1/a*b)^(1/2)*a*c*d*x)*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(-1/a*b)^(1/2)/d^2/b/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
977,1,129,137,0.022000," ","int(x^2/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\left(\EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, c}{\sqrt{-\frac{b}{a}}\, \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) d}"," ",0,"(-EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))+EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2)))*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)*c*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/d/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
978,1,224,170,0.026000," ","int(1/x^2/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\left(-\sqrt{-\frac{b}{a}}\, b d \,x^{4}-\sqrt{-\frac{b}{a}}\, a d \,x^{2}-\sqrt{-\frac{b}{a}}\, b c \,x^{2}+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{-\frac{b}{a}}\, a c \right) \sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}}{\sqrt{-\frac{b}{a}}\, \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) a c x}"," ",0,"(-(-1/a*b)^(1/2)*b*d*x^4-b*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*x*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))+b*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*x*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))-(-1/a*b)^(1/2)*a*d*x^2-(-1/a*b)^(1/2)*b*c*x^2-(-1/a*b)^(1/2)*a*c)*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)/x/c/(-1/a*b)^(1/2)/a/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
979,1,435,335,0.030000," ","int(1/x^4/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\left(2 \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{6}+2 \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{6}+2 \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{4}+3 \sqrt{-\frac{b}{a}}\, a b c d \,x^{4}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{4}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a^{2} c d \,x^{2}+\sqrt{-\frac{b}{a}}\, a b \,c^{2} x^{2}-\sqrt{-\frac{b}{a}}\, a^{2} c^{2}\right) \sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}}{3 \sqrt{-\frac{b}{a}}\, \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) a^{2} c^{2} x^{3}}"," ",0,"1/3*(2*(-1/a*b)^(1/2)*a*b*d^2*x^6+2*(-1/a*b)^(1/2)*b^2*c*d*x^6+b*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*c+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b*c*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2+2*(-1/a*b)^(1/2)*a^2*d^2*x^4+3*(-1/a*b)^(1/2)*a*b*c*d*x^4+2*(-1/a*b)^(1/2)*b^2*c^2*x^4+(-1/a*b)^(1/2)*a^2*c*d*x^2+(-1/a*b)^(1/2)*a*b*c^2*x^2-(-1/a*b)^(1/2)*a^2*c^2)*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)/(-1/a*b)^(1/2)/x^3/c^2/a^2/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
980,1,553,105,0.049000," ","int(x^5/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","-\frac{\left(3 a^{2} b \,d^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2 a \,b^{2} c d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-b^{3} c^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 a^{3} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2 a^{2} b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-a \,b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2 \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, \sqrt{b d}\, a b d \,x^{2}+2 \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, \sqrt{b d}\, b^{2} c \,x^{2}-6 \sqrt{b d}\, \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, a^{2} d +2 \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, \sqrt{b d}\, a b c \right) \sqrt{d \,x^{2}+c}}{4 \sqrt{b \,x^{2}+a}\, \sqrt{b d}\, \left(a d -b c \right) \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, b^{2} d}"," ",0,"-1/4*(3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a^2*b*d^2-2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b^2*c*d-ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^3*c^2-2*((b*x^2+a)*(d*x^2+c))^(1/2)*(b*d)^(1/2)*x^2*a*b*d+2*((b*x^2+a)*(d*x^2+c))^(1/2)*(b*d)^(1/2)*x^2*b^2*c+3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^3*d^2-2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2*b*c*d-ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*b^2*c^2-6*(b*d)^(1/2)*((b*x^2+a)*(d*x^2+c))^(1/2)*a^2*d+2*((b*x^2+a)*(d*x^2+c))^(1/2)*(b*d)^(1/2)*a*b*c)*(d*x^2+c)^(1/2)/b^2/(b*x^2+a)^(1/2)/d/(b*d)^(1/2)/(a*d-b*c)/((b*x^2+a)*(d*x^2+c))^(1/2)","B"
981,1,320,67,0.026000," ","int(x^3/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","\frac{\left(a b d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-b^{2} c \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+a^{2} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-a b c \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2 \sqrt{b d}\, \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, a \right) \sqrt{d \,x^{2}+c}}{2 \sqrt{b \,x^{2}+a}\, \sqrt{b d}\, \left(a d -b c \right) \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, b}"," ",0,"1/2*(ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b*d-ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^2*c+ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2*d-ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*b*c-2*(b*d)^(1/2)*((b*x^2+a)*(d*x^2+c))^(1/2)*a)/b*(d*x^2+c)^(1/2)/(b*x^2+a)^(1/2)/(b*d)^(1/2)/(a*d-b*c)/((b*x^2+a)*(d*x^2+c))^(1/2)","B"
982,1,30,30,0.005000," ","int(x/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}}{\sqrt{b \,x^{2}+a}\, \left(a d -b c \right)}"," ",0,"1/(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(a*d-b*c)","A"
983,1,651,113,0.046000," ","int(x^5/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","\frac{\left(-8 \sqrt{b d}\, a^{2} b \,d^{2} x^{4}+12 \sqrt{b d}\, a \,b^{2} c d \,x^{4}+3 \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, a^{2} b \,d^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-6 \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, a \,b^{2} c d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, b^{3} c^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-6 \sqrt{b d}\, a^{3} d^{2} x^{2}+2 \sqrt{b d}\, a^{2} b c d \,x^{2}+12 \sqrt{b d}\, a \,b^{2} c^{2} x^{2}+3 \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, a^{3} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-6 \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, a^{2} b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 \sqrt{\left(b \,x^{2}+a \right) \left(d \,x^{2}+c \right)}\, a \,b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-6 \sqrt{b d}\, a^{3} c d +10 \sqrt{b d}\, a^{2} b \,c^{2}\right) \sqrt{d \,x^{2}+c}}{6 \sqrt{b \,x^{2}+a}\, \sqrt{b d}\, \left(a d -b c \right)^{2} \left(x^{4} b d +a d \,x^{2}+b c \,x^{2}+a c \right) b^{2}}"," ",0,"1/6*(-8*(b*d)^(1/2)*x^4*a^2*b*d^2+12*x^4*a*b^2*c*d*(b*d)^(1/2)+3*((b*x^2+a)*(d*x^2+c))^(1/2)*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a^2*b*d^2-6*((b*x^2+a)*(d*x^2+c))^(1/2)*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b^2*c*d+3*((b*x^2+a)*(d*x^2+c))^(1/2)*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^3*c^2-6*x^2*a^3*d^2*(b*d)^(1/2)+2*(b*d)^(1/2)*x^2*a^2*b*c*d+12*x^2*a*b^2*c^2*(b*d)^(1/2)+3*((b*x^2+a)*(d*x^2+c))^(1/2)*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^3*d^2-6*((b*x^2+a)*(d*x^2+c))^(1/2)*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2*b*c*d+3*((b*x^2+a)*(d*x^2+c))^(1/2)*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*b^2*c^2-6*a^3*c*d*(b*d)^(1/2)+10*(b*d)^(1/2)*a^2*b*c^2)*(d*x^2+c)^(1/2)/b^2/(b*x^2+a)^(1/2)/(b*d)^(1/2)/(a*d-b*c)^2/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","B"
984,1,63,77,0.008000," ","int(x^3/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{d \,x^{2}+c}\, \left(-a d \,x^{2}+3 b c \,x^{2}+2 a c \right)}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right)}"," ",0,"-1/3*(d*x^2+c)^(1/2)*(-a*d*x^2+3*b*c*x^2+2*a*c)/(b*x^2+a)^(3/2)/(a^2*d^2-2*a*b*c*d+b^2*c^2)","A"
985,1,60,62,0.007000," ","int(x/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \left(2 b d \,x^{2}+3 a d -b c \right)}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right)}"," ",0,"1/3*(d*x^2+c)^(1/2)*(2*b*d*x^2+3*a*d-b*c)/(b*x^2+a)^(3/2)/(a^2*d^2-2*a*b*c*d+b^2*c^2)","A"
986,1,119,136,0.010000," ","int(x^5/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \left(3 a^{2} d^{2} x^{4}-10 a b c d \,x^{4}+15 b^{2} c^{2} x^{4}-4 a^{2} c d \,x^{2}+20 a b \,c^{2} x^{2}+8 a^{2} c^{2}\right)}{15 \left(b \,x^{2}+a \right)^{\frac{5}{2}} \left(a^{3} d^{3}-3 a^{2} c \,d^{2} b +3 a \,b^{2} c^{2} d -b^{3} c^{3}\right)}"," ",0,"1/15*(d*x^2+c)^(1/2)*(3*a^2*d^2*x^4-10*a*b*c*d*x^4+15*b^2*c^2*x^4-4*a^2*c*d*x^2+20*a*b*c^2*x^2+8*a^2*c^2)/(b*x^2+a)^(5/2)/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)","A"
987,1,125,120,0.012000," ","int(x^3/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{d \,x^{2}+c}\, \left(-2 a b \,d^{2} x^{4}+10 b^{2} c d \,x^{4}-5 a^{2} d^{2} x^{2}+26 a b c d \,x^{2}-5 b^{2} c^{2} x^{2}+10 a^{2} c d -2 a b \,c^{2}\right)}{15 \left(b \,x^{2}+a \right)^{\frac{5}{2}} \left(a^{3} d^{3}-3 a^{2} c \,d^{2} b +3 a \,b^{2} c^{2} d -b^{3} c^{3}\right)}"," ",0,"-1/15*(d*x^2+c)^(1/2)*(-2*a*b*d^2*x^4+10*b^2*c*d*x^4-5*a^2*d^2*x^2+26*a*b*c*d*x^2-5*b^2*c^2*x^2+10*a^2*c*d-2*a*b*c^2)/(b*x^2+a)^(5/2)/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)","A"
988,1,113,95,0.012000," ","int(x/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \left(8 b^{2} d^{2} x^{4}+20 a b \,d^{2} x^{2}-4 b^{2} c d \,x^{2}+15 a^{2} d^{2}-10 a b c d +3 b^{2} c^{2}\right)}{15 \left(b \,x^{2}+a \right)^{\frac{5}{2}} \left(a^{3} d^{3}-3 a^{2} c \,d^{2} b +3 a \,b^{2} c^{2} d -b^{3} c^{3}\right)}"," ",0,"1/15*(d*x^2+c)^(1/2)*(8*b^2*d^2*x^4+20*a*b*d^2*x^2-4*b^2*c*d*x^2+15*a^2*d^2-10*a*b*c*d+3*b^2*c^2)/(b*x^2+a)^(5/2)/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)","A"
989,1,213,193,0.013000," ","int(x^5/(b*x^2+a)^(9/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \left(6 a^{2} b \,d^{3} x^{6}-28 a \,b^{2} c \,d^{2} x^{6}+70 b^{3} c^{2} d \,x^{6}+21 a^{3} d^{3} x^{4}-101 a^{2} b c \,d^{2} x^{4}+259 a \,b^{2} c^{2} d \,x^{4}-35 b^{3} c^{3} x^{4}-28 a^{3} c \,d^{2} x^{2}+200 a^{2} b \,c^{2} d \,x^{2}-28 a \,b^{2} c^{3} x^{2}+56 a^{3} c^{2} d -8 a^{2} b \,c^{3}\right)}{105 \left(b \,x^{2}+a \right)^{\frac{7}{2}} \left(a^{4} d^{4}-4 a^{3} b c \,d^{3}+6 a^{2} c^{2} d^{2} b^{2}-4 a \,c^{3} d \,b^{3}+c^{4} b^{4}\right)}"," ",0,"1/105*(d*x^2+c)^(1/2)*(6*a^2*b*d^3*x^6-28*a*b^2*c*d^2*x^6+70*b^3*c^2*d*x^6+21*a^3*d^3*x^4-101*a^2*b*c*d^2*x^4+259*a*b^2*c^2*d*x^4-35*b^3*c^3*x^4-28*a^3*c*d^2*x^2+200*a^2*b*c^2*d*x^2-28*a*b^2*c^3*x^2+56*a^3*c^2*d-8*a^2*b*c^3)/(b*x^2+a)^(7/2)/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)","A"
990,1,108,35,0.046000," ","int(x/(-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \arctan \left(\frac{\sqrt{b d}\, \left(2 b d \,x^{2}-a d +b c \right)}{2 \sqrt{-x^{4} b d +a d \,x^{2}-b c \,x^{2}+a c}\, b d}\right)}{2 \sqrt{b d}\, \sqrt{-x^{4} b d +a d \,x^{2}-b c \,x^{2}+a c}}"," ",0,"1/2*arctan(1/2*(b*d)^(1/2)*(2*b*d*x^2-a*d+b*c)/b/d/(-b*d*x^4+a*d*x^2-b*c*x^2+a*c)^(1/2))*(-b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(b*d)^(1/2)/(-b*d*x^4+a*d*x^2-b*c*x^2+a*c)^(1/2)","B"
991,1,111,36,0.054000," ","int(x/(-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{-d \,x^{2}+c}\, \ln \left(\frac{2 b d \,x^{2}-a d -b c +2 \sqrt{x^{4} b d -a d \,x^{2}-b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)}{2 \sqrt{b d}\, \sqrt{x^{4} b d -a d \,x^{2}-b c \,x^{2}+a c}}"," ",0,"1/2*ln(1/2*(2*b*d*x^2+2*(b*d*x^4-a*d*x^2-b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)-a*d-b*c)/(b*d)^(1/2))*(-b*x^2+a)^(1/2)*(-d*x^2+c)^(1/2)/(b*d)^(1/2)/(b*d*x^4-a*d*x^2-b*c*x^2+a*c)^(1/2)","B"
992,1,70,125,0.029000," ","int(x^2/(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x)","\frac{\left(\EllipticE \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{b}{d}}}{2}\right)-\EllipticF \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{b}{d}}}{2}\right)\right) \sqrt{2}}{\sqrt{-d}\, b}"," ",0,"(-EllipticF(1/3*3^(1/2)*(-d)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(b/d)^(1/2))+EllipticE(1/3*3^(1/2)*(-d)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(b/d)^(1/2)))*2^(1/2)/(-d)^(1/2)/b","A"
993,1,59,81,0.048000," ","int(x^2/(-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\left(\EllipticE \left(\frac{x}{2}, 2 \sqrt{-\frac{d}{c}}\right)-\EllipticF \left(\frac{x}{2}, 2 \sqrt{-\frac{d}{c}}\right)\right) \sqrt{\frac{d \,x^{2}+c}{c}}\, c}{\sqrt{d \,x^{2}+c}\, d}"," ",0,"(-EllipticF(1/2*x,2*(-d/c)^(1/2))+EllipticE(1/2*x,2*(-d/c)^(1/2)))/(d*x^2+c)^(1/2)*c*((d*x^2+c)/c)^(1/2)/d","A"
994,1,76,85,0.046000," ","int(x^2/(x^2+4)^(1/2)/(d*x^2+c)^(1/2),x)","-\frac{2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \left(-\EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \frac{\sqrt{\frac{c}{d}}}{2}\right)+\EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \frac{\sqrt{\frac{c}{d}}}{2}\right)\right)}{\sqrt{d \,x^{2}+c}\, \sqrt{-\frac{d}{c}}}"," ",0,"-2/(d*x^2+c)^(1/2)*((d*x^2+c)/c)^(1/2)*(EllipticF(x*(-1/c*d)^(1/2),1/2*(c/d)^(1/2))-EllipticE(x*(-1/c*d)^(1/2),1/2*(c/d)^(1/2)))/(-1/c*d)^(1/2)","A"
995,1,25,27,0.048000," ","int(x^2/(-x^2+1)^(1/2)/(3*x^2+2)^(1/2),x)","-\frac{\left(-\EllipticE \left(x , \frac{i \sqrt{6}}{2}\right)+\EllipticF \left(x , \frac{i \sqrt{6}}{2}\right)\right) \sqrt{2}}{3}"," ",0,"-1/3*(EllipticF(x,1/2*I*6^(1/2))-EllipticE(x,1/2*I*6^(1/2)))*2^(1/2)","A"
996,1,23,25,0.029000," ","int(x^2/(-3*x^2+2)^(1/2)/(-x^2+1)^(1/2),x)","\frac{\sqrt{2}\, \left(-\EllipticE \left(x , \frac{\sqrt{6}}{2}\right)+\EllipticF \left(x , \frac{\sqrt{6}}{2}\right)\right)}{3}"," ",0,"1/3*2^(1/2)*(EllipticF(x,1/2*6^(1/2))-EllipticE(x,1/2*6^(1/2)))","A"
