1,1,28,27,0.037000," ","int(x^2*(b*x^3+a)*(B*x^3+A),x)","\frac{B b \,x^{9}}{9}+\frac{\left(A b +B a \right) x^{6}}{6}+\frac{A a \,x^{3}}{3}"," ",0,"1/3*A*a*x^3+1/6*(A*b+B*a)*x^6+1/9*b*B*x^9","A"
2,1,28,27,0.045000," ","int(x*(b*x^3+a)*(B*x^3+A),x)","\frac{B b \,x^{8}}{8}+\frac{\left(A b +B a \right) x^{5}}{5}+\frac{A a \,x^{2}}{2}"," ",0,"1/2*A*a*x^2+1/5*(A*b+B*a)*x^5+1/8*b*B*x^8","A"
3,1,25,24,0.036000," ","int((b*x^3+a)*(B*x^3+A),x)","\frac{B b \,x^{7}}{7}+\frac{\left(A b +B a \right) x^{4}}{4}+A a x"," ",0,"A*a*x+1/4*(A*b+B*a)*x^4+1/7*b*B*x^7","A"
4,1,28,25,0.038000," ","int((b*x^3+a)*(B*x^3+A)/x,x)","\frac{B b \,x^{6}}{6}+\frac{A b \,x^{3}}{3}+\frac{B a \,x^{3}}{3}+A a \ln \left(x \right)"," ",0,"1/6*b*B*x^6+1/3*A*x^3*b+1/3*B*a*x^3+A*a*ln(x)","A"
5,1,30,27,0.049000," ","int((b*x^3+a)*(B*x^3+A)/x^2,x)","\frac{B b \,x^{5}}{5}+\frac{A b \,x^{2}}{2}+\frac{B a \,x^{2}}{2}-\frac{A a}{x}"," ",0,"1/5*b*B*x^5+1/2*A*b*x^2+1/2*B*a*x^2-A*a/x","A"
6,1,24,24,0.044000," ","int((b*x^3+a)*(B*x^3+A)/x^3,x)","\frac{B b \,x^{4}}{4}+A b x +B a x -\frac{A a}{2 x^{2}}"," ",0,"1/4*b*B*x^4+A*b*x+B*a*x-1/2*A*a/x^2","A"
7,1,26,25,0.050000," ","int((b*x^3+a)*(B*x^3+A)/x^4,x)","\frac{B b \,x^{3}}{3}+A b \ln \left(x \right)+B a \ln \left(x \right)-\frac{A a}{3 x^{3}}"," ",0,"1/3*B*b*x^3-1/3*A*a/x^3+A*b*ln(x)+B*a*ln(x)","A"
8,1,28,28,0.046000," ","int((b*x^3+a)*(B*x^3+A)/x^5,x)","\frac{B b \,x^{2}}{2}-\frac{A b +B a}{x}-\frac{A a}{4 x^{4}}"," ",0,"1/2*b*B*x^2-1/4*a*A/x^4-(A*b+B*a)/x","A"
9,1,25,26,0.041000," ","int((b*x^3+a)*(B*x^3+A)/x^6,x)","B b x -\frac{A b +B a}{2 x^{2}}-\frac{A a}{5 x^{5}}"," ",0,"B*b*x-1/5*a*A/x^5-1/2*(A*b+B*a)/x^2","A"
10,1,28,27,0.044000," ","int((b*x^3+a)*(B*x^3+A)/x^7,x)","B b \ln \left(x \right)-\frac{A b}{3 x^{3}}-\frac{B a}{3 x^{3}}-\frac{A a}{6 x^{6}}"," ",0,"-1/3/x^3*A*b-1/3/x^3*B*a-1/6*a*A/x^6+B*b*ln(x)","A"
11,1,52,38,0.039000," ","int(x^2*(b*x^3+a)^2*(B*x^3+A),x)","\frac{B \,b^{2} x^{12}}{12}+\frac{\left(b^{2} A +2 a b B \right) x^{9}}{9}+\frac{A \,a^{2} x^{3}}{3}+\frac{\left(2 a b A +a^{2} B \right) x^{6}}{6}"," ",0,"1/12*b^2*B*x^12+1/9*(A*b^2+2*B*a*b)*x^9+1/6*(2*A*a*b+B*a^2)*x^6+1/3*A*a^2*x^3","A"
12,1,52,47,0.046000," ","int(x*(b*x^3+a)^2*(B*x^3+A),x)","\frac{B \,b^{2} x^{11}}{11}+\frac{\left(b^{2} A +2 a b B \right) x^{8}}{8}+\frac{A \,a^{2} x^{2}}{2}+\frac{\left(2 a b A +a^{2} B \right) x^{5}}{5}"," ",0,"1/11*b^2*B*x^11+1/8*(A*b^2+2*B*a*b)*x^8+1/5*(2*A*a*b+B*a^2)*x^5+1/2*a^2*A*x^2","A"
13,1,49,44,0.035000," ","int((b*x^3+a)^2*(B*x^3+A),x)","\frac{B \,b^{2} x^{10}}{10}+\frac{\left(b^{2} A +2 a b B \right) x^{7}}{7}+A \,a^{2} x +\frac{\left(2 a b A +a^{2} B \right) x^{4}}{4}"," ",0,"1/10*b^2*B*x^10+1/7*(A*b^2+2*B*a*b)*x^7+1/4*(2*A*a*b+B*a^2)*x^4+A*a^2*x","A"
14,1,52,40,0.042000," ","int((b*x^3+a)^2*(B*x^3+A)/x,x)","\frac{B \,b^{2} x^{9}}{9}+\frac{A \,b^{2} x^{6}}{6}+\frac{B a b \,x^{6}}{3}+\frac{2 A a b \,x^{3}}{3}+\frac{B \,a^{2} x^{3}}{3}+A \,a^{2} \ln \left(x \right)"," ",0,"1/9*B*b^2*x^9+1/6*A*b^2*x^6+1/3*B*x^6*a*b+2/3*a*A*b*x^3+1/3*B*a^2*x^3+A*a^2*ln(x)","A"
15,1,53,47,0.043000," ","int((b*x^3+a)^2*(B*x^3+A)/x^2,x)","\frac{B \,b^{2} x^{8}}{8}+\frac{A \,b^{2} x^{5}}{5}+\frac{2 B a b \,x^{5}}{5}+A a b \,x^{2}+\frac{B \,a^{2} x^{2}}{2}-\frac{A \,a^{2}}{x}"," ",0,"1/8*b^2*B*x^8+1/5*A*x^5*b^2+2/5*B*x^5*a*b+A*a*b*x^2+1/2*B*a^2*x^2-A*a^2/x","A"
16,1,49,44,0.045000," ","int((b*x^3+a)^2*(B*x^3+A)/x^3,x)","\frac{B \,b^{2} x^{7}}{7}+\frac{A \,b^{2} x^{4}}{4}+\frac{B a b \,x^{4}}{2}+2 A a b x +B \,a^{2} x -\frac{A \,a^{2}}{2 x^{2}}"," ",0,"1/7*b^2*B*x^7+1/4*A*b^2*x^4+1/2*B*x^4*a*b+2*a*b*A*x+B*a^2*x-1/2*A*a^2/x^2","A"
17,1,51,45,0.052000," ","int((b*x^3+a)^2*(B*x^3+A)/x^4,x)","\frac{B \,b^{2} x^{6}}{6}+\frac{A \,b^{2} x^{3}}{3}+\frac{2 B a b \,x^{3}}{3}+2 A a b \ln \left(x \right)+B \,a^{2} \ln \left(x \right)-\frac{A \,a^{2}}{3 x^{3}}"," ",0,"1/6*b^2*B*x^6+1/3*A*x^3*b^2+2/3*B*x^3*a*b-1/3*A*a^2/x^3+2*A*ln(x)*a*b+B*a^2*ln(x)","A"
18,1,50,47,0.049000," ","int((b*x^3+a)^2*(B*x^3+A)/x^5,x)","\frac{B \,b^{2} x^{5}}{5}+\frac{A \,b^{2} x^{2}}{2}+B a b \,x^{2}-\frac{\left(2 A b +B a \right) a}{x}-\frac{A \,a^{2}}{4 x^{4}}"," ",0,"1/5*b^2*B*x^5+1/2*A*x^2*b^2+B*a*b*x^2-1/4*a^2*A/x^4-a*(2*A*b+B*a)/x","A"
19,1,46,44,0.058000," ","int((b*x^3+a)^2*(B*x^3+A)/x^6,x)","\frac{B \,b^{2} x^{4}}{4}+A \,b^{2} x +2 B a b x -\frac{\left(2 A b +B a \right) a}{2 x^{2}}-\frac{A \,a^{2}}{5 x^{5}}"," ",0,"1/4*B*b^2*x^4+b^2*A*x+2*a*b*B*x-1/5*a^2*A/x^5-1/2*a*(2*A*b+B*a)/x^2","A"
20,1,51,45,0.067000," ","int((b*x^3+a)^2*(B*x^3+A)/x^7,x)","\frac{B \,b^{2} x^{3}}{3}+A \,b^{2} \ln \left(x \right)+2 B a b \ln \left(x \right)-\frac{2 A a b}{3 x^{3}}-\frac{B \,a^{2}}{3 x^{3}}-\frac{A \,a^{2}}{6 x^{6}}"," ",0,"1/3*b^2*B*x^3-2/3*a/x^3*A*b-1/3*a^2/x^3*B-1/6*a^2*A/x^6+A*ln(x)*b^2+2*B*ln(x)*a*b","A"
21,1,48,47,0.045000," ","int((b*x^3+a)^2*(B*x^3+A)/x^8,x)","\frac{B \,b^{2} x^{2}}{2}-\frac{\left(A b +2 B a \right) b}{x}-\frac{\left(2 A b +B a \right) a}{4 x^{4}}-\frac{A \,a^{2}}{7 x^{7}}"," ",0,"-1/7*a^2*A/x^7-1/4*a*(2*A*b+B*a)/x^4-b*(A*b+2*B*a)/x+1/2*b^2*B*x^2","A"
22,1,45,44,0.046000," ","int((b*x^3+a)^2*(B*x^3+A)/x^9,x)","B \,b^{2} x -\frac{\left(A b +2 B a \right) b}{2 x^{2}}-\frac{\left(2 A b +B a \right) a}{5 x^{5}}-\frac{A \,a^{2}}{8 x^{8}}"," ",0,"-1/8*a^2*A/x^8-1/5*a*(2*A*b+B*a)/x^5-1/2*b*(A*b+2*B*a)/x^2+b^2*B*x","A"
23,1,124,103,0.038000," ","int(x^9*(b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{28}}{28}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{25}}{25}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{22}}{22}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{19}}{19}+\frac{A \,a^{5} x^{10}}{10}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{16}}{16}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{13}}{13}"," ",0,"1/28*b^5*B*x^28+1/25*(A*b^5+5*B*a*b^4)*x^25+1/22*(5*A*a*b^4+10*B*a^2*b^3)*x^22+1/19*(10*A*a^2*b^3+10*B*a^3*b^2)*x^19+1/16*(10*A*a^3*b^2+5*B*a^4*b)*x^16+1/13*(5*A*a^4*b+B*a^5)*x^13+1/10*a^5*A*x^10","A"
24,1,124,87,0.038000," ","int(x^8*(b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{27}}{27}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{24}}{24}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{21}}{21}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{18}}{18}+\frac{A \,a^{5} x^{9}}{9}+\frac{\left(10 a^{3} b^{2} A +5 a^{4} b B \right) x^{15}}{15}+\frac{\left(5 a^{4} b A +a^{5} B \right) x^{12}}{12}"," ",0,"1/27*b^5*B*x^27+1/24*(A*b^5+5*B*a*b^4)*x^24+1/21*(5*A*a*b^4+10*B*a^2*b^3)*x^21+1/18*(10*A*a^2*b^3+10*B*a^3*b^2)*x^18+1/15*(10*A*a^3*b^2+5*B*a^4*b)*x^15+1/12*(5*A*a^4*b+B*a^5)*x^12+1/9*a^5*A*x^9","A"
25,1,124,103,0.042000," ","int(x^7*(b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{26}}{26}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{23}}{23}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{20}}{20}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{17}}{17}+\frac{A \,a^{5} x^{8}}{8}+\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^{11}}{11}"," ",0,"1/26*b^5*B*x^26+1/23*(A*b^5+5*B*a*b^4)*x^23+1/20*(5*A*a*b^4+10*B*a^2*b^3)*x^20+1/17*(10*A*a^2*b^3+10*B*a^3*b^2)*x^17+1/14*(10*A*a^3*b^2+5*B*a^4*b)*x^14+1/11*(5*A*a^4*b+B*a^5)*x^11+1/8*a^5*A*x^8","A"
26,1,124,103,0.033000," ","int(x^6*(b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{25}}{25}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{22}}{22}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{19}}{19}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{16}}{16}+\frac{A \,a^{5} x^{7}}{7}+\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^{10}}{10}"," ",0,"1/25*b^5*B*x^25+1/22*(A*b^5+5*B*a*b^4)*x^22+1/19*(5*A*a*b^4+10*B*a^2*b^3)*x^19+1/16*(10*A*a^2*b^3+10*B*a^3*b^2)*x^16+1/13*(10*A*a^3*b^2+5*B*a^4*b)*x^13+1/10*(5*A*a^4*b+B*a^5)*x^10+1/7*a^5*A*x^7","A"
27,1,124,61,0.040000," ","int(x^5*(b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{24}}{24}+\frac{\left(b^{5} A +5 a \,b^{4} B \right) x^{21}}{21}+\frac{\left(5 a \,b^{4} A +10 a^{2} b^{3} B \right) x^{18}}{18}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{15}}{15}+\frac{A \,a^{5} x^{6}}{6}+\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^{9}}{9}"," ",0,"1/24*b^5*B*x^24+1/21*(A*b^5+5*B*a*b^4)*x^21+1/18*(5*A*a*b^4+10*B*a^2*b^3)*x^18+1/15*(10*A*a^2*b^3+10*B*a^3*b^2)*x^15+1/12*(10*A*a^3*b^2+5*B*a^4*b)*x^12+1/9*(5*A*a^4*b+B*a^5)*x^9+1/6*a^5*A*x^6","B"
28,1,124,103,0.042000," ","int(x^4*(b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{23}}{23}+\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^{17}}{17}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{14}}{14}+\frac{A \,a^{5} x^{5}}{5}+\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^{8}}{8}"," ",0,"1/23*b^5*B*x^23+1/20*(A*b^5+5*B*a*b^4)*x^20+1/17*(5*A*a*b^4+10*B*a^2*b^3)*x^17+1/14*(10*A*a^2*b^3+10*B*a^3*b^2)*x^14+1/11*(10*A*a^3*b^2+5*B*a^4*b)*x^11+1/8*(5*A*a^4*b+B*a^5)*x^8+1/5*a^5*A*x^5","A"
29,1,124,103,0.039000," ","int(x^3*(b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{22}}{22}+\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^{16}}{16}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{13}}{13}+\frac{A \,a^{5} x^{4}}{4}+\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^{7}}{7}"," ",0,"1/22*b^5*B*x^22+1/19*(A*b^5+5*B*a*b^4)*x^19+1/16*(5*A*a*b^4+10*B*a^2*b^3)*x^16+1/13*(10*A*a^2*b^3+10*B*a^3*b^2)*x^13+1/10*(10*A*a^3*b^2+5*B*a^4*b)*x^10+1/7*(5*A*a^4*b+B*a^5)*x^7+1/4*a^5*A*x^4","A"
30,1,124,38,0.042000," ","int(x^2*(b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{21}}{21}+\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^{15}}{15}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{12}}{12}+\frac{A \,a^{5} x^{3}}{3}+\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^{6}}{6}"," ",0,"1/21*b^5*B*x^21+1/18*(A*b^5+5*B*a*b^4)*x^18+1/15*(5*A*a*b^4+10*B*a^2*b^3)*x^15+1/12*(10*A*a^2*b^3+10*B*a^3*b^2)*x^12+1/9*(10*A*a^3*b^2+5*B*a^4*b)*x^9+1/6*(5*A*a^4*b+B*a^5)*x^6+1/3*a^5*A*x^3","B"
31,1,124,103,0.043000," ","int(x*(b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{20}}{20}+\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^{14}}{14}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{11}}{11}+\frac{A \,a^{5} x^{2}}{2}+\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^{5}}{5}"," ",0,"1/20*b^5*B*x^20+1/17*(A*b^5+5*B*a*b^4)*x^17+1/14*(5*A*a*b^4+10*B*a^2*b^3)*x^14+1/11*(10*A*a^2*b^3+10*B*a^3*b^2)*x^11+1/8*(10*A*a^3*b^2+5*B*a^4*b)*x^8+1/5*(5*A*a^4*b+B*a^5)*x^5+1/2*a^5*A*x^2","A"
32,1,121,99,0.039000," ","int((b*x^3+a)^5*(B*x^3+A),x)","\frac{B \,b^{5} x^{19}}{19}+\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^{13}}{13}+\frac{\left(10 a^{2} b^{3} A +10 a^{3} b^{2} B \right) x^{10}}{10}+A \,a^{5} x +\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^{4}}{4}"," ",0,"1/19*b^5*B*x^19+1/16*(A*b^5+5*B*a*b^4)*x^16+1/13*(5*A*a*b^4+10*B*a^2*b^3)*x^13+1/10*(10*A*a^2*b^3+10*B*a^3*b^2)*x^10+1/7*(10*A*a^3*b^2+5*B*a^4*b)*x^7+1/4*(5*A*a^4*b+B*a^5)*x^4+a^5*A*x","A"
33,1,124,76,0.042000," ","int((b*x^3+a)^5*(B*x^3+A)/x,x)","\frac{B \,b^{5} x^{18}}{18}+\frac{A \,b^{5} x^{15}}{15}+\frac{B a \,b^{4} x^{15}}{3}+\frac{5 A a \,b^{4} x^{12}}{12}+\frac{5 B \,a^{2} b^{3} x^{12}}{6}+\frac{10 A \,a^{2} b^{3} x^{9}}{9}+\frac{10 B \,a^{3} b^{2} x^{9}}{9}+\frac{5 A \,a^{3} b^{2} x^{6}}{3}+\frac{5 B \,a^{4} b \,x^{6}}{6}+\frac{5 A \,a^{4} b \,x^{3}}{3}+\frac{B \,a^{5} x^{3}}{3}+A \,a^{5} \ln \left(x \right)"," ",0,"1/18*B*b^5*x^18+1/15*A*b^5*x^15+1/3*B*x^15*a*b^4+5/12*a*A*b^4*x^12+5/6*B*x^12*a^2*b^3+10/9*a^2*A*b^3*x^9+10/9*B*x^9*a^3*b^2+5/3*a^3*A*b^2*x^6+5/6*B*x^6*a^4*b+5/3*a^4*A*b*x^3+1/3*B*x^3*a^5+a^5*A*ln(x)","A"
34,1,125,102,0.049000," ","int((b*x^3+a)^5*(B*x^3+A)/x^2,x)","\frac{B \,b^{5} x^{17}}{17}+\frac{A \,b^{5} x^{14}}{14}+\frac{5 B a \,b^{4} x^{14}}{14}+\frac{5 A a \,b^{4} x^{11}}{11}+\frac{10 B \,a^{2} b^{3} x^{11}}{11}+\frac{5 A \,a^{2} b^{3} x^{8}}{4}+\frac{5 B \,a^{3} b^{2} x^{8}}{4}+2 A \,a^{3} b^{2} x^{5}+B \,a^{4} b \,x^{5}+\frac{5 A \,a^{4} b \,x^{2}}{2}+\frac{B \,a^{5} x^{2}}{2}-\frac{A \,a^{5}}{x}"," ",0,"1/17*b^5*B*x^17+1/14*A*x^14*b^5+5/14*B*x^14*a*b^4+5/11*A*x^11*a*b^4+10/11*B*x^11*a^2*b^3+5/4*A*x^8*a^2*b^3+5/4*B*x^8*a^3*b^2+2*A*x^5*a^3*b^2+B*x^5*a^4*b+5/2*A*x^2*a^4*b+1/2*B*x^2*a^5-a^5*A/x","A"
35,1,120,100,0.040000," ","int((b*x^3+a)^5*(B*x^3+A)/x^3,x)","\frac{B \,b^{5} x^{16}}{16}+\frac{A \,b^{5} x^{13}}{13}+\frac{5 B a \,b^{4} x^{13}}{13}+\frac{A a \,b^{4} x^{10}}{2}+B \,a^{2} b^{3} x^{10}+\frac{10 A \,a^{2} b^{3} x^{7}}{7}+\frac{10 B \,a^{3} b^{2} x^{7}}{7}+\frac{5 A \,a^{3} b^{2} x^{4}}{2}+\frac{5 B \,a^{4} b \,x^{4}}{4}+5 A \,a^{4} b x +B \,a^{5} x -\frac{A \,a^{5}}{2 x^{2}}"," ",0,"1/16*b^5*B*x^16+1/13*A*x^13*b^5+5/13*B*x^13*a*b^4+1/2*A*x^10*a*b^4+B*x^10*a^2*b^3+10/7*A*x^7*a^2*b^3+10/7*B*x^7*a^3*b^2+5/2*A*x^4*a^3*b^2+5/4*B*x^4*a^4*b+5*a^4*b*A*x+B*a^5*x-1/2*a^5*A/x^2","A"
36,1,123,101,0.054000," ","int((b*x^3+a)^5*(B*x^3+A)/x^4,x)","\frac{B \,b^{5} x^{15}}{15}+\frac{A \,b^{5} x^{12}}{12}+\frac{5 B a \,b^{4} x^{12}}{12}+\frac{5 A a \,b^{4} x^{9}}{9}+\frac{10 B \,a^{2} b^{3} x^{9}}{9}+\frac{5 A \,a^{2} b^{3} x^{6}}{3}+\frac{5 B \,a^{3} b^{2} x^{6}}{3}+\frac{10 A \,a^{3} b^{2} x^{3}}{3}+\frac{5 B \,a^{4} b \,x^{3}}{3}+5 A \,a^{4} b \ln \left(x \right)+B \,a^{5} \ln \left(x \right)-\frac{A \,a^{5}}{3 x^{3}}"," ",0,"1/15*b^5*B*x^15+1/12*A*x^12*b^5+5/12*B*x^12*a*b^4+5/9*A*x^9*a*b^4+10/9*B*x^9*a^2*b^3+5/3*A*x^6*a^2*b^3+5/3*B*x^6*a^3*b^2+10/3*A*x^3*a^3*b^2+5/3*B*x^3*a^4*b-1/3*a^5*A/x^3+5*A*ln(x)*a^4*b+B*ln(x)*a^5","A"
37,1,123,103,0.047000," ","int((b*x^3+a)^5*(B*x^3+A)/x^5,x)","\frac{B \,b^{5} x^{14}}{14}+\frac{A \,b^{5} x^{11}}{11}+\frac{5 B a \,b^{4} x^{11}}{11}+\frac{5 A a \,b^{4} x^{8}}{8}+\frac{5 B \,a^{2} b^{3} x^{8}}{4}+2 A \,a^{2} b^{3} x^{5}+2 B \,a^{3} b^{2} x^{5}+5 A \,a^{3} b^{2} x^{2}+\frac{5 B \,a^{4} b \,x^{2}}{2}-\frac{\left(5 A b +B a \right) a^{4}}{x}-\frac{A \,a^{5}}{4 x^{4}}"," ",0,"1/14*b^5*B*x^14+1/11*A*x^11*b^5+5/11*B*x^11*a*b^4+5/8*A*x^8*a*b^4+5/4*B*x^8*a^2*b^3+2*A*x^5*a^2*b^3+2*B*x^5*a^3*b^2+5*A*x^2*a^3*b^2+5/2*B*x^2*a^4*b-1/4*a^5*A/x^4-a^4*(5*A*b+B*a)/x","A"
38,1,119,101,0.043000," ","int((b*x^3+a)^5*(B*x^3+A)/x^6,x)","\frac{B \,b^{5} x^{13}}{13}+\frac{A \,b^{5} x^{10}}{10}+\frac{B a \,b^{4} x^{10}}{2}+\frac{5 A a \,b^{4} x^{7}}{7}+\frac{10 B \,a^{2} b^{3} x^{7}}{7}+\frac{5 A \,a^{2} b^{3} x^{4}}{2}+\frac{5 B \,a^{3} b^{2} x^{4}}{2}+10 A \,a^{3} b^{2} x +5 B \,a^{4} b x -\frac{\left(5 A b +B a \right) a^{4}}{2 x^{2}}-\frac{A \,a^{5}}{5 x^{5}}"," ",0,"1/13*b^5*B*x^13+1/10*A*x^10*b^5+1/2*B*x^10*a*b^4+5/7*A*x^7*a*b^4+10/7*B*x^7*a^2*b^3+5/2*A*x^4*a^2*b^3+5/2*B*x^4*a^3*b^2+10*A*a^3*b^2*x+5*B*a^4*b*x-1/5*a^5*A/x^5-1/2*a^4*(5*A*b+B*a)/x^2","A"
39,1,124,102,0.049000," ","int((b*x^3+a)^5*(B*x^3+A)/x^7,x)","\frac{B \,b^{5} x^{12}}{12}+\frac{A \,b^{5} x^{9}}{9}+\frac{5 B a \,b^{4} x^{9}}{9}+\frac{5 A a \,b^{4} x^{6}}{6}+\frac{5 B \,a^{2} b^{3} x^{6}}{3}+\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} \ln \left(x \right)+5 B \,a^{4} b \ln \left(x \right)-\frac{5 A \,a^{4} b}{3 x^{3}}-\frac{B \,a^{5}}{3 x^{3}}-\frac{A \,a^{5}}{6 x^{6}}"," ",0,"1/12*b^5*B*x^12+1/9*A*x^9*b^5+5/9*B*x^9*a*b^4+5/6*A*x^6*a*b^4+5/3*B*x^6*a^2*b^3+10/3*A*a^2*b^3*x^3+10/3*B*a^3*b^2*x^3-5/3*a^4/x^3*A*b-1/3*a^5/x^3*B-1/6*a^5*A/x^6+10*A*ln(x)*a^3*b^2+5*B*ln(x)*a^4*b","A"
40,1,117,102,0.047000," ","int((b*x^3+a)^5*(B*x^3+A)/x^8,x)","\frac{B \,b^{5} x^{11}}{11}+\frac{A \,b^{5} x^{8}}{8}+\frac{5 B a \,b^{4} x^{8}}{8}+A a \,b^{4} x^{5}+2 B \,a^{2} b^{3} x^{5}+5 A \,a^{2} b^{3} x^{2}+5 B \,a^{3} b^{2} x^{2}-\frac{5 \left(2 A b +B a \right) a^{3} b}{x}-\frac{\left(5 A b +B a \right) a^{4}}{4 x^{4}}-\frac{A \,a^{5}}{7 x^{7}}"," ",0,"1/11*b^5*B*x^11+1/8*A*x^8*b^5+5/8*B*x^8*a*b^4+A*a*b^4*x^5+2*B*a^2*b^3*x^5+5*A*x^2*a^2*b^3+5*B*x^2*a^3*b^2-1/4*a^4*(5*A*b+B*a)/x^4-1/7*a^5*A/x^7-5*a^3*b*(2*A*b+B*a)/x","A"
41,1,114,101,0.044000," ","int((b*x^3+a)^5*(B*x^3+A)/x^9,x)","\frac{B \,b^{5} x^{10}}{10}+\frac{A \,b^{5} x^{7}}{7}+\frac{5 B a \,b^{4} x^{7}}{7}+\frac{5 A a \,b^{4} x^{4}}{4}+\frac{5 B \,a^{2} b^{3} x^{4}}{2}+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}{2 x^{2}}-\frac{\left(5 A b +B a \right) a^{4}}{5 x^{5}}-\frac{A \,a^{5}}{8 x^{8}}"," ",0,"1/10*b^5*B*x^10+1/7*A*b^5*x^7+5/7*B*a*b^4*x^7+5/4*A*x^4*a*b^4+5/2*B*x^4*a^2*b^3+10*a^2*b^3*A*x+10*a^3*b^2*B*x-1/5*a^4*(5*A*b+B*a)/x^5-1/8*a^5*A/x^8-5/2*a^3*b*(2*A*b+B*a)/x^2","A"
42,1,124,102,0.049000," ","int((b*x^3+a)^5*(B*x^3+A)/x^10,x)","\frac{B \,b^{5} x^{9}}{9}+\frac{A \,b^{5} x^{6}}{6}+\frac{5 B a \,b^{4} x^{6}}{6}+\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} \ln \left(x \right)+10 B \,a^{3} b^{2} \ln \left(x \right)-\frac{10 A \,a^{3} b^{2}}{3 x^{3}}-\frac{5 B \,a^{4} b}{3 x^{3}}-\frac{5 A \,a^{4} b}{6 x^{6}}-\frac{B \,a^{5}}{6 x^{6}}-\frac{A \,a^{5}}{9 x^{9}}"," ",0,"1/9*B*b^5*x^9+1/6*A*x^6*b^5+5/6*B*x^6*a*b^4+5/3*A*x^3*a*b^4+10/3*B*x^3*a^2*b^3-10/3*a^3*b^2/x^3*A-5/3*a^4*b/x^3*B-1/9*a^5*A/x^9-5/6*a^4/x^6*A*b-1/6*a^5/x^6*B+10*A*ln(x)*a^2*b^3+10*B*ln(x)*a^3*b^2","A"
43,1,111,103,0.053000," ","int((b*x^3+a)^5*(B*x^3+A)/x^11,x)","\frac{B \,b^{5} x^{8}}{8}+\frac{A \,b^{5} x^{5}}{5}+B a \,b^{4} x^{5}+\frac{5 A a \,b^{4} x^{2}}{2}+5 B \,a^{2} b^{3} x^{2}-\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}{4 x^{4}}-\frac{\left(5 A b +B a \right) a^{4}}{7 x^{7}}-\frac{A \,a^{5}}{10 x^{10}}"," ",0,"1/8*b^5*B*x^8+1/5*A*x^5*b^5+B*x^5*a*b^4+5/2*A*x^2*a*b^4+5*B*x^2*a^2*b^3-5/4*a^3*b*(2*A*b+B*a)/x^4-1/7*a^4*(5*A*b+B*a)/x^7-10*a^2*b^2*(A*b+B*a)/x-1/10*a^5*A/x^10","A"
44,1,108,101,0.054000," ","int((b*x^3+a)^5*(B*x^3+A)/x^12,x)","\frac{B \,b^{5} x^{7}}{7}+\frac{A \,b^{5} x^{4}}{4}+\frac{5 B a \,b^{4} x^{4}}{4}+5 A a \,b^{4} x +10 B \,a^{2} b^{3} x -\frac{5 \left(A b +B a \right) a^{2} b^{2}}{x^{2}}-\frac{\left(2 A b +B a \right) a^{3} b}{x^{5}}-\frac{\left(5 A b +B a \right) a^{4}}{8 x^{8}}-\frac{A \,a^{5}}{11 x^{11}}"," ",0,"1/7*b^5*B*x^7+1/4*A*x^4*b^5+5/4*B*x^4*a*b^4+5*a*b^4*A*x+10*a^2*b^3*B*x-a^3*b*(2*A*b+B*a)/x^5-1/8*a^4*(5*A*b+B*a)/x^8-5*a^2*b^2*(A*b+B*a)/x^2-1/11*a^5*A/x^11","A"
45,1,124,102,0.051000," ","int((b*x^3+a)^5*(B*x^3+A)/x^13,x)","\frac{B \,b^{5} x^{6}}{6}+\frac{A \,b^{5} x^{3}}{3}+\frac{5 B a \,b^{4} x^{3}}{3}+5 A a \,b^{4} \ln \left(x \right)+10 B \,a^{2} b^{3} \ln \left(x \right)-\frac{10 A \,a^{2} b^{3}}{3 x^{3}}-\frac{10 B \,a^{3} b^{2}}{3 x^{3}}-\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}{9 x^{9}}-\frac{B \,a^{5}}{9 x^{9}}-\frac{A \,a^{5}}{12 x^{12}}"," ",0,"1/6*b^5*B*x^6+1/3*A*x^3*b^5+5/3*B*x^3*a*b^4-1/12*a^5*A/x^12-10/3*b^3*a^2/x^3*A-10/3*b^2*a^3/x^3*B-5/9*a^4/x^9*A*b-1/9*a^5/x^9*B-5/3*a^3*b^2/x^6*A-5/6*a^4*b/x^6*B+5*A*ln(x)*a*b^4+10*B*ln(x)*a^2*b^3","A"
46,1,107,103,0.058000," ","int((b*x^3+a)^5*(B*x^3+A)/x^14,x)","\frac{B \,b^{5} x^{5}}{5}+\frac{A \,b^{5} x^{2}}{2}+\frac{5 B a \,b^{4} x^{2}}{2}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{x}-\frac{5 \left(A b +B a \right) a^{2} b^{2}}{2 x^{4}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{7 x^{7}}-\frac{\left(5 A b +B a \right) a^{4}}{10 x^{10}}-\frac{A \,a^{5}}{13 x^{13}}"," ",0,"1/5*b^5*B*x^5+1/2*A*x^2*b^5+5/2*B*x^2*a*b^4-5/2*a^2*b^2*(A*b+B*a)/x^4-1/13*a^5*A/x^13-5/7*a^3*b*(2*A*b+B*a)/x^7-5*a*b^3*(A*b+2*B*a)/x-1/10*a^4*(5*A*b+B*a)/x^10","A"
47,1,102,100,0.052000," ","int((b*x^3+a)^5*(B*x^3+A)/x^15,x)","\frac{B \,b^{5} x^{4}}{4}+A \,b^{5} x +5 B a \,b^{4} x -\frac{5 \left(A b +2 B a \right) a \,b^{3}}{2 x^{2}}-\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}{8 x^{8}}-\frac{\left(5 A b +B a \right) a^{4}}{11 x^{11}}-\frac{A \,a^{5}}{14 x^{14}}"," ",0,"1/4*b^5*B*x^4+b^5*A*x+5*a*b^4*B*x-2*a^2*b^2*(A*b+B*a)/x^5-5/8*a^3*b*(2*A*b+B*a)/x^8-5/2*a*b^3*(A*b+2*B*a)/x^2-1/14*a^5*A/x^14-1/11*a^4*(5*A*b+B*a)/x^11","A"
48,1,123,101,0.049000," ","int((b*x^3+a)^5*(B*x^3+A)/x^16,x)","\frac{B \,b^{5} x^{3}}{3}+A \,b^{5} \ln \left(x \right)+5 B a \,b^{4} \ln \left(x \right)-\frac{5 A a \,b^{4}}{3 x^{3}}-\frac{10 B \,a^{2} b^{3}}{3 x^{3}}-\frac{5 A \,a^{2} b^{3}}{3 x^{6}}-\frac{5 B \,a^{3} b^{2}}{3 x^{6}}-\frac{10 A \,a^{3} b^{2}}{9 x^{9}}-\frac{5 B \,a^{4} b}{9 x^{9}}-\frac{5 A \,a^{4} b}{12 x^{12}}-\frac{B \,a^{5}}{12 x^{12}}-\frac{A \,a^{5}}{15 x^{15}}"," ",0,"1/3*b^5*B*x^3-5/12*a^4/x^12*A*b-1/12*a^5/x^12*B-5/3*a*b^4/x^3*A-10/3*a^2*b^3/x^3*B-1/15*a^5*A/x^15-10/9*a^3*b^2/x^9*A-5/9*a^4*b/x^9*B-5/3*b^3*a^2/x^6*A-5/3*b^2*a^3/x^6*B+A*ln(x)*b^5+5*B*ln(x)*a*b^4","A"
49,1,104,103,0.043000," ","int((b*x^3+a)^5*(B*x^3+A)/x^17,x)","\frac{B \,b^{5} x^{2}}{2}-\frac{\left(A b +5 B a \right) b^{4}}{x}-\frac{5 \left(A b +2 B a \right) a \,b^{3}}{4 x^{4}}-\frac{10 \left(A b +B a \right) a^{2} b^{2}}{7 x^{7}}-\frac{\left(2 A b +B a \right) a^{3} b}{2 x^{10}}-\frac{\left(5 A b +B a \right) a^{4}}{13 x^{13}}-\frac{A \,a^{5}}{16 x^{16}}"," ",0,"-1/16*a^5*A/x^16-1/13*a^4*(5*A*b+B*a)/x^13-1/2*a^3*b*(2*A*b+B*a)/x^10-10/7*a^2*b^2*(A*b+B*a)/x^7-5/4*a*b^3*(A*b+2*B*a)/x^4-b^4*(A*b+5*B*a)/x+1/2*b^5*B*x^2","A"
50,1,101,100,0.048000," ","int((b*x^3+a)^5*(B*x^3+A)/x^18,x)","B \,b^{5} x -\frac{\left(A b +5 B a \right) b^{4}}{2 x^{2}}-\frac{\left(A b +2 B a \right) a \,b^{3}}{x^{5}}-\frac{5 \left(A b +B a \right) a^{2} b^{2}}{4 x^{8}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{11 x^{11}}-\frac{\left(5 A b +B a \right) a^{4}}{14 x^{14}}-\frac{A \,a^{5}}{17 x^{17}}"," ",0,"-1/17*a^5*A/x^17-1/14*a^4*(5*A*b+B*a)/x^14-5/11*a^3*b*(2*A*b+B*a)/x^11-5/4*a^2*b^2*(A*b+B*a)/x^8-a*b^3*(A*b+2*B*a)/x^5-1/2*b^4*(A*b+5*B*a)/x^2+b^5*B*x","A"
51,1,124,79,0.047000," ","int((b*x^3+a)^5*(B*x^3+A)/x^19,x)","B \,b^{5} \ln \left(x \right)-\frac{A \,b^{5}}{3 x^{3}}-\frac{5 B a \,b^{4}}{3 x^{3}}-\frac{5 A a \,b^{4}}{6 x^{6}}-\frac{5 B \,a^{2} b^{3}}{3 x^{6}}-\frac{10 A \,a^{2} b^{3}}{9 x^{9}}-\frac{10 B \,a^{3} b^{2}}{9 x^{9}}-\frac{5 A \,a^{3} b^{2}}{6 x^{12}}-\frac{5 B \,a^{4} b}{12 x^{12}}-\frac{A \,a^{4} b}{3 x^{15}}-\frac{B \,a^{5}}{15 x^{15}}-\frac{A \,a^{5}}{18 x^{18}}"," ",0,"-5/6*a^3*b^2/x^12*A-5/12*a^4*b*B/x^12-1/3*b^5/x^3*A-5/3*a*b^4*B/x^3-1/18*A*a^5/x^18-1/3*a^4/x^15*A*b-1/15*a^5*B/x^15-10/9*b^3*a^2/x^9*A-10/9*a^3*b^2*B/x^9-5/6*a*b^4/x^6*A-5/3*a^2*b^3*B/x^6+b^5*B*ln(x)","A"
52,1,104,103,0.043000," ","int((b*x^3+a)^5*(B*x^3+A)/x^20,x)","-\frac{B \,b^{5}}{x}-\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}}{7 x^{7}}-\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}{13 x^{13}}-\frac{\left(5 A b +B a \right) a^{4}}{16 x^{16}}-\frac{A \,a^{5}}{19 x^{19}}"," ",0,"-1/19*a^5*A/x^19-1/16*a^4*(5*A*b+B*a)/x^16-5/13*a^3*b*(2*A*b+B*a)/x^13-a^2*b^2*(A*b+B*a)/x^10-5/7*a*b^3*(A*b+2*B*a)/x^7-1/4*b^4*(A*b+5*B*a)/x^4-b^5*B/x","A"
53,1,104,103,0.048000," ","int((b*x^3+a)^5*(B*x^3+A)/x^21,x)","-\frac{B \,b^{5}}{2 x^{2}}-\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}}{8 x^{8}}-\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}{14 x^{14}}-\frac{\left(5 A b +B a \right) a^{4}}{17 x^{17}}-\frac{A \,a^{5}}{20 x^{20}}"," ",0,"-1/20*a^5*A/x^20-1/17*a^4*(5*A*b+B*a)/x^17-5/14*a^3*b*(2*A*b+B*a)/x^14-10/11*a^2*b^2*(A*b+B*a)/x^11-5/8*a*b^3*(A*b+2*B*a)/x^8-1/5*b^4*(A*b+5*B*a)/x^5-1/2*b^5*B/x^2","A"
54,1,104,44,0.046000," ","int((b*x^3+a)^5*(B*x^3+A)/x^22,x)","-\frac{B \,b^{5}}{3 x^{3}}-\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}}{9 x^{9}}-\frac{5 \left(A b +B a \right) a^{2} b^{2}}{6 x^{12}}-\frac{\left(2 A b +B a \right) a^{3} b}{3 x^{15}}-\frac{\left(5 A b +B a \right) a^{4}}{18 x^{18}}-\frac{A \,a^{5}}{21 x^{21}}"," ",0,"-5/6*b^2*a^2*(A*b+B*a)/x^12-1/3*B*b^5/x^3-1/18*a^4*(5*A*b+B*a)/x^18-1/3*a^3*b*(2*A*b+B*a)/x^15-5/9*a*b^3*(A*b+2*B*a)/x^9-1/6*b^4*(A*b+5*B*a)/x^6-1/21*A*a^5/x^21","B"
55,1,104,103,0.049000," ","int((b*x^3+a)^5*(B*x^3+A)/x^23,x)","-\frac{B \,b^{5}}{4 x^{4}}-\frac{\left(A b +5 B a \right) b^{4}}{7 x^{7}}-\frac{\left(A b +2 B a \right) a \,b^{3}}{2 x^{10}}-\frac{10 \left(A b +B a \right) a^{2} b^{2}}{13 x^{13}}-\frac{5 \left(2 A b +B a \right) a^{3} b}{16 x^{16}}-\frac{\left(5 A b +B a \right) a^{4}}{19 x^{19}}-\frac{A \,a^{5}}{22 x^{22}}"," ",0,"-1/22*a^5*A/x^22-1/19*a^4*(5*A*b+B*a)/x^19-5/16*a^3*b*(2*A*b+B*a)/x^16-10/13*a^2*b^2*(A*b+B*a)/x^13-1/2*a*b^3*(A*b+2*B*a)/x^10-1/7*b^4*(A*b+5*B*a)/x^7-1/4*b^5*B/x^4","A"
56,1,249,142,0.044000," ","int(x^6*(B*x^3+A)/(b*x^3+a),x)","\frac{B \,x^{7}}{7 b}+\frac{A \,x^{4}}{4 b}-\frac{B a \,x^{4}}{4 b^{2}}+\frac{\sqrt{3}\, A \,a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{A \,a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{A \,a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{A a x}{b^{2}}-\frac{\sqrt{3}\, B \,a^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{B \,a^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{B \,a^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{B \,a^{2} x}{b^{3}}"," ",0,"1/7*B*x^7/b+1/4/b*A*x^4-1/4/b^2*B*x^4*a-1/b^2*a*A*x+1/b^3*a^2*B*x+1/3*a^2/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*A-1/3*a^3/b^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*B-1/6*a^2/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A+1/6*a^3/b^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B+1/3*a^2/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A-1/3*a^3/b^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B","A"
57,1,62,48,0.041000," ","int(x^5*(B*x^3+A)/(b*x^3+a),x)","\frac{B \,x^{6}}{6 b}+\frac{A \,x^{3}}{3 b}-\frac{B a \,x^{3}}{3 b^{2}}-\frac{A a \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{B \,a^{2} \ln \left(b \,x^{3}+a \right)}{3 b^{3}}"," ",0,"1/6*B*x^6/b+1/3/b*A*x^3-1/3/b^2*B*a*x^3-1/3*a/b^2*ln(b*x^3+a)*A+1/3*a^2/b^3*ln(b*x^3+a)*B","A"
58,1,226,127,0.045000," ","int(x^4*(B*x^3+A)/(b*x^3+a),x)","\frac{B \,x^{5}}{5 b}+\frac{A \,x^{2}}{2 b}-\frac{B a \,x^{2}}{2 b^{2}}-\frac{\sqrt{3}\, A a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{A a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{A a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{\sqrt{3}\, B \,a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{B \,a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{B \,a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}"," ",0,"1/5*B*x^5/b+1/2/b*A*x^2-1/2/b^2*B*x^2*a+1/3*a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*A-1/3*a^2/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*B-1/6*a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A+1/6*a^2/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B-1/3*a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+1/3*a^2/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B","A"
59,1,221,124,0.043000," ","int(x^3*(B*x^3+A)/(b*x^3+a),x)","\frac{B \,x^{4}}{4 b}-\frac{\sqrt{3}\, A a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{A a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{A a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{A x}{b}+\frac{\sqrt{3}\, B \,a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{B \,a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{B \,a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{B a x}{b^{2}}"," ",0,"1/4*B*x^4/b+1/b*A*x-1/b^2*B*a*x-1/3*a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*A+1/3*a^2/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*B+1/6*a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A-1/6*a^2/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B-1/3*a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+1/3*a^2/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B","A"
60,1,40,31,0.040000," ","int(x^2*(B*x^3+A)/(b*x^3+a),x)","\frac{B \,x^{3}}{3 b}+\frac{A \ln \left(b \,x^{3}+a \right)}{3 b}-\frac{B a \ln \left(b \,x^{3}+a \right)}{3 b^{2}}"," ",0,"1/3*B*x^3/b+1/3/b*ln(b*x^3+a)*A-1/3/b^2*ln(b*x^3+a)*B*a","A"
61,1,198,111,0.041000," ","int(x*(B*x^3+A)/(b*x^3+a),x)","\frac{B \,x^{2}}{2 b}+\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{\sqrt{3}\, B a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{B a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{B a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}"," ",0,"1/2*B*x^2/b-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*A+1/3/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*B*a+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A-1/6/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B*a+1/3/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A-1/3/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B*a","A"
62,1,195,108,0.045000," ","int((B*x^3+A)/(b*x^3+a),x)","\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{\sqrt{3}\, B a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{B a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{B a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{B x}{b}"," ",0,"B*x/b+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*A-1/3/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*B*a-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A+1/6/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B*a+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A-1/3/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B*a","A"
63,1,37,32,0.050000," ","int((B*x^3+A)/x/(b*x^3+a),x)","\frac{A \ln \left(x \right)}{a}-\frac{A \ln \left(b \,x^{3}+a \right)}{3 a}+\frac{B \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"-1/3/a*ln(b*x^3+a)*A+1/3/b*ln(b*x^3+a)*B+A/a*ln(x)","A"
64,1,195,111,0.057000," ","int((B*x^3+A)/x^2/(b*x^3+a),x)","-\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{A}{a x}"," ",0,"1/3/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*A-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*B-1/6/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B-1/3/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+1/3*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B-A/a/x","A"
65,1,195,111,0.048000," ","int((B*x^3+A)/x^3/(b*x^3+a),x)","-\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{A}{2 a \,x^{2}}"," ",0,"-1/3/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*A+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*B+1/6/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B-1/3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B-1/2*A/a/x^2","A"
66,1,56,46,0.048000," ","int((B*x^3+A)/x^4/(b*x^3+a),x)","-\frac{A b \ln \left(x \right)}{a^{2}}+\frac{A b \ln \left(b \,x^{3}+a \right)}{3 a^{2}}+\frac{B \ln \left(x \right)}{a}-\frac{B \ln \left(b \,x^{3}+a \right)}{3 a}-\frac{A}{3 a \,x^{3}}"," ",0,"1/3/a^2*ln(b*x^3+a)*A*b-1/3/a*ln(b*x^3+a)*B-1/3*A/a/x^3-1/a^2*ln(x)*A*b+B/a*ln(x)","A"
67,1,216,126,0.046000," ","int((B*x^3+A)/x^5/(b*x^3+a),x)","\frac{\sqrt{3}\, A b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{A b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{A b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{A b}{a^{2} x}-\frac{B}{a x}-\frac{A}{4 a \,x^{4}}"," ",0,"-1/3/a^2*b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*A+1/3/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*B+1/6/a^2*b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A-1/6/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B+1/3/a^2*b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A-1/3/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B-1/4*A/a/x^4+1/a^2/x*A*b-B/a/x","A"
68,1,217,127,0.048000," ","int((B*x^3+A)/x^6/(b*x^3+a),x)","\frac{\sqrt{3}\, A b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{A b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{A b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{A b}{2 a^{2} x^{2}}-\frac{B}{2 a \,x^{2}}-\frac{A}{5 a \,x^{5}}"," ",0,"1/3/a^2*b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*A-1/3/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*B-1/6/a^2*b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A+1/6/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B+1/3/a^2*b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A-1/3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B-1/5*A/a/x^5+1/2/a^2/x^2*A*b-1/2/a/x^2*B","A"
69,1,81,63,0.050000," ","int((B*x^3+A)/x^7/(b*x^3+a),x)","\frac{A \,b^{2} \ln \left(x \right)}{a^{3}}-\frac{A \,b^{2} \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{B b \ln \left(x \right)}{a^{2}}+\frac{B b \ln \left(b \,x^{3}+a \right)}{3 a^{2}}+\frac{A b}{3 a^{2} x^{3}}-\frac{B}{3 a \,x^{3}}-\frac{A}{6 a \,x^{6}}"," ",0,"-1/3*b^2/a^3*ln(b*x^3+a)*A+1/3*b/a^2*ln(b*x^3+a)*B-1/6*A/a/x^6+1/3/a^2/x^3*A*b-1/3/a/x^3*B+b^2/a^3*ln(x)*A-b/a^2*ln(x)*B","A"
70,1,247,144,0.057000," ","int((B*x^3+A)/x^8/(b*x^3+a),x)","-\frac{\sqrt{3}\, A \,b^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{A \,b^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{A \,b^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{\sqrt{3}\, B b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{B b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{B b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{A \,b^{2}}{a^{3} x}+\frac{B b}{a^{2} x}+\frac{A b}{4 a^{2} x^{4}}-\frac{B}{4 a \,x^{4}}-\frac{A}{7 a \,x^{7}}"," ",0,"1/3/a^3*b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*A-1/3/a^2*b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*B-1/6/a^3*b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A+1/6/a^2*b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B-1/3/a^3*b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+1/3/a^2*b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B-1/7*A/a/x^7+1/4/a^2/x^4*A*b-1/4/a/x^4*B-b^2/a^3/x*A+b/a^2/x*B","A"
71,1,288,186,0.057000," ","int(x^9*(B*x^3+A)/(b*x^3+a)^2,x)","\frac{B \,x^{7}}{7 b^{2}}+\frac{A \,x^{4}}{4 b^{2}}-\frac{B a \,x^{4}}{2 b^{3}}-\frac{A \,a^{2} x}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{B \,a^{3} x}{3 \left(b \,x^{3}+a \right) b^{4}}+\frac{7 \sqrt{3}\, A \,a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 A \,a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{7 A \,a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{2 A a x}{b^{3}}-\frac{10 \sqrt{3}\, B \,a^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{10 B \,a^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{5 B \,a^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{3 B \,a^{2} x}{b^{4}}"," ",0,"1/7/b^2*B*x^7+1/4/b^2*A*x^4-1/2/b^3*B*x^4*a-2/b^3*a*A*x+3/b^4*a^2*B*x-1/3*a^2/b^3*x/(b*x^3+a)*A+1/3*a^3/b^4*x/(b*x^3+a)*B+7/9*a^2/b^4*A/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-7/18*a^2/b^4*A/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+7/9*a^2/b^4*A/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-10/9*a^3/b^5*B/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+5/9*a^3/b^5*B/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-10/9*a^3/b^5*B/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
72,1,97,74,0.053000," ","int(x^8*(B*x^3+A)/(b*x^3+a)^2,x)","\frac{B \,x^{6}}{6 b^{2}}+\frac{A \,x^{3}}{3 b^{2}}-\frac{2 B a \,x^{3}}{3 b^{3}}-\frac{A \,a^{2}}{3 \left(b \,x^{3}+a \right) b^{3}}-\frac{2 A a \ln \left(b \,x^{3}+a \right)}{3 b^{3}}+\frac{B \,a^{3}}{3 \left(b \,x^{3}+a \right) b^{4}}+\frac{B \,a^{2} \ln \left(b \,x^{3}+a \right)}{b^{4}}"," ",0,"1/6*B*x^6/b^2+1/3/b^2*A*x^3-2/3/b^3*B*a*x^3-2/3*a/b^3*ln(b*x^3+a)*A+a^2/b^4*ln(b*x^3+a)*B-1/3*a^2/b^3/(b*x^3+a)*A+1/3*a^3/b^4/(b*x^3+a)*B","A"
73,1,266,170,0.048000," ","int(x^7*(B*x^3+A)/(b*x^3+a)^2,x)","\frac{B \,x^{5}}{5 b^{2}}+\frac{A a \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{B \,a^{2} x^{2}}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{A \,x^{2}}{2 b^{2}}-\frac{B a \,x^{2}}{b^{3}}-\frac{5 \sqrt{3}\, A a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 A a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 A a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{8 \sqrt{3}\, B \,a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{8 B \,a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{4 B \,a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}"," ",0,"1/5/b^2*B*x^5+1/2/b^2*A*x^2-1/b^3*B*x^2*a+1/3*a/b^2*x^2/(b*x^3+a)*A-1/3*a^2/b^3*x^2/(b*x^3+a)*B+5/9*a/b^3*A/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/18*a/b^3*A/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9*a/b^3*A*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-8/9*a^2/b^4*B/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+4/9*a^2/b^4*B/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+8/9*a^2/b^4*B*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
74,1,257,168,0.086000," ","int(x^6*(B*x^3+A)/(b*x^3+a)^2,x)","\frac{B \,x^{4}}{4 b^{2}}+\frac{A a x}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{B \,a^{2} x}{3 \left(b \,x^{3}+a \right) b^{3}}-\frac{4 \sqrt{3}\, A a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 A a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 A a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{A x}{b^{2}}+\frac{7 \sqrt{3}\, B \,a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 B \,a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{7 B \,a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{2 B a x}{b^{3}}"," ",0,"1/4/b^2*B*x^4+1/b^2*A*x-2/b^3*B*a*x+1/3*a/b^2*x/(b*x^3+a)*A-1/3*a^2/b^3*x/(b*x^3+a)*B-4/9*a/b^3*A/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+2/9*a/b^3*A/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9*a/b^3*A/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+7/9*a^2/b^4*B/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-7/18*a^2/b^4*B/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+7/9*a^2/b^4*B/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
75,1,74,54,0.052000," ","int(x^5*(B*x^3+A)/(b*x^3+a)^2,x)","\frac{B \,x^{3}}{3 b^{2}}+\frac{A a}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{A \ln \left(b \,x^{3}+a \right)}{3 b^{2}}-\frac{B \,a^{2}}{3 \left(b \,x^{3}+a \right) b^{3}}-\frac{2 B a \ln \left(b \,x^{3}+a \right)}{3 b^{3}}"," ",0,"1/3*B*x^3/b^2+1/3/b^2*ln(b*x^3+a)*A-2/3/b^3*ln(b*x^3+a)*B*a+1/3/b^2*a/(b*x^3+a)*A-1/3/b^3*a^2/(b*x^3+a)*B","A"
76,1,235,153,0.080000," ","int(x^4*(B*x^3+A)/(b*x^3+a)^2,x)","-\frac{A \,x^{2}}{3 \left(b \,x^{3}+a \right) b}+\frac{B a \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{B \,x^{2}}{2 b^{2}}+\frac{2 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{5 \sqrt{3}\, B a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 B a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 B a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}"," ",0,"1/2*B*x^2/b^2-1/3/b*x^2/(b*x^3+a)*A+1/3/b^2*x^2/(b*x^3+a)*B*a+5/9/b^3*B*a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/18/b^3*B*a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/b^3*B*a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/9/b^2*A/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/9/b^2*A/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/b^2*A*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
77,1,228,147,0.044000," ","int(x^3*(B*x^3+A)/(b*x^3+a)^2,x)","-\frac{A x}{3 \left(b \,x^{3}+a \right) b}+\frac{B a x}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{4 \sqrt{3}\, B a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 B a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 B a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{B x}{b^{2}}"," ",0,"B/b^2*x-1/3/b*x/(b*x^3+a)*A+1/3/b^2*x/(b*x^3+a)*B*a-4/9/b^3*B*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+2/9/b^3*B*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/b^3*B*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9/b^2*A/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/18/b^2*A/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/b^2*A/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
78,1,47,37,0.055000," ","int(x^2*(B*x^3+A)/(b*x^3+a)^2,x)","-\frac{A}{3 \left(b \,x^{3}+a \right) b}+\frac{B a}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{B \ln \left(b \,x^{3}+a \right)}{3 b^{2}}"," ",0,"1/3*B*ln(b*x^3+a)/b^2-1/3/b/(b*x^3+a)*A+1/3/b^2/(b*x^3+a)*B*a","A"
79,1,223,130,0.049000," ","int(x*(B*x^3+A)/(b*x^3+a)^2,x)","\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{2 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{\left(A b -B a \right) x^{2}}{3 \left(b \,x^{3}+a \right) a b}"," ",0,"1/3*(A*b-B*a)*x^2/a/b/(b*x^3+a)-1/9/b/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*A-2/9/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*B+1/18/b/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A+1/9/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B+1/9/b/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+2/9/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B","A"
80,1,221,128,0.057000," ","int((B*x^3+A)/(b*x^3+a)^2,x)","\frac{2 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{\left(A b -B a \right) x}{3 \left(b \,x^{3}+a \right) a b}"," ",0,"1/3*(A*b-B*a)*x/a/b/(b*x^3+a)+2/9/b/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*A+1/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*B-1/9/b/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A-1/18/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B+2/9/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+1/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B","A"
81,1,53,47,0.054000," ","int((B*x^3+A)/x/(b*x^3+a)^2,x)","\frac{A}{3 \left(b \,x^{3}+a \right) a}+\frac{A \ln \left(x \right)}{a^{2}}-\frac{A \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{B}{3 \left(b \,x^{3}+a \right) b}"," ",0,"-1/3*A*ln(b*x^3+a)/a^2+1/3/a/(b*x^3+a)*A-1/3/b/(b*x^3+a)*B+A/a^2*ln(x)","A"
82,1,241,152,0.052000," ","int((B*x^3+A)/x^2/(b*x^3+a)^2,x)","-\frac{A b \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{B \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{4 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{A}{a^{2} x}"," ",0,"-1/3/a^2*x^2/(b*x^3+a)*A*b+1/3/a*x^2/(b*x^3+a)*B+4/9/a^2*A/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-2/9/a^2*A/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/a^2*A*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/9/a*B/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/18/a*B/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/a*B*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-A/a^2/x","A"
83,1,237,153,0.048000," ","int((B*x^3+A)/x^3/(b*x^3+a)^2,x)","-\frac{A b x}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{B x}{3 \left(b \,x^{3}+a \right) a}-\frac{5 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{2 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{A}{2 a^{2} x^{2}}"," ",0,"-1/3/a^2*x/(b*x^3+a)*A*b+1/3/a*x/(b*x^3+a)*B-5/9/a^2*A/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+5/18/a^2*A/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/a^2*A/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/9/a*B/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/9/a*B/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/a*B/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/2*A/a^2/x^2","A"
84,1,87,70,0.060000," ","int((B*x^3+A)/x^4/(b*x^3+a)^2,x)","-\frac{A b}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{2 A b \ln \left(x \right)}{a^{3}}+\frac{2 A b \ln \left(b \,x^{3}+a \right)}{3 a^{3}}+\frac{B}{3 \left(b \,x^{3}+a \right) a}+\frac{B \ln \left(x \right)}{a^{2}}-\frac{B \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{A}{3 a^{2} x^{3}}"," ",0,"2/3*b/a^3*ln(b*x^3+a)*A-1/3/a^2*ln(b*x^3+a)*B-1/3*b/a^2/(b*x^3+a)*A+1/3/a/(b*x^3+a)*B-1/3*A/a^2/x^3-2/a^3*ln(x)*A*b+B/a^2*ln(x)","A"
85,1,257,170,0.057000," ","int((B*x^3+A)/x^5/(b*x^3+a)^2,x)","\frac{A \,b^{2} x^{2}}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{B b \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{7 \sqrt{3}\, A b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 A b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{7 A b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{4 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{2 A b}{a^{3} x}-\frac{B}{a^{2} x}-\frac{A}{4 a^{2} x^{4}}"," ",0,"1/3*b^2/a^3*x^2/(b*x^3+a)*A-1/3*b/a^2*x^2/(b*x^3+a)*B-7/9*b/a^3*A/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/18*b/a^3*A/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+7/9*b/a^3*A*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+4/9/a^2*B/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-2/9/a^2*B/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/a^2*B*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/4/a^2*A/x^4+2*A/a^3*b/x-B/a^2/x","A"
86,1,252,170,0.053000," ","int((B*x^3+A)/x^6/(b*x^3+a)^2,x)","\frac{A \,b^{2} x}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{B b x}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{8 \sqrt{3}\, A b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{8 A b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{4 A b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{5 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{A b}{a^{3} x^{2}}-\frac{B}{2 a^{2} x^{2}}-\frac{A}{5 a^{2} x^{5}}"," ",0,"1/3*b^2/a^3*x/(b*x^3+a)*A-1/3*b/a^2*x/(b*x^3+a)*B+8/9*b/a^3*A/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-4/9*b/a^3*A/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+8/9*b/a^3*A/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-5/9/a^2*B/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+5/18/a^2*B/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/a^2*B/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/5/a^2*A/x^5+1/a^3/x^2*A*b-1/2/a^2/x^2*B","A"
87,1,116,89,0.075000," ","int((B*x^3+A)/x^7/(b*x^3+a)^2,x)","\frac{A \,b^{2}}{3 \left(b \,x^{3}+a \right) a^{3}}+\frac{3 A \,b^{2} \ln \left(x \right)}{a^{4}}-\frac{A \,b^{2} \ln \left(b \,x^{3}+a \right)}{a^{4}}-\frac{B b}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{2 B b \ln \left(x \right)}{a^{3}}+\frac{2 B b \ln \left(b \,x^{3}+a \right)}{3 a^{3}}+\frac{2 A b}{3 a^{3} x^{3}}-\frac{B}{3 a^{2} x^{3}}-\frac{A}{6 a^{2} x^{6}}"," ",0,"-1/a^4*b^2*ln(b*x^3+a)*A+2/3/a^3*b*ln(b*x^3+a)*B+1/3/a^3*b^2/(b*x^3+a)*A-1/3/a^2*b/(b*x^3+a)*B-1/6*A/a^2/x^6+2/3/a^3/x^3*A*b-1/3/a^2/x^3*B+3*b^2/a^4*ln(x)*A-2*b/a^3*ln(x)*B","A"
88,1,134,99,0.054000," ","int(x^11*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{B \,x^{6}}{6 b^{3}}+\frac{A \,x^{3}}{3 b^{3}}-\frac{B a \,x^{3}}{b^{4}}+\frac{A \,a^{3}}{6 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{B \,a^{4}}{6 \left(b \,x^{3}+a \right)^{2} b^{5}}-\frac{A \,a^{2}}{\left(b \,x^{3}+a \right) b^{4}}-\frac{A a \ln \left(b \,x^{3}+a \right)}{b^{4}}+\frac{4 B \,a^{3}}{3 \left(b \,x^{3}+a \right) b^{5}}+\frac{2 B \,a^{2} \ln \left(b \,x^{3}+a \right)}{b^{5}}"," ",0,"1/6*B*x^6/b^3+1/3/b^3*A*x^3-1/b^4*B*a*x^3+1/6*a^3/b^4/(b*x^3+a)^2*A-1/6*a^4/b^5/(b*x^3+a)^2*B-a/b^4*ln(b*x^3+a)*A+2*a^2/b^5*ln(b*x^3+a)*B-a^2/b^4/(b*x^3+a)*A+4/3*a^3/b^5/(b*x^3+a)*B","A"
89,1,110,80,0.048000," ","int(x^8*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{B \,x^{3}}{3 b^{3}}-\frac{A \,a^{2}}{6 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{B \,a^{3}}{6 \left(b \,x^{3}+a \right)^{2} b^{4}}+\frac{2 A a}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{A \ln \left(b \,x^{3}+a \right)}{3 b^{3}}-\frac{B \,a^{2}}{\left(b \,x^{3}+a \right) b^{4}}-\frac{B a \ln \left(b \,x^{3}+a \right)}{b^{4}}"," ",0,"1/3*B*x^3/b^3-1/6/b^3*a^2/(b*x^3+a)^2*A+1/6/b^4*a^3/(b*x^3+a)^2*B+1/3/b^3*ln(b*x^3+a)*A-1/b^4*ln(b*x^3+a)*B*a+2/3/b^3*a/(b*x^3+a)*A-1/b^4*a^2/(b*x^3+a)*B","A"
90,1,81,61,0.051000," ","int(x^5*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{A a}{6 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{B \,a^{2}}{6 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{A}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{2 B a}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{B \ln \left(b \,x^{3}+a \right)}{3 b^{3}}"," ",0,"1/6*a/b^2/(b*x^3+a)^2*A-1/6*a^2/b^3/(b*x^3+a)^2*B+1/3*B*ln(b*x^3+a)/b^3-1/3/b^2/(b*x^3+a)*A+2/3/b^3/(b*x^3+a)*B*a","A"
91,1,39,30,0.053000," ","int(x^2*(B*x^3+A)/(b*x^3+a)^3,x)","-\frac{B}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{A b -B a}{6 \left(b \,x^{3}+a \right)^{2} b^{2}}"," ",0,"-1/6*(A*b-B*a)/b^2/(b*x^3+a)^2-1/3*B/b^2/(b*x^3+a)","A"
92,1,68,62,0.059000," ","int((B*x^3+A)/x/(b*x^3+a)^3,x)","\frac{A}{6 \left(b \,x^{3}+a \right)^{2} a}-\frac{B}{6 \left(b \,x^{3}+a \right)^{2} b}+\frac{A}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{A \ln \left(x \right)}{a^{3}}-\frac{A \ln \left(b \,x^{3}+a \right)}{3 a^{3}}"," ",0,"1/6/a/(b*x^3+a)^2*A-1/6/b/(b*x^3+a)^2*B-1/3*A*ln(b*x^3+a)/a^3+1/3*A/a^2/(b*x^3+a)+A/a^3*ln(x)","A"
93,1,117,92,0.060000," ","int((B*x^3+A)/x^4/(b*x^3+a)^3,x)","-\frac{A b}{6 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{B}{6 \left(b \,x^{3}+a \right)^{2} a}-\frac{2 A b}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{3 A b \ln \left(x \right)}{a^{4}}+\frac{A b \ln \left(b \,x^{3}+a \right)}{a^{4}}+\frac{B}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{B \ln \left(x \right)}{a^{3}}-\frac{B \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{A}{3 a^{3} x^{3}}"," ",0,"-1/6/a^2*b/(b*x^3+a)^2*A+1/6/a/(b*x^3+a)^2*B+1/a^4*b*ln(b*x^3+a)*A-1/3/a^3*ln(b*x^3+a)*B-2/3/a^3*b/(b*x^3+a)*A+1/3/a^2/(b*x^3+a)*B-1/3*A/a^3/x^3-3*A/a^4*b*ln(x)+B/a^3*ln(x)","A"
94,1,147,114,0.058000," ","int((B*x^3+A)/x^7/(b*x^3+a)^3,x)","\frac{A \,b^{2}}{6 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{B b}{6 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{A \,b^{2}}{\left(b \,x^{3}+a \right) a^{4}}+\frac{6 A \,b^{2} \ln \left(x \right)}{a^{5}}-\frac{2 A \,b^{2} \ln \left(b \,x^{3}+a \right)}{a^{5}}-\frac{2 B b}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{3 B b \ln \left(x \right)}{a^{4}}+\frac{B b \ln \left(b \,x^{3}+a \right)}{a^{4}}+\frac{A b}{a^{4} x^{3}}-\frac{B}{3 a^{3} x^{3}}-\frac{A}{6 a^{3} x^{6}}"," ",0,"1/6/a^3*b^2/(b*x^3+a)^2*A-1/6/a^2*b/(b*x^3+a)^2*B-2/a^5*b^2*ln(b*x^3+a)*A+1/a^4*b*ln(b*x^3+a)*B+1/a^4*b^2/(b*x^3+a)*A-2/3/a^3*b/(b*x^3+a)*B-1/6*A/a^3/x^6+1/a^4/x^3*A*b-1/3/a^3/x^3*B+6*b^2/a^5*ln(x)*A-3*b/a^4*ln(x)*B","A"
95,1,308,199,0.061000," ","int(x^10*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{7 A a \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{10 B \,a^{2} x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{B \,x^{5}}{5 b^{3}}+\frac{11 A \,a^{2} x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{17 B \,a^{3} x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{4}}+\frac{A \,x^{2}}{2 b^{3}}-\frac{3 B a \,x^{2}}{2 b^{4}}-\frac{20 \sqrt{3}\, A a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{20 A a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{10 A a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{44 \sqrt{3}\, B \,a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{44 B \,a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{22 B \,a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}"," ",0,"1/5/b^3*B*x^5+1/2/b^3*A*x^2-3/2/b^4*B*x^2*a+7/9*a/b^2/(b*x^3+a)^2*A*x^5-10/9*a^2/b^3/(b*x^3+a)^2*B*x^5+11/18*a^2/b^3/(b*x^3+a)^2*A*x^2-17/18*a^3/b^4/(b*x^3+a)^2*B*x^2+20/27*a/b^4*A/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-10/27*a/b^4*A/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-20/27*a/b^4*A*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-44/27*a^2/b^5*B/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+22/27*a^2/b^5*B/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+44/27*a^2/b^5*B*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
96,1,299,197,0.056000," ","int(x^9*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{13 A a \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{19 B \,a^{2} x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{B \,x^{4}}{4 b^{3}}+\frac{5 A \,a^{2} x}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{8 B \,a^{3} x}{9 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{14 \sqrt{3}\, A a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{14 A a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 A a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{A x}{b^{3}}+\frac{35 \sqrt{3}\, B \,a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{35 B \,a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{35 B \,a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{3 B a x}{b^{4}}"," ",0,"1/4/b^3*B*x^4+1/b^3*A*x-3/b^4*B*a*x+13/18*a/b^2/(b*x^3+a)^2*A*x^4-19/18*a^2/b^3/(b*x^3+a)^2*B*x^4+5/9*a^2/b^3/(b*x^3+a)^2*A*x-8/9*a^3/b^4/(b*x^3+a)^2*B*x-14/27*a/b^4*A/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+7/27*a/b^4*A/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-14/27*a/b^4*A/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+35/27*a^2/b^5*B/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-35/54*a^2/b^5*B/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+35/27*a^2/b^5*B/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
97,1,275,177,0.062000," ","int(x^7*(B*x^3+A)/(b*x^3+a)^3,x)","-\frac{4 A \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b}+\frac{7 B a \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{5 A a \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{11 B \,a^{2} x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{B \,x^{2}}{2 b^{3}}+\frac{5 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{20 \sqrt{3}\, B a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{20 B a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{10 B a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}"," ",0,"1/2*B/b^3*x^2-4/9/b/(b*x^3+a)^2*A*x^5+7/9/b^2/(b*x^3+a)^2*B*x^5*a-5/18/b^2/(b*x^3+a)^2*A*x^2*a+11/18/b^3/(b*x^3+a)^2*B*x^2*a^2-5/27/b^3*A/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+5/54/b^3*A/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/b^3*A*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+20/27/b^4*B*a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-10/27/b^4*B*a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-20/27/b^4*B*a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
98,1,268,175,0.054000," ","int(x^6*(B*x^3+A)/(b*x^3+a)^3,x)","-\frac{7 A \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b}+\frac{13 B a \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{2 A a x}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{5 B \,a^{2} x}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{2 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{14 \sqrt{3}\, B a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{14 B a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 B a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{B x}{b^{3}}"," ",0,"B/b^3*x-7/18/b/(b*x^3+a)^2*A*x^4+13/18/b^2/(b*x^3+a)^2*B*x^4*a-2/9/b^2/(b*x^3+a)^2*a*A*x+5/9/b^3/(b*x^3+a)^2*a^2*B*x+2/27/b^3*A/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/27/b^3*A/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/27/b^3*A/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-14/27/b^4*B*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+7/27/b^4*B*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-14/27/b^4*B*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
99,1,241,158,0.052000," ","int(x^4*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{5 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{\frac{\left(A b -4 B a \right) x^{5}}{9 a b}-\frac{\left(A b +5 B a \right) x^{2}}{18 b^{2}}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(1/9*(A*b-4*B*a)/a/b*x^5-1/18*(A*b+5*B*a)/b^2*x^2)/(b*x^3+a)^2-1/27/b^2/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*A-5/27/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*B+1/54/b^2/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A+5/54/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B+1/27/b^2/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+5/27/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B","A"
100,1,239,156,0.049000," ","int(x^3*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{\frac{\left(A b -7 B a \right) x^{4}}{18 a b}-\frac{\left(A b +2 B a \right) x}{9 b^{2}}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(1/18*(A*b-7*B*a)/a/b*x^4-1/9*(A*b+2*B*a)/b^2*x)/(b*x^3+a)^2+1/27/b^2/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*A+2/27/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*B-1/54/b^2/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A-1/27/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B+1/27/b^2/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+2/27/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B","A"
101,1,251,158,0.053000," ","int(x*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{2 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{\frac{\left(2 A b +B a \right) x^{5}}{9 a^{2}}+\frac{\left(7 A b -B a \right) x^{2}}{18 a b}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(1/9*(2*A*b+B*a)/a^2*x^5+1/18*(7*A*b-B*a)/a/b*x^2)/(b*x^3+a)^2-2/27/a^2/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*A-1/27/a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*B+1/27/a^2/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A+1/54/a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B+2/27/a^2/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+1/27/a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B","A"
102,1,249,154,0.056000," ","int((B*x^3+A)/(b*x^3+a)^3,x)","\frac{5 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{\frac{\left(5 A b +B a \right) x^{4}}{18 a^{2}}+\frac{\left(4 A b -B a \right) x}{9 a b}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(1/18*(5*A*b+B*a)/a^2*x^4+1/9*(4*A*b-B*a)/a/b*x)/(b*x^3+a)^2+5/27/a^2/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*A+1/27/a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*B-5/54/a^2/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*A-1/54/a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*B+5/27/a^2/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*A+1/27/a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*B","A"
103,1,281,182,0.063000," ","int((B*x^3+A)/x^2/(b*x^3+a)^3,x)","-\frac{5 A \,b^{2} x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{2 B b \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{13 A b \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{7 B \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{14 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{2 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{A}{a^{3} x}"," ",0,"-5/9/a^3/(b*x^3+a)^2*A*x^5*b^2+2/9/a^2/(b*x^3+a)^2*B*x^5*b-13/18/a^2/(b*x^3+a)^2*A*x^2*b+7/18/a/(b*x^3+a)^2*B*x^2+14/27/a^3*A/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-7/27/a^3*A/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-14/27/a^3*A*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/27/a^2*B/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/27/a^2*B/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/27/a^2*B*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-A/a^3/x","A"
104,1,277,182,0.054000," ","int((B*x^3+A)/x^3/(b*x^3+a)^3,x)","-\frac{11 A \,b^{2} x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{5 B b \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{7 A b x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{4 B x}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{20 \sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{5 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{A}{2 a^{3} x^{2}}"," ",0,"-11/18/a^3/(b*x^3+a)^2*A*x^4*b^2+5/18/a^2/(b*x^3+a)^2*B*x^4*b-7/9/a^2/(b*x^3+a)^2*b*A*x+4/9/a/(b*x^3+a)^2*B*x-20/27/a^3*A/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+10/27/a^3*A/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-20/27/a^3*A/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+5/27/a^2*B/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-5/54/a^2*B/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/a^2*B/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/2*A/a^3/x^2","A"
105,1,299,199,0.056000," ","int((B*x^3+A)/x^5/(b*x^3+a)^3,x)","\frac{8 A \,b^{3} x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{4}}-\frac{5 B \,b^{2} x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{19 A \,b^{2} x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{13 B b \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{35 \sqrt{3}\, A b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{35 A b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{35 A b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{14 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{3 A b}{a^{4} x}-\frac{B}{a^{3} x}-\frac{A}{4 a^{3} x^{4}}"," ",0,"8/9/a^4*b^3/(b*x^3+a)^2*x^5*A-5/9/a^3*b^2/(b*x^3+a)^2*x^5*B+19/18/a^3*b^2/(b*x^3+a)^2*A*x^2-13/18/a^2*b/(b*x^3+a)^2*B*x^2-35/27/a^4*b*A/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+35/54/a^4*b*A/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+35/27/a^4*b*A*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+14/27/a^3*B/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-7/27/a^3*B/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-14/27/a^3*B*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/4/a^3*A/x^4+3/a^4/x*A*b-B/a^3/x","A"