997,1,29,31,0.050000," ","int(x^2/(-x^2+4)^(1/2)/(3*x^2+2)^(1/2),x)","-\frac{\left(-\EllipticE \left(\frac{x}{2}, i \sqrt{6}\right)+\EllipticF \left(\frac{x}{2}, i \sqrt{6}\right)\right) \sqrt{2}}{3}"," ",0,"-1/3*(EllipticF(1/2*x,I*6^(1/2))-EllipticE(1/2*x,I*6^(1/2)))*2^(1/2)","A"
998,1,33,25,0.036000," ","int(x^2/(-3*x^2+2)^(1/2)/(-x^2+4)^(1/2),x)","\frac{2 \sqrt{3}\, \left(-\EllipticE \left(\frac{\sqrt{6}\, x}{2}, \frac{\sqrt{6}}{6}\right)+\EllipticF \left(\frac{\sqrt{6}\, x}{2}, \frac{\sqrt{6}}{6}\right)\right)}{3}"," ",0,"2/3*3^(1/2)*(EllipticF(1/2*x*6^(1/2),1/6*6^(1/2))-EllipticE(1/2*x*6^(1/2),1/6*6^(1/2)))","A"
999,1,29,31,0.046000," ","int(x^2/(-4*x^2+1)^(1/2)/(3*x^2+2)^(1/2),x)","-\frac{\left(-\EllipticE \left(2 x , \frac{i \sqrt{6}}{4}\right)+\EllipticF \left(2 x , \frac{i \sqrt{6}}{4}\right)\right) \sqrt{2}}{6}"," ",0,"-1/6*(EllipticF(2*x,1/4*I*6^(1/2))-EllipticE(2*x,1/4*I*6^(1/2)))*2^(1/2)","A"
1000,1,27,29,0.031000," ","int(x^2/(-4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \left(-\EllipticE \left(2 x , \frac{\sqrt{6}}{4}\right)+\EllipticF \left(2 x , \frac{\sqrt{6}}{4}\right)\right)}{6}"," ",0,"1/6*2^(1/2)*(EllipticF(2*x,1/4*6^(1/2))-EllipticE(2*x,1/4*6^(1/2)))","A"
1001,1,35,37,0.034000," ","int(x^2/(-3*x^2+2)^(1/2)/(x^2+1)^(1/2),x)","-\frac{\sqrt{3}\, \left(-\EllipticE \left(\frac{\sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{3}\right)+\EllipticF \left(\frac{\sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{3}\right)\right)}{3}"," ",0,"-1/3*3^(1/2)*(EllipticF(1/2*6^(1/2)*x,1/3*I*6^(1/2))-EllipticE(1/2*6^(1/2)*x,1/3*I*6^(1/2)))","A"
1002,1,35,37,0.029000," ","int(x^2/(-3*x^2+2)^(1/2)/(x^2+4)^(1/2),x)","-\frac{2 \sqrt{3}\, \left(-\EllipticE \left(\frac{\sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{6}\right)+\EllipticF \left(\frac{\sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{6}\right)\right)}{3}"," ",0,"-2/3*3^(1/2)*(EllipticF(1/2*6^(1/2)*x,1/6*I*6^(1/2))-EllipticE(1/2*6^(1/2)*x,1/6*I*6^(1/2)))","A"
1003,1,35,37,0.043000," ","int(x^2/(-3*x^2+2)^(1/2)/(4*x^2+1)^(1/2),x)","-\frac{\sqrt{3}\, \left(-\EllipticE \left(\frac{\sqrt{6}\, x}{2}, \frac{2 i \sqrt{6}}{3}\right)+\EllipticF \left(\frac{\sqrt{6}\, x}{2}, \frac{2 i \sqrt{6}}{3}\right)\right)}{12}"," ",0,"-1/12*3^(1/2)*(EllipticF(1/2*6^(1/2)*x,2/3*I*6^(1/2))-EllipticE(1/2*6^(1/2)*x,2/3*I*6^(1/2)))","A"
1004,1,30,76,0.029000," ","int(x^2/(x^2+1)^(1/2)/(3*x^2+2)^(1/2),x)","\frac{i \left(-\EllipticE \left(i x , \frac{\sqrt{6}}{2}\right)+\EllipticF \left(i x , \frac{\sqrt{6}}{2}\right)\right) \sqrt{2}}{3}"," ",0,"1/3*I*(EllipticF(I*x,1/2*6^(1/2))-EllipticE(I*x,1/2*6^(1/2)))*2^(1/2)","A"
1005,1,26,76,0.030000," ","int(x^2/(x^2+4)^(1/2)/(3*x^2+2)^(1/2),x)","\frac{i \left(-\EllipticE \left(\frac{i x}{2}, \sqrt{6}\right)+\EllipticF \left(\frac{i x}{2}, \sqrt{6}\right)\right) \sqrt{2}}{3}"," ",0,"1/3*I*(EllipticF(1/2*I*x,6^(1/2))-EllipticE(1/2*I*x,6^(1/2)))*2^(1/2)","A"
1006,1,36,84,0.044000," ","int(x^2/(3*x^2+2)^(1/2)/(4*x^2+1)^(1/2),x)","\frac{i \left(-\EllipticE \left(\frac{i \sqrt{6}\, x}{2}, \frac{2 \sqrt{6}}{3}\right)+\EllipticF \left(\frac{i \sqrt{6}\, x}{2}, \frac{2 \sqrt{6}}{3}\right)\right) \sqrt{3}}{12}"," ",0,"1/12*I*(EllipticF(1/2*I*x*6^(1/2),2/3*6^(1/2))-EllipticE(1/2*I*x*6^(1/2),2/3*6^(1/2)))*3^(1/2)","C"
1007,1,34,47,0.042000," ","int(x^2/(-x^2+1)^(1/2)/(2*x^2-1)^(1/2),x)","\frac{\left(-\EllipticE \left(x , \sqrt{2}\right)+\EllipticF \left(x , \sqrt{2}\right)\right) \sqrt{-2 x^{2}+1}}{2 \sqrt{2 x^{2}-1}}"," ",0,"1/2*(EllipticF(x,2^(1/2))-EllipticE(x,2^(1/2)))*(-2*x^2+1)^(1/2)/(2*x^2-1)^(1/2)","A"
1008,1,655,80,7.176000," ","int(x^5/(-x^2+1)^(1/3)/(x^2+3),x)","9 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(\frac{32 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+24 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-4 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-3 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+84 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+63 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)-9 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(-\frac{-16 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-10 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+5 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-21 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+42 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)-21 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)-\frac{9 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(-\frac{-16 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-10 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+5 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-21 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+42 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)-21 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{4}+\frac{3 \left(x^{2}-6\right) \left(x^{2}-1\right)}{10 \left(-x^{2}+1\right)^{\frac{1}{3}}}"," ",0,"3/10*(x^2-6)*(x^2-1)/(-x^2+1)^(1/3)-9/4*ln(-(8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-16*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-21*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)+5*RootOf(_Z^3-2)*x^2-10*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2-21*(-x^2+1)^(2/3)-21*RootOf(_Z^3-2)+42*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2))/(x^2+3))*RootOf(_Z^3-2)-9*ln(-(8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-16*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-21*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)+5*RootOf(_Z^3-2)*x^2-10*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2-21*(-x^2+1)^(2/3)-21*RootOf(_Z^3-2)+42*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2))/(x^2+3))*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+9*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*ln((24*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+32*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2+42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-3*RootOf(_Z^3-2)*x^2-4*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2+42*(-x^2+1)^(2/3)+63*RootOf(_Z^3-2)+84*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2))/(x^2+3))","C"
1009,1,754,69,7.982000," ","int(x^3/(-x^2+1)^(1/3)/(x^2+3),x)","-3 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3}+8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-x^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)+21 \RootOf \left(\textit{\_Z}^{3}+2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)-\frac{3 \RootOf \left(\textit{\_Z}^{3}+2\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3}+8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-x^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)+21 \RootOf \left(\textit{\_Z}^{3}+2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{4}+\frac{3 \RootOf \left(\textit{\_Z}^{3}+2\right) \ln \left(-\frac{96 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3}-60 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-5 x^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)+168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)+42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+252 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)+21 \RootOf \left(\textit{\_Z}^{3}+2\right)-42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{4}+\frac{\frac{3 x^{2}}{4}-\frac{3}{4}}{\left(-x^{2}+1\right)^{\frac{1}{3}}}"," ",0,"3/4*(x^2-1)/(-x^2+1)^(1/3)+3/4*RootOf(_Z^3+2)*ln(-(96*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)^2*RootOf(_Z^3+2)^2*x^2+8*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*RootOf(_Z^3+2)^3*x^2+168*RootOf(_Z^3+2)*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)-60*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*x^2+42*RootOf(_Z^3+2)^2*(-x^2+1)^(1/3)-5*RootOf(_Z^3+2)*x^2-42*(-x^2+1)^(2/3)+252*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)+21*RootOf(_Z^3+2))/(x^2+3))-3/4*ln((64*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)^2*RootOf(_Z^3+2)^2*x^2-8*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*RootOf(_Z^3+2)^3*x^2-168*RootOf(_Z^3+2)*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)+8*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*x^2-42*RootOf(_Z^3+2)^2*(-x^2+1)^(1/3)-RootOf(_Z^3+2)*x^2+42*(-x^2+1)^(2/3)-168*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)+21*RootOf(_Z^3+2))/(x^2+3))*RootOf(_Z^3+2)-3*ln((64*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)^2*RootOf(_Z^3+2)^2*x^2-8*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*RootOf(_Z^3+2)^3*x^2-168*RootOf(_Z^3+2)*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)+8*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*x^2-42*RootOf(_Z^3+2)^2*(-x^2+1)^(1/3)-RootOf(_Z^3+2)*x^2+42*(-x^2+1)^(2/3)-168*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)+21*RootOf(_Z^3+2))/(x^2+3))*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)","C"
1010,1,460,58,6.315000," ","int(x/(-x^2+1)^(1/3)/(x^2+3),x)","\RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+24 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}+40 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+15 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)+168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-63 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(-\frac{48 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-6 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-84 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)+126 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+21 \RootOf \left(\textit{\_Z}^{3}-2\right)-21 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{4}"," ",0,"1/4*RootOf(_Z^3-2)*ln(-(48*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2+8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-84*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-6*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2-RootOf(_Z^3-2)*x^2-21*(-x^2+1)^(2/3)+126*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+21*RootOf(_Z^3-2))/(x^2+3))+RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*ln((64*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2+24*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)+40*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2+15*RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)-168*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-63*RootOf(_Z^3-2))/(x^2+3))","C"
1011,0,0,102,1.504000," ","int(1/x/(-x^2+1)^(1/3)/(x^2+3),x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right) x}\, dx"," ",0,"int(1/x/(-x^2+1)^(1/3)/(x^2+3),x)","F"
1012,1,754,72,6.053000," ","int(1/x^3/(-x^2+1)^(1/3)/(x^2+3),x)","-\frac{\RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{9}+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{-96 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-60 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-5 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+252 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+21 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{36}-\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{36}+\frac{x^{2}-1}{6 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{2}}"," ",0,"1/6*(x^2-1)/x^2/(-x^2+1)^(1/3)-1/36*ln((64*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-8*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2+RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)+168*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-21*RootOf(_Z^3-2))/(x^2+3))*RootOf(_Z^3-2)-1/9*ln((64*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-8*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2+RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)+168*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-21*RootOf(_Z^3-2))/(x^2+3))*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+1/36*RootOf(_Z^3-2)*ln((-96*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-60*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2-5*RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)+252*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+21*RootOf(_Z^3-2))/(x^2+3))","C"
1013,0,0,130,1.638000," ","int(1/x^5/(-x^2+1)^(1/3)/(x^2+3),x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right) x^{5}}\, dx"," ",0,"int(1/x^5/(-x^2+1)^(1/3)/(x^2+3),x)","F"
1014,0,0,420,0.207000," ","int(x^4/(-x^2+1)^(1/3)/(x^2+3),x)","\int \frac{x^{4}}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)}\, dx"," ",0,"int(x^4/(-x^2+1)^(1/3)/(x^2+3),x)","F"
1015,0,0,407,0.082000," ","int(x^2/(-x^2+1)^(1/3)/(x^2+3),x)","\int \frac{x^{2}}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)}\, dx"," ",0,"int(x^2/(-x^2+1)^(1/3)/(x^2+3),x)","F"