106,1,295,199,0.062000," ","int((B*x^3+A)/x^6/(b*x^3+a)^3,x)","\frac{17 A \,b^{3} x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{4}}-\frac{11 B \,b^{2} x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{10 A \,b^{2} x}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{7 B b x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{44 \sqrt{3}\, A b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{44 A b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{22 A b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{20 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{3 A b}{2 a^{4} x^{2}}-\frac{B}{2 a^{3} x^{2}}-\frac{A}{5 a^{3} x^{5}}"," ",0,"17/18/a^4*b^3/(b*x^3+a)^2*A*x^4-11/18/a^3*b^2/(b*x^3+a)^2*B*x^4+10/9/a^3*b^2/(b*x^3+a)^2*A*x-7/9/a^2*b/(b*x^3+a)^2*B*x+44/27/a^4*b*A/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-22/27/a^4*b*A/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+44/27/a^4*b*A/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-20/27/a^3*B/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+10/27/a^3*B/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-20/27/a^3*B/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/5/a^3*A/x^5+3/2/a^4/x^2*A*b-1/2/a^3/x^2*B","A"
107,1,65,64,0.047000," ","int(x^8/(b*x^3+a)/(d*x^3+c),x)","-\frac{a^{2} \ln \left(b \,x^{3}+a \right)}{3 \left(a d -b c \right) b^{2}}+\frac{x^{3}}{3 b d}+\frac{c^{2} \ln \left(d \,x^{3}+c \right)}{3 \left(a d -b c \right) d^{2}}"," ",0,"1/3*x^3/b/d-1/3*a^2/b^2/(a*d-b*c)*ln(b*x^3+a)+1/3*c^2/d^2/(a*d-b*c)*ln(d*x^3+c)","A"
108,1,269,226,0.050000," ","int(x^7/(b*x^3+a)/(d*x^3+c),x)","-\frac{\sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{\sqrt{3}\, c^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} d^{2}}-\frac{c^{2} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} d^{2}}+\frac{c^{2} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} d^{2}}+\frac{x^{2}}{2 b d}"," ",0,"1/2*x^2/b/d+1/3*a^2/b^2/(a*d-b*c)/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-1/6*a^2/b^2/(a*d-b*c)/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*a^2/b^2/(a*d-b*c)*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*c^2/d^2/(a*d-b*c)/(c/d)^(1/3)*ln(x+(c/d)^(1/3))+1/6*c^2/d^2/(a*d-b*c)/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/3*c^2/d^2/(a*d-b*c)*3^(1/2)/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))","A"
109,1,266,223,0.052000," ","int(x^6/(b*x^3+a)/(d*x^3+c),x)","-\frac{\sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{\sqrt{3}\, c^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{c^{2} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}-\frac{c^{2} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{x}{b d}"," ",0,"x/b/d-1/3/b^2*a^2/(a*d-b*c)/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/6/b^2*a^2/(a*d-b*c)/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/b^2*a^2/(a*d-b*c)/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/d^2*c^2/(a*d-b*c)/(c/d)^(2/3)*ln(x+(c/d)^(1/3))-1/6/d^2*c^2/(a*d-b*c)/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/3/d^2*c^2/(a*d-b*c)/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))","A"
110,1,50,49,0.051000," ","int(x^5/(b*x^3+a)/(d*x^3+c),x)","\frac{a \ln \left(b \,x^{3}+a \right)}{3 \left(a d -b c \right) b}-\frac{c \ln \left(d \,x^{3}+c \right)}{3 \left(a d -b c \right) d}"," ",0,"1/3*a/(a*d-b*c)/b*ln(b*x^3+a)-1/3*c/(a*d-b*c)/d*ln(d*x^3+c)","A"
111,1,246,215,0.049000," ","int(x^4/(b*x^3+a)/(d*x^3+c),x)","\frac{\sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} d}+\frac{c \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} d}-\frac{c \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} d}"," ",0,"-1/3*a/(a*d-b*c)/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6*a/(a*d-b*c)/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*a/(a*d-b*c)*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*c/(a*d-b*c)/d/(c/d)^(1/3)*ln(x+(c/d)^(1/3))-1/6*c/(a*d-b*c)/d/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))-1/3*c/(a*d-b*c)*3^(1/2)/d/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))","A"
112,1,246,215,0.054000," ","int(x^3/(b*x^3+a)/(d*x^3+c),x)","\frac{\sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} d}-\frac{c \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} d}+\frac{c \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} d}"," ",0,"1/3*a/(a*d-b*c)/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/6*a/(a*d-b*c)/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*a/(a*d-b*c)/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*c/(a*d-b*c)/d/(c/d)^(2/3)*ln(x+(c/d)^(1/3))+1/6*c/(a*d-b*c)/d/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))-1/3*c/(a*d-b*c)/d/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))","A"
113,1,42,41,0.046000," ","int(x^2/(b*x^3+a)/(d*x^3+c),x)","-\frac{\ln \left(b \,x^{3}+a \right)}{3 \left(a d -b c \right)}+\frac{\ln \left(d \,x^{3}+c \right)}{3 a d -3 b c}"," ",0,"-1/3/(a*d-b*c)*ln(b*x^3+a)+1/3/(a*d-b*c)*ln(d*x^3+c)","A"
114,1,222,215,0.047000," ","int(x/(b*x^3+a)/(d*x^3+c),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}}}+\frac{\ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{\ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}}}-\frac{\ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{\ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}}}"," ",0,"1/3/(a*d-b*c)/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-1/6/(a*d-b*c)/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/(a*d-b*c)*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/(a*d-b*c)/(c/d)^(1/3)*ln(x+(c/d)^(1/3))+1/6/(a*d-b*c)/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/3/(a*d-b*c)*3^(1/2)/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))","A"
115,1,222,215,0.050000," ","int(1/(b*x^3+a)/(d*x^3+c),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}}}-\frac{\ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}}}+\frac{\ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"-1/3/(a*d-b*c)/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/6/(a*d-b*c)/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/(a*d-b*c)/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/(a*d-b*c)/(c/d)^(2/3)*ln(x+(c/d)^(1/3))-1/6/(a*d-b*c)/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/3/(a*d-b*c)/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))","A"
116,1,59,58,0.049000," ","int(1/x/(b*x^3+a)/(d*x^3+c),x)","\frac{b \ln \left(b \,x^{3}+a \right)}{3 \left(a d -b c \right) a}-\frac{d \ln \left(d \,x^{3}+c \right)}{3 \left(a d -b c \right) c}+\frac{\ln \left(x \right)}{a c}"," ",0,"1/3*b/a/(a*d-b*c)*ln(b*x^3+a)-1/3*d/c/(a*d-b*c)*ln(d*x^3+c)+ln(x)/a/c","A"
117,1,257,226,0.059000," ","int(1/x^2/(b*x^3+a)/(d*x^3+c),x)","\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} c}+\frac{d \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} c}-\frac{d \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} c}-\frac{1}{a c x}"," ",0,"-1/3*b/a/(a*d-b*c)/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6*b/a/(a*d-b*c)/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*b/a/(a*d-b*c)*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*d/c/(a*d-b*c)/(c/d)^(1/3)*ln(x+(c/d)^(1/3))-1/6*d/c/(a*d-b*c)/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))-1/3*d/c/(a*d-b*c)*3^(1/2)/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))-1/a/c/x","A"
118,1,257,226,0.052000," ","int(1/x^3/(b*x^3+a)/(d*x^3+c),x)","\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} c}-\frac{d \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} c}+\frac{d \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} c}-\frac{1}{2 a c \,x^{2}}"," ",0,"1/3/a*b/(a*d-b*c)/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/6/a*b/(a*d-b*c)/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/a*b/(a*d-b*c)/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/2/a/c/x^2-1/3/c*d/(a*d-b*c)/(c/d)^(2/3)*ln(x+(c/d)^(1/3))+1/6/c*d/(a*d-b*c)/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))-1/3/c*d/(a*d-b*c)/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))","A"
119,1,87,81,0.060000," ","int(1/x^4/(b*x^3+a)/(d*x^3+c),x)","-\frac{b^{2} \ln \left(b \,x^{3}+a \right)}{3 \left(a d -b c \right) a^{2}}+\frac{d^{2} \ln \left(d \,x^{3}+c \right)}{3 \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}{3 a c \,x^{3}}"," ",0,"-1/3*b^2/a^2/(a*d-b*c)*ln(b*x^3+a)+1/3*d^2/c^2/(a*d-b*c)*ln(d*x^3+c)-1/3/a/c/x^3-1/a/c^2*ln(x)*d-1/a^2/c*ln(x)*b","A"
120,1,291,243,0.052000," ","int(1/x^5/(b*x^3+a)/(d*x^3+c),x)","-\frac{\sqrt{3}\, b^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{b^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{b^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{\sqrt{3}\, d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} c^{2}}-\frac{d^{2} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} c^{2}}+\frac{d^{2} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} c^{2}}+\frac{d}{a \,c^{2} x}+\frac{b}{a^{2} c x}-\frac{1}{4 a c \,x^{4}}"," ",0,"1/3*b^2/a^2/(a*d-b*c)/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-1/6*b^2/a^2/(a*d-b*c)/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*b^2/a^2/(a*d-b*c)*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*d^2/c^2/(a*d-b*c)/(c/d)^(1/3)*ln(x+(c/d)^(1/3))+1/6*d^2/c^2/(a*d-b*c)/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/3*d^2/c^2/(a*d-b*c)*3^(1/2)/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))-1/4/a/c/x^4+1/a/c^2/x*d+1/a^2/c/x*b","A"
121,1,293,244,0.054000," ","int(1/x^6/(b*x^3+a)/(d*x^3+c),x)","-\frac{\sqrt{3}\, b^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{b^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{b^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{\sqrt{3}\, d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} c^{2}}+\frac{d^{2} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} c^{2}}-\frac{d^{2} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}} c^{2}}+\frac{d}{2 a \,c^{2} x^{2}}+\frac{b}{2 a^{2} c \,x^{2}}-\frac{1}{5 a c \,x^{5}}"," ",0,"-1/3/a^2*b^2/(a*d-b*c)/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/6/a^2*b^2/(a*d-b*c)/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/a^2*b^2/(a*d-b*c)/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/c^2*d^2/(a*d-b*c)/(c/d)^(2/3)*ln(x+(c/d)^(1/3))-1/6/c^2*d^2/(a*d-b*c)/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/3/c^2*d^2/(a*d-b*c)/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))-1/5/a/c/x^5+1/2/a/c^2/x^2*d+1/2/a^2/c/x^2*b","A"
122,1,124,111,0.056000," ","int(1/x^7/(b*x^3+a)/(d*x^3+c),x)","\frac{b^{3} \ln \left(b \,x^{3}+a \right)}{3 \left(a d -b c \right) a^{3}}-\frac{d^{3} \ln \left(d \,x^{3}+c \right)}{3 \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}{3 a \,c^{2} x^{3}}+\frac{b}{3 a^{2} c \,x^{3}}-\frac{1}{6 a c \,x^{6}}"," ",0,"1/3*b^3/a^3/(a*d-b*c)*ln(b*x^3+a)-1/3*d^3/c^3/(a*d-b*c)*ln(d*x^3+c)-1/6/a/c/x^6+1/3/a/c^2/x^3*d+1/3/a^2/c/x^3*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"
123,1,334,277,0.053000," ","int(1/x^8/(b*x^3+a)/(d*x^3+c),x)","\frac{\sqrt{3}\, b^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{b^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{b^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{\sqrt{3}\, d^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} c^{3}}+\frac{d^{3} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} c^{3}}-\frac{d^{3} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{3}} 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}{4 a \,c^{2} x^{4}}+\frac{b}{4 a^{2} c \,x^{4}}-\frac{1}{7 a c \,x^{7}}"," ",0,"-1/3*b^3/a^3/(a*d-b*c)/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6*b^3/a^3/(a*d-b*c)/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*b^3/a^3/(a*d-b*c)*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*d^3/c^3/(a*d-b*c)/(c/d)^(1/3)*ln(x+(c/d)^(1/3))-1/6*d^3/c^3/(a*d-b*c)/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))-1/3*d^3/c^3/(a*d-b*c)*3^(1/2)/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))-1/7/a/c/x^7+1/4/a/c^2/x^4*d+1/4/a^2/c/x^4*b-1/a/c^3/x*d^2-1/a^2/c^2/x*b*d-1/a^3/c/x*b^2","A"
124,1,1078,148,0.052000," ","int(x^m*(b*x^3+a)^5*(B*x^3+A),x)","\frac{\left(B \,b^{5} m^{6} x^{18}+51 B \,b^{5} m^{5} x^{18}+1005 B \,b^{5} m^{4} x^{18}+A \,b^{5} m^{6} x^{15}+5 B a \,b^{4} m^{6} x^{15}+9605 B \,b^{5} m^{3} x^{18}+54 A \,b^{5} m^{5} x^{15}+270 B a \,b^{4} m^{5} x^{15}+45474 B \,b^{5} m^{2} x^{18}+1110 A \,b^{5} m^{4} x^{15}+5550 B a \,b^{4} m^{4} x^{15}+95064 B \,b^{5} m \,x^{18}+5 A a \,b^{4} m^{6} x^{12}+10940 A \,b^{5} m^{3} x^{15}+10 B \,a^{2} b^{3} m^{6} x^{12}+54700 B a \,b^{4} m^{3} x^{15}+58240 b^{5} B \,x^{18}+285 A a \,b^{4} m^{5} x^{12}+52929 A \,b^{5} m^{2} x^{15}+570 B \,a^{2} b^{3} m^{5} x^{12}+264645 B a \,b^{4} m^{2} x^{15}+6165 A a \,b^{4} m^{4} x^{12}+112206 A \,b^{5} m \,x^{15}+12330 B \,a^{2} b^{3} m^{4} x^{12}+561030 B a \,b^{4} m \,x^{15}+10 A \,a^{2} b^{3} m^{6} x^{9}+63355 A a \,b^{4} m^{3} x^{12}+69160 A \,b^{5} x^{15}+10 B \,a^{3} b^{2} m^{6} x^{9}+126710 B \,a^{2} b^{3} m^{3} x^{12}+345800 B a \,b^{4} x^{15}+600 A \,a^{2} b^{3} m^{5} x^{9}+316230 A a \,b^{4} m^{2} x^{12}+600 B \,a^{3} b^{2} m^{5} x^{9}+632460 B \,a^{2} b^{3} m^{2} x^{12}+13740 A \,a^{2} b^{3} m^{4} x^{9}+684360 A a \,b^{4} m \,x^{12}+13740 B \,a^{3} b^{2} m^{4} x^{9}+1368720 B \,a^{2} b^{3} m \,x^{12}+10 A \,a^{3} b^{2} m^{6} x^{6}+149600 A \,a^{2} b^{3} m^{3} x^{9}+425600 A a \,b^{4} x^{12}+5 B \,a^{4} b \,m^{6} x^{6}+149600 B \,a^{3} b^{2} m^{3} x^{9}+851200 B \,a^{2} b^{3} x^{12}+630 A \,a^{3} b^{2} m^{5} x^{6}+783690 A \,a^{2} b^{3} m^{2} x^{9}+315 B \,a^{4} b \,m^{5} x^{6}+783690 B \,a^{3} b^{2} m^{2} x^{9}+15330 A \,a^{3} b^{2} m^{4} x^{6}+1753800 A \,a^{2} b^{3} m \,x^{9}+7665 B \,a^{4} b \,m^{4} x^{6}+1753800 B \,a^{3} b^{2} m \,x^{9}+5 A \,a^{4} b \,m^{6} x^{3}+179690 A \,a^{3} b^{2} m^{3} x^{6}+1106560 A \,a^{2} b^{3} x^{9}+B \,a^{5} m^{6} x^{3}+89845 B \,a^{4} b \,m^{3} x^{6}+1106560 B \,a^{3} b^{2} x^{9}+330 A \,a^{4} b \,m^{5} x^{3}+1021860 A \,a^{3} b^{2} m^{2} x^{6}+66 B \,a^{5} m^{5} x^{3}+510930 B \,a^{4} b \,m^{2} x^{6}+8550 A \,a^{4} b \,m^{4} x^{3}+2437680 A \,a^{3} b^{2} m \,x^{6}+1710 B \,a^{5} m^{4} x^{3}+1218840 B \,a^{4} b m \,x^{6}+A \,a^{5} m^{6}+109300 A \,a^{4} b \,m^{3} x^{3}+1580800 A \,a^{3} b^{2} x^{6}+21860 B \,a^{5} m^{3} x^{3}+790400 B \,a^{4} b \,x^{6}+69 A \,a^{5} m^{5}+702645 A \,a^{4} b \,m^{2} x^{3}+140529 B \,a^{5} m^{2} x^{3}+1905 A \,a^{5} m^{4}+1984770 A \,a^{4} b m \,x^{3}+396954 B \,a^{5} m \,x^{3}+26795 A \,a^{5} m^{3}+1383200 A \,a^{4} b \,x^{3}+276640 B \,a^{5} x^{3}+201174 A \,a^{5} m^{2}+757896 A \,a^{5} m +1106560 a^{5} A \right) x^{m +1}}{\left(m +1\right) \left(m +4\right) \left(m +7\right) \left(m +10\right) \left(m +13\right) \left(m +16\right) \left(m +19\right)}"," ",0,"x^(m+1)*(B*b^5*m^6*x^18+51*B*b^5*m^5*x^18+1005*B*b^5*m^4*x^18+A*b^5*m^6*x^15+5*B*a*b^4*m^6*x^15+9605*B*b^5*m^3*x^18+54*A*b^5*m^5*x^15+270*B*a*b^4*m^5*x^15+45474*B*b^5*m^2*x^18+1110*A*b^5*m^4*x^15+5550*B*a*b^4*m^4*x^15+95064*B*b^5*m*x^18+5*A*a*b^4*m^6*x^12+10940*A*b^5*m^3*x^15+10*B*a^2*b^3*m^6*x^12+54700*B*a*b^4*m^3*x^15+58240*B*b^5*x^18+285*A*a*b^4*m^5*x^12+52929*A*b^5*m^2*x^15+570*B*a^2*b^3*m^5*x^12+264645*B*a*b^4*m^2*x^15+6165*A*a*b^4*m^4*x^12+112206*A*b^5*m*x^15+12330*B*a^2*b^3*m^4*x^12+561030*B*a*b^4*m*x^15+10*A*a^2*b^3*m^6*x^9+63355*A*a*b^4*m^3*x^12+69160*A*b^5*x^15+10*B*a^3*b^2*m^6*x^9+126710*B*a^2*b^3*m^3*x^12+345800*B*a*b^4*x^15+600*A*a^2*b^3*m^5*x^9+316230*A*a*b^4*m^2*x^12+600*B*a^3*b^2*m^5*x^9+632460*B*a^2*b^3*m^2*x^12+13740*A*a^2*b^3*m^4*x^9+684360*A*a*b^4*m*x^12+13740*B*a^3*b^2*m^4*x^9+1368720*B*a^2*b^3*m*x^12+10*A*a^3*b^2*m^6*x^6+149600*A*a^2*b^3*m^3*x^9+425600*A*a*b^4*x^12+5*B*a^4*b*m^6*x^6+149600*B*a^3*b^2*m^3*x^9+851200*B*a^2*b^3*x^12+630*A*a^3*b^2*m^5*x^6+783690*A*a^2*b^3*m^2*x^9+315*B*a^4*b*m^5*x^6+783690*B*a^3*b^2*m^2*x^9+15330*A*a^3*b^2*m^4*x^6+1753800*A*a^2*b^3*m*x^9+7665*B*a^4*b*m^4*x^6+1753800*B*a^3*b^2*m*x^9+5*A*a^4*b*m^6*x^3+179690*A*a^3*b^2*m^3*x^6+1106560*A*a^2*b^3*x^9+B*a^5*m^6*x^3+89845*B*a^4*b*m^3*x^6+1106560*B*a^3*b^2*x^9+330*A*a^4*b*m^5*x^3+1021860*A*a^3*b^2*m^2*x^6+66*B*a^5*m^5*x^3+510930*B*a^4*b*m^2*x^6+8550*A*a^4*b*m^4*x^3+2437680*A*a^3*b^2*m*x^6+1710*B*a^5*m^4*x^3+1218840*B*a^4*b*m*x^6+A*a^5*m^6+109300*A*a^4*b*m^3*x^3+1580800*A*a^3*b^2*x^6+21860*B*a^5*m^3*x^3+790400*B*a^4*b*x^6+69*A*a^5*m^5+702645*A*a^4*b*m^2*x^3+140529*B*a^5*m^2*x^3+1905*A*a^5*m^4+1984770*A*a^4*b*m*x^3+396954*B*a^5*m*x^3+26795*A*a^5*m^3+1383200*A*a^4*b*x^3+276640*B*a^5*x^3+201174*A*a^5*m^2+757896*A*a^5*m+1106560*A*a^5)/(m+1)/(m+4)/(m+7)/(m+10)/(m+13)/(m+16)/(m+19)","B"
125,1,262,71,0.049000," ","int(x^m*(b*x^3+a)^2*(B*x^3+A),x)","\frac{\left(B \,b^{2} m^{3} x^{9}+12 B \,b^{2} m^{2} x^{9}+39 B \,b^{2} m \,x^{9}+A \,b^{2} m^{3} x^{6}+2 B a b \,m^{3} x^{6}+28 b^{2} B \,x^{9}+15 A \,b^{2} m^{2} x^{6}+30 B a b \,m^{2} x^{6}+54 A \,b^{2} m \,x^{6}+108 B a b m \,x^{6}+2 A a b \,m^{3} x^{3}+40 A \,b^{2} x^{6}+B \,a^{2} m^{3} x^{3}+80 B a b \,x^{6}+36 A a b \,m^{2} x^{3}+18 B \,a^{2} m^{2} x^{3}+174 A a b m \,x^{3}+87 B \,a^{2} m \,x^{3}+A \,a^{2} m^{3}+140 A a b \,x^{3}+70 B \,a^{2} x^{3}+21 A \,a^{2} m^{2}+138 A \,a^{2} m +280 a^{2} A \right) x^{m +1}}{\left(m +10\right) \left(m +7\right) \left(m +4\right) \left(m +1\right)}"," ",0,"x^(m+1)*(B*b^2*m^3*x^9+12*B*b^2*m^2*x^9+39*B*b^2*m*x^9+A*b^2*m^3*x^6+2*B*a*b*m^3*x^6+28*B*b^2*x^9+15*A*b^2*m^2*x^6+30*B*a*b*m^2*x^6+54*A*b^2*m*x^6+108*B*a*b*m*x^6+2*A*a*b*m^3*x^3+40*A*b^2*x^6+B*a^2*m^3*x^3+80*B*a*b*x^6+36*A*a*b*m^2*x^3+18*B*a^2*m^2*x^3+174*A*a*b*m*x^3+87*B*a^2*m*x^3+A*a^2*m^3+140*A*a*b*x^3+70*B*a^2*x^3+21*A*a^2*m^2+138*A*a^2*m+280*A*a^2)/(m+10)/(m+7)/(m+4)/(m+1)","B"
126,1,110,45,0.043000," ","int(x^m*(b*x^3+a)*(B*x^3+A),x)","\frac{\left(B b \,m^{2} x^{6}+5 B b m \,x^{6}+4 B b \,x^{6}+A b \,m^{2} x^{3}+B a \,m^{2} x^{3}+8 A b m \,x^{3}+8 B a m \,x^{3}+7 A b \,x^{3}+7 B a \,x^{3}+A a \,m^{2}+11 A a m +28 A a \right) x^{m +1}}{\left(m +7\right) \left(m +4\right) \left(m +1\right)}"," ",0,"x^(m+1)*(B*b*m^2*x^6+5*B*b*m*x^6+4*B*b*x^6+A*b*m^2*x^3+B*a*m^2*x^3+8*A*b*m*x^3+8*B*a*m*x^3+7*A*b*x^3+7*B*a*x^3+A*a*m^2+11*A*a*m+28*A*a)/(m+7)/(m+4)/(m+1)","B"
127,0,0,64,0.427000," ","int(x^m*(B*x^3+A)/(b*x^3+a),x)","\int \frac{\left(B \,x^{3}+A \right) x^{m}}{b \,x^{3}+a}\, dx"," ",0,"int(x^m*(B*x^3+A)/(b*x^3+a),x)","F"
128,0,0,87,0.416000," ","int(x^m*(B*x^3+A)/(b*x^3+a)^2,x)","\int \frac{\left(B \,x^{3}+A \right) x^{m}}{\left(b \,x^{3}+a \right)^{2}}\, dx"," ",0,"int(x^m*(B*x^3+A)/(b*x^3+a)^2,x)","F"
129,0,0,87,0.426000," ","int(x^m*(B*x^3+A)/(b*x^3+a)^3,x)","\int \frac{\left(B \,x^{3}+A \right) x^{m}}{\left(b \,x^{3}+a \right)^{3}}\, dx"," ",0,"int(x^m*(B*x^3+A)/(b*x^3+a)^3,x)","F"
130,0,0,108,0.616000," ","int((e*x)^m/(b*x^3+a)/(d*x^3+c),x)","\int \frac{\left(e x \right)^{m}}{\left(b \,x^{3}+a \right) \left(d \,x^{3}+c \right)}\, dx"," ",0,"int((e*x)^m/(b*x^3+a)/(d*x^3+c),x)","F"
131,1,32,27,0.046000," ","int(x^(7/2)*(b*x^3+a)*(B*x^3+A),x)","\frac{2 \left(15 B b \,x^{6}+21 A b \,x^{3}+21 B a \,x^{3}+35 A a \right) x^{\frac{9}{2}}}{315}"," ",0,"2/315*x^(9/2)*(15*B*b*x^6+21*A*b*x^3+21*B*a*x^3+35*A*a)","A"
132,1,32,27,0.045000," ","int(x^(5/2)*(b*x^3+a)*(B*x^3+A),x)","\frac{2 \left(91 B b \,x^{6}+133 A b \,x^{3}+133 B a \,x^{3}+247 A a \right) x^{\frac{7}{2}}}{1729}"," ",0,"2/1729*x^(7/2)*(91*B*b*x^6+133*A*b*x^3+133*B*a*x^3+247*A*a)","A"
133,1,32,27,0.046000," ","int(x^(3/2)*(b*x^3+a)*(B*x^3+A),x)","\frac{2 \left(55 B b \,x^{6}+85 A b \,x^{3}+85 B a \,x^{3}+187 A a \right) x^{\frac{5}{2}}}{935}"," ",0,"2/935*x^(5/2)*(55*B*b*x^6+85*A*b*x^3+85*B*a*x^3+187*A*a)","A"
134,1,32,27,0.045000," ","int((b*x^3+a)*(B*x^3+A)*x^(1/2),x)","\frac{2 \left(3 B b \,x^{6}+5 A b \,x^{3}+5 B a \,x^{3}+15 A a \right) x^{\frac{3}{2}}}{45}"," ",0,"2/45*x^(3/2)*(3*B*b*x^6+5*A*b*x^3+5*B*a*x^3+15*A*a)","A"
135,1,32,27,0.045000," ","int((b*x^3+a)*(B*x^3+A)/x^(1/2),x)","\frac{2 \left(7 B b \,x^{6}+13 A b \,x^{3}+13 B a \,x^{3}+91 A a \right) \sqrt{x}}{91}"," ",0,"2/91*x^(1/2)*(7*B*b*x^6+13*A*b*x^3+13*B*a*x^3+91*A*a)","A"
136,1,32,27,0.044000," ","int((b*x^3+a)*(B*x^3+A)/x^(3/2),x)","-\frac{2 \left(-5 B b \,x^{6}-11 A b \,x^{3}-11 B a \,x^{3}+55 A a \right)}{55 \sqrt{x}}"," ",0,"-2/55*(-5*B*b*x^6-11*A*b*x^3-11*B*a*x^3+55*A*a)/x^(1/2)","A"
137,1,32,27,0.042000," ","int((b*x^3+a)*(B*x^3+A)/x^(5/2),x)","-\frac{2 \left(-B b \,x^{6}-3 A b \,x^{3}-3 B a \,x^{3}+3 A a \right)}{9 x^{\frac{3}{2}}}"," ",0,"-2/9*(-B*b*x^6-3*A*b*x^3-3*B*a*x^3+3*A*a)/x^(3/2)","A"
138,1,32,27,0.041000," ","int((b*x^3+a)*(B*x^3+A)/x^(7/2),x)","-\frac{2 \left(-5 B b \,x^{6}-35 A b \,x^{3}-35 B a \,x^{3}+7 A a \right)}{35 x^{\frac{5}{2}}}"," ",0,"-2/35*(-5*B*b*x^6-35*A*b*x^3-35*B*a*x^3+7*A*a)/x^(5/2)","A"
139,1,56,47,0.049000," ","int(x^(7/2)*(b*x^3+a)^2*(B*x^3+A),x)","\frac{2 \left(35 b^{2} B \,x^{9}+45 A \,b^{2} x^{6}+90 B a b \,x^{6}+126 A a b \,x^{3}+63 B \,a^{2} x^{3}+105 a^{2} A \right) x^{\frac{9}{2}}}{945}"," ",0,"2/945*x^(9/2)*(35*B*b^2*x^9+45*A*b^2*x^6+90*B*a*b*x^6+126*A*a*b*x^3+63*B*a^2*x^3+105*A*a^2)","A"
140,1,56,47,0.043000," ","int(x^(5/2)*(b*x^3+a)^2*(B*x^3+A),x)","\frac{2 \left(1729 b^{2} B \,x^{9}+2275 A \,b^{2} x^{6}+4550 B a b \,x^{6}+6650 A a b \,x^{3}+3325 B \,a^{2} x^{3}+6175 a^{2} A \right) x^{\frac{7}{2}}}{43225}"," ",0,"2/43225*x^(7/2)*(1729*B*b^2*x^9+2275*A*b^2*x^6+4550*B*a*b*x^6+6650*A*a*b*x^3+3325*B*a^2*x^3+6175*A*a^2)","A"
141,1,56,47,0.045000," ","int(x^(3/2)*(b*x^3+a)^2*(B*x^3+A),x)","\frac{2 \left(935 b^{2} B \,x^{9}+1265 A \,b^{2} x^{6}+2530 B a b \,x^{6}+3910 A a b \,x^{3}+1955 B \,a^{2} x^{3}+4301 a^{2} A \right) x^{\frac{5}{2}}}{21505}"," ",0,"2/21505*x^(5/2)*(935*B*b^2*x^9+1265*A*b^2*x^6+2530*B*a*b*x^6+3910*A*a*b*x^3+1955*B*a^2*x^3+4301*A*a^2)","A"
142,1,56,47,0.043000," ","int((b*x^3+a)^2*(B*x^3+A)*x^(1/2),x)","\frac{2 \left(15 b^{2} B \,x^{9}+21 A \,b^{2} x^{6}+42 B a b \,x^{6}+70 A a b \,x^{3}+35 B \,a^{2} x^{3}+105 a^{2} A \right) x^{\frac{3}{2}}}{315}"," ",0,"2/315*x^(3/2)*(15*B*b^2*x^9+21*A*b^2*x^6+42*B*a*b*x^6+70*A*a*b*x^3+35*B*a^2*x^3+105*A*a^2)","A"
143,1,56,47,0.046000," ","int((b*x^3+a)^2*(B*x^3+A)/x^(1/2),x)","\frac{2 \left(91 b^{2} B \,x^{9}+133 A \,b^{2} x^{6}+266 B a b \,x^{6}+494 A a b \,x^{3}+247 B \,a^{2} x^{3}+1729 a^{2} A \right) \sqrt{x}}{1729}"," ",0,"2/1729*x^(1/2)*(91*B*b^2*x^9+133*A*b^2*x^6+266*B*a*b*x^6+494*A*a*b*x^3+247*B*a^2*x^3+1729*A*a^2)","A"
144,1,56,47,0.049000," ","int((b*x^3+a)^2*(B*x^3+A)/x^(3/2),x)","-\frac{2 \left(-55 b^{2} B \,x^{9}-85 A \,b^{2} x^{6}-170 B a b \,x^{6}-374 A a b \,x^{3}-187 B \,a^{2} x^{3}+935 a^{2} A \right)}{935 \sqrt{x}}"," ",0,"-2/935*(-55*B*b^2*x^9-85*A*b^2*x^6-170*B*a*b*x^6-374*A*a*b*x^3-187*B*a^2*x^3+935*A*a^2)/x^(1/2)","A"
145,1,56,47,0.054000," ","int((b*x^3+a)^2*(B*x^3+A)/x^(5/2),x)","-\frac{2 \left(-3 b^{2} B \,x^{9}-5 A \,b^{2} x^{6}-10 B a b \,x^{6}-30 A a b \,x^{3}-15 B \,a^{2} x^{3}+15 a^{2} A \right)}{45 x^{\frac{3}{2}}}"," ",0,"-2/45*(-3*B*b^2*x^9-5*A*b^2*x^6-10*B*a*b*x^6-30*A*a*b*x^3-15*B*a^2*x^3+15*A*a^2)/x^(3/2)","A"
146,1,56,47,0.047000," ","int((b*x^3+a)^2*(B*x^3+A)/x^(7/2),x)","-\frac{2 \left(-35 b^{2} B \,x^{9}-65 A \,b^{2} x^{6}-130 B a b \,x^{6}-910 A a b \,x^{3}-455 B \,a^{2} x^{3}+91 a^{2} A \right)}{455 x^{\frac{5}{2}}}"," ",0,"-2/455*(-35*B*b^2*x^9-65*A*b^2*x^6-130*B*a*b*x^6-910*A*a*b*x^3-455*B*a^2*x^3+91*A*a^2)/x^(5/2)","A"
147,1,80,65,0.043000," ","int(x^(7/2)*(b*x^3+a)^3*(B*x^3+A),x)","\frac{2 \left(315 B \,b^{3} x^{12}+385 x^{9} A \,b^{3}+1155 x^{9} B a \,b^{2}+1485 x^{6} A a \,b^{2}+1485 x^{6} B \,a^{2} b +2079 x^{3} A \,a^{2} b +693 B \,a^{3} x^{3}+1155 A \,a^{3}\right) x^{\frac{9}{2}}}{10395}"," ",0,"2/10395*x^(9/2)*(315*B*b^3*x^12+385*A*b^3*x^9+1155*B*a*b^2*x^9+1485*A*a*b^2*x^6+1485*B*a^2*b*x^6+2079*A*a^2*b*x^3+693*B*a^3*x^3+1155*A*a^3)","A"
148,1,80,65,0.043000," ","int(x^(5/2)*(b*x^3+a)^3*(B*x^3+A),x)","\frac{2 \left(43225 B \,b^{3} x^{12}+53599 x^{9} A \,b^{3}+160797 x^{9} B a \,b^{2}+211575 x^{6} A a \,b^{2}+211575 x^{6} B \,a^{2} b +309225 x^{3} A \,a^{2} b +103075 B \,a^{3} x^{3}+191425 A \,a^{3}\right) x^{\frac{7}{2}}}{1339975}"," ",0,"2/1339975*x^(7/2)*(43225*B*b^3*x^12+53599*A*b^3*x^9+160797*B*a*b^2*x^9+211575*A*a*b^2*x^6+211575*B*a^2*b*x^6+309225*A*a^2*b*x^3+103075*B*a^3*x^3+191425*A*a^3)","A"
149,1,80,65,0.049000," ","int(x^(3/2)*(b*x^3+a)^3*(B*x^3+A),x)","\frac{2 \left(21505 B \,b^{3} x^{12}+27115 x^{9} A \,b^{3}+81345 x^{9} B a \,b^{2}+110055 x^{6} A a \,b^{2}+110055 x^{6} B \,a^{2} b +170085 x^{3} A \,a^{2} b +56695 B \,a^{3} x^{3}+124729 A \,a^{3}\right) x^{\frac{5}{2}}}{623645}"," ",0,"2/623645*x^(5/2)*(21505*B*b^3*x^12+27115*A*b^3*x^9+81345*B*a*b^2*x^9+110055*A*a*b^2*x^6+110055*B*a^2*b*x^6+170085*A*a^2*b*x^3+56695*B*a^3*x^3+124729*A*a^3)","A"
150,1,80,65,0.046000," ","int((b*x^3+a)^3*(B*x^3+A)*x^(1/2),x)","\frac{2 \left(35 B \,b^{3} x^{12}+45 x^{9} A \,b^{3}+135 x^{9} B a \,b^{2}+189 x^{6} A a \,b^{2}+189 x^{6} B \,a^{2} b +315 x^{3} A \,a^{2} b +105 B \,a^{3} x^{3}+315 A \,a^{3}\right) x^{\frac{3}{2}}}{945}"," ",0,"2/945*x^(3/2)*(35*B*b^3*x^12+45*A*b^3*x^9+135*B*a*b^2*x^9+189*A*a*b^2*x^6+189*B*a^2*b*x^6+315*A*a^2*b*x^3+105*B*a^3*x^3+315*A*a^3)","A"
151,1,80,65,0.041000," ","int((b*x^3+a)^3*(B*x^3+A)/x^(1/2),x)","\frac{2 \left(1729 B \,b^{3} x^{12}+2275 x^{9} A \,b^{3}+6825 x^{9} B a \,b^{2}+9975 x^{6} A a \,b^{2}+9975 x^{6} B \,a^{2} b +18525 x^{3} A \,a^{2} b +6175 B \,a^{3} x^{3}+43225 A \,a^{3}\right) \sqrt{x}}{43225}"," ",0,"2/43225*x^(1/2)*(1729*B*b^3*x^12+2275*A*b^3*x^9+6825*B*a*b^2*x^9+9975*A*a*b^2*x^6+9975*B*a^2*b*x^6+18525*A*a^2*b*x^3+6175*B*a^3*x^3+43225*A*a^3)","A"
152,1,80,65,0.045000," ","int((b*x^3+a)^3*(B*x^3+A)/x^(3/2),x)","-\frac{2 \left(-935 B \,b^{3} x^{12}-1265 x^{9} A \,b^{3}-3795 x^{9} B a \,b^{2}-5865 x^{6} A a \,b^{2}-5865 x^{6} B \,a^{2} b -12903 x^{3} A \,a^{2} b -4301 B \,a^{3} x^{3}+21505 A \,a^{3}\right)}{21505 \sqrt{x}}"," ",0,"-2/21505*(-935*B*b^3*x^12-1265*A*b^3*x^9-3795*B*a*b^2*x^9-5865*A*a*b^2*x^6-5865*B*a^2*b*x^6-12903*A*a^2*b*x^3-4301*B*a^3*x^3+21505*A*a^3)/x^(1/2)","A"
153,1,80,65,0.043000," ","int((b*x^3+a)^3*(B*x^3+A)/x^(5/2),x)","-\frac{2 \left(-5 B \,b^{3} x^{12}-7 x^{9} A \,b^{3}-21 x^{9} B a \,b^{2}-35 x^{6} A a \,b^{2}-35 x^{6} B \,a^{2} b -105 x^{3} A \,a^{2} b -35 B \,a^{3} x^{3}+35 A \,a^{3}\right)}{105 x^{\frac{3}{2}}}"," ",0,"-2/105*(-5*B*b^3*x^12-7*A*b^3*x^9-21*B*a*b^2*x^9-35*A*a*b^2*x^6-35*B*a^2*b*x^6-105*A*a^2*b*x^3-35*B*a^3*x^3+35*A*a^3)/x^(3/2)","A"
154,1,80,65,0.041000," ","int((b*x^3+a)^3*(B*x^3+A)/x^(7/2),x)","-\frac{2 \left(-455 B \,b^{3} x^{12}-665 x^{9} A \,b^{3}-1995 x^{9} B a \,b^{2}-3705 x^{6} A a \,b^{2}-3705 x^{6} B \,a^{2} b -25935 x^{3} A \,a^{2} b -8645 B \,a^{3} x^{3}+1729 A \,a^{3}\right)}{8645 x^{\frac{5}{2}}}"," ",0,"-2/8645*(-455*B*b^3*x^12-665*A*b^3*x^9-1995*B*a*b^2*x^9-3705*A*a*b^2*x^6-3705*B*a^2*b*x^6-25935*A*a^2*b*x^3-8645*B*a^3*x^3+1729*A*a^3)/x^(5/2)","A"
155,1,78,53,0.047000," ","int(x^(7/2)*(B*x^3+A)/(b*x^3+a),x)","\frac{2 B \,x^{\frac{9}{2}}}{9 b}-\frac{2 A a \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}\, b}+\frac{2 B \,a^{2} \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}\, b^{2}}+\frac{2 A \,x^{\frac{3}{2}}}{3 b}-\frac{2 B a \,x^{\frac{3}{2}}}{3 b^{2}}"," ",0,"2/9*B*x^(9/2)/b+2/3/b*A*x^(3/2)-2/3/b^2*B*a*x^(3/2)-2/3*a/b/(a*b)^(1/2)*arctan(x^(3/2)*b/(a*b)^(1/2))*A+2/3*a^2/b^2/(a*b)^(1/2)*arctan(x^(3/2)*b/(a*b)^(1/2))*B","A"
156,1,377,204,0.178000," ","int(x^(5/2)*(B*x^3+A)/(b*x^3+a),x)","\frac{2 B \,x^{\frac{7}{2}}}{7 b}-\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 b}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 b}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 b}+\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{6}} B a \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} B a \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} B a \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 b^{2}}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B a \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 b^{2}}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B a \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 b^{2}}+\frac{2 A \sqrt{x}}{b}-\frac{2 B a \sqrt{x}}{b^{2}}"," ",0,"2/7*B*x^(7/2)/b+2/b*A*x^(1/2)-2/b^2*B*a*x^(1/2)-2/3/b*(a/b)^(1/6)*arctan(x^(1/2)/(a/b)^(1/6))*A+2/3*a/b^2*(a/b)^(1/6)*arctan(x^(1/2)/(a/b)^(1/6))*B+1/6/b*3^(1/2)*(a/b)^(1/6)*ln(3^(1/2)*(a/b)^(1/6)*x^(1/2)-x-(a/b)^(1/3))*A-1/6*a/b^2*3^(1/2)*(a/b)^(1/6)*ln(3^(1/2)*(a/b)^(1/6)*x^(1/2)-x-(a/b)^(1/3))*B-1/3/b*(a/b)^(1/6)*arctan(-3^(1/2)+2*x^(1/2)/(a/b)^(1/6))*A+1/3*a/b^2*(a/b)^(1/6)*arctan(-3^(1/2)+2*x^(1/2)/(a/b)^(1/6))*B-1/6/b*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A+1/6*a/b^2*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B-1/3/b*(a/b)^(1/6)*arctan(2*x^(1/2)/(a/b)^(1/6)+3^(1/2))*A+1/3*a/b^2*(a/b)^(1/6)*arctan(2*x^(1/2)/(a/b)^(1/6)+3^(1/2))*B","A"