1016,1,938,81,42.308000," ","int(1/(-x^2+1)^(1/3)/(x^2+3),x)","-\frac{\RootOf \left(\textit{\_Z}^{6}+108\right)^{4} \ln \left(\frac{x^{6} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+72 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+225 x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+36 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-72 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-189 x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+864 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+648 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{4}-648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+27 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+4536 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{3}-324 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+1944 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{2}-1944 \left(-x^{2}+1\right)^{\frac{2}{3}} x}{\left(x^{2}+3\right)^{3}}\right)}{432}+\frac{\RootOf \left(\textit{\_Z}^{6}+108\right) \ln \left(\frac{x^{6} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+72 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+225 x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+36 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-72 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-189 x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+864 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+648 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{4}-648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+27 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+4536 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{3}-324 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+1944 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{2}-1944 \left(-x^{2}+1\right)^{\frac{2}{3}} x}{\left(x^{2}+3\right)^{3}}\right)}{72}+\frac{\RootOf \left(\textit{\_Z}^{6}+108\right) \ln \left(\frac{-x^{6} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}-6 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}-72 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}-108 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}-225 x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}-144 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}-18 x^{6} \RootOf \left(\textit{\_Z}^{6}+108\right)-36 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+72 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+108 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}-1296 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)-648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+189 x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+54 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}-4050 x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)-864 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+1296 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{4}+1296 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)+648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-27 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+9072 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{3}+3402 x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)+324 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+3888 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{2}-3888 \left(-x^{2}+1\right)^{\frac{2}{3}} x -486 \RootOf \left(\textit{\_Z}^{6}+108\right)}{\left(x^{2}+3\right)^{3}}\right)}{36}"," ",0,"-1/432*ln((RootOf(_Z^6+108)^4*x^6+72*RootOf(_Z^6+108)^4*x^5+36*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^5+225*RootOf(_Z^6+108)^4*x^4+648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^4-72*RootOf(_Z^6+108)^4*x^3+648*(-x^2+1)^(2/3)*x^4+864*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^3-189*RootOf(_Z^6+108)^4*x^2+4536*(-x^2+1)^(2/3)*x^3-648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^2+1944*(-x^2+1)^(2/3)*x^2-324*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x+27*RootOf(_Z^6+108)^4-1944*x*(-x^2+1)^(2/3))/(x^2+3)^3)*RootOf(_Z^6+108)^4+1/72*ln((RootOf(_Z^6+108)^4*x^6+72*RootOf(_Z^6+108)^4*x^5+36*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^5+225*RootOf(_Z^6+108)^4*x^4+648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^4-72*RootOf(_Z^6+108)^4*x^3+648*(-x^2+1)^(2/3)*x^4+864*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^3-189*RootOf(_Z^6+108)^4*x^2+4536*(-x^2+1)^(2/3)*x^3-648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^2+1944*(-x^2+1)^(2/3)*x^2-324*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x+27*RootOf(_Z^6+108)^4-1944*x*(-x^2+1)^(2/3))/(x^2+3)^3)*RootOf(_Z^6+108)+1/36*RootOf(_Z^6+108)*ln((1296*(-x^2+1)^(2/3)*x^4+9072*(-x^2+1)^(2/3)*x^3+3888*(-x^2+1)^(2/3)*x^2-486*RootOf(_Z^6+108)-3888*x*(-x^2+1)^(2/3)+189*RootOf(_Z^6+108)^4*x^2+3402*RootOf(_Z^6+108)*x^2+72*RootOf(_Z^6+108)^4*x^3+1296*RootOf(_Z^6+108)*x^3-1296*RootOf(_Z^6+108)*x^5-4050*RootOf(_Z^6+108)*x^4-RootOf(_Z^6+108)^4*x^6-72*RootOf(_Z^6+108)^4*x^5-225*RootOf(_Z^6+108)^4*x^4-18*RootOf(_Z^6+108)*x^6-144*(-x^2+1)^(1/3)*RootOf(_Z^6+108)^5*x^3+108*(-x^2+1)^(1/3)*RootOf(_Z^6+108)^5*x^2+54*(-x^2+1)^(1/3)*RootOf(_Z^6+108)^5*x-36*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^5-648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^4-864*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^3+648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^2+324*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x-6*(-x^2+1)^(1/3)*RootOf(_Z^6+108)^5*x^5-108*(-x^2+1)^(1/3)*RootOf(_Z^6+108)^5*x^4-27*RootOf(_Z^6+108)^4)/(x^2+3)^3)","C"
1017,0,0,422,0.096000," ","int(1/x^2/(-x^2+1)^(1/3)/(x^2+3),x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right) x^{2}}\, dx"," ",0,"int(1/x^2/(-x^2+1)^(1/3)/(x^2+3),x)","F"
1018,0,0,436,0.087000," ","int(1/x^4/(-x^2+1)^(1/3)/(x^2+3),x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right) x^{4}}\, dx"," ",0,"int(1/x^4/(-x^2+1)^(1/3)/(x^2+3),x)","F"
1019,1,770,104,5.976000," ","int(x^7/(-x^2+1)^(1/3)/(x^2+3)^2,x)","-\frac{99 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{4}+\frac{99 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{-96 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-60 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-5 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+252 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+21 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{16}-\frac{99 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{16}+\frac{\frac{3}{10} x^{6}-\frac{69}{20} x^{4}-\frac{99}{8} x^{2}+\frac{621}{40}}{\left(x^{2}+3\right) \left(-x^{2}+1\right)^{\frac{1}{3}}}"," ",0,"3/40*(4*x^6-46*x^4-165*x^2+207)/(x^2+3)/(-x^2+1)^(1/3)+99/16*RootOf(_Z^3-2)*ln((-96*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-60*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2-5*RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)+252*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+21*RootOf(_Z^3-2))/(x^2+3))-99/16*ln((64*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-8*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2+RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)+168*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-21*RootOf(_Z^3-2))/(x^2+3))*RootOf(_Z^3-2)-99/4*ln((64*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-8*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2+RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)+168*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-21*RootOf(_Z^3-2))/(x^2+3))*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)","C"
1020,1,490,87,6.766000," ","int(x^5/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\frac{21 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+24 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3}-40 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-15 x^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)+168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)+168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)+63 \RootOf \left(\textit{\_Z}^{3}+2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{4}+\frac{21 \RootOf \left(\textit{\_Z}^{3}+2\right) \ln \left(-\frac{48 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3}+6 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)+x^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)-84 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)-126 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}+2\right)-21 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{16}+\frac{\frac{3}{4} x^{4}+\frac{21}{8} x^{2}-\frac{27}{8}}{\left(x^{2}+3\right) \left(-x^{2}+1\right)^{\frac{1}{3}}}"," ",0,"3/8*(2*x^4+7*x^2-9)/(x^2+3)/(-x^2+1)^(1/3)+21/16*RootOf(_Z^3+2)*ln(-(48*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)^2*RootOf(_Z^3+2)^2*x^2+8*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*RootOf(_Z^3+2)^3*x^2-84*RootOf(_Z^3+2)*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)+6*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*x^2+RootOf(_Z^3+2)*x^2-21*(-x^2+1)^(2/3)-126*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)-21*RootOf(_Z^3+2))/(x^2+3))+21/4*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*ln((64*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)^2*RootOf(_Z^3+2)^2*x^2+24*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*RootOf(_Z^3+2)^3*x^2+168*RootOf(_Z^3+2)*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)-40*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)*x^2-15*RootOf(_Z^3+2)*x^2+42*(-x^2+1)^(2/3)+168*RootOf(RootOf(_Z^3+2)^2+4*_Z*RootOf(_Z^3+2)+16*_Z^2)+63*RootOf(_Z^3+2))/(x^2+3))","C"
1021,1,758,76,5.052000," ","int(x^3/(-x^2+1)^(1/3)/(x^2+3)^2,x)","-\frac{3 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{4}+\frac{3 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{-96 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-60 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-5 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+252 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+21 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{16}-\frac{3 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{64 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-168 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+168 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{16}-\frac{3 \left(x^{2}-1\right)}{8 \left(x^{2}+3\right) \left(-x^{2}+1\right)^{\frac{1}{3}}}"," ",0,"-3/8*(x^2-1)/(x^2+3)/(-x^2+1)^(1/3)+3/16*RootOf(_Z^3-2)*ln((-96*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-60*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2-5*RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)+252*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+21*RootOf(_Z^3-2))/(x^2+3))-3/16*ln((64*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-8*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2+RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)+168*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-21*RootOf(_Z^3-2))/(x^2+3))*RootOf(_Z^3-2)-3/4*ln((64*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-168*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)-42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-8*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2+RootOf(_Z^3-2)*x^2+42*(-x^2+1)^(2/3)+168*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-21*RootOf(_Z^3-2))/(x^2+3))*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)","C"
1022,1,657,76,4.947000," ","int(x/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\frac{\RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(\frac{32 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+24 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-4 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-3 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+84 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+63 \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{12}-\frac{\RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(-\frac{-16 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-10 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+5 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-21 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+42 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)-21 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(-\frac{-16 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+8 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-10 x^{2} \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+5 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-21 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+42 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-21 \RootOf \left(\textit{\_Z}^{3}-2\right)-21 \left(-x^{2}+1\right)^{\frac{2}{3}}}{x^{2}+3}\right)}{48}+\frac{x^{2}-1}{8 \left(x^{2}+3\right) \left(-x^{2}+1\right)^{\frac{1}{3}}}"," ",0,"1/8*(x^2-1)/(x^2+3)/(-x^2+1)^(1/3)-1/48*ln(-(8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-16*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-21*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)+5*RootOf(_Z^3-2)*x^2-10*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2-21*(-x^2+1)^(2/3)-21*RootOf(_Z^3-2)+42*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2))/(x^2+3))*RootOf(_Z^3-2)-1/12*ln(-(8*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)-16*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-21*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)+5*RootOf(_Z^3-2)*x^2-10*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2-21*(-x^2+1)^(2/3)-21*RootOf(_Z^3-2)+42*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2))/(x^2+3))*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+1/12*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*ln((24*x^2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)+32*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^2+42*RootOf(_Z^3-2)^2*(-x^2+1)^(1/3)-3*RootOf(_Z^3-2)*x^2-4*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^2+42*(-x^2+1)^(2/3)+63*RootOf(_Z^3-2)+84*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2))/(x^2+3))","C"
1023,0,0,120,1.632000," ","int(1/x/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)^{2} x}\, dx"," ",0,"int(1/x/(-x^2+1)^(1/3)/(x^2+3)^2,x)","F"
1024,0,0,141,1.669000," ","int(1/x^3/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)^{2} x^{3}}\, dx"," ",0,"int(1/x^3/(-x^2+1)^(1/3)/(x^2+3)^2,x)","F"
1025,0,0,162,1.687000," ","int(1/x^5/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)^{2} x^{5}}\, dx"," ",0,"int(1/x^5/(-x^2+1)^(1/3)/(x^2+3)^2,x)","F"
1026,0,0,427,0.303000," ","int(x^4/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\int \frac{x^{4}}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)^{2}}\, dx"," ",0,"int(x^4/(-x^2+1)^(1/3)/(x^2+3)^2,x)","F"
1027,0,0,427,0.194000," ","int(x^2/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\int \frac{x^{2}}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)^{2}}\, dx"," ",0,"int(x^2/(-x^2+1)^(1/3)/(x^2+3)^2,x)","F"
1028,0,0,427,0.101000," ","int(1/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)^{2}}\, dx"," ",0,"int(1/(-x^2+1)^(1/3)/(x^2+3)^2,x)","F"
1029,0,0,443,0.185000," ","int(1/x^2/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)^{2} x^{2}}\, dx"," ",0,"int(1/x^2/(-x^2+1)^(1/3)/(x^2+3)^2,x)","F"
1030,0,0,457,0.262000," ","int(1/x^4/(-x^2+1)^(1/3)/(x^2+3)^2,x)","\int \frac{1}{\left(-x^{2}+1\right)^{\frac{1}{3}} \left(x^{2}+3\right)^{2} x^{4}}\, dx"," ",0,"int(1/x^4/(-x^2+1)^(1/3)/(x^2+3)^2,x)","F"
1031,1,217,102,2.848000," ","int(x^7/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","\frac{16 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}-6 x^{2}+2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}-4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{3 x^{2}-4}\right)}{81}-\frac{16 \RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(\frac{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}-6 x^{2}-2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)}{3 x^{2}-4}\right)}{81}-\frac{2 \left(189 x^{4}+540 x^{2}+1712\right) \left(3 x^{2}-2\right)}{18711 \left(-3 x^{2}+2\right)^{\frac{1}{4}}}"," ",0,"-2/18711*(189*x^4+540*x^2+1712)*(3*x^2-2)/(-3*x^2+2)^(1/4)-16/81*RootOf(_Z^4+8)*ln((RootOf(_Z^4+8)^3*(-3*x^2+2)^(3/4)-2*RootOf(_Z^4+8)^2*(-3*x^2+2)^(1/2)+4*RootOf(_Z^4+8)*(-3*x^2+2)^(1/4)-6*x^2)/(3*x^2-4))+16/81*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(-3*x^2+2)^(3/4)+2*RootOf(_Z^4+8)^2*(-3*x^2+2)^(1/2)-4*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(-3*x^2+2)^(1/4)-6*x^2)/(3*x^2-4))","C"
1032,1,211,91,2.513000," ","int(x^5/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+6 x^{2}-2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}-4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{3 x^{2}-4}\right)}{27}-\frac{4 \RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(\frac{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}-6 x^{2}-2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)}{3 x^{2}-4}\right)}{27}-\frac{2 \left(x^{2}+4\right) \left(3 x^{2}-2\right)}{63 \left(-3 x^{2}+2\right)^{\frac{1}{4}}}"," ",0,"-2/63*(x^2+4)*(3*x^2-2)/(-3*x^2+2)^(1/4)-4/27*RootOf(_Z^4+8)*ln((RootOf(_Z^4+8)^3*(-3*x^2+2)^(3/4)-2*RootOf(_Z^4+8)^2*(-3*x^2+2)^(1/2)+4*RootOf(_Z^4+8)*(-3*x^2+2)^(1/4)-6*x^2)/(3*x^2-4))-4/27*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(-3*x^2+2)^(3/4)-2*RootOf(_Z^4+8)^2*(-3*x^2+2)^(1/2)-4*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(-3*x^2+2)^(1/4)+6*x^2)/(3*x^2-4))","C"
1033,1,206,80,1.725000," ","int(x^3/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+6 x^{2}-2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}-4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{3 x^{2}-4}\right)}{9}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(\frac{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}-6 x^{2}-2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)}{3 x^{2}-4}\right)}{9}-\frac{2 \left(3 x^{2}-2\right)}{27 \left(-3 x^{2}+2\right)^{\frac{1}{4}}}"," ",0,"-2/27*(3*x^2-2)/(-3*x^2+2)^(1/4)-1/9*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(-3*x^2+2)^(3/4)-2*RootOf(_Z^4+8)^2*(-3*x^2+2)^(1/2)-4*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(-3*x^2+2)^(1/4)+6*x^2)/(3*x^2-4))-1/9*RootOf(_Z^4+8)*ln((RootOf(_Z^4+8)^3*(-3*x^2+2)^(3/4)-2*RootOf(_Z^4+8)^2*(-3*x^2+2)^(1/2)+4*RootOf(_Z^4+8)*(-3*x^2+2)^(1/4)-6*x^2)/(3*x^2-4))","C"
1034,1,189,69,3.965000," ","int(x/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+6 x^{2}-2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}-4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{3 x^{2}-4}\right)}{12}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}+6 x^{2}+2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)}{3 x^{2}-4}\right)}{12}"," ",0,"1/12*RootOf(_Z^4+8)*ln(-(RootOf(_Z^4+8)^3*(-3*x^2+2)^(3/4)+2*RootOf(_Z^4+8)^2*(-3*x^2+2)^(1/2)+4*RootOf(_Z^4+8)*(-3*x^2+2)^(1/4)+6*x^2)/(3*x^2-4))-1/12*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(-3*x^2+2)^(3/4)-2*RootOf(_Z^4+8)^2*(-3*x^2+2)^(1/2)-4*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(-3*x^2+2)^(1/4)+6*x^2)/(3*x^2-4))","C"
1035,0,0,109,11.909000," ","int(1/x/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","\int \frac{1}{\left(-3 x^{2}+2\right)^{\frac{1}{4}} \left(-3 x^{2}+4\right) x}\, dx"," ",0,"int(1/x/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","F"
1036,0,0,123,9.181000," ","int(1/x^3/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","\int \frac{1}{\left(-3 x^{2}+2\right)^{\frac{1}{4}} \left(-3 x^{2}+4\right) x^{3}}\, dx"," ",0,"int(1/x^3/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","F"
1037,0,0,148,0.144000," ","int(x^4/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","\int \frac{x^{4}}{\left(-3 x^{2}+2\right)^{\frac{1}{4}} \left(-3 x^{2}+4\right)}\, dx"," ",0,"int(x^4/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","F"
1038,0,0,136,0.191000," ","int(x^2/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","\int \frac{x^{2}}{\left(-3 x^{2}+2\right)^{\frac{1}{4}} \left(-3 x^{2}+4\right)}\, dx"," ",0,"int(x^2/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","F"
1039,1,186,90,2.055000," ","int(1/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+72\right)^{2}\right) \ln \left(\frac{3 x \RootOf \left(\textit{\_Z}^{4}+72\right)^{2}+\left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+72\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+72\right)^{2}+18 \sqrt{-3 x^{2}+2}\, x +6 \left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+72\right)^{2}\right)}{3 x^{2}-4}\right)}{24}+\frac{\RootOf \left(\textit{\_Z}^{4}+72\right) \ln \left(\frac{-3 x \RootOf \left(\textit{\_Z}^{4}+72\right)^{2}-\left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+72\right)^{3}+18 \sqrt{-3 x^{2}+2}\, x +6 \left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+72\right)}{3 x^{2}-4}\right)}{24}"," ",0,"1/24*RootOf(_Z^4+72)*ln((6*(-3*x^2+2)^(3/4)*RootOf(_Z^4+72)-(-3*x^2+2)^(1/4)*RootOf(_Z^4+72)^3+18*(-3*x^2+2)^(1/2)*x-3*RootOf(_Z^4+72)^2*x)/(3*x^2-4))+1/24*RootOf(_Z^2+RootOf(_Z^4+72)^2)*ln((6*(-3*x^2+2)^(3/4)*RootOf(_Z^2+RootOf(_Z^4+72)^2)+(-3*x^2+2)^(1/4)*RootOf(_Z^4+72)^2*RootOf(_Z^2+RootOf(_Z^4+72)^2)+18*(-3*x^2+2)^(1/2)*x+3*RootOf(_Z^4+72)^2*x)/(3*x^2-4))","C"
1040,0,0,150,0.090000," ","int(1/x^2/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","\int \frac{1}{\left(-3 x^{2}+2\right)^{\frac{1}{4}} \left(-3 x^{2}+4\right) x^{2}}\, dx"," ",0,"int(1/x^2/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","F"
1041,0,0,164,0.094000," ","int(1/x^4/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","\int \frac{1}{\left(-3 x^{2}+2\right)^{\frac{1}{4}} \left(-3 x^{2}+4\right) x^{4}}\, dx"," ",0,"int(1/x^4/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","F"
1042,1,148,58,1.080000," ","int(x^7/(3*x^2-2)/(3*x^2-1)^(1/4),x)","\frac{4 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{3 x^{2}-1}}{3 x^{2}-2}\right)}{81}+\frac{4 \ln \left(\frac{-3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{3 x^{2}-1}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{81}+\frac{2 \left(189 x^{4}+270 x^{2}+428\right) \left(3 x^{2}-1\right)^{\frac{3}{4}}}{18711}"," ",0,"2/18711*(189*x^4+270*x^2+428)*(3*x^2-1)^(3/4)+4/81*RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*(3*x^2-1)^(3/4)-2*RootOf(_Z^2+1)*(3*x^2-1)^(1/4)-2*(3*x^2-1)^(1/2)+3*x^2)/(3*x^2-2))+4/81*ln((2*(3*x^2-1)^(3/4)-2*(3*x^2-1)^(1/2)-3*x^2+2*(3*x^2-1)^(1/4))/(3*x^2-2))","C"
1043,1,141,47,0.965000," ","int(x^5/(3*x^2-2)/(3*x^2-1)^(1/4),x)","\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{3 x^{2}-1}}{3 x^{2}-2}\right)}{27}+\frac{2 \ln \left(\frac{-3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{3 x^{2}-1}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{27}+\frac{2 \left(x^{2}+2\right) \left(3 x^{2}-1\right)^{\frac{3}{4}}}{63}"," ",0,"2/63*(x^2+2)*(3*x^2-1)^(3/4)+2/27*RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*(3*x^2-1)^(3/4)-2*RootOf(_Z^2+1)*(3*x^2-1)^(1/4)-2*(3*x^2-1)^(1/2)+3*x^2)/(3*x^2-2))+2/27*ln((-3*x^2+2*(3*x^2-1)^(3/4)-2*(3*x^2-1)^(1/2)+2*(3*x^2-1)^(1/4))/(3*x^2-2))","C"
1044,1,136,36,1.013000," ","int(x^3/(3*x^2-2)/(3*x^2-1)^(1/4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{3 x^{2}-1}}{3 x^{2}-2}\right)}{9}-\frac{\ln \left(-\frac{3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}+2 \sqrt{3 x^{2}-1}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{9}+\frac{2 \left(3 x^{2}-1\right)^{\frac{3}{4}}}{27}"," ",0,"2/27*(3*x^2-1)^(3/4)-1/9*ln(-(2*(3*x^2-1)^(3/4)+2*(3*x^2-1)^(1/2)+3*x^2+2*(3*x^2-1)^(1/4))/(3*x^2-2))-1/9*RootOf(_Z^2+1)*ln((2*RootOf(_Z^2+1)*(3*x^2-1)^(3/4)+2*(3*x^2-1)^(1/2)-2*RootOf(_Z^2+1)*(3*x^2-1)^(1/4)-3*x^2)/(3*x^2-2))","C"
1045,1,125,25,0.928000," ","int(x/(3*x^2-2)/(3*x^2-1)^(1/4),x)","\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{3 x^{2}-1}}{3 x^{2}-2}\right)}{6}+\frac{\ln \left(\frac{-3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{3 x^{2}-1}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{6}"," ",0,"1/6*ln((-3*x^2+2*(3*x^2-1)^(3/4)-2*(3*x^2-1)^(1/2)+2*(3*x^2-1)^(1/4))/(3*x^2-2))+1/6*RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*(3*x^2-1)^(3/4)-2*RootOf(_Z^2+1)*(3*x^2-1)^(1/4)-2*(3*x^2-1)^(1/2)+3*x^2)/(3*x^2-2))","C"
1046,1,301,128,5.782000," ","int(1/x/(3*x^2-2)/(3*x^2-1)^(1/4),x)","\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \sqrt{3 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}}{x^{2}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \ln \left(-\frac{-3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \sqrt{3 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}-2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{-3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \sqrt{3 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)-2 \left(3 x^{2}-1\right)^{\frac{3}{4}}}{x^{2}}\right)}{4}+\frac{\ln \left(-\frac{-3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{3 x^{2}-1}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{4}"," ",0,"1/4*RootOf(_Z^4+1)*ln((2*(3*x^2-1)^(1/2)*RootOf(_Z^4+1)^3+2*RootOf(_Z^4+1)^2*(3*x^2-1)^(1/4)-3*RootOf(_Z^4+1)*x^2-2*(3*x^2-1)^(3/4)+2*RootOf(_Z^4+1))/x^2)+1/4*RootOf(_Z^4+1)^3*ln(-(3*RootOf(_Z^4+1)^3*x^2-2*RootOf(_Z^4+1)^3+2*RootOf(_Z^4+1)^2*(3*x^2-1)^(1/4)-2*(3*x^2-1)^(1/2)*RootOf(_Z^4+1)+2*(3*x^2-1)^(3/4))/x^2)+1/4*ln(-(-3*x^2+2*(3*x^2-1)^(3/4)-2*(3*x^2-1)^(1/2)+2*(3*x^2-1)^(1/4))/(3*x^2-2))+1/4*RootOf(_Z^4+1)^2*ln(-(2*(3*x^2-1)^(1/2)*RootOf(_Z^4+1)^2-3*RootOf(_Z^4+1)^2*x^2+2*(3*x^2-1)^(3/4)-2*(3*x^2-1)^(1/4))/(3*x^2-2))","C"
1047,1,315,142,5.086000," ","int(1/x^3/(3*x^2-2)/(3*x^2-1)^(1/4),x)","-\frac{9 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{-3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \sqrt{3 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}}{x^{2}}\right)}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \ln \left(-\frac{-3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \sqrt{3 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}-2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{8}+\frac{9 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{-3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \sqrt{3 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)-2 \left(3 x^{2}-1\right)^{\frac{3}{4}}}{x^{2}}\right)}{16}+\frac{3 \ln \left(-\frac{-3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{3 x^{2}-1}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{8}-\frac{\left(3 x^{2}-1\right)^{\frac{3}{4}}}{4 x^{2}}"," ",0,"-1/4*(3*x^2-1)^(3/4)/x^2+9/16*RootOf(_Z^4+1)*ln((2*(3*x^2-1)^(1/2)*RootOf(_Z^4+1)^3+2*RootOf(_Z^4+1)^2*(3*x^2-1)^(1/4)-3*RootOf(_Z^4+1)*x^2-2*(3*x^2-1)^(3/4)+2*RootOf(_Z^4+1))/x^2)-9/16*RootOf(_Z^4+1)^3*ln(-(-3*RootOf(_Z^4+1)^3*x^2+2*(3*x^2-1)^(3/4)+2*(3*x^2-1)^(1/2)*RootOf(_Z^4+1)+2*RootOf(_Z^4+1)^2*(3*x^2-1)^(1/4)+2*RootOf(_Z^4+1)^3)/x^2)+3/8*RootOf(_Z^4+1)^2*ln(-(2*(3*x^2-1)^(1/2)*RootOf(_Z^4+1)^2-3*RootOf(_Z^4+1)^2*x^2+2*(3*x^2-1)^(3/4)-2*(3*x^2-1)^(1/4))/(3*x^2-2))+3/8*ln(-(-3*x^2+2*(3*x^2-1)^(3/4)-2*(3*x^2-1)^(1/2)+2*(3*x^2-1)^(1/4))/(3*x^2-2))","C"
1048,0,0,258,0.192000," ","int(x^4/(3*x^2-2)/(3*x^2-1)^(1/4),x)","\int \frac{x^{4}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{\frac{1}{4}}}\, dx"," ",0,"int(x^4/(3*x^2-2)/(3*x^2-1)^(1/4),x)","F"
1049,0,0,246,0.125000," ","int(x^2/(3*x^2-2)/(3*x^2-1)^(1/4),x)","\int \frac{x^{2}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{\frac{1}{4}}}\, dx"," ",0,"int(x^2/(3*x^2-2)/(3*x^2-1)^(1/4),x)","F"
1050,1,137,43,1.292000," ","int(1/(3*x^2-2)/(3*x^2-1)^(1/4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{3 \sqrt{3 x^{2}-1}\, x +3 x +\left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)+\left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)}{3 x^{2}-2}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{2}+6\right) \ln \left(\frac{3 \sqrt{3 x^{2}-1}\, x -3 x +\left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)-\left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)}{3 x^{2}-2}\right)}{12}"," ",0,"-1/12*RootOf(_Z^2+6)*ln((RootOf(_Z^2+6)*(3*x^2-1)^(3/4)+3*(3*x^2-1)^(1/2)*x-RootOf(_Z^2+6)*(3*x^2-1)^(1/4)-3*x)/(3*x^2-2))-1/12*RootOf(_Z^2-6)*ln((RootOf(_Z^2-6)*(3*x^2-1)^(3/4)+3*(3*x^2-1)^(1/2)*x+RootOf(_Z^2-6)*(3*x^2-1)^(1/4)+3*x)/(3*x^2-2))","C"
1051,0,0,260,0.186000," ","int(1/x^2/(3*x^2-2)/(3*x^2-1)^(1/4),x)","\int \frac{1}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{\frac{1}{4}} x^{2}}\, dx"," ",0,"int(1/x^2/(3*x^2-2)/(3*x^2-1)^(1/4),x)","F"
1052,0,0,274,0.101000," ","int(1/x^4/(3*x^2-2)/(3*x^2-1)^(1/4),x)","\int \frac{1}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{\frac{1}{4}} x^{4}}\, dx"," ",0,"int(1/x^4/(3*x^2-2)/(3*x^2-1)^(1/4),x)","F"