157,1,356,188,0.164000," ","int(x^(3/2)*(B*x^3+A)/(b*x^3+a),x)","\frac{2 B \,x^{\frac{5}{2}}}{5 b}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a}+\frac{2 A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} b}+\frac{A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} b}+\frac{A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} b}-\frac{2 B a \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} b^{2}}-\frac{B a \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} b^{2}}-\frac{B a \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} b^{2}}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 b}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 b}"," ",0,"2/5*B*x^(5/2)/b+2/3/b/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*A-2/3/b^2/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*B*a+1/6/a*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*A-1/6/b*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*B+1/3/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*A-1/3/b^2/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*B*a-1/6/a*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A+1/6/b*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B+1/3/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*A-1/3/b^2/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*B*a","A"
158,1,53,37,0.054000," ","int((B*x^3+A)*x^(1/2)/(b*x^3+a),x)","\frac{2 A \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}}-\frac{2 B a \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}\, b}+\frac{2 B \,x^{\frac{3}{2}}}{3 b}"," ",0,"2/3*B*x^(3/2)/b+2/3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*A-2/3/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*B*a","A"
159,1,353,188,0.151000," ","int((B*x^3+A)/(b*x^3+a)/x^(1/2),x)","\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 a}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a}-\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 b}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 b}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 b}+\frac{2 B \sqrt{x}}{b}"," ",0,"2*B*x^(1/2)/b+2/3/a*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*A-2/3/b*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*B-1/6/a*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*A+1/6/b*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*B+1/3/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*A-1/3/b*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*B+1/6/a*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A-1/6/b*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B+1/3/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*A-1/3/b*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*B","A"
160,1,355,188,0.157000," ","int((B*x^3+A)/x^(3/2)/(b*x^3+a),x)","-\frac{2 A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} a}-\frac{A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} a}-\frac{A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} a}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A b \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a^{2}}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A b \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a^{2}}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a}+\frac{2 B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} b}+\frac{B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} b}+\frac{B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{6}} b}-\frac{2 A}{a \sqrt{x}}"," ",0,"-2/3/a/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*A+2/3/b/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*B-1/6/a^2*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*A*b+1/6/a*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*B-1/3/a/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*A+1/3/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*B+1/6/a^2*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A*b-1/6/a*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B-1/3/a/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*A+1/3/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*B-2*A/a/x^(1/2)","A"
161,1,53,37,0.056000," ","int((B*x^3+A)/x^(5/2)/(b*x^3+a),x)","-\frac{2 A b \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}\, a}+\frac{2 B \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}}-\frac{2 A}{3 a \,x^{\frac{3}{2}}}"," ",0,"-2/3*A/a/x^(3/2)-2/3/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*A*b+2/3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*B","A"
162,1,358,188,0.175000," ","int((B*x^3+A)/x^(7/2)/(b*x^3+a),x)","-\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 a^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} A b \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 a^{2}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} A b \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 a^{2}}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a^{2}}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a^{2}}+\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{3 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{3 a}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 a}-\frac{2 A}{5 a \,x^{\frac{5}{2}}}"," ",0,"-2/5*A/a/x^(5/2)-2/3/a^2*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*A*b+2/3/a*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*B+1/6/a^2*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*A*b-1/6/a*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*B-1/3/a^2*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*A*b+1/3/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*B-1/6/a^2*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A*b+1/6/a*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B-1/3/a^2*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*A*b+1/3/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*B","A"
163,1,93,75,0.064000," ","int(x^(7/2)*(B*x^3+A)/(b*x^3+a)^2,x)","-\frac{A \,x^{\frac{3}{2}}}{3 \left(b \,x^{3}+a \right) b}+\frac{B a \,x^{\frac{3}{2}}}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{A \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}\, b}-\frac{B a \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}+\frac{2 B \,x^{\frac{3}{2}}}{3 b^{2}}"," ",0,"2/3*B*x^(3/2)/b^2-1/3/b*x^(3/2)/(b*x^3+a)*A+1/3/b^2*x^(3/2)/(b*x^3+a)*B*a+1/3/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*A-1/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*B*a","A"
164,1,405,226,0.166000," ","int(x^(5/2)*(B*x^3+A)/(b*x^3+a)^2,x)","-\frac{A \sqrt{x}}{3 \left(b \,x^{3}+a \right) b}+\frac{B a \sqrt{x}}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 a b}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a b}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a b}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 b^{2}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 b^{2}}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 b^{2}}-\frac{7 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 b^{2}}+\frac{7 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 b^{2}}+\frac{2 B \sqrt{x}}{b^{2}}"," ",0,"2*B/b^2*x^(1/2)-1/3/b*x^(1/2)/(b*x^3+a)*A+1/3/b^2*x^(1/2)/(b*x^3+a)*B*a-7/9/b^2*B*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))+7/36/b^2*B*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))-7/18/b^2*B*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))-7/36/b^2*B*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))-7/18/b^2*B*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))+1/9/b*A/a*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))-1/36/b*A/a*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))+1/18/b*A/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))+1/36/b*A/a*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))+1/18/b*A/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))","A"
165,1,387,207,0.164000," ","int(x^(3/2)*(B*x^3+A)/(b*x^3+a)^2,x)","\frac{\left(A b -B a \right) x^{\frac{5}{2}}}{3 \left(b \,x^{3}+a \right) a b}+\frac{A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{6}} a b}+\frac{A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{6}} a b}+\frac{A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{6}} a b}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{2}}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{2}}-\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a b}+\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a b}+\frac{5 B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{6}} b^{2}}+\frac{5 B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{6}} b^{2}}+\frac{5 B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{6}} b^{2}}"," ",0,"1/3*(A*b-B*a)*x^(5/2)/a/b/(b*x^3+a)+1/9/b/a/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*A+5/9/b^2/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*B+1/36/a^2*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*A+5/36/b/a*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*B+1/18/b/a/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*A+5/18/b^2/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*B-1/36/a^2*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A-5/36/b/a*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B+1/18/b/a/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*A+5/18/b^2/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*B","A"
166,1,74,55,0.056000," ","int((B*x^3+A)*x^(1/2)/(b*x^3+a)^2,x)","\frac{A \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}\, a}+\frac{B \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}\, b}+\frac{\left(A b -B a \right) x^{\frac{3}{2}}}{3 \left(b \,x^{3}+a \right) a b}"," ",0,"1/3*(A*b-B*a)*x^(3/2)/a/b/(b*x^3+a)+1/3/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*A+1/3/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*B","A"
167,1,387,207,0.163000," ","int((B*x^3+A)/(b*x^3+a)^2/x^(1/2),x)","\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 a^{2}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 a^{2}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 a^{2}}+\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{2}}-\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 a b}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a b}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a b}+\frac{\left(A b -B a \right) \sqrt{x}}{3 \left(b \,x^{3}+a \right) a b}"," ",0,"1/3*(A*b-B*a)*x^(1/2)/a/b/(b*x^3+a)+5/9/a^2*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*A+1/9/b/a*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*B-5/36/a^2*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*A-1/36/b/a*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*B+5/18/a^2*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*A+1/18/b/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*B+5/36/a^2*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A+1/36/b/a*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B+5/18/a^2*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*A+1/18/b/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*B","A"
168,1,401,231,0.162000," ","int((B*x^3+A)/x^(3/2)/(b*x^3+a)^2,x)","-\frac{A b \,x^{\frac{5}{2}}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{B \,x^{\frac{5}{2}}}{3 \left(b \,x^{3}+a \right) a}-\frac{7 A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{2}}-\frac{7 A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{2}}-\frac{7 A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{2}}+\frac{7 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A b \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{3}}-\frac{7 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A b \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{3}}+\frac{B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{6}} a b}+\frac{B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{6}} a b}+\frac{B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{6}} a b}-\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{2}}+\frac{\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{2}}-\frac{2 A}{a^{2} \sqrt{x}}"," ",0,"-1/3/a^2*x^(5/2)/(b*x^3+a)*A*b+1/3/a*x^(5/2)/(b*x^3+a)*B-7/9/a^2*A/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))-7/36/a^3*A*b*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))-7/18/a^2*A/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))+7/36/a^3*A*b*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))-7/18/a^2*A/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))+1/9/a*B/b/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))+1/36/a^2*B*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))+1/18/a*B/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))-1/36/a^2*B*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))+1/18/a*B/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))-2*A/a^2/x^(1/2)","A"
169,1,93,76,0.066000," ","int((B*x^3+A)/x^(5/2)/(b*x^3+a)^2,x)","-\frac{A b \,x^{\frac{3}{2}}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{B \,x^{\frac{3}{2}}}{3 \left(b \,x^{3}+a \right) a}-\frac{A b \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{2}}+\frac{B \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{3 \sqrt{a b}\, a}-\frac{2 A}{3 a^{2} x^{\frac{3}{2}}}"," ",0,"-1/3/a^2*x^(3/2)/(b*x^3+a)*A*b+1/3/a*x^(3/2)/(b*x^3+a)*B-1/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*A*b+1/3/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*B-2/3*A/a^2/x^(3/2)","A"
170,1,395,232,0.159000," ","int((B*x^3+A)/x^(7/2)/(b*x^3+a)^2,x)","-\frac{A b \sqrt{x}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{B \sqrt{x}}{3 \left(b \,x^{3}+a \right) a}-\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 a^{3}}-\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 a^{3}}-\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 a^{3}}-\frac{11 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{3}}+\frac{11 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{3}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{9 a^{2}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{18 a^{2}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{18 a^{2}}+\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{2}}-\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{36 a^{2}}-\frac{2 A}{5 a^{2} x^{\frac{5}{2}}}"," ",0,"-1/3/a^2*x^(1/2)/(b*x^3+a)*A*b+1/3/a*x^(1/2)/(b*x^3+a)*B-11/9/a^3*A*b*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))+11/36/a^3*A*b*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))-11/18/a^3*A*b*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))-11/36/a^3*A*b*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))-11/18/a^3*A*b*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))+5/9/a^2*B*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))-5/36/a^2*B*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))+5/18/a^2*B*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))+5/36/a^2*B*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))+5/18/a^2*B*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))-2/5/a^2*A/x^(5/2)","A"
171,1,96,84,0.066000," ","int(x^(7/2)*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{A \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{12 \sqrt{a b}\, a b}+\frac{B \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{4 \sqrt{a b}\, b^{2}}+\frac{\frac{\left(A b -5 B a \right) x^{\frac{9}{2}}}{12 a b}-\frac{\left(A b +3 B a \right) x^{\frac{3}{2}}}{12 b^{2}}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"2/3*(1/8*(A*b-5*B*a)/a/b*x^(9/2)-1/8*(A*b+3*B*a)/b^2*x^(3/2))/(b*x^3+a)^2+1/12/b/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*A+1/4/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*B","A"
172,1,416,241,0.161000," ","int(x^(5/2)*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 a^{2} b}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 a^{2} b}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 a^{2} b}-\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(x -\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{2} b}+\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{2} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 a \,b^{2}}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 a \,b^{2}}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 a \,b^{2}}-\frac{7 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(x -\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a \,b^{2}}+\frac{7 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a \,b^{2}}+\frac{\frac{\left(A b -13 B a \right) x^{\frac{7}{2}}}{36 a b}-\frac{\left(5 A b +7 B a \right) \sqrt{x}}{36 b^{2}}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"2*(1/72*(A*b-13*B*a)/a/b*x^(7/2)-1/72*(5*A*b+7*B*a)/b^2*x^(1/2))/(b*x^3+a)^2+5/108/b/a^2*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*A+7/108/b^2/a*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*B-5/432/b/a^2*3^(1/2)*(a/b)^(1/6)*ln(x-3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A-7/432/b^2/a*3^(1/2)*(a/b)^(1/6)*ln(x-3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B+5/216/b/a^2*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*A+7/216/b^2/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*B+5/432/b/a^2*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A+7/432/b^2/a*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B+5/216/b/a^2*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*A+7/216/b^2/a*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*B","A"
173,1,411,241,0.161000," ","int(x^(3/2)*(B*x^3+A)/(b*x^3+a)^3,x)","\frac{7 A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{2} b}+\frac{7 A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{2} b}+\frac{7 A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{2} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{5}{6}} \sqrt{3}\, A \ln \left(x -\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{3}}-\frac{7 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{3}}+\frac{5 B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 \left(\frac{a}{b}\right)^{\frac{1}{6}} a \,b^{2}}+\frac{5 B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 \left(\frac{a}{b}\right)^{\frac{1}{6}} a \,b^{2}}+\frac{5 B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 \left(\frac{a}{b}\right)^{\frac{1}{6}} a \,b^{2}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{5}{6}} \sqrt{3}\, B \ln \left(x -\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{2} b}-\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{2} b}+\frac{\frac{\left(7 A b +5 B a \right) x^{\frac{11}{2}}}{36 a^{2}}+\frac{\left(13 A b -B a \right) x^{\frac{5}{2}}}{36 a b}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"2*(1/72*(7*A*b+5*B*a)/a^2*x^(11/2)+1/72*(13*A*b-B*a)/a/b*x^(5/2))/(b*x^3+a)^2+7/108/a^2/b/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*A+5/108/a/b^2/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*B+7/432/a^3*(a/b)^(5/6)*3^(1/2)*ln(x-3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A+5/432/a^2/b*(a/b)^(5/6)*3^(1/2)*ln(x-3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B+7/216/a^2/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*A+5/216/a/b^2/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*B-7/432/a^3*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A-5/432/a^2/b*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B+7/216/a^2/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*A+5/216/a/b^2/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*B","A"
174,1,97,84,0.067000," ","int((B*x^3+A)*x^(1/2)/(b*x^3+a)^3,x)","\frac{A \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{4 \sqrt{a b}\, a^{2}}+\frac{B \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{12 \sqrt{a b}\, a b}+\frac{\frac{\left(3 A b +B a \right) x^{\frac{9}{2}}}{12 a^{2}}+\frac{\left(5 A b -B a \right) x^{\frac{3}{2}}}{12 a b}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"2/3*(1/8*(3*A*b+B*a)/a^2*x^(9/2)+1/8*(5*A*b-B*a)/a/b*x^(3/2))/(b*x^3+a)^2+1/4/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*A+1/12/a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*B","A"
175,1,407,235,0.169000," ","int((B*x^3+A)/(b*x^3+a)^3/x^(1/2),x)","\frac{55 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 a^{3}}+\frac{55 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 a^{3}}+\frac{55 \left(\frac{a}{b}\right)^{\frac{1}{6}} A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 a^{3}}+\frac{55 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{3}}-\frac{55 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{3}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 a^{2} b}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 a^{2} b}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 a^{2} b}+\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{2} b}-\frac{5 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{2} b}+\frac{\frac{\left(11 A b +B a \right) x^{\frac{7}{2}}}{36 a^{2}}+\frac{\left(17 A b -5 B a \right) \sqrt{x}}{36 a b}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"2*(1/72*(11*A*b+B*a)/a^2*x^(7/2)+1/72*(17*A*b-5*B*a)/a/b*x^(1/2))/(b*x^3+a)^2+55/108/a^3*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*A+5/108/a^2/b*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))*B-55/432/a^3*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*A-5/432/a^2/b*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))*B+55/216/a^3*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*A+5/216/a^2/b*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))*B+55/432/a^3*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*A+5/432/a^2/b*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))*B+55/216/a^3*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*A+5/216/a^2/b*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))*B","A"
176,1,441,261,0.170000," ","int((B*x^3+A)/x^(3/2)/(b*x^3+a)^3,x)","-\frac{19 A \,b^{2} x^{\frac{11}{2}}}{36 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{7 B b \,x^{\frac{11}{2}}}{36 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{25 A b \,x^{\frac{5}{2}}}{36 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{13 B \,x^{\frac{5}{2}}}{36 \left(b \,x^{3}+a \right)^{2} a}-\frac{91 A \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{3}}-\frac{91 A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{3}}-\frac{91 A \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{3}}+\frac{91 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A b \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{4}}-\frac{91 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} A b \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{4}}+\frac{7 B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{2} b}+\frac{7 B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{2} b}+\frac{7 B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 \left(\frac{a}{b}\right)^{\frac{1}{6}} a^{2} b}-\frac{7 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{3}}+\frac{7 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{5}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{3}}-\frac{2 A}{a^{3} \sqrt{x}}"," ",0,"-19/36/a^3/(b*x^3+a)^2*x^(11/2)*b^2*A+7/36/a^2/(b*x^3+a)^2*x^(11/2)*B*b-25/36/a^2/(b*x^3+a)^2*A*x^(5/2)*b+13/36/a/(b*x^3+a)^2*B*x^(5/2)-91/108/a^3*A/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))-91/432/a^4*A*b*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))-91/216/a^3*A/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))+91/432/a^4*A*b*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))-91/216/a^3*A/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))+7/108/a^2*B/b/(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))+7/432/a^3*B*3^(1/2)*(a/b)^(5/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))+7/216/a^2*B/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))-7/432/a^3*B*3^(1/2)*(a/b)^(5/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))+7/216/a^2*B/b/(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))-2*A/a^3/x^(1/2)","A"
177,1,133,105,0.072000," ","int((B*x^3+A)/x^(5/2)/(b*x^3+a)^3,x)","-\frac{7 A \,b^{2} x^{\frac{9}{2}}}{12 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{B b \,x^{\frac{9}{2}}}{4 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{3 A b \,x^{\frac{3}{2}}}{4 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{5 B \,x^{\frac{3}{2}}}{12 \left(b \,x^{3}+a \right)^{2} a}-\frac{5 A b \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{4 \sqrt{a b}\, a^{3}}+\frac{B \arctan \left(\frac{b \,x^{\frac{3}{2}}}{\sqrt{a b}}\right)}{4 \sqrt{a b}\, a^{2}}-\frac{2 A}{3 a^{3} x^{\frac{3}{2}}}"," ",0,"-7/12/a^3/(b*x^3+a)^2*x^(9/2)*b^2*A+1/4/a^2/(b*x^3+a)^2*x^(9/2)*B*b-3/4/a^2/(b*x^3+a)^2*A*x^(3/2)*b+5/12/a/(b*x^3+a)^2*B*x^(3/2)-5/4/a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*A*b+1/4/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^(3/2))*B-2/3/a^3*A/x^(3/2)","A"
178,1,435,261,0.171000," ","int((B*x^3+A)/x^(7/2)/(b*x^3+a)^3,x)","-\frac{23 A \,b^{2} x^{\frac{7}{2}}}{36 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{11 B b \,x^{\frac{7}{2}}}{36 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{29 A b \sqrt{x}}{36 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{17 B \sqrt{x}}{36 \left(b \,x^{3}+a \right)^{2} a}-\frac{187 \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 a^{4}}-\frac{187 \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 a^{4}}-\frac{187 \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 a^{4}}-\frac{187 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{4}}+\frac{187 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} A b \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{4}}+\frac{55 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{\sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{108 a^{3}}+\frac{55 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{216 a^{3}}+\frac{55 \left(\frac{a}{b}\right)^{\frac{1}{6}} B \arctan \left(\frac{2 \sqrt{x}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{216 a^{3}}+\frac{55 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{3}}-\frac{55 \sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} B \ln \left(-x +\sqrt{3}\, \left(\frac{a}{b}\right)^{\frac{1}{6}} \sqrt{x}-\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{432 a^{3}}-\frac{2 A}{5 a^{3} x^{\frac{5}{2}}}"," ",0,"-23/36/a^3/(b*x^3+a)^2*x^(7/2)*b^2*A+11/36/a^2/(b*x^3+a)^2*x^(7/2)*B*b-29/36/a^2/(b*x^3+a)^2*A*x^(1/2)*b+17/36/a/(b*x^3+a)^2*B*x^(1/2)-187/108/a^4*A*b*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))+187/432/a^4*A*b*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))-187/216/a^4*A*b*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))-187/432/a^4*A*b*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))-187/216/a^4*A*b*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))+55/108/a^3*B*(a/b)^(1/6)*arctan(1/(a/b)^(1/6)*x^(1/2))-55/432/a^3*B*3^(1/2)*(a/b)^(1/6)*ln(-x+3^(1/2)*(a/b)^(1/6)*x^(1/2)-(a/b)^(1/3))+55/216/a^3*B*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)-3^(1/2))+55/432/a^3*B*3^(1/2)*(a/b)^(1/6)*ln(x+3^(1/2)*(a/b)^(1/6)*x^(1/2)+(a/b)^(1/3))+55/216/a^3*B*(a/b)^(1/6)*arctan(2/(a/b)^(1/6)*x^(1/2)+3^(1/2))-2/5*A/a^3/x^(5/2)","A"
179,1,77,87,0.047000," ","int(x^8*(B*x^3+A)*(b*x^3+a)^(1/2),x)","\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} \left(35 B \,x^{9} b^{3}+45 A \,b^{3} x^{6}-30 B a \,b^{2} x^{6}-36 A a \,b^{2} x^{3}+24 B \,a^{2} b \,x^{3}+24 A \,a^{2} b -16 B \,a^{3}\right)}{945 b^{4}}"," ",0,"2/945*(b*x^3+a)^(3/2)*(35*B*b^3*x^9+45*A*b^3*x^6-30*B*a*b^2*x^6-36*A*a*b^2*x^3+24*B*a^2*b*x^3+24*A*a^2*b-16*B*a^3)/b^4","A"
180,1,53,61,0.041000," ","int(x^5*(B*x^3+A)*(b*x^3+a)^(1/2),x)","-\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} \left(-15 B \,b^{2} x^{6}-21 A \,b^{2} x^{3}+12 B a b \,x^{3}+14 A a b -8 B \,a^{2}\right)}{315 b^{3}}"," ",0,"-2/315*(b*x^3+a)^(3/2)*(-15*B*b^2*x^6-21*A*b^2*x^3+12*B*a*b*x^3+14*A*a*b-8*B*a^2)/b^3","A"
181,1,31,38,0.041000," ","int(x^2*(B*x^3+A)*(b*x^3+a)^(1/2),x)","\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} \left(3 B b \,x^{3}+5 A b -2 B a \right)}{45 b^{2}}"," ",0,"2/45*(b*x^3+a)^(3/2)*(3*B*b*x^3+5*A*b-2*B*a)/b^2","A"
182,1,50,48,0.046000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x,x)","\left(-\frac{2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{2 \sqrt{b \,x^{3}+a}}{3}\right) A +\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} B}{9 b}"," ",0,"2/9*B*(b*x^3+a)^(3/2)/b+A*(-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2)+2/3*(b*x^3+a)^(1/2))","A"
183,1,72,68,0.048000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^4,x)","\left(-\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{\sqrt{b \,x^{3}+a}}{3 x^{3}}\right) A +\left(-\frac{2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{2 \sqrt{b \,x^{3}+a}}{3}\right) B"," ",0,"A*(-1/3*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)-1/3*(b*x^3+a)^(1/2)/x^3)+B*(-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2)+2/3*(b*x^3+a)^(1/2))","A"
184,1,96,72,0.049000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^7,x)","\left(\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{12 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{3}+a}\, b}{12 a \,x^{3}}-\frac{\sqrt{b \,x^{3}+a}}{6 x^{6}}\right) A +\left(-\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{\sqrt{b \,x^{3}+a}}{3 x^{3}}\right) B"," ",0,"B*(-1/3*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)-1/3*(b*x^3+a)^(1/2)/x^3)+A*(1/12*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2)-1/6*(b*x^3+a)^(1/2)/x^6-1/12*(b*x^3+a)^(1/2)/a*b/x^3)","A"
185,1,658,236,0.053000," ","int(x^3*(B*x^3+A)*(b*x^3+a)^(1/2),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11}+\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{6 \sqrt{b \,x^{3}+a}\, a x}{55 b}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{7}}{17}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187 b}-\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{3}}-\frac{48 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b^{2}}\right) B"," ",0,"B*(2/17*(b*x^3+a)^(1/2)*x^7+6/187*(b*x^3+a)^(1/2)*a/b*x^4-48/935*(b*x^3+a)^(1/2)*a^2/b^2*x-32/935*I*a^3/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(2/11*(b*x^3+a)^(1/2)*x^4+6/55*(b*x^3+a)^(1/2)*a/b*x+4/55*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