1053,1,186,93,7.444000," ","int(x^2/(3*x^2+2)^(3/4)/(3*x^2+4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+18\right)^{2}\right) \ln \left(\frac{3 x \RootOf \left(\textit{\_Z}^{4}+18\right)^{2}+\left(3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+18\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+18\right)^{2}+9 \sqrt{3 x^{2}+2}\, x -6 \left(3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+18\right)^{2}\right)}{3 x^{2}+4}\right)}{18}-\frac{\RootOf \left(\textit{\_Z}^{4}+18\right) \ln \left(-\frac{3 x \RootOf \left(\textit{\_Z}^{4}+18\right)^{2}+\left(3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+18\right)^{3}-9 \sqrt{3 x^{2}+2}\, x +6 \left(3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+18\right)}{3 x^{2}+4}\right)}{18}"," ",0,"-1/18*RootOf(_Z^2+RootOf(_Z^4+18)^2)*ln((RootOf(_Z^4+18)^2*RootOf(_Z^2+RootOf(_Z^4+18)^2)*(3*x^2+2)^(3/4)+3*RootOf(_Z^4+18)^2*x+9*(3*x^2+2)^(1/2)*x-6*RootOf(_Z^2+RootOf(_Z^4+18)^2)*(3*x^2+2)^(1/4))/(3*x^2+4))-1/18*RootOf(_Z^4+18)*ln(-((3*x^2+2)^(3/4)*RootOf(_Z^4+18)^3+3*RootOf(_Z^4+18)^2*x-9*(3*x^2+2)^(1/2)*x+6*(3*x^2+2)^(1/4)*RootOf(_Z^4+18))/(3*x^2+4))","C"
1054,1,186,90,7.247000," ","int(x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+18\right)^{2}\right) \ln \left(\frac{-3 x \RootOf \left(\textit{\_Z}^{4}+18\right)^{2}+\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+18\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+18\right)^{2}+9 \sqrt{-3 x^{2}+2}\, x +6 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+18\right)^{2}\right)}{3 x^{2}-4}\right)}{18}-\frac{\RootOf \left(\textit{\_Z}^{4}+18\right) \ln \left(-\frac{-3 x \RootOf \left(\textit{\_Z}^{4}+18\right)^{2}+\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+18\right)^{3}-9 \sqrt{-3 x^{2}+2}\, x -6 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+18\right)}{3 x^{2}-4}\right)}{18}"," ",0,"-1/18*RootOf(_Z^4+18)*ln(-((-3*x^2+2)^(3/4)*RootOf(_Z^4+18)^3-3*RootOf(_Z^4+18)^2*x-9*(-3*x^2+2)^(1/2)*x-6*RootOf(_Z^4+18)*(-3*x^2+2)^(1/4))/(3*x^2-4))-1/18*RootOf(_Z^2+RootOf(_Z^4+18)^2)*ln((RootOf(_Z^4+18)^2*RootOf(_Z^2+RootOf(_Z^4+18)^2)*(-3*x^2+2)^(3/4)-3*RootOf(_Z^4+18)^2*x+9*(-3*x^2+2)^(1/2)*x+6*RootOf(_Z^2+RootOf(_Z^4+18)^2)*(-3*x^2+2)^(1/4))/(3*x^2-4))","C"
1055,0,0,93,0.283000," ","int(x^2/(b*x^2+2)^(3/4)/(b*x^2+4),x)","\int \frac{x^{2}}{\left(b \,x^{2}+2\right)^{\frac{3}{4}} \left(b \,x^{2}+4\right)}\, dx"," ",0,"int(x^2/(b*x^2+2)^(3/4)/(b*x^2+4),x)","F"
1056,0,0,94,0.088000," ","int(x^2/(-b*x^2+2)^(3/4)/(-b*x^2+4),x)","\int \frac{x^{2}}{\left(-b \,x^{2}+2\right)^{\frac{3}{4}} \left(-b \,x^{2}+4\right)}\, dx"," ",0,"int(x^2/(-b*x^2+2)^(3/4)/(-b*x^2+4),x)","F"
1057,0,0,90,0.095000," ","int(x^2/(3*x^2+a)^(3/4)/(3*x^2+2*a),x)","\int \frac{x^{2}}{\left(3 x^{2}+a \right)^{\frac{3}{4}} \left(3 x^{2}+2 a \right)}\, dx"," ",0,"int(x^2/(3*x^2+a)^(3/4)/(3*x^2+2*a),x)","F"
1058,0,0,90,0.171000," ","int(x^2/(-3*x^2+a)^(3/4)/(-3*x^2+2*a),x)","\int \frac{x^{2}}{\left(-3 x^{2}+a \right)^{\frac{3}{4}} \left(-3 x^{2}+2 a \right)}\, dx"," ",0,"int(x^2/(-3*x^2+a)^(3/4)/(-3*x^2+2*a),x)","F"
1059,0,0,87,0.321000," ","int(x^2/(b*x^2+a)^(3/4)/(b*x^2+2*a),x)","\int \frac{x^{2}}{\left(b \,x^{2}+a \right)^{\frac{3}{4}} \left(b \,x^{2}+2 a \right)}\, dx"," ",0,"int(x^2/(b*x^2+a)^(3/4)/(b*x^2+2*a),x)","F"
1060,0,0,91,0.149000," ","int(x^2/(-b*x^2+a)^(3/4)/(-b*x^2+2*a),x)","\int \frac{x^{2}}{\left(-b \,x^{2}+a \right)^{\frac{3}{4}} \left(-b \,x^{2}+2 a \right)}\, dx"," ",0,"int(x^2/(-b*x^2+a)^(3/4)/(-b*x^2+2*a),x)","F"
1061,1,541,137,2.974000," ","int(x^7/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","-\frac{2 \left(45 x^{4}+156 x^{2}+1136\right) \left(3 x^{2}-2\right)}{3645 \left(-3 x^{2}+2\right)^{\frac{3}{4}}}-\frac{\left(\frac{16 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(-\frac{27 x^{6}-18 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)-36 x^{4}-6 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+24 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)+2 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+12 x^{2}+4 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{\left(3 x^{2}-4\right) \left(3 x^{2}-2\right)^{2}}\right)}{81}+\frac{16 \RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(\frac{-27 x^{6}+18 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}+2\right)+36 x^{4}-6 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-24 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{4}+2\right)+2 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{3}-12 x^{2}+4 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)}{\left(3 x^{2}-4\right) \left(3 x^{2}-2\right)^{2}}\right)}{81}\right) \left(-\left(3 x^{2}-2\right)^{3}\right)^{\frac{1}{4}}}{\left(-3 x^{2}+2\right)^{\frac{3}{4}}}"," ",0,"-2/3645*(45*x^4+156*x^2+1136)*(3*x^2-2)/(-3*x^2+2)^(3/4)-(16/81*RootOf(_Z^4+2)*ln((2*RootOf(_Z^4+2)^3*(-27*x^6+54*x^4-36*x^2+8)^(3/4)-6*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*x^2+18*RootOf(_Z^4+2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^4-27*x^6+4*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)-24*RootOf(_Z^4+2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^2+36*x^4+8*RootOf(_Z^4+2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)-12*x^2)/(3*x^2-4)/(3*x^2-2)^2)+16/81*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln(-(2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(3/4)-18*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^4-6*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*x^2+27*x^6+24*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^2+4*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)-36*x^4-8*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)+12*x^2)/(3*x^2-4)/(3*x^2-2)^2))/(-3*x^2+2)^(3/4)*(-(3*x^2-2)^3)^(1/4)","C"
1062,1,536,126,2.165000," ","int(x^5/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","-\frac{2 \left(3 x^{2}+28\right) \left(3 x^{2}-2\right)}{135 \left(-3 x^{2}+2\right)^{\frac{3}{4}}}-\frac{\left(\frac{4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(-\frac{27 x^{6}-18 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)-36 x^{4}-6 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+24 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)+2 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+12 x^{2}+4 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{\left(3 x^{2}-4\right) \left(3 x^{2}-2\right)^{2}}\right)}{27}+\frac{4 \RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(\frac{-27 x^{6}+18 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}+2\right)+36 x^{4}-6 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-24 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{4}+2\right)+2 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{3}-12 x^{2}+4 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)}{\left(3 x^{2}-4\right) \left(3 x^{2}-2\right)^{2}}\right)}{27}\right) \left(-\left(3 x^{2}-2\right)^{3}\right)^{\frac{1}{4}}}{\left(-3 x^{2}+2\right)^{\frac{3}{4}}}"," ",0,"-2/135*(3*x^2+28)*(3*x^2-2)/(-3*x^2+2)^(3/4)-(4/27*RootOf(_Z^4+2)*ln((2*RootOf(_Z^4+2)^3*(-27*x^6+54*x^4-36*x^2+8)^(3/4)-6*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*x^2+18*RootOf(_Z^4+2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^4-27*x^6+4*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)-24*RootOf(_Z^4+2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^2+36*x^4+8*RootOf(_Z^4+2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)-12*x^2)/(3*x^2-4)/(3*x^2-2)^2)+4/27*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln(-(2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(3/4)-18*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^4-6*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*x^2+27*x^6+24*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^2+4*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)-36*x^4-8*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)+12*x^2)/(3*x^2-4)/(3*x^2-2)^2))/(-3*x^2+2)^(3/4)*(-(3*x^2-2)^3)^(1/4)","C"
1063,1,528,115,2.393000," ","int(x^3/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","-\frac{2 \left(3 x^{2}-2\right)}{9 \left(-3 x^{2}+2\right)^{\frac{3}{4}}}-\frac{\left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(\frac{-27 x^{6}-18 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)+36 x^{4}+6 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+24 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)+2 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-12 x^{2}-4 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{\left(3 x^{2}-4\right) \left(3 x^{2}-2\right)^{2}}\right)}{9}+\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(\frac{-27 x^{6}+18 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}+2\right)+36 x^{4}-6 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-24 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{4}+2\right)+2 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{3}-12 x^{2}+4 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)}{\left(3 x^{2}-4\right) \left(3 x^{2}-2\right)^{2}}\right)}{9}\right) \left(-\left(3 x^{2}-2\right)^{3}\right)^{\frac{1}{4}}}{\left(-3 x^{2}+2\right)^{\frac{3}{4}}}"," ",0,"-2/9*(3*x^2-2)/(-3*x^2+2)^(3/4)-(1/9*RootOf(_Z^4+2)*ln((2*RootOf(_Z^4+2)^3*(-27*x^6+54*x^4-36*x^2+8)^(3/4)-6*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*x^2+18*RootOf(_Z^4+2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^4-27*x^6+4*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)-24*RootOf(_Z^4+2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^2+36*x^4+8*RootOf(_Z^4+2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)-12*x^2)/(3*x^2-4)/(3*x^2-2)^2)-1/9*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln((2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(3/4)-18*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^4+6*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*x^2-27*x^6+24*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*x^2-4*RootOf(_Z^4+2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/2)+36*x^4-8*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)-12*x^2)/(3*x^2-4)/(3*x^2-2)^2))/(-3*x^2+2)^(3/4)*(-(3*x^2-2)^3)^(1/4)","C"
1064,1,189,104,1.801000," ","int(x/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(\frac{2 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-3 x^{2}-2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-2 \left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{3 x^{2}-4}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(\frac{2 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{3}-3 x^{2}+2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+2 \left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)}{3 x^{2}-4}\right)}{12}"," ",0,"1/12*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln((2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*(-3*x^2+2)^(1/4)-2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(-3*x^2+2)^(3/4)-2*RootOf(_Z^4+2)^2*(-3*x^2+2)^(1/2)-3*x^2)/(3*x^2-4))-1/12*RootOf(_Z^4+2)*ln((2*RootOf(_Z^4+2)^3*(-3*x^2+2)^(1/4)+2*RootOf(_Z^4+2)^2*(-3*x^2+2)^(1/2)+2*RootOf(_Z^4+2)*(-3*x^2+2)^(3/4)-3*x^2)/(3*x^2-4))","C"
1065,1,560,144,15.084000," ","int(1/x/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \ln \left(\frac{3 x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)-4 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)+4 \left(-3 x^{2}+2\right)^{\frac{3}{4}}}{3 x^{2}-4}\right)}{32}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \ln \left(\frac{3 x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)+3 x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)+2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-2 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)+4 \left(-3 x^{2}+2\right)^{\frac{3}{4}}}{3 x^{2}-4}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \ln \left(\frac{3 x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)-4 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)+4 \left(-3 x^{2}+2\right)^{\frac{3}{4}}}{3 x^{2}-4}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{3 x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+4 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)-4 \left(-3 x^{2}+2\right)^{\frac{3}{4}}}{x^{2}}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(-\frac{3 x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+4 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-4 \sqrt{-3 x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}-2\right)+4 \left(-3 x^{2}+2\right)^{\frac{3}{4}}}{x^{2}}\right)}{16}"," ",0,"1/16*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((3*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(-3*x^2+2)^(1/2)-4*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)-4*(-3*x^2+2)^(3/4)+4*RootOf(_Z^4-2)^2*(-3*x^2+2)^(1/4))/x^2)+1/16*RootOf(_Z^4-2)*ln(-(3*RootOf(_Z^4-2)^3*x^2+4*(-3*x^2+2)^(3/4)-4*(-3*x^2+2)^(1/2)*RootOf(_Z^4-2)+4*RootOf(_Z^4-2)^2*(-3*x^2+2)^(1/4)-4*RootOf(_Z^4-2)^3)/x^2)+1/32*ln((-4*RootOf(_Z^4-2)^3*(-3*x^2+2)^(1/2)+4*(-3*x^2+2)^(3/4)+4*RootOf(_Z^4-2)^2*(-3*x^2+2)^(1/4)+3*RootOf(_Z^4-2)*x^2-4*RootOf(_Z^4-2))/(3*x^2-4))*RootOf(_Z^4-2)^3+1/32*ln((-4*RootOf(_Z^4-2)^3*(-3*x^2+2)^(1/2)+4*(-3*x^2+2)^(3/4)+4*RootOf(_Z^4-2)^2*(-3*x^2+2)^(1/4)+3*RootOf(_Z^4-2)*x^2-4*RootOf(_Z^4-2))/(3*x^2-4))*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)-1/16*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((2*(-3*x^2+2)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2-2*RootOf(_Z^4-2)^3*(-3*x^2+2)^(1/2)-4*(-3*x^2+2)^(1/4)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)+3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+4*(-3*x^2+2)^(3/4)+3*RootOf(_Z^4-2)*x^2)/(3*x^2-4))","C"
1066,1,1540,158,23.050000," ","int(1/x^3/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","\frac{3 x^{2}-2}{16 \left(-3 x^{2}+2\right)^{\frac{3}{4}} x^{2}}-\frac{\left(-\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \ln \left(\frac{27 x^{6} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-27 x^{6} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-36 x^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+36 x^{4} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-36 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)+12 x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-12 x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+48 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)+12 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)+12 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)-16 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)-8 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)-8 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}-2\right)-8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}}}{\left(3 x^{2}-4\right) \left(3 x^{2}-2\right)^{2}}\right)}{64}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \ln \left(-\frac{-27 x^{6} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+72 x^{4} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+36 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-60 x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-48 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-24 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)+16 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+16 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+16 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}-2\right)+8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}}}{\left(3 x^{2}-4\right) \left(3 x^{2}-2\right)^{2}}\right)}{128}+\frac{3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \ln \left(-\frac{-27 x^{6} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+72 x^{4} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+36 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-60 x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-48 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-24 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)+16 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+16 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+16 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}-2\right)+8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}}}{\left(3 x^{2}-4\right) \left(3 x^{2}-2\right)^{2}}\right)}{128}+\frac{15 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{-27 x^{6} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)-18 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+72 x^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)+6 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+24 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-60 x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)-4 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+16 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)+4 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}}}{\left(3 x^{2}-2\right)^{2} x^{2}}\right)}{128}+\frac{15 \RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{-27 x^{6} \RootOf \left(\textit{\_Z}^{4}-2\right)+18 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+72 x^{4} \RootOf \left(\textit{\_Z}^{4}-2\right)-6 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-24 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-60 x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)+4 \sqrt{-27 x^{6}+54 x^{4}-36 x^{2}+8}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+8 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+16 \RootOf \left(\textit{\_Z}^{4}-2\right)+4 \left(-27 x^{6}+54 x^{4}-36 x^{2}+8\right)^{\frac{3}{4}}}{\left(3 x^{2}-2\right)^{2} x^{2}}\right)}{128}\right) \left(-\left(3 x^{2}-2\right)^{3}\right)^{\frac{1}{4}}}{\left(-3 x^{2}+2\right)^{\frac{3}{4}}}"," ",0,"1/16*(3*x^2-2)/x^2/(-3*x^2+2)^(3/4)-(15/128*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((6*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^4-2)^2*x^2-27*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^6-18*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)^2*x^4-4*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2+72*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4+24*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)^2*x^2-60*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+4*(-27*x^6+54*x^4-36*x^2+8)^(3/4)-8*RootOf(_Z^4-2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/4)+16*RootOf(_Z^2+RootOf(_Z^4-2)^2))/(3*x^2-2)^2/x^2)+15/128*RootOf(_Z^4-2)*ln((-6*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^4-2)^3*x^2+18*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)^2*x^4-27*RootOf(_Z^4-2)*x^6+4*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^4-2)^3-24*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)^2*x^2+72*RootOf(_Z^4-2)*x^4+4*(-27*x^6+54*x^4-36*x^2+8)^(3/4)+8*RootOf(_Z^4-2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/4)-60*RootOf(_Z^4-2)*x^2+16*RootOf(_Z^4-2))/(3*x^2-2)^2/x^2)+3/128*ln(-(-27*x^6*RootOf(_Z^4-2)^3+36*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)^2*x^4+72*RootOf(_Z^4-2)^3*x^4-24*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^4-2)*x^2-48*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)^2*x^2-60*RootOf(_Z^4-2)^3*x^2+8*(-27*x^6+54*x^4-36*x^2+8)^(3/4)+16*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^4-2)+16*RootOf(_Z^4-2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/4)+16*RootOf(_Z^4-2)^3)/(3*x^2-4)/(3*x^2-2)^2)*RootOf(_Z^4-2)^3+3/128*ln(-(-27*x^6*RootOf(_Z^4-2)^3+36*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)^2*x^4+72*RootOf(_Z^4-2)^3*x^4-24*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^4-2)*x^2-48*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)^2*x^2-60*RootOf(_Z^4-2)^3*x^2+8*(-27*x^6+54*x^4-36*x^2+8)^(3/4)+16*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^4-2)+16*RootOf(_Z^4-2)^2*(-27*x^6+54*x^4-36*x^2+8)^(1/4)+16*RootOf(_Z^4-2)^3)/(3*x^2-4)/(3*x^2-2)^2)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)-3/64*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((27*x^6*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2-27*x^6*RootOf(_Z^4-2)^3-36*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)*x^4-36*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4+36*RootOf(_Z^4-2)^3*x^4+12*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*x^2+48*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^4-2)*x^2+12*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+12*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^4-2)*x^2-12*RootOf(_Z^4-2)^3*x^2-8*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16*(-27*x^6+54*x^4-36*x^2+8)^(1/4)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)-8*(-27*x^6+54*x^4-36*x^2+8)^(3/4)-8*(-27*x^6+54*x^4-36*x^2+8)^(1/2)*RootOf(_Z^4-2))/(3*x^2-4)/(3*x^2-2)^2))/(-3*x^2+2)^(3/4)*(-(3*x^2-2)^3)^(1/4)","C"
1067,0,0,162,10.347000," ","int(x^6/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","\int \frac{x^{6}}{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \left(-3 x^{2}+4\right)}\, dx"," ",0,"int(x^6/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","F"
1068,0,0,148,6.569000," ","int(x^4/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","\int \frac{x^{4}}{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \left(-3 x^{2}+4\right)}\, dx"," ",0,"int(x^4/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","F"
1069,1,186,90,0.000000," ","int(x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+18\right)^{2}\right) \ln \left(\frac{-3 x \RootOf \left(\textit{\_Z}^{4}+18\right)^{2}+\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+18\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+18\right)^{2}+9 \sqrt{-3 x^{2}+2}\, x +6 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+18\right)^{2}\right)}{3 x^{2}-4}\right)}{18}-\frac{\RootOf \left(\textit{\_Z}^{4}+18\right) \ln \left(-\frac{-3 x \RootOf \left(\textit{\_Z}^{4}+18\right)^{2}+\left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+18\right)^{3}-9 \sqrt{-3 x^{2}+2}\, x -6 \left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+18\right)}{3 x^{2}-4}\right)}{18}"," ",0,"-1/18*RootOf(_Z^4+18)*ln(-((-3*x^2+2)^(3/4)*RootOf(_Z^4+18)^3-3*RootOf(_Z^4+18)^2*x-9*(-3*x^2+2)^(1/2)*x-6*RootOf(_Z^4+18)*(-3*x^2+2)^(1/4))/(3*x^2-4))-1/18*RootOf(_Z^2+RootOf(_Z^4+18)^2)*ln((RootOf(_Z^4+18)^2*RootOf(_Z^2+RootOf(_Z^4+18)^2)*(-3*x^2+2)^(3/4)-3*RootOf(_Z^4+18)^2*x+9*(-3*x^2+2)^(1/2)*x+6*RootOf(_Z^2+RootOf(_Z^4+18)^2)*(-3*x^2+2)^(1/4))/(3*x^2-4))","C"
1070,0,0,136,9.602000," ","int(1/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","\int \frac{1}{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \left(-3 x^{2}+4\right)}\, dx"," ",0,"int(1/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","F"
1071,0,0,150,5.895000," ","int(1/x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","\int \frac{1}{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \left(-3 x^{2}+4\right) x^{2}}\, dx"," ",0,"int(1/x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","F"
1072,0,0,164,5.462000," ","int(1/x^4/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","\int \frac{1}{\left(-3 x^{2}+2\right)^{\frac{3}{4}} \left(-3 x^{2}+4\right) x^{4}}\, dx"," ",0,"int(1/x^4/(-3*x^2+2)^(3/4)/(-3*x^2+4),x)","F"
1073,1,137,43,1.283000," ","int(x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{3 \sqrt{3 x^{2}-1}\, x +3 x +\left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)+\left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)}{3 x^{2}-2}\right)}{18}+\frac{\RootOf \left(\textit{\_Z}^{2}+6\right) \ln \left(\frac{3 \sqrt{3 x^{2}-1}\, x -3 x +\left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)-\left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)}{3 x^{2}-2}\right)}{18}"," ",0,"1/18*RootOf(_Z^2+6)*ln((RootOf(_Z^2+6)*(3*x^2-1)^(3/4)+3*(3*x^2-1)^(1/2)*x-RootOf(_Z^2+6)*(3*x^2-1)^(1/4)-3*x)/(3*x^2-2))-1/18*RootOf(_Z^2-6)*ln((RootOf(_Z^2-6)*(3*x^2-1)^(3/4)+3*(3*x^2-1)^(1/2)*x+RootOf(_Z^2-6)*(3*x^2-1)^(1/4)+3*x)/(3*x^2-2))","C"
1074,1,138,43,1.324000," ","int(x^2/(-3*x^2-2)/(-3*x^2-1)^(3/4),x)","\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(-\frac{-3 \sqrt{-3 x^{2}-1}\, x +3 x +\left(-3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)-\left(-3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)}{3 x^{2}+2}\right)}{18}+\frac{\RootOf \left(\textit{\_Z}^{2}+6\right) \ln \left(\frac{3 \sqrt{-3 x^{2}-1}\, x +3 x +\left(-3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)+\left(-3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)}{3 x^{2}+2}\right)}{18}"," ",0,"1/18*RootOf(_Z^2+6)*ln(((-3*x^2-1)^(3/4)*RootOf(_Z^2+6)+3*(-3*x^2-1)^(1/2)*x+RootOf(_Z^2+6)*(-3*x^2-1)^(1/4)+3*x)/(3*x^2+2))+1/18*RootOf(_Z^2-6)*ln(-((-3*x^2-1)^(3/4)*RootOf(_Z^2-6)-3*(-3*x^2-1)^(1/2)*x-RootOf(_Z^2-6)*(-3*x^2-1)^(1/4)+3*x)/(3*x^2+2))","C"
1075,0,0,55,0.089000," ","int(x^2/(b*x^2-2)/(b*x^2-1)^(3/4),x)","\int \frac{x^{2}}{\left(b \,x^{2}-2\right) \left(b \,x^{2}-1\right)^{\frac{3}{4}}}\, dx"," ",0,"int(x^2/(b*x^2-2)/(b*x^2-1)^(3/4),x)","F"
1076,0,0,57,0.086000," ","int(x^2/(-b*x^2-2)/(-b*x^2-1)^(3/4),x)","\int \frac{x^{2}}{\left(-b \,x^{2}-2\right) \left(-b \,x^{2}-1\right)^{\frac{3}{4}}}\, dx"," ",0,"int(x^2/(-b*x^2-2)/(-b*x^2-1)^(3/4),x)","F"
1077,0,0,59,0.084000," ","int(x^2/(3*x^2-2*a)/(3*x^2-a)^(3/4),x)","\int \frac{x^{2}}{\left(3 x^{2}-2 a \right) \left(3 x^{2}-a \right)^{\frac{3}{4}}}\, dx"," ",0,"int(x^2/(3*x^2-2*a)/(3*x^2-a)^(3/4),x)","F"
1078,0,0,59,0.084000," ","int(x^2/(-3*x^2-2*a)/(-3*x^2-a)^(3/4),x)","\int \frac{x^{2}}{\left(-3 x^{2}-2 a \right) \left(-3 x^{2}-a \right)^{\frac{3}{4}}}\, dx"," ",0,"int(x^2/(-3*x^2-2*a)/(-3*x^2-a)^(3/4),x)","F"
1079,0,0,71,0.091000," ","int(x^2/(b*x^2-2*a)/(b*x^2-a)^(3/4),x)","\int \frac{x^{2}}{\left(b \,x^{2}-2 a \right) \left(b \,x^{2}-a \right)^{\frac{3}{4}}}\, dx"," ",0,"int(x^2/(b*x^2-2*a)/(b*x^2-a)^(3/4),x)","F"
1080,0,0,73,0.082000," ","int(x^2/(-b*x^2-2*a)/(-b*x^2-a)^(3/4),x)","\int \frac{x^{2}}{\left(-b \,x^{2}-2 a \right) \left(-b \,x^{2}-a \right)^{\frac{3}{4}}}\, dx"," ",0,"int(x^2/(-b*x^2-2*a)/(-b*x^2-a)^(3/4),x)","F"
1081,1,424,58,0.864000," ","int(x^7/(3*x^2-2)/(3*x^2-1)^(3/4),x)","\frac{2 \left(45 x^{4}+78 x^{2}+284\right) \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3645}+\frac{\left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-27 x^{6}-18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{2}+1\right)+18 x^{4}+12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{2}+1\right)+6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2}-3 x^{2}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{2}}\right)}{81}-\frac{4 \ln \left(-\frac{27 x^{6}+18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4}-18 x^{4}+6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2}-12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2}+3 x^{2}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{2}}\right)}{81}\right) \left(\left(3 x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(3 x^{2}-1\right)^{\frac{3}{4}}}"," ",0,"2/3645*(45*x^4+78*x^2+284)*(3*x^2-1)^(1/4)+(-4/81*ln(-(27*x^6+18*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4+6*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2-18*x^4+2*(27*x^6-27*x^4+9*x^2-1)^(3/4)-12*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2-2*(27*x^6-27*x^4+9*x^2-1)^(1/2)+3*x^2+2*(27*x^6-27*x^4+9*x^2-1)^(1/4))/(3*x^2-2)/(3*x^2-1)^2)-4/81*RootOf(_Z^2+1)*ln((-18*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4-27*x^6+2*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(3/4)+6*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2+12*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2+18*x^4-2*(27*x^6-27*x^4+9*x^2-1)^(1/2)-2*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(1/4)-3*x^2)/(3*x^2-2)/(3*x^2-1)^2))/(3*x^2-1)^(3/4)*((3*x^2-1)^3)^(1/4)","C"