186,1,618,205,0.048000," ","int((B*x^3+A)*(b*x^3+a)^(1/2),x)","\left(-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{5 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11}+\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{6 \sqrt{b \,x^{3}+a}\, a x}{55 b}\right) B"," ",0,"B*(2/11*(b*x^3+a)^(1/2)*x^4+6/55*(b*x^3+a)^(1/2)*a/b*x+4/55*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(2/5*(b*x^3+a)^(1/2)*x-2/5*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
187,1,596,206,0.050000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^3,x)","\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{2 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}}{2 x^{2}}\right) A +\left(-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{5 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5}\right) B"," ",0,"B*(2/5*(b*x^3+a)^(1/2)*x-2/5*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(-1/2*(b*x^3+a)^(1/2)/x^2-1/2*I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
188,1,616,209,0.054000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^6,x)","\left(\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{20 a \,x^{2}}-\frac{\sqrt{b \,x^{3}+a}}{5 x^{5}}\right) A +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{2 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}}{2 x^{2}}\right) B"," ",0,"A*(-1/5*(b*x^3+a)^(1/2)/x^5-3/20*(b*x^3+a)^(1/2)/a*b/x^2+1/20*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+B*(-1/2*(b*x^3+a)^(1/2)/x^2-1/2*I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
189,1,660,238,0.054000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^9,x)","\left(-\frac{7 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{320 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{21 \sqrt{b \,x^{3}+a}\, b^{2}}{320 a^{2} x^{2}}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{80 a \,x^{5}}-\frac{\sqrt{b \,x^{3}+a}}{8 x^{8}}\right) A +\left(\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{20 a \,x^{2}}-\frac{\sqrt{b \,x^{3}+a}}{5 x^{5}}\right) B"," ",0,"B*(-1/5*(b*x^3+a)^(1/2)/x^5-3/20*(b*x^3+a)^(1/2)/a*b/x^2+1/20*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(-1/8*(b*x^3+a)^(1/2)/x^8-3/80*(b*x^3+a)^(1/2)/a*b/x^5+21/320*(b*x^3+a)^(1/2)/a^2*b^2/x^2-7/320*I*b^2/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
190,1,966,439,0.046000," ","int(x^4*(B*x^3+A)*(b*x^3+a)^(1/2),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{5}}{13}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b^{2}}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{8}}{19}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{5}}{247 b}-\frac{60 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{1729 b^{2}}-\frac{80 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{3}}{1729 \sqrt{b \,x^{3}+a}\, b^{3}}\right) B"," ",0,"B*(2/19*(b*x^3+a)^(1/2)*x^8+6/247*(b*x^3+a)^(1/2)*a/b*x^5-60/1729*(b*x^3+a)^(1/2)*a^2/b^2*x^2-80/1729*I*a^3/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(2/13*(b*x^3+a)^(1/2)*x^5+6/91*(b*x^3+a)^(1/2)*a/b*x^2+8/91*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
191,1,926,410,0.047000," ","int(x*(B*x^3+A)*(b*x^3+a)^(1/2),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}\, b}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{5}}{13}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b^{2}}\right) B"," ",0,"B*(2/13*(b*x^3+a)^(1/2)*x^5+6/91*(b*x^3+a)^(1/2)*a/b*x^2+8/91*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(2/7*(b*x^3+a)^(1/2)*x^2-2/7*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
192,1,902,409,0.062000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^2,x)","\left(-\frac{\sqrt{b \,x^{3}+a}}{x}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{\sqrt{b \,x^{3}+a}}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}\, b}\right) B"," ",0,"B*(2/7*(b*x^3+a)^(1/2)*x^2-2/7*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-(b*x^3+a)^(1/2)/x-I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
193,1,920,408,0.056000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^5,x)","\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{8 a x}-\frac{\sqrt{b \,x^{3}+a}}{4 x^{4}}\right) A +\left(-\frac{\sqrt{b \,x^{3}+a}}{x}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{\sqrt{b \,x^{3}+a}}\right) B"," ",0,"A*(-1/4*(b*x^3+a)^(1/2)/x^4-3/8*(b*x^3+a)^(1/2)/a*b/x-1/8*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+B*(-(b*x^3+a)^(1/2)/x-I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
194,1,964,439,0.093000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^8,x)","\left(\frac{5 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{15 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a^{2} x}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{56 a \,x^{4}}-\frac{\sqrt{b \,x^{3}+a}}{7 x^{7}}\right) A +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{8 a x}-\frac{\sqrt{b \,x^{3}+a}}{4 x^{4}}\right) B"," ",0,"B*(-1/4*(b*x^3+a)^(1/2)/x^4-3/8*(b*x^3+a)^(1/2)/a*b/x-1/8*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-1/7*(b*x^3+a)^(1/2)/x^7-3/56/a*b*(b*x^3+a)^(1/2)/x^4+15/112/a^2*b^2*(b*x^3+a)^(1/2)/x+5/112*I*b^2/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
195,1,1006,468,0.083000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^11,x)","\left(-\frac{11 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{3}}{448 \sqrt{b \,x^{3}+a}\, a^{3}}-\frac{33 \sqrt{b \,x^{3}+a}\, b^{3}}{448 a^{3} x}+\frac{33 \sqrt{b \,x^{3}+a}\, b^{2}}{1120 a^{2} x^{4}}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{140 a \,x^{7}}-\frac{\sqrt{b \,x^{3}+a}}{10 x^{10}}\right) A +\left(\frac{5 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{15 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a^{2} x}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{56 a \,x^{4}}-\frac{\sqrt{b \,x^{3}+a}}{7 x^{7}}\right) B"," ",0,"B*(-1/7*(b*x^3+a)^(1/2)/x^7-3/56*(b*x^3+a)^(1/2)/a*b/x^4+15/112*(b*x^3+a)^(1/2)/a^2*b^2/x+5/112*I*b^2/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-1/10*(b*x^3+a)^(1/2)/x^10-3/140/a*b*(b*x^3+a)^(1/2)/x^7+33/1120/a^2*b^2*(b*x^3+a)^(1/2)/x^4-33/448/a^3*b^3*(b*x^3+a)^(1/2)/x-11/448*I/a^3*b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
196,1,77,87,0.051000," ","int(x^8*(b*x^3+a)^(3/2)*(B*x^3+A),x)","\frac{2 \left(b \,x^{3}+a \right)^{\frac{5}{2}} \left(315 B \,x^{9} b^{3}+385 A \,b^{3} x^{6}-210 B a \,b^{2} x^{6}-220 A a \,b^{2} x^{3}+120 B \,a^{2} b \,x^{3}+88 A \,a^{2} b -48 B \,a^{3}\right)}{10395 b^{4}}"," ",0,"2/10395*(b*x^3+a)^(5/2)*(315*B*b^3*x^9+385*A*b^3*x^6-210*B*a*b^2*x^6-220*A*a*b^2*x^3+120*B*a^2*b*x^3+88*A*a^2*b-48*B*a^3)/b^4","A"
197,1,53,61,0.047000," ","int(x^5*(b*x^3+a)^(3/2)*(B*x^3+A),x)","-\frac{2 \left(b \,x^{3}+a \right)^{\frac{5}{2}} \left(-35 B \,b^{2} x^{6}-45 A \,b^{2} x^{3}+20 B a b \,x^{3}+18 A a b -8 B \,a^{2}\right)}{945 b^{3}}"," ",0,"-2/945*(b*x^3+a)^(5/2)*(-35*B*b^2*x^6-45*A*b^2*x^3+20*B*a*b*x^3+18*A*a*b-8*B*a^2)/b^3","A"
198,1,31,38,0.047000," ","int(x^2*(b*x^3+a)^(3/2)*(B*x^3+A),x)","\frac{2 \left(b \,x^{3}+a \right)^{\frac{5}{2}} \left(5 B b \,x^{3}+7 A b -2 B a \right)}{105 b^{2}}"," ",0,"2/105*(b*x^3+a)^(5/2)*(5*B*b*x^3+7*A*b-2*B*a)/b^2","A"
199,1,66,61,0.049000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x,x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{3}}{9}-\frac{2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{8 \sqrt{b \,x^{3}+a}\, a}{9}\right) A +\frac{2 \left(b \,x^{3}+a \right)^{\frac{5}{2}} B}{15 b}"," ",0,"2/15*B*(b*x^3+a)^(5/2)/b+A*(2/9*(b*x^3+a)^(1/2)*b*x^3+8/9*(b*x^3+a)^(1/2)*a-2/3*a^(3/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))","A"
200,1,101,90,0.049000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x^4,x)","\left(-\sqrt{a}\, b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)+\frac{2 \sqrt{b \,x^{3}+a}\, b}{3}-\frac{\sqrt{b \,x^{3}+a}\, a}{3 x^{3}}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{3}}{9}-\frac{2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{8 \sqrt{b \,x^{3}+a}\, a}{9}\right) B"," ",0,"A*(-1/3*(b*x^3+a)^(1/2)*a/x^3+2/3*(b*x^3+a)^(1/2)*b-b*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2))+B*(2/9*(b*x^3+a)^(1/2)*b*x^3+8/9*(b*x^3+a)^(1/2)*a-2/3*a^(3/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))","A"
201,1,107,95,0.052000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x^7,x)","\left(-\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{5 \sqrt{b \,x^{3}+a}\, b}{12 x^{3}}-\frac{\sqrt{b \,x^{3}+a}\, a}{6 x^{6}}\right) A +\left(-\sqrt{a}\, b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)+\frac{2 \sqrt{b \,x^{3}+a}\, b}{3}-\frac{\sqrt{b \,x^{3}+a}\, a}{3 x^{3}}\right) B"," ",0,"B*(-1/3*(b*x^3+a)^(1/2)*a/x^3+2/3*(b*x^3+a)^(1/2)*b-b*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2))+A*(-1/6*a*(b*x^3+a)^(1/2)/x^6-5/12*(b*x^3+a)^(1/2)*b/x^3-1/4*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2))","A"
202,1,694,265,0.053000," ","int(x^3*(b*x^3+a)^(3/2)*(B*x^3+A),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{7}}{17}+\frac{40 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187}+\frac{36 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{10}}{23}+\frac{52 \sqrt{b \,x^{3}+a}\, a \,x^{7}}{391}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{4}}{4301 b}-\frac{288 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{4} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{21505 \sqrt{b \,x^{3}+a}\, b^{3}}-\frac{432 \sqrt{b \,x^{3}+a}\, a^{3} x}{21505 b^{2}}\right) B"," ",0,"B*(2/23*(b*x^3+a)^(1/2)*b*x^10+52/391*(b*x^3+a)^(1/2)*a*x^7+54/4301*(b*x^3+a)^(1/2)*a^2/b*x^4-432/21505*(b*x^3+a)^(1/2)*a^3/b^2*x-288/21505*I*a^4/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(2/17*b*x^7*(b*x^3+a)^(1/2)+40/187*(b*x^3+a)^(1/2)*a*x^4+54/935*(b*x^3+a)^(1/2)*a^2/b*x+36/935*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
203,1,654,232,0.043000," ","int((b*x^3+a)^(3/2)*(B*x^3+A),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{4}}{11}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b}+\frac{28 \sqrt{b \,x^{3}+a}\, a x}{55}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{7}}{17}+\frac{40 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187}+\frac{36 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b}\right) B"," ",0,"B*(2/17*(b*x^3+a)^(1/2)*b*x^7+40/187*(b*x^3+a)^(1/2)*a*x^4+54/935*(b*x^3+a)^(1/2)*a^2/b*x+36/935*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(2/11*(b*x^3+a)^(1/2)*b*x^4+28/55*(b*x^3+a)^(1/2)*a*x-18/55*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
204,1,629,228,0.053000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x^3,x)","\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{10 \sqrt{b \,x^{3}+a}}+\frac{2 \sqrt{b \,x^{3}+a}\, b x}{5}-\frac{\sqrt{b \,x^{3}+a}\, a}{2 x^{2}}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{4}}{11}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b}+\frac{28 \sqrt{b \,x^{3}+a}\, a x}{55}\right) B"," ",0,"B*(2/11*(b*x^3+a)^(1/2)*b*x^4+28/55*(b*x^3+a)^(1/2)*a*x-18/55*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(-1/2*a*(b*x^3+a)^(1/2)/x^2+2/5*(b*x^3+a)^(1/2)*b*x-9/10*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
205,1,626,230,0.051000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x^6,x)","\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}}-\frac{13 \sqrt{b \,x^{3}+a}\, b}{20 x^{2}}-\frac{\sqrt{b \,x^{3}+a}\, a}{5 x^{5}}\right) A +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{10 \sqrt{b \,x^{3}+a}}+\frac{2 \sqrt{b \,x^{3}+a}\, b x}{5}-\frac{\sqrt{b \,x^{3}+a}\, a}{2 x^{2}}\right) B"," ",0,"A*(-1/5*a*(b*x^3+a)^(1/2)/x^5-13/20*(b*x^3+a)^(1/2)*b/x^2-9/20*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+B*(-1/2*(b*x^3+a)^(1/2)*a/x^2+2/5*(b*x^3+a)^(1/2)*b*x-9/10*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
206,1,653,235,0.093000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x^9,x)","\left(\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{320 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{320 a \,x^{2}}-\frac{19 \sqrt{b \,x^{3}+a}\, b}{80 x^{5}}-\frac{\sqrt{b \,x^{3}+a}\, a}{8 x^{8}}\right) A +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}}-\frac{13 \sqrt{b \,x^{3}+a}\, b}{20 x^{2}}-\frac{\sqrt{b \,x^{3}+a}\, a}{5 x^{5}}\right) B"," ",0,"B*(-1/5*(b*x^3+a)^(1/2)*a/x^5-13/20*(b*x^3+a)^(1/2)*b/x^2-9/20*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(-1/8*a*(b*x^3+a)^(1/2)/x^8-19/80*b*(b*x^3+a)^(1/2)/x^5-27/320*b^2/a*(b*x^3+a)^(1/2)/x^2+9/320*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
207,1,1002,468,0.052000," ","int(x^4*(b*x^3+a)^(3/2)*(B*x^3+A),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{8}}{19}+\frac{44 \sqrt{b \,x^{3}+a}\, a \,x^{5}}{247}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{1729 b}+\frac{72 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{3}}{1729 \sqrt{b \,x^{3}+a}\, b^{2}}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{11}}{25}+\frac{56 \sqrt{b \,x^{3}+a}\, a \,x^{8}}{475}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{5}}{6175 b}-\frac{108 \sqrt{b \,x^{3}+a}\, a^{3} x^{2}}{8645 b^{2}}-\frac{144 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{4}}{8645 \sqrt{b \,x^{3}+a}\, b^{3}}\right) B"," ",0,"B*(2/25*b*x^11*(b*x^3+a)^(1/2)+56/475*(b*x^3+a)^(1/2)*a*x^8+54/6175*(b*x^3+a)^(1/2)*a^2/b*x^5-108/8645*(b*x^3+a)^(1/2)*a^3/b^2*x^2-144/8645*I*a^4/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(2/19*b*x^8*(b*x^3+a)^(1/2)+44/247*(b*x^3+a)^(1/2)*a*x^5+54/1729*(b*x^3+a)^(1/2)*a^2/b*x^2+72/1729*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
208,1,962,439,0.043000," ","int(x*(b*x^3+a)^(3/2)*(B*x^3+A),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{5}}{13}+\frac{32 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{8}}{19}+\frac{44 \sqrt{b \,x^{3}+a}\, a \,x^{5}}{247}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{1729 b}+\frac{72 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{3}}{1729 \sqrt{b \,x^{3}+a}\, b^{2}}\right) B"," ",0,"B*(2/19*(b*x^3+a)^(1/2)*b*x^8+44/247*(b*x^3+a)^(1/2)*a*x^5+54/1729*(b*x^3+a)^(1/2)*a^2/b*x^2+72/1729*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(2/13*b*x^5*(b*x^3+a)^(1/2)+32/91*(b*x^3+a)^(1/2)*a*x^2-18/91*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
209,1,937,433,0.057000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x^2,x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}\, a}{x}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{5}}{13}+\frac{32 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b}\right) B"," ",0,"B*(2/13*(b*x^3+a)^(1/2)*b*x^5+32/91*(b*x^3+a)^(1/2)*a*x^2-18/91*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-a*(b*x^3+a)^(1/2)/x+2/7*(b*x^3+a)^(1/2)*b*x^2-9/7*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
210,1,932,436,0.053000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x^5,x)","\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}}-\frac{11 \sqrt{b \,x^{3}+a}\, b}{8 x}-\frac{\sqrt{b \,x^{3}+a}\, a}{4 x^{4}}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}\, a}{x}\right) B"," ",0,"A*(-1/4*a*(b*x^3+a)^(1/2)/x^4-11/8*(b*x^3+a)^(1/2)*b/x-9/8*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+B*(-(b*x^3+a)^(1/2)*a/x+2/7*(b*x^3+a)^(1/2)*b*x^2-9/7*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
211,1,957,434,0.095000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x^8,x)","\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a x}-\frac{17 \sqrt{b \,x^{3}+a}\, b}{56 x^{4}}-\frac{\sqrt{b \,x^{3}+a}\, a}{7 x^{7}}\right) A +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}}-\frac{11 \sqrt{b \,x^{3}+a}\, b}{8 x}-\frac{\sqrt{b \,x^{3}+a}\, a}{4 x^{4}}\right) B"," ",0,"B*(-1/4*(b*x^3+a)^(1/2)*a/x^4-11/8*(b*x^3+a)^(1/2)*b/x-9/8*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-1/7*a*(b*x^3+a)^(1/2)/x^7-17/56*b*(b*x^3+a)^(1/2)/x^4-27/112*b^2/a*(b*x^3+a)^(1/2)/x-9/112*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
212,1,1002,462,0.099000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/x^11,x)","\left(\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{3}}{448 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{27 \sqrt{b \,x^{3}+a}\, b^{3}}{448 a^{2} x}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{1120 a \,x^{4}}-\frac{23 \sqrt{b \,x^{3}+a}\, b}{140 x^{7}}-\frac{\sqrt{b \,x^{3}+a}\, a}{10 x^{10}}\right) A +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a x}-\frac{17 \sqrt{b \,x^{3}+a}\, b}{56 x^{4}}-\frac{\sqrt{b \,x^{3}+a}\, a}{7 x^{7}}\right) B"," ",0,"B*(-1/7*(b*x^3+a)^(1/2)*a/x^7-17/56*(b*x^3+a)^(1/2)*b/x^4-27/112*(b*x^3+a)^(1/2)/a*b^2/x-9/112*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-1/10*a*(b*x^3+a)^(1/2)/x^10-23/140*b*(b*x^3+a)^(1/2)/x^7-27/1120*b^2/a*(b*x^3+a)^(1/2)/x^4+27/448*b^3/a^2*(b*x^3+a)^(1/2)/x+9/448*I*b^3/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
213,1,77,87,0.043000," ","int(x^8*(B*x^3+A)/(b*x^3+a)^(1/2),x)","\frac{2 \sqrt{b \,x^{3}+a}\, \left(15 B \,x^{9} b^{3}+21 A \,b^{3} x^{6}-18 B a \,b^{2} x^{6}-28 A a \,b^{2} x^{3}+24 B \,a^{2} b \,x^{3}+56 A \,a^{2} b -48 B \,a^{3}\right)}{315 b^{4}}"," ",0,"2/315*(b*x^3+a)^(1/2)*(15*B*b^3*x^9+21*A*b^3*x^6-18*B*a*b^2*x^6-28*A*a*b^2*x^3+24*B*a^2*b*x^3+56*A*a^2*b-48*B*a^3)/b^4","A"
214,1,53,61,0.047000," ","int(x^5*(B*x^3+A)/(b*x^3+a)^(1/2),x)","-\frac{2 \sqrt{b \,x^{3}+a}\, \left(-3 B \,b^{2} x^{6}-5 A \,b^{2} x^{3}+4 B a b \,x^{3}+10 A a b -8 B \,a^{2}\right)}{45 b^{3}}"," ",0,"-2/45*(b*x^3+a)^(1/2)*(-3*B*b^2*x^6-5*A*b^2*x^3+4*B*a*b*x^3+10*A*a*b-8*B*a^2)/b^3","A"
215,1,30,38,0.043000," ","int(x^2*(B*x^3+A)/(b*x^3+a)^(1/2),x)","\frac{2 \sqrt{b \,x^{3}+a}\, \left(B b \,x^{3}+3 A b -2 B a \right)}{9 b^{2}}"," ",0,"2/9*(b*x^3+a)^(1/2)*(B*b*x^3+3*A*b-2*B*a)/b^2","A"
216,1,37,36,0.044000," ","int((B*x^3+A)/x/(b*x^3+a)^(1/2),x)","-\frac{2 A \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}+\frac{2 \sqrt{b \,x^{3}+a}\, B}{3 b}"," ",0,"-2/3*A*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)+2/3*B*(b*x^3+a)^(1/2)/b","A"
217,1,62,46,0.053000," ","int((B*x^3+A)/x^4/(b*x^3+a)^(1/2),x)","-\frac{2 B \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}+\left(\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{3}+a}}{3 a \,x^{3}}\right) A"," ",0,"A*(1/3*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2)-1/3*(b*x^3+a)^(1/2)/a/x^3)-2/3*B*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)","A"
218,1,102,74,0.075000," ","int((B*x^3+A)/x^7/(b*x^3+a)^(1/2),x)","\left(-\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{4 a^{\frac{5}{2}}}+\frac{\sqrt{b \,x^{3}+a}\, b}{4 a^{2} x^{3}}-\frac{\sqrt{b \,x^{3}+a}}{6 a \,x^{6}}\right) A +\left(\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{3}+a}}{3 a \,x^{3}}\right) B"," ",0,"B*(1/3*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2)-1/3*(b*x^3+a)^(1/2)/a/x^3)+A*(-1/4*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(5/2)-1/6*(b*x^3+a)^(1/2)/a/x^6+1/4*(b*x^3+a)^(1/2)/a^2*b/x^3)","A"
219,1,624,207,0.050000," ","int(x^3*(B*x^3+A)/(b*x^3+a)^(1/2),x)","\left(\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{15 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11 b}-\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{165 \sqrt{b \,x^{3}+a}\, b^{3}}-\frac{16 \sqrt{b \,x^{3}+a}\, a x}{55 b^{2}}\right) B"," ",0,"B*(2/11*(b*x^3+a)^(1/2)/b*x^4-16/55*(b*x^3+a)^(1/2)*a/b^2*x-32/165*I*a^2/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(2/5*(b*x^3+a)^(1/2)/b*x+4/15*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
220,1,586,180,0.053000," ","int((B*x^3+A)/(b*x^3+a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, A \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}+\left(\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{15 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b}\right) B"," ",0,"B*(2/5*(b*x^3+a)^(1/2)/b*x+4/15*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*I*A*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
221,1,587,184,0.052000," ","int((B*x^3+A)/x^3/(b*x^3+a)^(1/2),x)","\left(\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{6 \sqrt{b \,x^{3}+a}\, a}-\frac{\sqrt{b \,x^{3}+a}}{2 a \,x^{2}}\right) A -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, B \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"-2/3*I*B*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+A*(-1/2*(b*x^3+a)^(1/2)/a/x^2+1/6*I/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
222,1,625,211,0.052000," ","int((B*x^3+A)/x^6/(b*x^3+a)^(1/2),x)","\left(-\frac{7 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{60 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{7 \sqrt{b \,x^{3}+a}\, b}{20 a^{2} x^{2}}-\frac{\sqrt{b \,x^{3}+a}}{5 a \,x^{5}}\right) A +\left(\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{6 \sqrt{b \,x^{3}+a}\, a}-\frac{\sqrt{b \,x^{3}+a}}{2 a \,x^{2}}\right) B"," ",0,"A*(-1/5*(b*x^3+a)^(1/2)/a/x^5+7/20*(b*x^3+a)^(1/2)/a^2*b/x^2-7/60*I/a^2*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+B*(-1/2*(b*x^3+a)^(1/2)/a/x^2+1/6*I/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
223,1,932,410,0.051000," ","int(x^4*(B*x^3+A)/(b*x^3+a)^(1/2),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{21 \sqrt{b \,x^{3}+a}\, b^{2}}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{5}}{13 b}-\frac{20 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91 b^{2}}-\frac{80 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{273 \sqrt{b \,x^{3}+a}\, b^{3}}\right) B"," ",0,"B*(2/13*(b*x^3+a)^(1/2)/b*x^5-20/91*(b*x^3+a)^(1/2)*a/b^2*x^2-80/273*I*a^2/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(2/7*(b*x^3+a)^(1/2)/b*x^2+8/21*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
224,1,892,383,0.052000," ","int(x*(B*x^3+A)/(b*x^3+a)^(1/2),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{21 \sqrt{b \,x^{3}+a}\, b^{2}}\right) B -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) A}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"B*(2/7*(b*x^3+a)^(1/2)/b*x^2+8/21*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))-2/3*I*A*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
225,1,891,382,0.059000," ","int((B*x^3+A)/x^2/(b*x^3+a)^(1/2),x)","\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, a}-\frac{\sqrt{b \,x^{3}+a}}{a x}\right) A -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) B}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"-2/3*I*B*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(-(b*x^3+a)^(1/2)/a/x-1/3*I/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
226,1,929,412,0.055000," ","int((B*x^3+A)/x^5/(b*x^3+a)^(1/2),x)","\left(\frac{5 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{24 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{5 \sqrt{b \,x^{3}+a}\, b}{8 a^{2} x}-\frac{\sqrt{b \,x^{3}+a}}{4 a \,x^{4}}\right) A +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, a}-\frac{\sqrt{b \,x^{3}+a}}{a x}\right) B"," ",0,"A*(-1/4*(b*x^3+a)^(1/2)/a/x^4+5/8*(b*x^3+a)^(1/2)/a^2*b/x+5/24*I/a^2*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+B*(-(b*x^3+a)^(1/2)/a/x-1/3*I/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
227,1,970,439,0.083000," ","int((B*x^3+A)/x^8/(b*x^3+a)^(1/2),x)","\left(-\frac{55 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{336 \sqrt{b \,x^{3}+a}\, a^{3}}-\frac{55 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a^{3} x}+\frac{11 \sqrt{b \,x^{3}+a}\, b}{56 a^{2} x^{4}}-\frac{\sqrt{b \,x^{3}+a}}{7 a \,x^{7}}\right) A +\left(\frac{5 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{24 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{5 \sqrt{b \,x^{3}+a}\, b}{8 a^{2} x}-\frac{\sqrt{b \,x^{3}+a}}{4 a \,x^{4}}\right) B"," ",0,"B*(-1/4*(b*x^3+a)^(1/2)/a/x^4+5/8*(b*x^3+a)^(1/2)/a^2*b/x+5/24*I/a^2*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-1/7/a*(b*x^3+a)^(1/2)/x^7+11/56/a^2*b*(b*x^3+a)^(1/2)/x^4-55/112/a^3*b^2*(b*x^3+a)^(1/2)/x-55/336*I/a^3*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
228,1,77,87,0.045000," ","int(x^8*(B*x^3+A)/(b*x^3+a)^(3/2),x)","-\frac{2 \left(-3 B \,x^{9} b^{3}-5 A \,b^{3} x^{6}+6 B a \,b^{2} x^{6}+20 A a \,b^{2} x^{3}-24 B \,a^{2} b \,x^{3}+40 A \,a^{2} b -48 B \,a^{3}\right)}{45 \sqrt{b \,x^{3}+a}\, b^{4}}"," ",0,"-2/45/(b*x^3+a)^(1/2)*(-3*B*b^3*x^9-5*A*b^3*x^6+6*B*a*b^2*x^6+20*A*a*b^2*x^3-24*B*a^2*b*x^3+40*A*a^2*b-48*B*a^3)/b^4","A"
229,1,52,61,0.049000," ","int(x^5*(B*x^3+A)/(b*x^3+a)^(3/2),x)","\frac{\frac{2}{9} B \,b^{2} x^{6}+\frac{2}{3} A \,b^{2} x^{3}-\frac{8}{9} B a b \,x^{3}+\frac{4}{3} A a b -\frac{16}{9} B \,a^{2}}{\sqrt{b \,x^{3}+a}\, b^{3}}"," ",0,"2/9/(b*x^3+a)^(1/2)*(B*b^2*x^6+3*A*b^2*x^3-4*B*a*b*x^3+6*A*a*b-8*B*a^2)/b^3","A"
230,1,30,38,0.046000," ","int(x^2*(B*x^3+A)/(b*x^3+a)^(3/2),x)","-\frac{2 \left(-B b \,x^{3}+A b -2 B a \right)}{3 \sqrt{b \,x^{3}+a}\, b^{2}}"," ",0,"-2/3/(b*x^3+a)^(1/2)*(-B*b*x^3+A*b-2*B*a)/b^2","A"
231,1,57,46,0.047000," ","int((B*x^3+A)/x/(b*x^3+a)^(3/2),x)","\left(-\frac{2 \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 a^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}\right) A -\frac{2 B}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"-2/3*B/b/(b*x^3+a)^(1/2)+A*(2/3/a/((x^3+a/b)*b)^(1/2)-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2))","A"
232,1,100,70,0.061000," ","int((B*x^3+A)/x^4/(b*x^3+a)^(3/2),x)","\left(\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{a^{\frac{5}{2}}}-\frac{2 b}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}-\frac{\sqrt{b \,x^{3}+a}}{3 a^{2} x^{3}}\right) A +\left(-\frac{2 \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 a^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}\right) B"," ",0,"A*(-1/3*(b*x^3+a)^(1/2)/a^2/x^3-2/3/((x^3+a/b)*b)^(1/2)/a^2*b+b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(5/2))+B*(2/3/((x^3+a/b)*b)^(1/2)/a-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2))","A"
233,1,141,98,0.048000," ","int((B*x^3+A)/x^7/(b*x^3+a)^(3/2),x)","\left(-\frac{5 b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{4 a^{\frac{7}{2}}}+\frac{2 b^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}+\frac{7 \sqrt{b \,x^{3}+a}\, b}{12 a^{3} x^{3}}-\frac{\sqrt{b \,x^{3}+a}}{6 a^{2} x^{6}}\right) A +\left(\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{a^{\frac{5}{2}}}-\frac{2 b}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}-\frac{\sqrt{b \,x^{3}+a}}{3 a^{2} x^{3}}\right) B"," ",0,"B*(-1/3*(b*x^3+a)^(1/2)/a^2/x^3-2/3/((x^3+a/b)*b)^(1/2)/a^2*b+b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(5/2))+A*(-1/6*(b*x^3+a)^(1/2)/a^2/x^6+7/12*(b*x^3+a)^(1/2)/a^3*b/x^3+2/3/((x^3+a/b)*b)^(1/2)/a^3*b^2-5/4*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(7/2))","A"
234,1,666,233,0.081000," ","int(x^6*(B*x^3+A)/(b*x^3+a)^(3/2),x)","\left(\frac{2 a x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{45 \sqrt{b \,x^{3}+a}\, b^{3}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b^{2}}\right) A +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11 b^{2}}-\frac{2 a^{2} x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{3}}-\frac{448 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{495 \sqrt{b \,x^{3}+a}\, b^{4}}-\frac{38 \sqrt{b \,x^{3}+a}\, a x}{55 b^{3}}\right) B"," ",0,"B*(-2/3/b^3*a^2*x/((x^3+a/b)*b)^(1/2)+2/11/b^2*x^4*(b*x^3+a)^(1/2)-38/55*a/b^3*x*(b*x^3+a)^(1/2)-448/495*I*a^2/b^4*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(2/3/((x^3+a/b)*b)^(1/2)*a/b^2*x+2/5*(b*x^3+a)^(1/2)/b^2*x+32/45*I*a/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
235,1,627,206,0.049000," ","int(x^3*(B*x^3+A)/(b*x^3+a)^(3/2),x)","\left(-\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) A +\left(\frac{2 a x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{45 \sqrt{b \,x^{3}+a}\, b^{3}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b^{2}}\right) B"," ",0,"B*(2/3/((x^3+a/b)*b)^(1/2)*a/b^2*x+2/5*(b*x^3+a)^(1/2)/b^2*x+32/45*I*a/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(-2/3/((x^3+a/b)*b)^(1/2)/b*x-4/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
236,1,613,192,0.056000," ","int((B*x^3+A)/(b*x^3+a)^(3/2),x)","\left(\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) A +\left(-\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) B"," ",0,"B*(-2/3/((x^3+a/b)*b)^(1/2)/b*x-4/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(2/3/((x^3+a/b)*b)^(1/2)/a*x-2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
237,1,631,209,0.055000," ","int((B*x^3+A)/x^3/(b*x^3+a)^(3/2),x)","\left(-\frac{2 b x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{7 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{18 \sqrt{b \,x^{3}+a}\, a^{2}}-\frac{\sqrt{b \,x^{3}+a}}{2 a^{2} x^{2}}\right) A +\left(\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) B"," ",0,"B*(2/3/((x^3+a/b)*b)^(1/2)/a*x-2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(-2/3/((x^3+a/b)*b)^(1/2)/a^2*b*x-1/2*(b*x^3+a)^(1/2)/a^2/x^2+7/18*I/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
238,1,667,237,0.048000," ","int((B*x^3+A)/x^6/(b*x^3+a)^(3/2),x)","\left(\frac{2 b^{2} x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}-\frac{91 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{180 \sqrt{b \,x^{3}+a}\, a^{3}}+\frac{17 \sqrt{b \,x^{3}+a}\, b}{20 a^{3} x^{2}}-\frac{\sqrt{b \,x^{3}+a}}{5 a^{2} x^{5}}\right) A +\left(-\frac{2 b x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{7 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{18 \sqrt{b \,x^{3}+a}\, a^{2}}-\frac{\sqrt{b \,x^{3}+a}}{2 a^{2} x^{2}}\right) B"," ",0,"A*(-1/5*(b*x^3+a)^(1/2)/a^2/x^5+17/20*(b*x^3+a)^(1/2)/a^3*b/x^2+2/3*b^2/a^3*x/((x^3+a/b)*b)^(1/2)-91/180*I/a^3*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+B*(-2/3/((x^3+a/b)*b)^(1/2)/a^2*b*x-1/2*(b*x^3+a)^(1/2)/a^2/x^2+7/18*I/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
239,1,937,409,0.055000," ","int(x^4*(B*x^3+A)/(b*x^3+a)^(3/2),x)","\left(-\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) A +\left(\frac{2 a \,x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7 b^{2}}+\frac{80 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{63 \sqrt{b \,x^{3}+a}\, b^{3}}\right) B"," ",0,"B*(2/3/b^2*a*x^2/((x^3+a/b)*b)^(1/2)+2/7*(b*x^3+a)^(1/2)/b^2*x^2+80/63*I*a/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-2/3/b*x^2/((x^3+a/b)*b)^(1/2)-8/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