1082,1,420,47,0.828000," ","int(x^5/(3*x^2-2)/(3*x^2-1)^(3/4),x)","\frac{2 \left(3 x^{2}+14\right) \left(3 x^{2}-1\right)^{\frac{1}{4}}}{135}+\frac{\left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{27 x^{6}-18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{2}+1\right)-18 x^{4}+12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{2}+1\right)-6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2}+3 x^{2}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{2}}\right)}{27}-\frac{2 \ln \left(-\frac{27 x^{6}+18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4}-18 x^{4}+6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2}-12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2}+3 x^{2}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{2}}\right)}{27}\right) \left(\left(3 x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(3 x^{2}-1\right)^{\frac{3}{4}}}"," ",0,"2/135*(3*x^2+14)*(3*x^2-1)^(1/4)+(-2/27*ln(-(27*x^6+18*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4-18*x^4+6*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2-12*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2+3*x^2+2*(27*x^6-27*x^4+9*x^2-1)^(3/4)-2*(27*x^6-27*x^4+9*x^2-1)^(1/2)+2*(27*x^6-27*x^4+9*x^2-1)^(1/4))/(3*x^2-2)/(3*x^2-1)^2)+2/27*RootOf(_Z^2+1)*ln(-(-18*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4+27*x^6+2*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(3/4)-6*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2+12*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2-18*x^4+2*(27*x^6-27*x^4+9*x^2-1)^(1/2)-2*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(1/4)+3*x^2)/(3*x^2-2)/(3*x^2-1)^2))/(3*x^2-1)^(3/4)*((3*x^2-1)^3)^(1/4)","C"
1083,1,412,36,0.757000," ","int(x^3/(3*x^2-2)/(3*x^2-1)^(3/4),x)","\frac{2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{9}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{27 x^{6}-18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{2}+1\right)-18 x^{4}+12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{2}+1\right)-6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2}+3 x^{2}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{2}}\right)}{9}+\frac{\ln \left(\frac{-27 x^{6}+18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4}+18 x^{4}-6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2}-12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2}-3 x^{2}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}}+2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{2}}\right)}{9}\right) \left(\left(3 x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(3 x^{2}-1\right)^{\frac{3}{4}}}"," ",0,"2/9*(3*x^2-1)^(1/4)+(1/9*RootOf(_Z^2+1)*ln(-(-18*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4+27*x^6+2*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(3/4)-6*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2+12*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2-18*x^4+2*(27*x^6-27*x^4+9*x^2-1)^(1/2)-2*RootOf(_Z^2+1)*(27*x^6-27*x^4+9*x^2-1)^(1/4)+3*x^2)/(3*x^2-2)/(3*x^2-1)^2)+1/9*ln((-27*x^6+18*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4-6*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2+18*x^4+2*(27*x^6-27*x^4+9*x^2-1)^(3/4)-12*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2+2*(27*x^6-27*x^4+9*x^2-1)^(1/2)-3*x^2+2*(27*x^6-27*x^4+9*x^2-1)^(1/4))/(3*x^2-2)/(3*x^2-1)^2))/(3*x^2-1)^(3/4)*((3*x^2-1)^3)^(1/4)","C"
1084,1,125,25,0.530000," ","int(x/(3*x^2-2)/(3*x^2-1)^(3/4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{3 x^{2}-1}}{3 x^{2}-2}\right)}{6}+\frac{\ln \left(\frac{-3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{3 x^{2}-1}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{6}"," ",0,"1/6*ln((-3*x^2+2*(3*x^2-1)^(3/4)-2*(3*x^2-1)^(1/2)+2*(3*x^2-1)^(1/4))/(3*x^2-2))-1/6*RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*(3*x^2-1)^(3/4)-2*RootOf(_Z^2+1)*(3*x^2-1)^(1/4)-2*(3*x^2-1)^(1/2)+3*x^2)/(3*x^2-2))","C"
1085,1,299,128,3.500000," ","int(1/x/(3*x^2-2)/(3*x^2-1)^(3/4),x)","\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \sqrt{3 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)-2 \left(3 x^{2}-1\right)^{\frac{3}{4}}}{x^{2}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \ln \left(\frac{-3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \sqrt{3 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \left(3 x^{2}-1\right)^{\frac{3}{4}}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \sqrt{3 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)-2 \left(3 x^{2}-1\right)^{\frac{3}{4}}}{x^{2}}\right)}{4}-\frac{\ln \left(-\frac{3 x^{2}+2 \left(3 x^{2}-1\right)^{\frac{3}{4}}+2 \sqrt{3 x^{2}-1}+2 \left(3 x^{2}-1\right)^{\frac{1}{4}}}{3 x^{2}-2}\right)}{4}"," ",0,"1/4*RootOf(_Z^4+1)^3*ln((2*(3*x^2-1)^(1/2)*RootOf(_Z^4+1)^3+2*RootOf(_Z^4+1)^2*(3*x^2-1)^(1/4)-3*RootOf(_Z^4+1)*x^2-2*(3*x^2-1)^(3/4)+2*RootOf(_Z^4+1))/x^2)-1/4*RootOf(_Z^4+1)*ln((3*RootOf(_Z^4+1)^3*x^2-2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1)^2*(3*x^2-1)^(1/4)-2*(3*x^2-1)^(1/2)*RootOf(_Z^4+1)-2*(3*x^2-1)^(3/4))/x^2)-1/4*ln(-(3*x^2+2*(3*x^2-1)^(3/4)+2*(3*x^2-1)^(1/2)+2*(3*x^2-1)^(1/4))/(3*x^2-2))+1/4*RootOf(_Z^4+1)^2*ln((2*(3*x^2-1)^(1/2)*RootOf(_Z^4+1)^2-3*RootOf(_Z^4+1)^2*x^2-2*(3*x^2-1)^(3/4)+2*(3*x^2-1)^(1/4))/(3*x^2-2))","C"
1086,1,916,142,5.956000," ","int(1/x^3/(3*x^2-2)/(3*x^2-1)^(3/4),x)","-\frac{\left(3 x^{2}-1\right)^{\frac{1}{4}}}{4 x^{2}}+\frac{\left(\frac{15 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{27 x^{6} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-36 x^{4} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+15 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}}}{\left(3 x^{2}-1\right)^{2} x^{2}}\right)}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \ln \left(\frac{-27 x^{6} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+18 x^{4} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4}+6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-3 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2}-2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}}-2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}}}{\left(3 x^{2}-1\right)^{2} \left(3 x^{2}-2\right)}\right)}{8}+\frac{15 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{27 x^{6} \RootOf \left(\textit{\_Z}^{4}+1\right)-18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-36 x^{4} \RootOf \left(\textit{\_Z}^{4}+1\right)+6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+15 x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)-2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}}}{\left(3 x^{2}-1\right)^{2} x^{2}}\right)}{16}+\frac{3 \ln \left(\frac{-27 x^{6}+18 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{4}+18 x^{4}-6 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}\, x^{2}-12 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}} x^{2}-3 x^{2}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{3}{4}}+2 \sqrt{27 x^{6}-27 x^{4}+9 x^{2}-1}+2 \left(27 x^{6}-27 x^{4}+9 x^{2}-1\right)^{\frac{1}{4}}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{2}}\right)}{8}\right) \left(\left(3 x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(3 x^{2}-1\right)^{\frac{3}{4}}}"," ",0,"-1/4*(3*x^2-1)^(1/4)/x^2+(15/16*RootOf(_Z^4+1)^3*ln((27*x^6*RootOf(_Z^4+1)^3-36*RootOf(_Z^4+1)^3*x^4+18*RootOf(_Z^4+1)^2*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4+15*RootOf(_Z^4+1)^3*x^2-12*RootOf(_Z^4+1)^2*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2+6*RootOf(_Z^4+1)*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2-2*RootOf(_Z^4+1)^3+2*RootOf(_Z^4+1)^2*(27*x^6-27*x^4+9*x^2-1)^(1/4)-2*(27*x^6-27*x^4+9*x^2-1)^(1/2)*RootOf(_Z^4+1)+2*(27*x^6-27*x^4+9*x^2-1)^(3/4))/x^2/(3*x^2-1)^2)+15/16*RootOf(_Z^4+1)*ln((6*RootOf(_Z^4+1)^3*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2-18*RootOf(_Z^4+1)^2*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4+27*x^6*RootOf(_Z^4+1)-2*(27*x^6-27*x^4+9*x^2-1)^(1/2)*RootOf(_Z^4+1)^3+12*RootOf(_Z^4+1)^2*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2-36*RootOf(_Z^4+1)*x^4-2*RootOf(_Z^4+1)^2*(27*x^6-27*x^4+9*x^2-1)^(1/4)+15*RootOf(_Z^4+1)*x^2+2*(27*x^6-27*x^4+9*x^2-1)^(3/4)-2*RootOf(_Z^4+1))/x^2/(3*x^2-1)^2)+3/8*ln((-27*x^6+18*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4+18*x^4-6*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2-12*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2-3*x^2+2*(27*x^6-27*x^4+9*x^2-1)^(3/4)+2*(27*x^6-27*x^4+9*x^2-1)^(1/2)+2*(27*x^6-27*x^4+9*x^2-1)^(1/4))/(3*x^2-2)/(3*x^2-1)^2)+3/8*RootOf(_Z^4+1)^2*ln((-27*RootOf(_Z^4+1)^2*x^6+6*RootOf(_Z^4+1)^2*(27*x^6-27*x^4+9*x^2-1)^(1/2)*x^2+18*RootOf(_Z^4+1)^2*x^4-18*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^4-2*RootOf(_Z^4+1)^2*(27*x^6-27*x^4+9*x^2-1)^(1/2)-3*RootOf(_Z^4+1)^2*x^2+2*(27*x^6-27*x^4+9*x^2-1)^(3/4)+12*(27*x^6-27*x^4+9*x^2-1)^(1/4)*x^2-2*(27*x^6-27*x^4+9*x^2-1)^(1/4))/(3*x^2-1)^2/(3*x^2-2)))/(3*x^2-1)^(3/4)*((3*x^2-1)^3)^(1/4)","C"
1087,0,0,158,2.240000," ","int(x^6/(3*x^2-2)/(3*x^2-1)^(3/4),x)","\int \frac{x^{6}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{\frac{3}{4}}}\, dx"," ",0,"int(x^6/(3*x^2-2)/(3*x^2-1)^(3/4),x)","F"
1088,0,0,144,1.954000," ","int(x^4/(3*x^2-2)/(3*x^2-1)^(3/4),x)","\int \frac{x^{4}}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{\frac{3}{4}}}\, dx"," ",0,"int(x^4/(3*x^2-2)/(3*x^2-1)^(3/4),x)","F"
1089,1,137,43,0.000000," ","int(x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{3 \sqrt{3 x^{2}-1}\, x +3 x +\left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)+\left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)}{3 x^{2}-2}\right)}{18}+\frac{\RootOf \left(\textit{\_Z}^{2}+6\right) \ln \left(\frac{3 \sqrt{3 x^{2}-1}\, x -3 x +\left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)-\left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)}{3 x^{2}-2}\right)}{18}"," ",0,"1/18*RootOf(_Z^2+6)*ln((RootOf(_Z^2+6)*(3*x^2-1)^(3/4)+3*(3*x^2-1)^(1/2)*x-RootOf(_Z^2+6)*(3*x^2-1)^(1/4)-3*x)/(3*x^2-2))-1/18*RootOf(_Z^2-6)*ln((RootOf(_Z^2-6)*(3*x^2-1)^(3/4)+3*(3*x^2-1)^(1/2)*x+RootOf(_Z^2-6)*(3*x^2-1)^(1/4)+3*x)/(3*x^2-2))","C"
1090,0,0,132,1.959000," ","int(1/(3*x^2-2)/(3*x^2-1)^(3/4),x)","\int \frac{1}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/(3*x^2-2)/(3*x^2-1)^(3/4),x)","F"
1091,0,0,146,2.092000," ","int(1/x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x)","\int \frac{1}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{\frac{3}{4}} x^{2}}\, dx"," ",0,"int(1/x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x)","F"
1092,0,0,160,1.756000," ","int(1/x^4/(3*x^2-2)/(3*x^2-1)^(3/4),x)","\int \frac{1}{\left(3 x^{2}-2\right) \left(3 x^{2}-1\right)^{\frac{3}{4}} x^{4}}\, dx"," ",0,"int(1/x^4/(3*x^2-2)/(3*x^2-1)^(3/4),x)","F"
1093,0,0,133,0.115000," ","int((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x)","\int \frac{\left(e x \right)^{\frac{5}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x)","F"
1094,0,0,102,0.060000," ","int((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x)","\int \frac{\sqrt{e x}\, \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x)","F"
1095,0,0,85,0.064000," ","int((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(3/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{3}{2}} \left(b \,x^{2}+a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(3/4),x)","F"
1096,1,39,55,0.007000," ","int((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(3/4),x)","-\frac{2 \left(b \,x^{2}+a \right)^{\frac{1}{4}} \left(5 a d \,x^{2}-4 b c \,x^{2}+a c \right) x}{5 \left(e x \right)^{\frac{7}{2}} a^{2}}"," ",0,"-2/5*(b*x^2+a)^(1/4)*x*(5*a*d*x^2-4*b*c*x^2+a*c)/a^2/(e*x)^(7/2)","A"
1097,1,62,86,0.006000," ","int((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(3/4),x)","-\frac{2 \left(b \,x^{2}+a \right)^{\frac{1}{4}} \left(-36 a b d \,x^{4}+32 b^{2} c \,x^{4}+9 a^{2} d \,x^{2}-8 a b c \,x^{2}+5 c \,a^{2}\right) x}{45 \left(e x \right)^{\frac{11}{2}} a^{3}}"," ",0,"-2/45*(b*x^2+a)^(1/4)*x*(-36*a*b*d*x^4+32*b^2*c*x^4+9*a^2*d*x^2-8*a*b*c*x^2+5*a^2*c)/a^3/(e*x)^(11/2)","A"
1098,1,86,117,0.008000," ","int((d*x^2+c)/(e*x)^(15/2)/(b*x^2+a)^(3/4),x)","-\frac{2 \left(b \,x^{2}+a \right)^{\frac{1}{4}} \left(416 a \,b^{2} d \,x^{6}-384 b^{3} c \,x^{6}-104 a^{2} b d \,x^{4}+96 a \,b^{2} c \,x^{4}+65 a^{3} d \,x^{2}-60 a^{2} b c \,x^{2}+45 c \,a^{3}\right) x}{585 \left(e x \right)^{\frac{15}{2}} a^{4}}"," ",0,"-2/585*(b*x^2+a)^(1/4)*x*(416*a*b^2*d*x^6-384*b^3*c*x^6-104*a^2*b*d*x^4+96*a*b^2*c*x^4+65*a^3*d*x^2-60*a^2*b*c*x^2+45*a^3*c)/a^4/(e*x)^(15/2)","A"
1099,0,0,177,0.069000," ","int((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x)","\int \frac{\left(e x \right)^{\frac{7}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x)","F"
1100,0,0,142,0.060000," ","int((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x)","\int \frac{\left(e x \right)^{\frac{3}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x)","F"
1101,0,0,115,0.064000," ","int((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(3/4),x)","\int \frac{d \,x^{2}+c}{\sqrt{e x}\, \left(b \,x^{2}+a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(3/4),x)","F"
1102,0,0,116,0.071000," ","int((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(3/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{5}{2}} \left(b \,x^{2}+a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(3/4),x)","F"
1103,0,0,147,0.069000," ","int((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(3/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{9}{2}} \left(b \,x^{2}+a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(3/4),x)","F"