240,1,921,393,0.047000," ","int(x*(B*x^3+A)/(b*x^3+a)^(3/2),x)","\left(\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}+\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) A +\left(-\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) B"," ",0,"B*(-2/3/((x^3+a/b)*b)^(1/2)/b*x^2-8/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(2/3/((x^3+a/b)*b)^(1/2)/a*x^2+2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
241,1,939,412,0.046000," ","int((B*x^3+A)/x^2/(b*x^3+a)^(3/2),x)","\left(-\frac{2 b \,x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}-\frac{5 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a^{2}}-\frac{\sqrt{b \,x^{3}+a}}{a^{2} x}\right) A +\left(\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}+\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) B"," ",0,"B*(2/3/((x^3+a/b)*b)^(1/2)/a*x^2+2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-2/3/((x^3+a/b)*b)^(1/2)/a^2*b*x^2-(b*x^3+a)^(1/2)/a^2/x-5/9*I/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
242,1,975,438,0.051000," ","int((B*x^3+A)/x^5/(b*x^3+a)^(3/2),x)","\left(\frac{2 b^{2} x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}+\frac{55 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{72 \sqrt{b \,x^{3}+a}\, a^{3}}+\frac{13 \sqrt{b \,x^{3}+a}\, b}{8 a^{3} x}-\frac{\sqrt{b \,x^{3}+a}}{4 a^{2} x^{4}}\right) A +\left(-\frac{2 b \,x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}-\frac{5 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a^{2}}-\frac{\sqrt{b \,x^{3}+a}}{a^{2} x}\right) B"," ",0,"A*(2/3/((x^3+a/b)*b)^(1/2)/a^3*b^2*x^2-1/4*(b*x^3+a)^(1/2)/a^2/x^4+13/8*(b*x^3+a)^(1/2)/a^3*b/x+55/72*I/a^3*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+B*(-2/3/((x^3+a/b)*b)^(1/2)/a^2*b*x^2-(b*x^3+a)^(1/2)/a^2/x-5/9*I/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
243,1,1018,465,0.095000," ","int((B*x^3+A)/x^8/(b*x^3+a)^(3/2),x)","\left(-\frac{2 b^{3} x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{4}}-\frac{935 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{1008 \sqrt{b \,x^{3}+a}\, a^{4}}-\frac{237 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a^{4} x}+\frac{25 \sqrt{b \,x^{3}+a}\, b}{56 a^{3} x^{4}}-\frac{\sqrt{b \,x^{3}+a}}{7 a^{2} x^{7}}\right) A +\left(\frac{2 b^{2} x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}+\frac{55 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{72 \sqrt{b \,x^{3}+a}\, a^{3}}+\frac{13 \sqrt{b \,x^{3}+a}\, b}{8 a^{3} x}-\frac{\sqrt{b \,x^{3}+a}}{4 a^{2} x^{4}}\right) B"," ",0,"B*(2/3/((x^3+a/b)*b)^(1/2)/a^3*b^2*x^2-1/4*(b*x^3+a)^(1/2)/a^2/x^4+13/8*(b*x^3+a)^(1/2)/a^3*b/x+55/72*I/a^3*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-1/7/a^2*(b*x^3+a)^(1/2)/x^7+25/56*b/a^3*(b*x^3+a)^(1/2)/x^4-237/112/a^4*b^2*(b*x^3+a)^(1/2)/x-2/3*b^3/a^4*x^2/((x^3+a/b)*b)^(1/2)-935/1008*I/a^4*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
244,1,76,87,0.048000," ","int(x^8*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\frac{\frac{2}{9} B \,x^{9} b^{3}+\frac{2}{3} A \,b^{3} x^{6}-\frac{4}{3} B a \,b^{2} x^{6}+\frac{8}{3} A a \,b^{2} x^{3}-\frac{16}{3} B \,a^{2} b \,x^{3}+\frac{16}{9} A \,a^{2} b -\frac{32}{9} B \,a^{3}}{\left(b \,x^{3}+a \right)^{\frac{3}{2}} b^{4}}"," ",0,"2/9/(b*x^3+a)^(3/2)*(B*b^3*x^9+3*A*b^3*x^6-6*B*a*b^2*x^6+12*A*a*b^2*x^3-24*B*a^2*b*x^3+8*A*a^2*b-16*B*a^3)/b^4","A"
245,1,53,61,0.050000," ","int(x^5*(B*x^3+A)/(b*x^3+a)^(5/2),x)","-\frac{2 \left(-3 B \,b^{2} x^{6}+3 A \,b^{2} x^{3}-12 B a b \,x^{3}+2 A a b -8 B \,a^{2}\right)}{9 \left(b \,x^{3}+a \right)^{\frac{3}{2}} b^{3}}"," ",0,"-2/9/(b*x^3+a)^(3/2)*(-3*B*b^2*x^6+3*A*b^2*x^3-12*B*a*b*x^3+2*A*a*b-8*B*a^2)/b^3","A"
246,1,30,38,0.046000," ","int(x^2*(B*x^3+A)/(b*x^3+a)^(5/2),x)","-\frac{2 \left(3 B b \,x^{3}+A b +2 B a \right)}{9 \left(b \,x^{3}+a \right)^{\frac{3}{2}} b^{2}}"," ",0,"-2/9/(b*x^3+a)^(3/2)*(3*B*b*x^3+A*b+2*B*a)/b^2","A"
247,1,85,61,0.086000," ","int((B*x^3+A)/x/(b*x^3+a)^(5/2),x)","\left(-\frac{2 \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 a^{\frac{5}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}\right) A -\frac{2 B}{9 \left(b \,x^{3}+a \right)^{\frac{3}{2}} b}"," ",0,"-2/9*B/b/(b*x^3+a)^(3/2)+A*(2/9/a/b^2*(b*x^3+a)^(1/2)/(x^3+a/b)^2+2/3/a^2/((x^3+a/b)*b)^(1/2)-2/3/a^(5/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))","A"
248,1,157,93,0.091000," ","int((B*x^3+A)/x^4/(b*x^3+a)^(5/2),x)","\left(\frac{5 b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 a^{\frac{7}{2}}}-\frac{4 b}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}-\frac{2 \sqrt{b \,x^{3}+a}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b}-\frac{\sqrt{b \,x^{3}+a}}{3 a^{3} x^{3}}\right) A +\left(-\frac{2 \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 a^{\frac{5}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}\right) B"," ",0,"A*(-1/3/a^3*(b*x^3+a)^(1/2)/x^3-2/9/a^2/b*(b*x^3+a)^(1/2)/(x^3+a/b)^2-4/3*b/a^3/((x^3+a/b)*b)^(1/2)+5/3*b/a^(7/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))+B*(2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a/b^2+2/3/((x^3+a/b)*b)^(1/2)/a^2-2/3/a^(5/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))","A"
249,1,683,232,0.098000," ","int(x^6*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\left(-\frac{22 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, a x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{4}}-\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, b^{3}}\right) A +\left(\frac{40 a x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{3}}-\frac{2 \sqrt{b \,x^{3}+a}\, a^{2} x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{5}}+\frac{448 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{405 \sqrt{b \,x^{3}+a}\, b^{4}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b^{3}}\right) B"," ",0,"B*(-2/9*a^2*x/b^5*(b*x^3+a)^(1/2)/(x^3+a/b)^2+40/27/b^3*a*x/((x^3+a/b)*b)^(1/2)+2/5/b^3*x*(b*x^3+a)^(1/2)+448/405*I*a/b^4*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(2/9*a*x/b^4*(b*x^3+a)^(1/2)/(x^3+a/b)^2-22/27/b^2*x/((x^3+a/b)*b)^(1/2)-32/81*I/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
250,1,669,220,0.077000," ","int(x^3*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\left(\frac{4 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, a \,b^{2}}-\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{3}}\right) A +\left(-\frac{22 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, a x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{4}}-\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, b^{3}}\right) B"," ",0,"B*(2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2*a/b^4*x-22/27/((x^3+a/b)*b)^(1/2)/b^2*x-32/81*I/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(-2/9*x/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^2+4/27/b/a*x/((x^3+a/b)*b)^(1/2)-4/81*I/b^2/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
251,1,674,220,0.073000," ","int((B*x^3+A)/(b*x^3+a)^(5/2),x)","\left(\frac{14 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}-\frac{14 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{2} b}\right) A +\left(\frac{4 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, a \,b^{2}}-\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{3}}\right) B"," ",0,"B*(-2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/b^3*x+4/27/((x^3+a/b)*b)^(1/2)/a/b*x-4/81*I/b^2/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(2/9/a*x/b^2*(b*x^3+a)^(1/2)/(x^3+a/b)^2+14/27/a^2*x/((x^3+a/b)*b)^(1/2)-14/81*I/a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
252,1,689,233,0.082000," ","int((B*x^3+A)/x^3/(b*x^3+a)^(5/2),x)","\left(-\frac{32 b x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}-\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b}+\frac{91 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{162 \sqrt{b \,x^{3}+a}\, a^{3}}-\frac{\sqrt{b \,x^{3}+a}}{2 a^{3} x^{2}}\right) A +\left(\frac{14 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}-\frac{14 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{2} b}\right) B"," ",0,"B*(2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a/b^2*x+14/27/((x^3+a/b)*b)^(1/2)/a^2*x-14/81*I/a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+A*(-2/9/a^2*x/b*(b*x^3+a)^(1/2)/(x^3+a/b)^2-32/27*b/a^3*x/((x^3+a/b)*b)^(1/2)-1/2/a^3*(b*x^3+a)^(1/2)/x^2+91/162*I/a^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
253,1,722,263,0.086000," ","int((B*x^3+A)/x^6/(b*x^3+a)^(5/2),x)","\left(\frac{50 b^{2} x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{4}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a^{3}}-\frac{1729 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{1620 \sqrt{b \,x^{3}+a}\, a^{4}}+\frac{27 \sqrt{b \,x^{3}+a}\, b}{20 a^{4} x^{2}}-\frac{\sqrt{b \,x^{3}+a}}{5 a^{3} x^{5}}\right) A +\left(-\frac{32 b x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}-\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b}+\frac{91 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{162 \sqrt{b \,x^{3}+a}\, a^{3}}-\frac{\sqrt{b \,x^{3}+a}}{2 a^{3} x^{2}}\right) B"," ",0,"A*(-1/5/a^3*(b*x^3+a)^(1/2)/x^5+27/20/a^4*b*(b*x^3+a)^(1/2)/x^2+2/9/a^3*x*(b*x^3+a)^(1/2)/(x^3+a/b)^2+50/27*b^2/a^4*x/((x^3+a/b)*b)^(1/2)-1729/1620*I/a^4*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+B*(-2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a^2/b*x-32/27/((x^3+a/b)*b)^(1/2)/a^3*b*x-1/2*(b*x^3+a)^(1/2)/a^3/x^2+91/162*I/a^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
254,1,997,435,0.099000," ","int(x^7*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\left(-\frac{26 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{4}}-\frac{80 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, b^{3}}\right) A +\left(\frac{44 a \,x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{3}}-\frac{2 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{5}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7 b^{3}}+\frac{1280 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{567 \sqrt{b \,x^{3}+a}\, b^{4}}\right) B"," ",0,"B*(-2/9*a^2*x^2/b^5*(b*x^3+a)^(1/2)/(x^3+a/b)^2+44/27/b^3*a*x^2/((x^3+a/b)*b)^(1/2)+2/7/b^3*x^2*(b*x^3+a)^(1/2)+1280/567*I*a/b^4*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(2/9*a*x^2/b^4*(b*x^3+a)^(1/2)/(x^3+a/b)^2-26/27/b^2*x^2/((x^3+a/b)*b)^(1/2)-80/81*I/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
255,1,981,421,0.082000," ","int(x^4*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\left(\frac{8 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a b}-\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{3}}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a \,b^{2}}\right) A +\left(-\frac{26 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{4}}-\frac{80 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, b^{3}}\right) B"," ",0,"B*(2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2*a/b^4*x^2-26/27/((x^3+a/b)*b)^(1/2)/b^2*x^2-80/81*I/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-2/9*x^2/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^2+8/27/b/a*x^2/((x^3+a/b)*b)^(1/2)+8/81*I/b^2/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
256,1,986,425,0.077000," ","int(x*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\left(\frac{10 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}+\frac{10 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{2} b}\right) A +\left(\frac{8 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a b}-\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{3}}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a \,b^{2}}\right) B"," ",0,"B*(-2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/b^3*x^2+8/27/((x^3+a/b)*b)^(1/2)/a/b*x^2+8/81*I/b^2/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(2/9/a*x^2/b^2*(b*x^3+a)^(1/2)/(x^3+a/b)^2+10/27/a^2*x^2/((x^3+a/b)*b)^(1/2)+10/81*I/a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
257,1,1001,438,0.096000," ","int((B*x^3+A)/x^2/(b*x^3+a)^(5/2),x)","\left(-\frac{28 b \,x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}-\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b}-\frac{55 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{3}}-\frac{\sqrt{b \,x^{3}+a}}{a^{3} x}\right) A +\left(\frac{10 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}+\frac{10 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{2} b}\right) B"," ",0,"B*(2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a/b^2*x^2+10/27/((x^3+a/b)*b)^(1/2)/a^2*x^2+10/81*I/a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+A*(-2/9/a^2*x^2/b*(b*x^3+a)^(1/2)/(x^3+a/b)^2-28/27*b/a^3*x^2/((x^3+a/b)*b)^(1/2)-1/a^3*(b*x^3+a)^(1/2)/x-55/81*I/a^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
258,1,1034,464,0.115000," ","int((B*x^3+A)/x^5/(b*x^3+a)^(5/2),x)","\left(\frac{46 b^{2} x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{4}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a^{3}}+\frac{935 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{648 \sqrt{b \,x^{3}+a}\, a^{4}}+\frac{21 \sqrt{b \,x^{3}+a}\, b}{8 a^{4} x}-\frac{\sqrt{b \,x^{3}+a}}{4 a^{3} x^{4}}\right) A +\left(-\frac{28 b \,x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}-\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b}-\frac{55 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{3}}-\frac{\sqrt{b \,x^{3}+a}}{a^{3} x}\right) B"," ",0,"A*(-1/4/a^3*(b*x^3+a)^(1/2)/x^4+21/8/a^4*b*(b*x^3+a)^(1/2)/x+2/9/a^3*x^2*(b*x^3+a)^(1/2)/(x^3+a/b)^2+46/27*b^2/a^4*x^2/((x^3+a/b)*b)^(1/2)+935/648*I/a^4*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+B*(-2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a^2/b*x^2-28/27/((x^3+a/b)*b)^(1/2)/a^3*b*x^2-(b*x^3+a)^(1/2)/a^3/x-55/81*I/a^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
259,1,506,76,4.458000," ","int(x^8*(d*x^3+c)^(1/2)/(d*x^3+4*c),x)","\frac{16 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{2}}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{6}}{15}+\frac{2 \sqrt{d \,x^{3}+c}\, c \,x^{3}}{45 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c^{2}}{45 d^{2}}\right) d -\frac{8 \left(d \,x^{3}+c \right)^{\frac{3}{2}} c}{9 d}}{d^{2}}"," ",0,"1/d^2*(d*(2/15*x^6*(d*x^3+c)^(1/2)+2/45*c/d*x^3*(d*x^3+c)^(1/2)-4/45*c^2*(d*x^3+c)^(1/2)/d^2)-8/9*c/d*(d*x^3+c)^(3/2))+16*c^2/d^2*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*d*(2*x+1/d*(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3)))/(-c*d^2)^(1/3))^(1/2)*(d*(x-1/d*(-c*d^2)^(1/3))/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3)))^(1/2)*(-1/2*I*d*(2*x+1/d*(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3)))/(-c*d^2)^(1/3))^(1/2)/(d*x^3+c)^(1/2)*(I*(-c*d^2)^(1/3)*_alpha*3^(1/2)*d-I*3^(1/2)*(-c*d^2)^(2/3)+2*_alpha^2*d^2-(-c*d^2)^(1/3)*_alpha*d-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/d*(-c*d^2)^(1/3)-1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2),1/6/d*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha+I*3^(1/2)*c*d-3*(-c*d^2)^(2/3)*_alpha-3*c*d)/c,(I*3^(1/2)/d*(-c*d^2)^(1/3)/(-3/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*d+4*c)))","C"
260,1,446,59,0.170000," ","int(x^5*(d*x^3+c)^(1/2)/(d*x^3+4*c),x)","-\frac{4 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d}+\frac{2 \left(d \,x^{3}+c \right)^{\frac{3}{2}}}{9 d^{2}}"," ",0,"2/9*(d*x^3+c)^(3/2)/d^2-4*c/d*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c)))","C"
261,1,425,44,0.152000," ","int(x^2*(d*x^3+c)^(1/2)/(d*x^3+4*c),x)","\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
262,1,468,46,0.187000," ","int((d*x^3+c)^(1/2)/x/(d*x^3+4*c),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) d}{4 c}+\frac{-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}}{4 c}"," ",0,"-1/4/c*d*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c)))+1/4/c*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
263,1,511,65,0.191000," ","int((d*x^3+c)^(1/2)/x^4/(d*x^3+4*c),x)","\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{16 c^{2}}+\frac{-\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 \sqrt{c}}-\frac{\sqrt{d \,x^{3}+c}}{3 x^{3}}}{4 c}-\frac{\left(-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}\right) d}{16 c^{2}}"," ",0,"1/4/c*(-1/3*(d*x^3+c)^(1/2)/x^3-1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2))+1/16*d^2/c^2*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c)))-1/16/c^2*d*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
264,1,1309,494,0.257000," ","int(x^4*(d*x^3+c)^(1/2)/(d*x^3+4*c),x)","-\frac{4 \left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}\right) c}{d}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}\, d}}{d}"," ",0,"1/d*(2/7*x^2*(d*x^3+c)^(1/2)-2/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-4*c/d*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c)))","C"
265,1,848,476,0.227000," ","int(x*(d*x^3+c)^(1/2)/(d*x^3+4*c),x)","-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}"," ",0,"-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
266,1,1306,496,0.255000," ","int((d*x^3+c)^(1/2)/x^2/(d*x^3+4*c),x)","-\frac{\left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}\right) d}{4 c}+\frac{-\frac{\sqrt{d \,x^{3}+c}}{x}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{\sqrt{d \,x^{3}+c}}}{4 c}"," ",0,"-1/4/c*d*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c)))+1/4/c*(-(d*x^3+c)^(1/2)/x-I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
267,1,1003,52,0.260000," ","int(x^3*(d*x^3+c)^(1/2)/(d*x^3+4*c),x)","-\frac{4 \left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2}}\right) c}{d}+\frac{-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{5 \sqrt{d \,x^{3}+c}\, d}+\frac{2 \sqrt{d \,x^{3}+c}\, x}{5}}{d}"," ",0,"1/d*(2/5*x*(d*x^3+c)^(1/2)-2/5*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-4*c/d*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c)))","C"
268,1,696,50,0.145000," ","int((d*x^3+c)^(1/2)/(d*x^3+4*c),x)","-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2}}"," ",0,"-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
269,1,1002,52,0.191000," ","int((d*x^3+c)^(1/2)/x^3/(d*x^3+4*c),x)","-\frac{\left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2}}\right) d}{4 c}+\frac{-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}}{2 x^{2}}}{4 c}"," ",0,"-1/4/c*d*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c)))+1/4/c*(-1/2*(d*x^3+c)^(1/2)/x^2-1/2*I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))","C"
270,1,467,59,0.245000," ","int(x^8/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c}{9 d^{2}}\right) d -\frac{8 \sqrt{d \,x^{3}+c}\, c}{3 d}}{d^{2}}-\frac{16 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 d^{5} \sqrt{d \,x^{3}+c}}"," ",0,"1/d^2*(d*(2/9/d*x^3*(d*x^3+c)^(1/2)-4/9*c*(d*x^3+c)^(1/2)/d^2)-8/3*c*(d*x^3+c)^(1/2)/d)-16/9*I*c/d^5*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
271,1,425,44,0.180000," ","int(x^5/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","\frac{2 \sqrt{d \,x^{3}+c}}{3 d^{2}}+\frac{4 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 d^{4} \sqrt{d \,x^{3}+c}}"," ",0,"2/3*(d*x^3+c)^(1/2)/d^2+4/9*I/d^4*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
272,1,413,29,0.175000," ","int(x^2/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 c \,d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"-1/9*I/d^3/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
273,1,433,46,0.192000," ","int(1/x/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","-\frac{\arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{6 c^{\frac{3}{2}}}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{36 c^{2} d^{2} \sqrt{d \,x^{3}+c}}"," ",0,"1/36*I/c^2/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))-1/6*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2)","C"
274,1,477,65,0.227000," ","int(1/x^4/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{24 c^{\frac{5}{2}}}+\frac{\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}-\frac{\sqrt{d \,x^{3}+c}}{3 c \,x^{3}}}{4 c}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{144 c^{3} d \sqrt{d \,x^{3}+c}}"," ",0,"1/4/c*(-1/3*(d*x^3+c)^(1/2)/c/x^3+1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))-1/144*I/d/c^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))+1/24*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2)","C"
275,1,848,476,0.252000," ","int(x^4/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d^{2}}+\frac{4 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 d^{4} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}"," ",0,"-2/3*I/d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+4/9*I/d^4*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
276,1,416,139,0.178000," ","int(x/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 c \,d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}"," ",0,"-1/9*I/d^3/c*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
277,1,874,496,0.191000," ","int(1/x^2/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","\frac{-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{c x}}{4 c}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{36 c^{2} d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}"," ",0,"1/36*I/c^2/d^2*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))+1/4/c*(-(d*x^3+c)^(1/2)/c/x-1/3*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
278,1,696,52,0.239000," ","int(x^3/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d^{2}}+\frac{4 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 d^{4} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2}}"," ",0,"-2/3*I/d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+4/9*I/d^4*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
279,1,416,50,0.151000," ","int(1/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 c \,d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2}}"," ",0,"-1/9*I/d^3/c*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))","C"
280,1,722,52,0.191000," ","int(1/x^3/(d*x^3+4*c)/(d*x^3+c)^(1/2),x)","\frac{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{2 c \,x^{2}}}{4 c}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)}{6 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{36 c^{2} d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}+4 c \right)^{2}}"," ",0,"1/36*I/c^2/d^2*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/6*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d+4*c))+1/4/c*(-1/2/c*(d*x^3+c)^(1/2)/x^2+1/6*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))","C"
281,1,164,92,0.796000," ","int(x/(-x^3+4)/(-x^3+1)^(1/2),x)","\frac{i \sqrt{i \left(2 x +1-i \sqrt{3}\right)}\, \sqrt{\frac{x -1}{i \sqrt{3}-3}}\, \sqrt{-\frac{i \left(2 x +1+i \sqrt{3}\right)}{2}}\, \left(-2 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\RootOf \left(\textit{\_Z}^{3}-4\right)+1+i \sqrt{3}\, \left(-\RootOf \left(\textit{\_Z}^{3}-4\right)+1\right)\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, -\frac{i \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}}{3}+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right)}{2}+\frac{i \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3}-4\right)}{6}-\frac{1}{2}+\frac{i \sqrt{3}}{6}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{36 \sqrt{-x^{3}+1}}"," ",0,"1/36*I*2^(1/2)*sum(_alpha^2*(1/2*I*(2*x+1-I*3^(1/2)))^(1/2)*((x-1)/(I*3^(1/2)-3))^(1/2)*(-1/2*I*(2*x+1+I*3^(1/2)))^(1/2)/(-x^3+1)^(1/2)*(-2*_alpha^2+_alpha+1+I*3^(1/2)*(1-_alpha))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),1/2*_alpha-1/3*I*_alpha^2*3^(1/2)-1/2+1/6*I*_alpha*3^(1/2)+1/6*I*3^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2)),_alpha=RootOf(_Z^3-4))","C"
282,1,582,87,0.354000," ","int(x^11*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x)","-\frac{512 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) c^{3}}{d^{3}}-\frac{8 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{6}}{15}+\frac{2 \sqrt{d \,x^{3}+c}\, c \,x^{3}}{45 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c^{2}}{45 d^{2}}\right) c}{d^{2}}-\frac{\frac{2 \sqrt{d \,x^{3}+c}\, x^{9}}{21}+\frac{2 \sqrt{d \,x^{3}+c}\, c \,x^{6}}{105 d}-\frac{8 \sqrt{d \,x^{3}+c}\, c^{2} x^{3}}{315 d^{2}}+\frac{16 \sqrt{d \,x^{3}+c}\, c^{3}}{315 d^{3}}}{d}-\frac{128 \left(d \,x^{3}+c \right)^{\frac{3}{2}} c^{2}}{9 d^{4}}"," ",0,"-1/d*(2/21*x^9*(d*x^3+c)^(1/2)+2/105*c/d*x^6*(d*x^3+c)^(1/2)-8/315*c^2/d^2*x^3*(d*x^3+c)^(1/2)+16/315*c^3*(d*x^3+c)^(1/2)/d^3)-8*c/d^2*(2/15*(d*x^3+c)^(1/2)*x^6+2/45*(d*x^3+c)^(1/2)*c/d*x^3-4/45*(d*x^3+c)^(1/2)*c^2/d^2)-128/9*c^2*(d*x^3+c)^(3/2)/d^4-512*c^3/d^3*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
283,1,507,70,0.161000," ","int(x^8*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x)","-\frac{64 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{2}}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{6}}{15}+\frac{2 \sqrt{d \,x^{3}+c}\, c \,x^{3}}{45 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c^{2}}{45 d^{2}}\right) d +\frac{16 \left(d \,x^{3}+c \right)^{\frac{3}{2}} c}{9 d}}{d^{2}}"," ",0,"-1/d^2*((2/15*(d*x^3+c)^(1/2)*x^6+2/45*(d*x^3+c)^(1/2)*c/d*x^3-4/45*(d*x^3+c)^(1/2)*c^2/d^2)*d+16/9*(d*x^3+c)^(3/2)*c/d)-64*c^2/d^2*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
284,1,446,53,0.180000," ","int(x^5*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x)","-\frac{8 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d}-\frac{2 \left(d \,x^{3}+c \right)^{\frac{3}{2}}}{9 d^{2}}"," ",0,"-2/9*(d*x^3+c)^(3/2)/d^2-8*c/d*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
285,1,425,38,0.152000," ","int(x^2*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x)","-\frac{2 \sqrt{d \,x^{3}+c}}{3 d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"-2/3*(d*x^3+c)^(1/2)/d-1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
286,1,468,40,0.158000," ","int((d*x^3+c)^(1/2)/x/(-d*x^3+8*c),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) d}{8 c}+\frac{-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}}{8 c}"," ",0,"-1/8/c*d*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/8/c*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
287,1,511,59,0.176000," ","int((d*x^3+c)^(1/2)/x^4/(-d*x^3+8*c),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{64 c^{2}}+\frac{-\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 \sqrt{c}}-\frac{\sqrt{d \,x^{3}+c}}{3 x^{3}}}{8 c}+\frac{\left(-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}\right) d}{64 c^{2}}"," ",0,"1/8/c*(-1/3*(d*x^3+c)^(1/2)/x^3-1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2))-1/64*d^2/c^2*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*d*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
288,1,574,81,0.186000," ","int((d*x^3+c)^(1/2)/x^7/(-d*x^3+8*c),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{512 c^{3}}+\frac{\frac{d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{12 c^{\frac{3}{2}}}-\frac{\sqrt{d \,x^{3}+c}\, d}{12 c \,x^{3}}-\frac{\sqrt{d \,x^{3}+c}}{6 x^{6}}}{8 c}+\frac{\left(-\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 \sqrt{c}}-\frac{\sqrt{d \,x^{3}+c}}{3 x^{3}}\right) d}{64 c^{2}}+\frac{\left(-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}\right) d^{2}}{512 c^{3}}"," ",0,"1/64/c^2*d*(-1/3*(d*x^3+c)^(1/2)/x^3-1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2))+1/8/c*(-1/6*(d*x^3+c)^(1/2)/x^6-1/12*d*(d*x^3+c)^(1/2)/c/x^3+1/12*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))-1/512/c^3*d^3*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/512/c^3*d^2*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
289,1,1788,470,0.237000," ","int(x^7*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x)","-\frac{64 \left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c^{2}}{d^{2}}-\frac{8 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}\, d}\right) c +\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{5}}{13}+\frac{6 \sqrt{d \,x^{3}+c}\, c \,x^{2}}{91 d}+\frac{8 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c^{2}}{91 \sqrt{d \,x^{3}+c}\, d^{2}}\right) d}{d^{2}}"," ",0,"-1/d^2*(d*(2/13*x^5*(d*x^3+c)^(1/2)+6/91*c*x^2*(d*x^3+c)^(1/2)/d+8/91*I*c^2/d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+8*c*(2/7*(d*x^3+c)^(1/2)*x^2-2/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))))-64*c^2/d^2*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
290,1,1310,450,0.171000," ","int(x^4*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x)","-\frac{8 \left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c}{d}-\frac{\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}\, d}}{d}"," ",0,"-1/d*(2/7*(d*x^3+c)^(1/2)*x^2-2/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-8*c/d*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
291,1,848,431,0.156000," ","int(x*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x)","\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
292,1,1306,452,0.168000," ","int((d*x^3+c)^(1/2)/x^2/(-d*x^3+8*c),x)","-\frac{\left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) d}{8 c}+\frac{-\frac{\sqrt{d \,x^{3}+c}}{x}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{\sqrt{d \,x^{3}+c}}}{8 c}"," ",0,"1/8/c*(-(d*x^3+c)^(1/2)/x-I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/8/c*d*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
293,1,1782,470,0.178000," ","int((d*x^3+c)^(1/2)/x^5/(-d*x^3+8*c),x)","-\frac{\left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) d^{2}}{64 c^{2}}+\frac{-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) d}{8 \sqrt{d \,x^{3}+c}\, c}-\frac{3 \sqrt{d \,x^{3}+c}\, d}{8 c x}-\frac{\sqrt{d \,x^{3}+c}}{4 x^{4}}}{8 c}+\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{x}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{\sqrt{d \,x^{3}+c}}\right) d}{64 c^{2}}"," ",0,"1/8/c*(-1/4*(d*x^3+c)^(1/2)/x^4-3/8*d*(d*x^3+c)^(1/2)/c/x-1/8*I*d/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/64/c^2*d*(-(d*x^3+c)^(1/2)/x-I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/64*d^2/c^2*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