1104,0,0,179,0.072000," ","int((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(3/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{13}{2}} \left(b \,x^{2}+a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(3/4),x)","F"
1105,0,0,131,0.121000," ","int((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x)","\int \frac{\left(e x \right)^{\frac{3}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x)","F"
1106,0,0,94,0.060000," ","int((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(5/4),x)","\int \frac{d \,x^{2}+c}{\sqrt{e x}\, \left(b \,x^{2}+a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(5/4),x)","F"
1107,1,39,55,0.007000," ","int((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(5/4),x)","-\frac{2 \left(-3 a d \,x^{2}+4 b c \,x^{2}+a c \right) x}{3 \left(b \,x^{2}+a \right)^{\frac{1}{4}} \left(e x \right)^{\frac{5}{2}} a^{2}}"," ",0,"-2/3*x*(-3*a*d*x^2+4*b*c*x^2+a*c)/(b*x^2+a)^(1/4)/a^2/(e*x)^(5/2)","A"
1108,1,62,86,0.007000," ","int((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(5/4),x)","-\frac{2 \left(28 a b d \,x^{4}-32 b^{2} c \,x^{4}+7 a^{2} d \,x^{2}-8 a b c \,x^{2}+3 c \,a^{2}\right) x}{21 \left(b \,x^{2}+a \right)^{\frac{1}{4}} \left(e x \right)^{\frac{9}{2}} a^{3}}"," ",0,"-2/21*x*(28*a*b*d*x^4-32*b^2*c*x^4+7*a^2*d*x^2-8*a*b*c*x^2+3*a^2*c)/(b*x^2+a)^(1/4)/a^3/(e*x)^(9/2)","A"
1109,1,86,117,0.008000," ","int((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(5/4),x)","-\frac{2 \left(-352 a \,b^{2} d \,x^{6}+384 b^{3} c \,x^{6}-88 a^{2} b d \,x^{4}+96 a \,b^{2} c \,x^{4}+33 a^{3} d \,x^{2}-36 a^{2} b c \,x^{2}+21 c \,a^{3}\right) x}{231 \left(b \,x^{2}+a \right)^{\frac{1}{4}} \left(e x \right)^{\frac{13}{2}} a^{4}}"," ",0,"-2/231*x*(-352*a*b^2*d*x^6+384*b^3*c*x^6-88*a^2*b*d*x^4+96*a*b^2*c*x^4+33*a^3*d*x^2-36*a^2*b*c*x^2+21*a^3*c)/(b*x^2+a)^(1/4)/a^4/(e*x)^(13/2)","A"
1110,0,0,177,0.113000," ","int((e*x)^(9/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x)","\int \frac{\left(e x \right)^{\frac{9}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((e*x)^(9/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x)","F"
1111,0,0,145,0.112000," ","int((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x)","\int \frac{\left(e x \right)^{\frac{5}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x)","F"
1112,0,0,112,0.058000," ","int((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x)","\int \frac{\sqrt{e x}\, \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x)","F"
1113,0,0,116,0.105000," ","int((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(5/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{3}{2}} \left(b \,x^{2}+a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(5/4),x)","F"
1114,0,0,147,0.105000," ","int((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(5/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{7}{2}} \left(b \,x^{2}+a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(5/4),x)","F"
1115,0,0,179,0.111000," ","int((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(5/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{11}{2}} \left(b \,x^{2}+a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(5/4),x)","F"
1116,0,0,144,0.111000," ","int((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x)","\int \frac{\left(e x \right)^{\frac{5}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{7}{4}}}\, dx"," ",0,"int((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x)","F"
1117,0,0,95,0.054000," ","int((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x)","\int \frac{\sqrt{e x}\, \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{7}{4}}}\, dx"," ",0,"int((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x)","F"
1118,1,40,55,0.006000," ","int((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(7/4),x)","-\frac{2 \left(-a d \,x^{2}+4 b c \,x^{2}+3 a c \right) x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{4}} \left(e x \right)^{\frac{3}{2}} a^{2}}"," ",0,"-2/3*x*(-a*d*x^2+4*b*c*x^2+3*a*c)/(b*x^2+a)^(3/4)/a^2/(e*x)^(3/2)","A"
1119,1,62,86,0.008000," ","int((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(7/4),x)","-\frac{2 \left(20 a b d \,x^{4}-32 b^{2} c \,x^{4}+15 a^{2} d \,x^{2}-24 a b c \,x^{2}+3 c \,a^{2}\right) x}{15 \left(b \,x^{2}+a \right)^{\frac{3}{4}} \left(e x \right)^{\frac{7}{2}} a^{3}}"," ",0,"-2/15*x*(20*a*b*d*x^4-32*b^2*c*x^4+15*a^2*d*x^2-24*a*b*c*x^2+3*a^2*c)/(b*x^2+a)^(3/4)/a^3/(e*x)^(7/2)","A"
1120,1,86,117,0.007000," ","int((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(7/4),x)","-\frac{2 \left(-96 a \,b^{2} d \,x^{6}+128 b^{3} c \,x^{6}-72 a^{2} b d \,x^{4}+96 a \,b^{2} c \,x^{4}+9 a^{3} d \,x^{2}-12 a^{2} b c \,x^{2}+5 c \,a^{3}\right) x}{45 \left(b \,x^{2}+a \right)^{\frac{3}{4}} \left(e x \right)^{\frac{11}{2}} a^{4}}"," ",0,"-2/45*x*(-96*a*b^2*d*x^6+128*b^3*c*x^6-72*a^2*b*d*x^4+96*a*b^2*c*x^4+9*a^3*d*x^2-12*a^2*b*c*x^2+5*a^3*c)/(b*x^2+a)^(3/4)/a^4/(e*x)^(11/2)","A"
1121,0,0,189,0.103000," ","int((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x)","\int \frac{\left(e x \right)^{\frac{7}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{7}{4}}}\, dx"," ",0,"int((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x)","F"
1122,0,0,155,0.105000," ","int((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x)","\int \frac{\left(e x \right)^{\frac{3}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{7}{4}}}\, dx"," ",0,"int((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x)","F"
1123,0,0,125,0.056000," ","int((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(7/4),x)","\int \frac{d \,x^{2}+c}{\sqrt{e x}\, \left(b \,x^{2}+a \right)^{\frac{7}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(7/4),x)","F"
1124,0,0,147,0.106000," ","int((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(7/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{5}{2}} \left(b \,x^{2}+a \right)^{\frac{7}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(7/4),x)","F"
1125,0,0,178,0.102000," ","int((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(7/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{9}{2}} \left(b \,x^{2}+a \right)^{\frac{7}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(7/4),x)","F"
1126,0,0,175,0.112000," ","int((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","\int \frac{\left(e x \right)^{\frac{7}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","F"
1127,0,0,115,0.058000," ","int((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","\int \frac{\left(e x \right)^{\frac{3}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","F"
1128,1,39,67,0.006000," ","int((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(9/4),x)","\frac{2 \left(a d \,x^{2}+4 b c \,x^{2}+5 a c \right) x}{5 \left(b \,x^{2}+a \right)^{\frac{5}{4}} \sqrt{e x}\, a^{2}}"," ",0,"2/5*x*(a*d*x^2+4*b*c*x^2+5*a*c)/(b*x^2+a)^(5/4)/a^2/(e*x)^(1/2)","A"
1129,1,62,86,0.007000," ","int((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(9/4),x)","-\frac{2 \left(-12 a b d \,x^{4}+32 b^{2} c \,x^{4}-15 a^{2} d \,x^{2}+40 a b c \,x^{2}+5 c \,a^{2}\right) x}{15 \left(b \,x^{2}+a \right)^{\frac{5}{4}} \left(e x \right)^{\frac{5}{2}} a^{3}}"," ",0,"-2/15*x*(-12*a*b*d*x^4+32*b^2*c*x^4-15*a^2*d*x^2+40*a*b*c*x^2+5*a^2*c)/(b*x^2+a)^(5/4)/a^3/(e*x)^(5/2)","A"
1130,1,86,117,0.007000," ","int((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(9/4),x)","-\frac{2 \left(224 a \,b^{2} d \,x^{6}-384 b^{3} c \,x^{6}+280 a^{2} b d \,x^{4}-480 a \,b^{2} c \,x^{4}+35 a^{3} d \,x^{2}-60 a^{2} b c \,x^{2}+15 c \,a^{3}\right) x}{105 \left(b \,x^{2}+a \right)^{\frac{5}{4}} \left(e x \right)^{\frac{9}{2}} a^{4}}"," ",0,"-2/105*x*(224*a*b^2*d*x^6-384*b^3*c*x^6+280*a^2*b*d*x^4-480*a*b^2*c*x^4+35*a^3*d*x^2-60*a^2*b*c*x^2+15*a^3*c)/(b*x^2+a)^(5/4)/a^4/(e*x)^(9/2)","A"
1131,1,110,148,0.008000," ","int((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(9/4),x)","-\frac{2 \left(-1408 a \,b^{3} d \,x^{8}+2048 b^{4} c \,x^{8}-1760 a^{2} b^{2} d \,x^{6}+2560 a \,b^{3} c \,x^{6}-220 a^{3} b d \,x^{4}+320 a^{2} b^{2} c \,x^{4}+55 a^{4} d \,x^{2}-80 a^{3} b c \,x^{2}+35 c \,a^{4}\right) x}{385 \left(b \,x^{2}+a \right)^{\frac{5}{4}} \left(e x \right)^{\frac{13}{2}} a^{5}}"," ",0,"-2/385*x*(-1408*a*b^3*d*x^8+2048*b^4*c*x^8-1760*a^2*b^2*d*x^6+2560*a*b^3*c*x^6-220*a^3*b*d*x^4+320*a^2*b^2*c*x^4+55*a^4*d*x^2-80*a^3*b*c*x^2+35*a^4*c)/(b*x^2+a)^(5/4)/a^5/(e*x)^(13/2)","A"
1132,0,0,221,0.133000," ","int((e*x)^(13/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","\int \frac{\left(e x \right)^{\frac{13}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((e*x)^(13/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","F"
1133,0,0,189,0.125000," ","int((e*x)^(9/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","\int \frac{\left(e x \right)^{\frac{9}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((e*x)^(9/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","F"
1134,0,0,158,0.059000," ","int((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","\int \frac{\left(e x \right)^{\frac{5}{2}} \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","F"
1135,0,0,123,0.056000," ","int((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","\int \frac{\sqrt{e x}\, \left(d \,x^{2}+c \right)}{\left(b \,x^{2}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x)","F"
1136,0,0,147,0.120000," ","int((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(9/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{3}{2}} \left(b \,x^{2}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(9/4),x)","F"
1137,0,0,178,0.134000," ","int((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(9/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{7}{2}} \left(b \,x^{2}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(9/4),x)","F"
1138,0,0,210,0.133000," ","int((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(9/4),x)","\int \frac{d \,x^{2}+c}{\left(e x \right)^{\frac{11}{2}} \left(b \,x^{2}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(9/4),x)","F"
1139,0,0,97,0.174000," ","int((e*x)^m*(b*x^2+a)^p*(d*x^2+c)^q,x)","\int \left(e x \right)^{m} \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int((e*x)^m*(b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1140,0,0,78,0.077000," ","int(x^4*(b*x^2+a)^p*(d*x^2+c)^q,x)","\int x^{4} \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int(x^4*(b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1141,0,0,78,0.065000," ","int(x^2*(b*x^2+a)^p*(d*x^2+c)^q,x)","\int x^{2} \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int(x^2*(b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1142,0,0,75,0.079000," ","int((b*x^2+a)^p*(d*x^2+c)^q,x)","\int \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1143,0,0,78,0.063000," ","int((b*x^2+a)^p*(d*x^2+c)^q/x^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}}{x^{2}}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q/x^2,x)","F"
1144,0,0,78,0.064000," ","int((b*x^2+a)^p*(d*x^2+c)^q/x^4,x)","\int \frac{\left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}}{x^{4}}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q/x^4,x)","F"
1145,0,0,238,0.063000," ","int(x^5*(b*x^2+a)^p*(d*x^2+c)^q,x)","\int x^{5} \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int(x^5*(b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1146,0,0,144,0.062000," ","int(x^3*(b*x^2+a)^p*(d*x^2+c)^q,x)","\int x^{3} \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int(x^3*(b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1147,0,0,85,0.071000," ","int(x*(b*x^2+a)^p*(d*x^2+c)^q,x)","\int x \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int(x*(b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1148,0,0,95,0.070000," ","int((b*x^2+a)^p*(d*x^2+c)^q/x,x)","\int \frac{\left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}}{x}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q/x,x)","F"
1149,0,0,96,0.074000," ","int((b*x^2+a)^p*(d*x^2+c)^q/x^3,x)","\int \frac{\left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}}{x^{3}}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q/x^3,x)","F"
1150,0,0,98,0.074000," ","int((b*x^2+a)^p*(d*x^2+c)^q/x^5,x)","\int \frac{\left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}}{x^{5}}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q/x^5,x)","F"
1151,0,0,83,0.069000," ","int((e*x)^(5/2)*(b*x^2+a)^p*(d*x^2+c)^q,x)","\int \left(e x \right)^{\frac{5}{2}} \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int((e*x)^(5/2)*(b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1152,0,0,83,0.070000," ","int((e*x)^(3/2)*(b*x^2+a)^p*(d*x^2+c)^q,x)","\int \left(e x \right)^{\frac{3}{2}} \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int((e*x)^(3/2)*(b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1153,0,0,83,0.069000," ","int((e*x)^(1/2)*(b*x^2+a)^p*(d*x^2+c)^q,x)","\int \sqrt{e x}\, \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int((e*x)^(1/2)*(b*x^2+a)^p*(d*x^2+c)^q,x)","F"
1154,0,0,83,0.079000," ","int((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(1/2),x)","\int \frac{\left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}}{\sqrt{e x}}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(1/2),x)","F"
1155,0,0,83,0.079000," ","int((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(3/2),x)","\int \frac{\left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}}{\left(e x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(3/2),x)","F"
1156,0,0,83,0.071000," ","int((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(5/2),x)","\int \frac{\left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}}{\left(e x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(5/2),x)","F"