294,1,2280,490,0.180000," ","int((d*x^3+c)^(1/2)/x^8/(-d*x^3+8*c),x)","\text{Expression too large to display}"," ",0,"1/64/c^2*d*(-1/4*(d*x^3+c)^(1/2)/x^4-3/8*(d*x^3+c)^(1/2)/c*d/x-1/8*I*d/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/8/c*(-1/7*(d*x^3+c)^(1/2)/x^7-3/56*d*(d*x^3+c)^(1/2)/c/x^4+15/112*d^2*(d*x^3+c)^(1/2)/c^2/x+5/112*I*d^2/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/512/c^3*d^2*(-(d*x^3+c)^(1/2)/x-I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/512/c^3*d^3*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
295,1,634,104,0.252000," ","int(x^11*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x)","-\frac{512 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) c^{3}}{d^{3}}-\frac{8 \left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{9}}{21}+\frac{16 \sqrt{d \,x^{3}+c}\, c \,x^{6}}{105}+\frac{2 \sqrt{d \,x^{3}+c}\, c^{2} x^{3}}{105 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c^{3}}{105 d^{2}}\right) c}{d^{2}}-\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{12}}{27}+\frac{20 \sqrt{d \,x^{3}+c}\, c \,x^{9}}{189}+\frac{2 \sqrt{d \,x^{3}+c}\, c^{2} x^{6}}{315 d}-\frac{8 \sqrt{d \,x^{3}+c}\, c^{3} x^{3}}{945 d^{2}}+\frac{16 \sqrt{d \,x^{3}+c}\, c^{4}}{945 d^{3}}}{d}-\frac{128 \left(d \,x^{3}+c \right)^{\frac{5}{2}} c^{2}}{15 d^{4}}"," ",0,"-1/d*(2/27*d*x^12*(d*x^3+c)^(1/2)+20/189*c*x^9*(d*x^3+c)^(1/2)+2/315*c^2/d*x^6*(d*x^3+c)^(1/2)-8/945*c^3/d^2*x^3*(d*x^3+c)^(1/2)+16/945*c^4/d^3*(d*x^3+c)^(1/2))-8*c/d^2*(2/21*d*x^9*(d*x^3+c)^(1/2)+16/105*c*x^6*(d*x^3+c)^(1/2)+2/105*c^2/d*x^3*(d*x^3+c)^(1/2)-4/105*c^3/d^2*(d*x^3+c)^(1/2))-128/15*c^2*(d*x^3+c)^(5/2)/d^4-512*c^3/d^3*(2/9*x^3*(d*x^3+c)^(1/2)+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
296,1,541,87,0.157000," ","int(x^8*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x)","-\frac{64 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{2}}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{9}}{21}+\frac{16 \sqrt{d \,x^{3}+c}\, c \,x^{6}}{105}+\frac{2 \sqrt{d \,x^{3}+c}\, c^{2} x^{3}}{105 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c^{3}}{105 d^{2}}\right) d +\frac{16 \left(d \,x^{3}+c \right)^{\frac{5}{2}} c}{15 d}}{d^{2}}"," ",0,"-1/d^2*(d*(2/21*(d*x^3+c)^(1/2)*d*x^9+16/105*(d*x^3+c)^(1/2)*c*x^6+2/105*(d*x^3+c)^(1/2)*c^2/d*x^3-4/105*(d*x^3+c)^(1/2)*c^3/d^2)+16/15*c/d*(d*x^3+c)^(5/2))-64*c^2/d^2*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
297,1,462,70,0.176000," ","int(x^5*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x)","-\frac{8 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d}-\frac{2 \left(d \,x^{3}+c \right)^{\frac{5}{2}}}{15 d^{2}}"," ",0,"-2/15*(d*x^3+c)^(5/2)/d^2-8*c/d*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
298,1,441,53,0.158000," ","int(x^2*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x)","-\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}-\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}-\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"-2/9*(d*x^3+c)^(1/2)*x^3-56/9*(d*x^3+c)^(1/2)*c/d-3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
299,1,500,51,0.189000," ","int((d*x^3+c)^(3/2)/x/(-d*x^3+8*c),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) d}{8 c}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}}{8 c}"," ",0,"-1/8/c*d*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/8/c*(2/9*d*x^3*(d*x^3+c)^(1/2)+8/9*c*(d*x^3+c)^(1/2)-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
300,1,556,56,0.262000," ","int((d*x^3+c)^(3/2)/x^4/(-d*x^3+8*c),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{64 c^{2}}+\frac{-\sqrt{c}\, d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)+\frac{2 \sqrt{d \,x^{3}+c}\, d}{3}-\frac{\sqrt{d \,x^{3}+c}\, c}{3 x^{3}}}{8 c}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}\right) d}{64 c^{2}}"," ",0,"1/8/c*(-1/3*c*(d*x^3+c)^(1/2)/x^3+2/3*d*(d*x^3+c)^(1/2)-c^(1/2)*d*arctanh((d*x^3+c)^(1/2)/c^(1/2)))-1/64*d^2/c^2*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*d*(2/9*(d*x^3+c)^(1/2)*d*x^3+8/9*(d*x^3+c)^(1/2)*c-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
301,1,617,78,0.235000," ","int((d*x^3+c)^(3/2)/x^7/(-d*x^3+8*c),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{512 c^{3}}+\frac{-\frac{d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{4 \sqrt{c}}-\frac{5 \sqrt{d \,x^{3}+c}\, d}{12 x^{3}}-\frac{\sqrt{d \,x^{3}+c}\, c}{6 x^{6}}}{8 c}+\frac{\left(-\sqrt{c}\, d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)+\frac{2 \sqrt{d \,x^{3}+c}\, d}{3}-\frac{\sqrt{d \,x^{3}+c}\, c}{3 x^{3}}\right) d}{64 c^{2}}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}\right) d^{2}}{512 c^{3}}"," ",0,"1/64/c^2*d*(-1/3*(d*x^3+c)^(1/2)*c/x^3+2/3*(d*x^3+c)^(1/2)*d-c^(1/2)*d*arctanh((d*x^3+c)^(1/2)/c^(1/2)))+1/8/c*(-1/6*c*(d*x^3+c)^(1/2)/x^6-5/12*d*(d*x^3+c)^(1/2)/x^3-1/4*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2))-1/512/c^3*d^3*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/512/c^3*d^2*(2/9*(d*x^3+c)^(1/2)*d*x^3+8/9*(d*x^3+c)^(1/2)*c-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
302,1,1840,487,0.275000," ","int(x^7*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x)","-\frac{64 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7}-\frac{44 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}\, d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c^{2}}{d^{2}}-\frac{8 \left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{5}}{13}+\frac{32 \sqrt{d \,x^{3}+c}\, c \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c^{2}}{91 \sqrt{d \,x^{3}+c}\, d}\right) c +\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{8}}{19}+\frac{44 \sqrt{d \,x^{3}+c}\, c \,x^{5}}{247}+\frac{54 \sqrt{d \,x^{3}+c}\, c^{2} x^{2}}{1729 d}+\frac{72 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c^{3}}{1729 \sqrt{d \,x^{3}+c}\, d^{2}}\right) d}{d^{2}}"," ",0,"-1/d^2*(d*(2/19*d*x^8*(d*x^3+c)^(1/2)+44/247*c*x^5*(d*x^3+c)^(1/2)+54/1729*c^2/d*x^2*(d*x^3+c)^(1/2)+72/1729*I*c^3/d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+8*c*(2/13*x^5*d*(d*x^3+c)^(1/2)+32/91*c*x^2*(d*x^3+c)^(1/2)-18/91*I*c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))))-64*c^2/d^2*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
303,1,1344,467,0.164000," ","int(x^4*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x)","-\frac{8 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7}-\frac{44 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}\, d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c}{d}-\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{5}}{13}+\frac{32 \sqrt{d \,x^{3}+c}\, c \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c^{2}}{91 \sqrt{d \,x^{3}+c}\, d}}{d}"," ",0,"-1/d*(2/13*(d*x^3+c)^(1/2)*d*x^5+32/91*(d*x^3+c)^(1/2)*c*x^2-18/91*I*c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-8*c/d*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
304,1,864,447,0.179000," ","int(x*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x)","-\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7}+\frac{44 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}\, d}-\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"-2/7*(d*x^3+c)^(1/2)*x^2+44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
305,1,1339,446,0.209000," ","int((d*x^3+c)^(3/2)/x^2/(-d*x^3+8*c),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7}-\frac{44 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}\, d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) d}{8 c}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}\, c}{x}}{8 c}"," ",0,"1/8/c*(-c*(d*x^3+c)^(1/2)/x+2/7*d*x^2*(d*x^3+c)^(1/2)-9/7*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/8/c*d*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
306,1,1810,467,0.214000," ","int((d*x^3+c)^(3/2)/x^5/(-d*x^3+8*c),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7}-\frac{44 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}\, d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) d^{2}}{64 c^{2}}+\frac{-\frac{9 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) d}{8 \sqrt{d \,x^{3}+c}}-\frac{11 \sqrt{d \,x^{3}+c}\, d}{8 x}-\frac{\sqrt{d \,x^{3}+c}\, c}{4 x^{4}}}{8 c}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}\, c}{x}\right) d}{64 c^{2}}"," ",0,"1/8/c*(-1/4*c*(d*x^3+c)^(1/2)/x^4-11/8*d*(d*x^3+c)^(1/2)/x-9/8*I*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/64/c^2*d*(-(d*x^3+c)^(1/2)*c/x+2/7*(d*x^3+c)^(1/2)*d*x^2-9/7*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/64*d^2/c^2*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
307,1,2306,487,0.201000," ","int((d*x^3+c)^(3/2)/x^8/(-d*x^3+8*c),x)","\text{Expression too large to display}"," ",0,"1/64/c^2*d*(-1/4*(d*x^3+c)^(1/2)*c/x^4-11/8*(d*x^3+c)^(1/2)*d/x-9/8*I*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/8/c*(-1/7*c*(d*x^3+c)^(1/2)/x^7-17/56*d*(d*x^3+c)^(1/2)/x^4-27/112*d^2/c*(d*x^3+c)^(1/2)/x-9/112*I/c*d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/512/c^3*d^2*(-(d*x^3+c)^(1/2)*c/x+2/7*(d*x^3+c)^(1/2)*d*x^2-9/7*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/512/c^3*d^3*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
308,1,528,70,0.281000," ","int(x^11/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{8 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c}{9 d^{2}}\right) c}{d^{2}}-\frac{\frac{2 \sqrt{d \,x^{3}+c}\, x^{6}}{15 d}-\frac{8 \sqrt{d \,x^{3}+c}\, c \,x^{3}}{45 d^{2}}+\frac{16 \sqrt{d \,x^{3}+c}\, c^{2}}{45 d^{3}}}{d}-\frac{128 \sqrt{d \,x^{3}+c}\, c^{2}}{3 d^{4}}-\frac{512 i c^{2} \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 d^{6} \sqrt{d \,x^{3}+c}}"," ",0,"-1/d*(2/15/d*x^6*(d*x^3+c)^(1/2)-8/45*c/d^2*x^3*(d*x^3+c)^(1/2)+16/45*c^2*(d*x^3+c)^(1/2)/d^3)-8*c/d^2*(2/9*(d*x^3+c)^(1/2)/d*x^3-4/9*(d*x^3+c)^(1/2)*c/d^2)-128/3*c^2*(d*x^3+c)^(1/2)/d^4-512/27*I*c^2/d^6*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
309,1,468,53,0.158000," ","int(x^8/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c}{9 d^{2}}\right) d +\frac{16 \sqrt{d \,x^{3}+c}\, c}{3 d}}{d^{2}}-\frac{64 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 d^{5} \sqrt{d \,x^{3}+c}}"," ",0,"-1/d^2*((2/9*(d*x^3+c)^(1/2)/d*x^3-4/9*(d*x^3+c)^(1/2)*c/d^2)*d+16/3*(d*x^3+c)^(1/2)*c/d)-64/27*I*c/d^5*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
310,1,425,38,0.168000," ","int(x^5/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{2 \sqrt{d \,x^{3}+c}}{3 d^{2}}-\frac{8 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 d^{4} \sqrt{d \,x^{3}+c}}"," ",0,"-2/3*(d*x^3+c)^(1/2)/d^2-8/27*I/d^4*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
311,1,413,23,0.195000," ","int(x^2/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 c \,d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"-1/27*I/d^3/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
312,1,433,40,0.174000," ","int(1/x/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{\arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{12 c^{\frac{3}{2}}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{216 c^{2} d^{2} \sqrt{d \,x^{3}+c}}"," ",0,"-1/216*I/c^2/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))-1/12*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2)","C"
313,1,477,59,0.186000," ","int(1/x^4/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{96 c^{\frac{5}{2}}}+\frac{\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}-\frac{\sqrt{d \,x^{3}+c}}{3 c \,x^{3}}}{8 c}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1728 c^{3} d \sqrt{d \,x^{3}+c}}"," ",0,"1/8/c*(-1/3*(d*x^3+c)^(1/2)/c/x^3+1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))-1/1728*I/d/c^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))-1/96*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2)","C"
314,1,540,81,0.207000," ","int(1/x^7/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{768 c^{\frac{7}{2}}}+\frac{-\frac{d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{4 c^{\frac{5}{2}}}+\frac{\sqrt{d \,x^{3}+c}\, d}{4 c^{2} x^{3}}-\frac{\sqrt{d \,x^{3}+c}}{6 c \,x^{6}}}{8 c}+\frac{\left(\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}-\frac{\sqrt{d \,x^{3}+c}}{3 c \,x^{3}}\right) d}{64 c^{2}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{13824 c^{4} \sqrt{d \,x^{3}+c}}"," ",0,"1/64/c^2*d*(-1/3*(d*x^3+c)^(1/2)/c/x^3+1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))+1/8/c*(-1/6*(d*x^3+c)^(1/2)/c/x^6+1/4*d*(d*x^3+c)^(1/2)/c^2/x^3-1/4*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2))-1/13824*I/c^4*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))-1/768*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(7/2)","C"
315,1,1311,450,0.237000," ","int(x^7/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7 d}+\frac{8 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{21 \sqrt{d \,x^{3}+c}\, d^{2}}\right) d -\frac{16 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{3 \sqrt{d \,x^{3}+c}\, d}}{d^{2}}-\frac{64 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 d^{5} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"-1/d^2*(d*(2/7*x^2*(d*x^3+c)^(1/2)/d+8/21*I*c/d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-16/3*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-64/27*I*c/d^5*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
316,1,848,431,0.170000," ","int(x^4/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d^{2}}-\frac{8 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 d^{4} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"2/3*I/d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-8/27*I/d^4*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
317,1,416,95,0.165000," ","int(x/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 c \,d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"-1/27*I/d^3/c*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
318,1,874,452,0.167000," ","int(1/x^2/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","\frac{-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{c x}}{8 c}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{216 c^{2} d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"1/8/c*(-(d*x^3+c)^(1/2)/c/x-1/3*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/216*I/c^2/d^2*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
319,1,1351,470,0.199000," ","int(1/x^5/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","\frac{\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) d}{24 \sqrt{d \,x^{3}+c}\, c^{2}}+\frac{5 \sqrt{d \,x^{3}+c}\, d}{8 c^{2} x}-\frac{\sqrt{d \,x^{3}+c}}{4 c \,x^{4}}}{8 c}+\frac{\left(-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{c x}\right) d}{64 c^{2}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1728 c^{3} d \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"1/8/c*(-1/4*(d*x^3+c)^(1/2)/c/x^4+5/8*d*(d*x^3+c)^(1/2)/c^2/x+5/24*I/c^2*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/64/c^2*d*(-(d*x^3+c)^(1/2)/c/x-1/3*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/1728*I/c^3/d*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
320,1,1849,490,0.201000," ","int(1/x^8/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","\frac{-\frac{55 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) d^{2}}{336 \sqrt{d \,x^{3}+c}\, c^{3}}-\frac{55 \sqrt{d \,x^{3}+c}\, d^{2}}{112 c^{3} x}+\frac{11 \sqrt{d \,x^{3}+c}\, d}{56 c^{2} x^{4}}-\frac{\sqrt{d \,x^{3}+c}}{7 c \,x^{7}}}{8 c}+\frac{\left(\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) d}{24 \sqrt{d \,x^{3}+c}\, c^{2}}+\frac{5 \sqrt{d \,x^{3}+c}\, d}{8 c^{2} x}-\frac{\sqrt{d \,x^{3}+c}}{4 c \,x^{4}}\right) d}{64 c^{2}}+\frac{\left(-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{c x}\right) d^{2}}{512 c^{3}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{13824 c^{4} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"1/64/c^2*d*(-1/4*(d*x^3+c)^(1/2)/c/x^4+5/8*(d*x^3+c)^(1/2)/c^2*d/x+5/24*I/c^2*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/8/c*(-1/7*(d*x^3+c)^(1/2)/c/x^7+11/56*d*(d*x^3+c)^(1/2)/c^2/x^4-55/112*d^2*(d*x^3+c)^(1/2)/c^3/x-55/336*I/c^3*d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/512/c^3*d^2*(-(d*x^3+c)^(1/2)/c/x-1/3*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/13824*I/c^4*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
321,1,696,52,0.240000," ","int(x^3/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d^{2}}-\frac{8 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 d^{4} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"2/3*I/d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-8/27*I/d^4*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
322,1,416,50,0.163000," ","int(1/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 c \,d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"-1/27*I/d^3/c*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
323,1,722,52,0.154000," ","int(1/x^3/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","\frac{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{2 c \,x^{2}}}{8 c}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{216 c^{2} d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"1/8/c*(-1/2/c*(d*x^3+c)^(1/2)/x^2+1/6*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/216*I/c^2/d^2*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
324,1,1047,52,0.196000," ","int(1/x^6/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x)","\frac{-\frac{7 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{60 \sqrt{d \,x^{3}+c}\, c^{2}}+\frac{7 \sqrt{d \,x^{3}+c}\, d}{20 c^{2} x^{2}}-\frac{\sqrt{d \,x^{3}+c}}{5 c \,x^{5}}}{8 c}+\frac{\left(\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{2 c \,x^{2}}\right) d}{64 c^{2}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1728 c^{3} d \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"1/8/c*(-1/5/c*(d*x^3+c)^(1/2)/x^5+7/20/c^2*d*(d*x^3+c)^(1/2)/x^2-7/60*I/c^2*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/64/c^2*d*(-1/2*(d*x^3+c)^(1/2)/c/x^2+1/6*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/1728*I/c^3/d*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
325,1,560,70,0.297000," ","int(x^11/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{512 \left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) c^{3}}{d^{3}}-\frac{8 \left(\frac{2 c}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, d^{2}}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d^{2}}\right) c}{d^{2}}-\frac{\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9 d^{2}}-\frac{2 c^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, d^{3}}-\frac{10 \sqrt{d \,x^{3}+c}\, c}{9 d^{3}}}{d}+\frac{128 c^{2}}{3 \sqrt{d \,x^{3}+c}\, d^{4}}"," ",0,"-1/d*(-2/3/d^3*c^2/((x^3+c/d)*d)^(1/2)+2/9/d^2*x^3*(d*x^3+c)^(1/2)-10/9*c*(d*x^3+c)^(1/2)/d^3)-8*c/d^2*(2/3/d^2*c/((x^3+c/d)*d)^(1/2)+2/3*(d*x^3+c)^(1/2)/d^2)+128/3*c^2/d^4/(d*x^3+c)^(1/2)-512*c^3/d^3*(2/27/d/c/((x^3+c/d)*d)^(1/2)+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
326,1,501,53,0.170000," ","int(x^8/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{64 \left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{2}}-\frac{\left(\frac{2 c}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, d^{2}}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d^{2}}\right) d -\frac{16 c}{3 \sqrt{d \,x^{3}+c}\, d}}{d^{2}}"," ",0,"-1/d^2*(d*(2/3/((x^3+c/d)*d)^(1/2)*c/d^2+2/3*(d*x^3+c)^(1/2)/d^2)-16/3*c/d/(d*x^3+c)^(1/2))-64*c^2/d^2*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
327,1,456,38,0.184000," ","int(x^5/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{8 \left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d}+\frac{2}{3 \sqrt{d \,x^{3}+c}\, d^{2}}"," ",0,"2/3/d^2/(d*x^3+c)^(1/2)-8*c/d*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
328,1,435,41,0.214000," ","int(x^2/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"-2/27/((x^3+c/d)*d)^(1/2)/c/d-1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
329,1,485,54,0.189000," ","int(1/x/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{\left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) d}{8 c}+\frac{-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}}{8 c}"," ",0,"-1/8/c*d*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/8/c*(2/3/c/((x^3+c/d)*d)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
330,1,549,74,0.188000," ","int(1/x^4/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{\left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{64 c^{2}}+\frac{\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{c^{\frac{5}{2}}}-\frac{2 d}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{3 c^{2} x^{3}}}{8 c}+\frac{\left(-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}\right) d}{64 c^{2}}"," ",0,"1/8/c*(-1/3*(d*x^3+c)^(1/2)/c^2/x^3-2/3*d/c^2/((x^3+c/d)*d)^(1/2)+d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2))-1/64/c^2*d^2*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*d*(2/3/((x^3+c/d)*d)^(1/2)/c-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
331,1,636,98,0.217000," ","int(1/x^7/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{\left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{512 c^{3}}+\frac{-\frac{5 d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{4 c^{\frac{7}{2}}}+\frac{2 d^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}+\frac{7 \sqrt{d \,x^{3}+c}\, d}{12 c^{3} x^{3}}-\frac{\sqrt{d \,x^{3}+c}}{6 c^{2} x^{6}}}{8 c}+\frac{\left(\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{c^{\frac{5}{2}}}-\frac{2 d}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{3 c^{2} x^{3}}\right) d}{64 c^{2}}+\frac{\left(-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}\right) d^{2}}{512 c^{3}}"," ",0,"1/64/c^2*d*(-1/3*(d*x^3+c)^(1/2)/c^2/x^3-2/3/((x^3+c/d)*d)^(1/2)/c^2*d+d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2))+1/8/c*(-1/6*(d*x^3+c)^(1/2)/c^2/x^6+7/12*d*(d*x^3+c)^(1/2)/c^3/x^3+2/3*d^2/c^3/((x^3+c/d)*d)^(1/2)-5/4*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(7/2))-1/512/c^3*d^3*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/512/c^3*d^2*(2/3/((x^3+c/d)*d)^(1/2)/c-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
332,1,1810,449,0.281000," ","int(x^7/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{64 \left(-\frac{2 x^{2}}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c^{2}}{d^{2}}-\frac{8 \left(\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \sqrt{d \,x^{3}+c}\, c d}\right) c +\left(-\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, d}-\frac{8 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \sqrt{d \,x^{3}+c}\, d^{2}}\right) d}{d^{2}}"," ",0,"-1/d^2*(d*(-2/3/d*x^2/((x^3+c/d)*d)^(1/2)-8/9*I/d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+8*c*(2/3/c*x^2/((x^3+c/d)*d)^(1/2)+2/9*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))))-64*c^2/d^2*(-2/27/c^2*x^2/((x^3+c/d)*d)^(1/2)-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
333,1,1346,455,0.162000," ","int(x^4/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{8 \left(-\frac{2 x^{2}}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c}{d}-\frac{\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \sqrt{d \,x^{3}+c}\, c d}}{d}"," ",0,"-1/d*(2/3/((x^3+c/d)*d)^(1/2)/c*x^2+2/9*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-8*c/d*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
334,1,875,452,0.171000," ","int(x/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","\frac{2 x^{2}}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2+2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
335,1,1361,469,0.225000," ","int(1/x^2/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{\left(-\frac{2 x^{2}}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) d}{8 c}+\frac{-\frac{2 d \,x^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \sqrt{d \,x^{3}+c}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{c^{2} x}}{8 c}"," ",0,"1/8/c*(-2/3*d/c^2*x^2/((x^3+c/d)*d)^(1/2)-(d*x^3+c)^(1/2)/c^2/x-5/9*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/8/c*d*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
336,1,1864,487,0.216000," ","int(1/x^5/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{\left(-\frac{2 x^{2}}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) d^{2}}{64 c^{2}}+\frac{\frac{2 d^{2} x^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}+\frac{55 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) d}{72 \sqrt{d \,x^{3}+c}\, c^{3}}+\frac{13 \sqrt{d \,x^{3}+c}\, d}{8 c^{3} x}-\frac{\sqrt{d \,x^{3}+c}}{4 c^{2} x^{4}}}{8 c}+\frac{\left(-\frac{2 d \,x^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \sqrt{d \,x^{3}+c}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{c^{2} x}\right) d}{64 c^{2}}"," ",0,"1/8/c*(-1/4*(d*x^3+c)^(1/2)/c^2/x^4+13/8*d*(d*x^3+c)^(1/2)/c^3/x+2/3*d^2/c^3*x^2/((x^3+c/d)*d)^(1/2)+55/72*I/c^3*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/64/c^2*d*(-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x^2-(d*x^3+c)^(1/2)/c^2/x-5/9*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/64/c^2*d^2*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
337,1,2389,507,0.199000," ","int(1/x^8/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/64/c^2*d*(-1/4*(d*x^3+c)^(1/2)/c^2/x^4+13/8*(d*x^3+c)^(1/2)/c^3*d/x+2/3/((x^3+c/d)*d)^(1/2)/c^3*d^2*x^2+55/72*I/c^3*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/8/c*(-1/7*(d*x^3+c)^(1/2)/c^2/x^7+25/56*d*(d*x^3+c)^(1/2)/c^3/x^4-237/112*d^2*(d*x^3+c)^(1/2)/c^4/x-2/3*d^3/c^4*x^2/((x^3+c/d)*d)^(1/2)-935/1008*I/c^4*d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/512/c^3*d^2*(-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x^2-(d*x^3+c)^(1/2)/c^2/x-5/9*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/512/c^3*d^3*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
338,1,1038,52,0.243000," ","int(x^3/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{8 \left(-\frac{2 x}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) c}{d}-\frac{\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \sqrt{d \,x^{3}+c}\, c d}}{d}"," ",0,"-1/d*(2/3/c*x/((x^3+c/d)*d)^(1/2)-2/9*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-8*c/d*(-2/27/c^2*x/((x^3+c/d)*d)^(1/2)+2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
339,1,721,50,0.161000," ","int(1/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","\frac{2 x}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"2/27/((x^3+c/d)*d)^(1/2)/c^2*x-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
340,1,1053,52,0.200000," ","int(1/x^3/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{\left(-\frac{2 x}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) d}{8 c}+\frac{-\frac{2 d x}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{7 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 \sqrt{d \,x^{3}+c}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{2 c^{2} x^{2}}}{8 c}"," ",0,"1/8/c*(-1/2/c^2*(d*x^3+c)^(1/2)/x^2-2/3*d/c^2*x/((x^3+c/d)*d)^(1/2)+7/18*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/8/c*d*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x+2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
341,1,1402,52,0.191000," ","int(1/x^6/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x)","-\frac{\left(-\frac{2 x}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) d^{2}}{64 c^{2}}+\frac{\frac{2 d^{2} x}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}-\frac{91 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{180 \sqrt{d \,x^{3}+c}\, c^{3}}+\frac{17 \sqrt{d \,x^{3}+c}\, d}{20 c^{3} x^{2}}-\frac{\sqrt{d \,x^{3}+c}}{5 c^{2} x^{5}}}{8 c}+\frac{\left(-\frac{2 d x}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{7 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 \sqrt{d \,x^{3}+c}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{2 c^{2} x^{2}}\right) d}{64 c^{2}}"," ",0,"1/8/c*(-1/5/c^2*(d*x^3+c)^(1/2)/x^5+17/20/c^3*d*(d*x^3+c)^(1/2)/x^2+2/3*d^2/c^3*x/((x^3+c/d)*d)^(1/2)-91/180*I/c^3*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/64/c^2*d*(-1/2*(d*x^3+c)^(1/2)/c^2/x^2-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x+7/18*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/64/c^2*d^2*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x+2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
342,1,977,531,0.775000," ","int(x*(b*x^3+a)^(1/2)/(b*x^3+2*a*(5+3*3^(1/2))),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, b}+\frac{i \left(2 \sqrt{3}+3\right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b^{2}-6 \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b^{2}-3 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b -2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +6 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +3 \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +3 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-6 i \left(-a \,b^{2}\right)^{\frac{2}{3}}+3 \left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b -4 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b +i \sqrt{3}\, a b +2 \sqrt{3}\, a b -2 i a b -3 a b -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)+2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)+2 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)}{6 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 b^{3} \sqrt{b \,x^{3}+a}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)}"," ",0,"-2/3*I*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+1/9*I/b^3*2^(1/2)*sum(1/_alpha*(2*3^(1/2)+3)*(-a*b^2)^(1/3)*(1/2*I*b*(2*x+1/b*((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(b*(x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*b*(2*x+1/b*((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(b*x^3+a)^(1/2)*(-3*I*(-a*b^2)^(1/3)*_alpha*3^(1/2)*b+4*b^2*_alpha^2*3^(1/2)+3*I*(-a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(-a*b^2)^(1/3)*_alpha*b+6*I*(-a*b^2)^(1/3)*_alpha*b-6*b^2*_alpha^2-2*3^(1/2)*(-a*b^2)^(2/3)-6*I*(-a*b^2)^(2/3)+3*(-a*b^2)^(1/3)*_alpha*b+3*(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/6/b*(2*I*3^(1/2)*(-a*b^2)^(1/3)*_alpha^2*b-I*3^(1/2)*(-a*b^2)^(2/3)*_alpha-4*I*(-a*b^2)^(1/3)*_alpha^2*b+2*3^(1/2)*(-a*b^2)^(2/3)*_alpha+I*3^(1/2)*a*b+2*I*(-a*b^2)^(2/3)*_alpha+2*3^(1/2)*a*b-3*(-a*b^2)^(2/3)*_alpha-2*I*a*b-3*a*b)/a,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(b*_Z^3+6*a*3^(1/2)+10*a))","C"
343,1,924,551,4.354000," ","int(x*(-b*x^3+a)^(1/2)/(-b*x^3+2*a*(5+3*3^(1/2))),x)","\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}+a}\, b}-\frac{i \left(2 \sqrt{3}+3\right) \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b^{2}-6 \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b^{2}+3 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -6 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b +3 \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -3 i \left(a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}+6 i \left(a \,b^{2}\right)^{\frac{2}{3}}-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}}+3 \left(a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b +4 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b +i \sqrt{3}\, a b -2 i a b -2 \sqrt{3}\, a b +3 a b +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)-2 i \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)+2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)-3 \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 b^{3} \sqrt{-b \,x^{3}+a}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)}"," ",0,"2/3*I*3^(1/2)/b*(a*b^2)^(1/3)*(-I*(x+1/2/b*(a*b^2)^(1/3)+1/2*I*3^(1/2)/b*(a*b^2)^(1/3))*3^(1/2)*b/(a*b^2)^(1/3))^(1/2)*((x-1/b*(a*b^2)^(1/3))/(-3/2/b*(a*b^2)^(1/3)-1/2*I*3^(1/2)/b*(a*b^2)^(1/3)))^(1/2)*(I*(x+1/2/b*(a*b^2)^(1/3)-1/2*I*3^(1/2)/b*(a*b^2)^(1/3))*3^(1/2)*b/(a*b^2)^(1/3))^(1/2)/(-b*x^3+a)^(1/2)*((-3/2/b*(a*b^2)^(1/3)-1/2*I*3^(1/2)/b*(a*b^2)^(1/3))*EllipticE(1/3*3^(1/2)*(-I*(x+1/2/b*(a*b^2)^(1/3)+1/2*I*3^(1/2)/b*(a*b^2)^(1/3))*3^(1/2)*b/(a*b^2)^(1/3))^(1/2),(-I*3^(1/2)/b*(a*b^2)^(1/3)/(-3/2/b*(a*b^2)^(1/3)-1/2*I*3^(1/2)/b*(a*b^2)^(1/3)))^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2/b*(a*b^2)^(1/3)+1/2*I*3^(1/2)/b*(a*b^2)^(1/3))*3^(1/2)*b/(a*b^2)^(1/3))^(1/2),(-I*3^(1/2)/b*(a*b^2)^(1/3)/(-3/2/b*(a*b^2)^(1/3)-1/2*I*3^(1/2)/b*(a*b^2)^(1/3)))^(1/2)))-1/9*I/b^3*2^(1/2)*sum(1/_alpha*(2*3^(1/2)+3)*(a*b^2)^(1/3)*(-1/2*I*b*(2*x+1/b*(I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3)))/(a*b^2)^(1/3))^(1/2)*(b*(x-1/b*(a*b^2)^(1/3))/(-3*(a*b^2)^(1/3)-I*3^(1/2)*(a*b^2)^(1/3)))^(1/2)*(1/2*I*b*(2*x+1/b*(-I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3)))/(a*b^2)^(1/3))^(1/2)/(-b*x^3+a)^(1/2)*(3*I*(a*b^2)^(1/3)*_alpha*3^(1/2)*b+4*3^(1/2)*_alpha^2*b^2-3*I*(a*b^2)^(2/3)*3^(1/2)-6*I*(a*b^2)^(1/3)*_alpha*b-2*3^(1/2)*(a*b^2)^(1/3)*_alpha*b-6*_alpha^2*b^2+6*I*(a*b^2)^(2/3)-2*3^(1/2)*(a*b^2)^(2/3)+3*(a*b^2)^(1/3)*_alpha*b+3*(a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2/b*(a*b^2)^(1/3)+1/2*I*3^(1/2)/b*(a*b^2)^(1/3))*3^(1/2)*b/(a*b^2)^(1/3))^(1/2),1/6/b*(-2*I*3^(1/2)*(a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*(a*b^2)^(2/3)*_alpha+4*I*(a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b-2*I*(a*b^2)^(2/3)*_alpha+2*3^(1/2)*(a*b^2)^(2/3)*_alpha-2*I*a*b-2*3^(1/2)*a*b-3*(a*b^2)^(2/3)*_alpha+3*a*b)/a,(-I*3^(1/2)/b*(a*b^2)^(1/3)/(-3/2/b*(a*b^2)^(1/3)-1/2*I*3^(1/2)/b*(a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*b-6*3^(1/2)*a-10*a))","C"
344,1,926,569,0.365000," ","int(x*(b*x^3-a)^(1/2)/(b*x^3-2*a*(5+3*3^(1/2))),x)","\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}-a}\, b}-\frac{i \left(2 \sqrt{3}+3\right) \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b^{2}-6 \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b^{2}+3 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -6 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b +3 \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -3 i \left(a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}+6 i \left(a \,b^{2}\right)^{\frac{2}{3}}-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}}+3 \left(a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b +4 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b +i \sqrt{3}\, a b -2 i a b -2 \sqrt{3}\, a b +3 a b +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)-2 i \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)+2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)-3 \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 b^{3} \sqrt{b \,x^{3}-a}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)}"," ",0,"2/3*I*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))-1/9*I/b^3*2^(1/2)*sum(1/_alpha*(2*3^(1/2)+3)*(a*b^2)^(1/3)*(-1/2*I*(2*x+(I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3*(a*b^2)^(1/3)-I*3^(1/2)*(a*b^2)^(1/3))*b)^(1/2)*(1/2*I*(2*x+(-I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2-6*_alpha^2*b^2+3*I*(a*b^2)^(1/3)*3^(1/2)*_alpha*b-6*I*(a*b^2)^(1/3)*_alpha*b-2*3^(1/2)*(a*b^2)^(1/3)*_alpha*b+3*(a*b^2)^(1/3)*_alpha*b-3*I*(a*b^2)^(2/3)*3^(1/2)+6*I*(a*b^2)^(2/3)-2*3^(1/2)*(a*b^2)^(2/3)+3*(a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),1/6*(-2*I*3^(1/2)*(a*b^2)^(1/3)*_alpha^2*b+4*I*(a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b-2*I*a*b-2*3^(1/2)*a*b+3*a*b+I*3^(1/2)*(a*b^2)^(2/3)*_alpha-2*I*(a*b^2)^(2/3)*_alpha+2*3^(1/2)*(a*b^2)^(2/3)*_alpha-3*(a*b^2)^(2/3)*_alpha)/a/b,(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b-6*3^(1/2)*a-10*a))","C"
345,1,983,563,0.368000," ","int(x*(-b*x^3-a)^(1/2)/(-b*x^3-2*a*(5+3*3^(1/2))),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}-a}\, b}+\frac{i \left(2 \sqrt{3}+3\right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b^{2}-6 \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b^{2}-3 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b -2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +6 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +3 \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +3 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-6 i \left(-a \,b^{2}\right)^{\frac{2}{3}}+3 \left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b -4 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b +i \sqrt{3}\, a b +2 \sqrt{3}\, a b -2 i a b -3 a b -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)+2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)+2 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)}{6 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 b^{3} \sqrt{-b \,x^{3}-a}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)}"," ",0,"-2/3*I*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+1/9*I/b^3*2^(1/2)*sum(1/_alpha*(2*3^(1/2)+3)*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2-6*_alpha^2*b^2-3*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-2*3^(1/2)*(-a*b^2)^(1/3)*_alpha*b+6*I*(-a*b^2)^(1/3)*_alpha*b+3*(-a*b^2)^(1/3)*_alpha*b+3*I*(-a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(-a*b^2)^(2/3)-6*I*(-a*b^2)^(2/3)+3*(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/6*(2*I*3^(1/2)*(-a*b^2)^(1/3)*_alpha^2*b-4*I*(-a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b+2*3^(1/2)*a*b-2*I*a*b-3*a*b-I*3^(1/2)*(-a*b^2)^(2/3)*_alpha+2*3^(1/2)*(-a*b^2)^(2/3)*_alpha+2*I*(-a*b^2)^(2/3)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/a/b,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b+6*3^(1/2)*a+10*a))","C"
346,1,977,531,0.741000," ","int(x*(b*x^3+a)^(1/2)/(b*x^3+2*a*(5-3*3^(1/2))),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, b}+\frac{i \left(2 \sqrt{3}-3\right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b^{2}+6 \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b^{2}+3 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b +6 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -3 \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -3 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-6 i \left(-a \,b^{2}\right)^{\frac{2}{3}}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b +4 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b +i \sqrt{3}\, a b -2 \sqrt{3}\, a b +2 i a b -3 a b -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-2 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)}{6 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 b^{3} \sqrt{b \,x^{3}+a}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)}"," ",0,"-2/3*I*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+1/9*I/b^3*2^(1/2)*sum(1/_alpha*(2*3^(1/2)-3)*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(3*I*(-a*b^2)^(1/3)*_alpha*3^(1/2)*b+4*3^(1/2)*_alpha^2*b^2-3*I*(-a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(-a*b^2)^(1/3)*_alpha*b+6*I*(-a*b^2)^(1/3)*_alpha*b+6*_alpha^2*b^2-2*3^(1/2)*(-a*b^2)^(2/3)-6*I*(-a*b^2)^(2/3)-3*(-a*b^2)^(1/3)*_alpha*b-3*(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/6/b*(2*I*3^(1/2)*(-a*b^2)^(1/3)*_alpha^2*b-I*3^(1/2)*(-a*b^2)^(2/3)*_alpha+4*I*(-a*b^2)^(1/3)*_alpha^2*b-2*3^(1/2)*(-a*b^2)^(2/3)*_alpha+I*3^(1/2)*a*b-2*I*(-a*b^2)^(2/3)*_alpha-2*3^(1/2)*a*b-3*(-a*b^2)^(2/3)*_alpha+2*I*a*b-3*a*b)/a,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b-6*3^(1/2)*a+10*a))","C"
347,1,924,551,0.768000," ","int(x*(-b*x^3+a)^(1/2)/(-b*x^3+2*a*(5-3*3^(1/2))),x)","\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}+a}\, b}-\frac{i \left(2 \sqrt{3}-3\right) \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b^{2}+6 \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b^{2}-3 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -6 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -3 \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b +3 i \left(a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}}+6 i \left(a \,b^{2}\right)^{\frac{2}{3}}-3 \left(a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b -4 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b +i \sqrt{3}\, a b +2 \sqrt{3}\, a b +2 i a b +3 a b +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)+2 i \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)-3 \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 b^{3} \sqrt{-b \,x^{3}+a}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)}"," ",0,"2/3*I*3^(1/2)/b*(a*b^2)^(1/3)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))-1/9*I/b^3*2^(1/2)*sum(1/_alpha*(2*3^(1/2)-3)*(a*b^2)^(1/3)*(-1/2*I*(2*x+(I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3*(a*b^2)^(1/3)-I*3^(1/2)*(a*b^2)^(1/3))*b)^(1/2)*(1/2*I*(2*x+(-I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*(-3*I*(a*b^2)^(1/3)*_alpha*3^(1/2)*b+4*3^(1/2)*_alpha^2*b^2+3*I*(a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(a*b^2)^(1/3)*_alpha*b-6*I*(a*b^2)^(1/3)*_alpha*b+6*_alpha^2*b^2-2*3^(1/2)*(a*b^2)^(2/3)+6*I*(a*b^2)^(2/3)-3*(a*b^2)^(1/3)*_alpha*b-3*(a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),1/6/b*(-2*I*3^(1/2)*(a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*(a*b^2)^(2/3)*_alpha-4*I*(a*b^2)^(1/3)*_alpha^2*b-2*3^(1/2)*(a*b^2)^(2/3)*_alpha+I*3^(1/2)*a*b+2*I*(a*b^2)^(2/3)*_alpha+2*3^(1/2)*a*b-3*(a*b^2)^(2/3)*_alpha+2*I*a*b+3*a*b)/a,(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b+6*3^(1/2)*a-10*a))","C"
348,1,926,570,0.390000," ","int(x*(b*x^3-a)^(1/2)/(-b*x^3+2*a*(5-3*3^(1/2))),x)","-\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}-a}\, b}+\frac{i \left(2 \sqrt{3}-3\right) \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b^{2}+6 \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b^{2}-3 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -6 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -3 \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b +3 i \left(a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}}+6 i \left(a \,b^{2}\right)^{\frac{2}{3}}-3 \left(a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b -4 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b +i \sqrt{3}\, a b +2 \sqrt{3}\, a b +2 i a b +3 a b +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)+2 i \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)-3 \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 b^{3} \sqrt{b \,x^{3}-a}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)}"," ",0,"-2/3*I*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))+1/9*I/b^3*2^(1/2)*sum(1/_alpha*(2*3^(1/2)-3)*(a*b^2)^(1/3)*(-1/2*I*(2*x+(I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3*(a*b^2)^(1/3)-I*3^(1/2)*(a*b^2)^(1/3))*b)^(1/2)*(1/2*I*(2*x+(-I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2+6*_alpha^2*b^2-3*I*(a*b^2)^(1/3)*3^(1/2)*_alpha*b-2*3^(1/2)*(a*b^2)^(1/3)*_alpha*b-6*I*(a*b^2)^(1/3)*_alpha*b-3*(a*b^2)^(1/3)*_alpha*b+3*I*(a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(a*b^2)^(2/3)+6*I*(a*b^2)^(2/3)-3*(a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),1/6*(-2*I*3^(1/2)*(a*b^2)^(1/3)*_alpha^2*b-4*I*(a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b+2*3^(1/2)*a*b+2*I*a*b+3*a*b+I*3^(1/2)*(a*b^2)^(2/3)*_alpha-2*3^(1/2)*(a*b^2)^(2/3)*_alpha+2*I*(a*b^2)^(2/3)*_alpha-3*(a*b^2)^(2/3)*_alpha)/a/b,(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b+6*3^(1/2)*a-10*a))","C"
349,1,983,564,0.418000," ","int(x*(-b*x^3-a)^(1/2)/(b*x^3+2*a*(5-3*3^(1/2))),x)","\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}-a}\, b}-\frac{i \left(2 \sqrt{3}-3\right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b^{2}+6 \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b^{2}+3 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b +6 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -3 \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -3 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-6 i \left(-a \,b^{2}\right)^{\frac{2}{3}}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b +4 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b +i \sqrt{3}\, a b -2 \sqrt{3}\, a b +2 i a b -3 a b -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-2 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)}{6 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 b^{3} \sqrt{-b \,x^{3}-a}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)}"," ",0,"2/3*I*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-1/9*I/b^3*2^(1/2)*sum(1/_alpha*(2*3^(1/2)-3)*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2+6*_alpha^2*b^2+3*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-2*3^(1/2)*(-a*b^2)^(1/3)*_alpha*b+6*I*(-a*b^2)^(1/3)*_alpha*b-3*(-a*b^2)^(1/3)*_alpha*b-3*I*(-a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(-a*b^2)^(2/3)-6*I*(-a*b^2)^(2/3)-3*(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/6*(2*I*3^(1/2)*(-a*b^2)^(1/3)*_alpha^2*b+4*I*(-a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b-2*3^(1/2)*a*b+2*I*a*b-3*a*b-I*3^(1/2)*(-a*b^2)^(2/3)*_alpha-2*3^(1/2)*(-a*b^2)^(2/3)*_alpha-2*I*(-a*b^2)^(2/3)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/a/b,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b-6*3^(1/2)*a+10*a))","C"
350,1,538,222,0.388000," ","int(x/(b*x^3+2*a*(5+3*3^(1/2)))/(b*x^3+a)^(1/2),x)","-\frac{i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b^{2}-6 \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b^{2}-3 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b -2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +6 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +3 \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +3 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-6 i \left(-a \,b^{2}\right)^{\frac{2}{3}}+3 \left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b -4 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b +i \sqrt{3}\, a b +2 \sqrt{3}\, a b -2 i a b -3 a b -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)+2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)+2 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)}{6 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{27 a \,b^{3} \sqrt{b \,x^{3}+a}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)}"," ",0,"-1/27*I/b^3/a*2^(1/2)*sum(1/_alpha*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2-6*_alpha^2*b^2-3*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-2*3^(1/2)*(-a*b^2)^(1/3)*_alpha*b+6*I*(-a*b^2)^(1/3)*_alpha*b+3*(-a*b^2)^(1/3)*_alpha*b+3*I*(-a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(-a*b^2)^(2/3)-6*I*(-a*b^2)^(2/3)+3*(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/6*(2*I*3^(1/2)*(-a*b^2)^(1/3)*_alpha^2*b-4*I*(-a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b+2*3^(1/2)*a*b-2*I*a*b-3*a*b-I*3^(1/2)*(-a*b^2)^(2/3)*_alpha+2*3^(1/2)*(-a*b^2)^(2/3)*_alpha+2*I*(-a*b^2)^(2/3)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/a/b,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b+6*3^(1/2)*a+10*a))","C"
351,1,509,228,0.410000," ","int(x/(-b*x^3+2*a*(5+3*3^(1/2)))/(-b*x^3+a)^(1/2),x)","\frac{i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b^{2}-6 \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b^{2}+3 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -6 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b +3 \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -3 i \left(a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}+6 i \left(a \,b^{2}\right)^{\frac{2}{3}}-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}}+3 \left(a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b +4 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b +i \sqrt{3}\, a b -2 i a b -2 \sqrt{3}\, a b +3 a b +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)-2 i \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)+2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)-3 \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{27 a \,b^{3} \sqrt{-b \,x^{3}+a}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)}"," ",0,"1/27*I/b^3/a*2^(1/2)*sum(1/_alpha*(a*b^2)^(1/3)*(-1/2*I*(2*x+(I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3*(a*b^2)^(1/3)-I*3^(1/2)*(a*b^2)^(1/3))*b)^(1/2)*(1/2*I*(2*x+(-I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2-6*_alpha^2*b^2+3*I*(a*b^2)^(1/3)*3^(1/2)*_alpha*b-6*I*(a*b^2)^(1/3)*_alpha*b-2*3^(1/2)*(a*b^2)^(1/3)*_alpha*b+3*(a*b^2)^(1/3)*_alpha*b-3*I*(a*b^2)^(2/3)*3^(1/2)+6*I*(a*b^2)^(2/3)-2*3^(1/2)*(a*b^2)^(2/3)+3*(a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),1/6*(-2*I*3^(1/2)*(a*b^2)^(1/3)*_alpha^2*b+4*I*(a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b-2*I*a*b-2*3^(1/2)*a*b+3*a*b+I*3^(1/2)*(a*b^2)^(2/3)*_alpha-2*I*(a*b^2)^(2/3)*_alpha+2*3^(1/2)*(a*b^2)^(2/3)*_alpha-3*(a*b^2)^(2/3)*_alpha)/a/b,(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b-6*3^(1/2)*a-10*a))","C"
352,1,510,232,0.413000," ","int(x/(b*x^3-2*a*(5+3*3^(1/2)))/(b*x^3-a)^(1/2),x)","-\frac{i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b^{2}-6 \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b^{2}+3 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -6 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b +3 \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right) b -3 i \left(a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}+6 i \left(a \,b^{2}\right)^{\frac{2}{3}}-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}}+3 \left(a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b +4 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)^{2} b +i \sqrt{3}\, a b -2 i a b -2 \sqrt{3}\, a b +3 a b +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)-2 i \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)+2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)-3 \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{27 a \,b^{3} \sqrt{b \,x^{3}-a}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a -10 a \right)}"," ",0,"-1/27*I/b^3/a*2^(1/2)*sum(1/_alpha*(a*b^2)^(1/3)*(-1/2*I*(2*x+(I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3*(a*b^2)^(1/3)-I*3^(1/2)*(a*b^2)^(1/3))*b)^(1/2)*(1/2*I*(2*x+(-I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2-6*_alpha^2*b^2+3*I*(a*b^2)^(1/3)*3^(1/2)*_alpha*b-6*I*(a*b^2)^(1/3)*_alpha*b-2*3^(1/2)*(a*b^2)^(1/3)*_alpha*b+3*(a*b^2)^(1/3)*_alpha*b-3*I*(a*b^2)^(2/3)*3^(1/2)+6*I*(a*b^2)^(2/3)-2*3^(1/2)*(a*b^2)^(2/3)+3*(a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),1/6*(-2*I*3^(1/2)*(a*b^2)^(1/3)*_alpha^2*b+4*I*(a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b-2*I*a*b-2*3^(1/2)*a*b+3*a*b+I*3^(1/2)*(a*b^2)^(2/3)*_alpha-2*I*(a*b^2)^(2/3)*_alpha+2*3^(1/2)*(a*b^2)^(2/3)*_alpha-3*(a*b^2)^(2/3)*_alpha)/a/b,(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b-6*3^(1/2)*a-10*a))","C"
353,1,541,234,0.365000," ","int(x/(-b*x^3-2*a*(5+3*3^(1/2)))/(-b*x^3-a)^(1/2),x)","\frac{i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b^{2}-6 \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b^{2}-3 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b -2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +6 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +3 \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right) b +3 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-6 i \left(-a \,b^{2}\right)^{\frac{2}{3}}+3 \left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b -4 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)^{2} b +i \sqrt{3}\, a b +2 \sqrt{3}\, a b -2 i a b -3 a b -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)+2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)+2 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)}{6 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{27 a \,b^{3} \sqrt{-b \,x^{3}-a}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a +10 a \right)}"," ",0,"1/27*I/b^3/a*2^(1/2)*sum(1/_alpha*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2-6*_alpha^2*b^2-3*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-2*3^(1/2)*(-a*b^2)^(1/3)*_alpha*b+6*I*(-a*b^2)^(1/3)*_alpha*b+3*(-a*b^2)^(1/3)*_alpha*b+3*I*(-a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(-a*b^2)^(2/3)-6*I*(-a*b^2)^(2/3)+3*(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/6*(2*I*3^(1/2)*(-a*b^2)^(1/3)*_alpha^2*b-4*I*(-a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b+2*3^(1/2)*a*b-2*I*a*b-3*a*b-I*3^(1/2)*(-a*b^2)^(2/3)*_alpha+2*3^(1/2)*(-a*b^2)^(2/3)*_alpha+2*I*(-a*b^2)^(2/3)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/a/b,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b+6*3^(1/2)*a+10*a))","C"
354,1,538,214,0.425000," ","int(x/(b*x^3+2*a*(5-3*3^(1/2)))/(b*x^3+a)^(1/2),x)","\frac{i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b^{2}+6 \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b^{2}+3 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b +6 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -3 \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -3 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-6 i \left(-a \,b^{2}\right)^{\frac{2}{3}}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b +4 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b +i \sqrt{3}\, a b -2 \sqrt{3}\, a b +2 i a b -3 a b -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-2 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)}{6 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{27 a \,b^{3} \sqrt{b \,x^{3}+a}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)}"," ",0,"1/27*I/b^3/a*2^(1/2)*sum(1/_alpha*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2+6*_alpha^2*b^2+3*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-2*3^(1/2)*(-a*b^2)^(1/3)*_alpha*b+6*I*(-a*b^2)^(1/3)*_alpha*b-3*(-a*b^2)^(1/3)*_alpha*b-3*I*(-a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(-a*b^2)^(2/3)-6*I*(-a*b^2)^(2/3)-3*(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/6*(2*I*3^(1/2)*(-a*b^2)^(1/3)*_alpha^2*b+4*I*(-a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b-2*3^(1/2)*a*b+2*I*a*b-3*a*b-I*3^(1/2)*(-a*b^2)^(2/3)*_alpha-2*3^(1/2)*(-a*b^2)^(2/3)*_alpha-2*I*(-a*b^2)^(2/3)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/a/b,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b-6*3^(1/2)*a+10*a))","C"
355,1,509,220,0.372000," ","int(x/(-b*x^3+2*a*(5-3*3^(1/2)))/(-b*x^3+a)^(1/2),x)","-\frac{i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b^{2}+6 \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b^{2}-3 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -6 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -3 \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b +3 i \left(a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}}+6 i \left(a \,b^{2}\right)^{\frac{2}{3}}-3 \left(a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b -4 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b +i \sqrt{3}\, a b +2 \sqrt{3}\, a b +2 i a b +3 a b +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)+2 i \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)-3 \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{27 a \,b^{3} \sqrt{-b \,x^{3}+a}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)}"," ",0,"-1/27*I/b^3/a*2^(1/2)*sum(1/_alpha*(a*b^2)^(1/3)*(-1/2*I*(2*x+(I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3*(a*b^2)^(1/3)-I*3^(1/2)*(a*b^2)^(1/3))*b)^(1/2)*(1/2*I*(2*x+(-I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2+6*_alpha^2*b^2-3*I*(a*b^2)^(1/3)*3^(1/2)*_alpha*b-2*3^(1/2)*(a*b^2)^(1/3)*_alpha*b-6*I*(a*b^2)^(1/3)*_alpha*b-3*(a*b^2)^(1/3)*_alpha*b+3*I*(a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(a*b^2)^(2/3)+6*I*(a*b^2)^(2/3)-3*(a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),1/6*(-2*I*3^(1/2)*(a*b^2)^(1/3)*_alpha^2*b-4*I*(a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b+2*3^(1/2)*a*b+2*I*a*b+3*a*b+I*3^(1/2)*(a*b^2)^(2/3)*_alpha-2*3^(1/2)*(a*b^2)^(2/3)*_alpha+2*I*(a*b^2)^(2/3)*_alpha-3*(a*b^2)^(2/3)*_alpha)/a/b,(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b+6*3^(1/2)*a-10*a))","C"
356,1,510,224,0.364000," ","int(x/(-b*x^3+2*a*(5-3*3^(1/2)))/(b*x^3-a)^(1/2),x)","-\frac{i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b^{2}+6 \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b^{2}-3 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -6 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b -3 \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right) b +3 i \left(a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}}+6 i \left(a \,b^{2}\right)^{\frac{2}{3}}-3 \left(a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b -4 i \left(a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)^{2} b +i \sqrt{3}\, a b +2 \sqrt{3}\, a b +2 i a b +3 a b +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)-2 \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)+2 i \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)-3 \left(a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{27 a \,b^{3} \sqrt{b \,x^{3}-a}\, \RootOf \left(\textit{\_Z}^{3} b +6 \sqrt{3}\, a -10 a \right)}"," ",0,"-1/27*I/b^3/a*2^(1/2)*sum(1/_alpha*(a*b^2)^(1/3)*(-1/2*I*(2*x+(I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3*(a*b^2)^(1/3)-I*3^(1/2)*(a*b^2)^(1/3))*b)^(1/2)*(1/2*I*(2*x+(-I*3^(1/2)*(a*b^2)^(1/3)+(a*b^2)^(1/3))/b)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2+6*_alpha^2*b^2-3*I*(a*b^2)^(1/3)*3^(1/2)*_alpha*b-2*3^(1/2)*(a*b^2)^(1/3)*_alpha*b-6*I*(a*b^2)^(1/3)*_alpha*b-3*(a*b^2)^(1/3)*_alpha*b+3*I*(a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(a*b^2)^(2/3)+6*I*(a*b^2)^(2/3)-3*(a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),1/6*(-2*I*3^(1/2)*(a*b^2)^(1/3)*_alpha^2*b-4*I*(a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b+2*3^(1/2)*a*b+2*I*a*b+3*a*b+I*3^(1/2)*(a*b^2)^(2/3)*_alpha-2*3^(1/2)*(a*b^2)^(2/3)*_alpha+2*I*(a*b^2)^(2/3)*_alpha-3*(a*b^2)^(2/3)*_alpha)/a/b,(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b+6*3^(1/2)*a-10*a))","C"
357,1,541,226,0.392000," ","int(x/(b*x^3+2*a*(5-3*3^(1/2)))/(-b*x^3-a)^(1/2),x)","\frac{i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(4 \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b^{2}+6 \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b^{2}+3 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b +6 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -3 \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right) b -3 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-6 i \left(-a \,b^{2}\right)^{\frac{2}{3}}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b +4 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)^{2} b +i \sqrt{3}\, a b -2 \sqrt{3}\, a b +2 i a b -3 a b -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-2 \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-2 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)}{6 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{27 a \,b^{3} \sqrt{-b \,x^{3}-a}\, \RootOf \left(\textit{\_Z}^{3} b -6 \sqrt{3}\, a +10 a \right)}"," ",0,"1/27*I/b^3/a*2^(1/2)*sum(1/_alpha*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*(4*3^(1/2)*_alpha^2*b^2+6*_alpha^2*b^2+3*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-2*3^(1/2)*(-a*b^2)^(1/3)*_alpha*b+6*I*(-a*b^2)^(1/3)*_alpha*b-3*(-a*b^2)^(1/3)*_alpha*b-3*I*(-a*b^2)^(2/3)*3^(1/2)-2*3^(1/2)*(-a*b^2)^(2/3)-6*I*(-a*b^2)^(2/3)-3*(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/6*(2*I*3^(1/2)*(-a*b^2)^(1/3)*_alpha^2*b+4*I*(-a*b^2)^(1/3)*_alpha^2*b+I*3^(1/2)*a*b-2*3^(1/2)*a*b+2*I*a*b-3*a*b-I*3^(1/2)*(-a*b^2)^(2/3)*_alpha-2*3^(1/2)*(-a*b^2)^(2/3)*_alpha-2*I*(-a*b^2)^(2/3)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/a/b,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b-6*3^(1/2)*a+10*a))","C"
358,1,514,101,0.425000," ","int(x^8*(d*x^3+c)^(1/2)/(b*x^3+a),x)","\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}}\right) a^{2}}{b^{2}}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{6}}{15}+\frac{2 \sqrt{d \,x^{3}+c}\, c \,x^{3}}{45 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c^{2}}{45 d^{2}}\right) b -\frac{2 \left(d \,x^{3}+c \right)^{\frac{3}{2}} a}{9 d}}{b^{2}}"," ",0,"1/b^2*(b*(2/15*(d*x^3+c)^(1/2)*x^6+2/45*(d*x^3+c)^(1/2)*c/d*x^3-4/45*(d*x^3+c)^(1/2)*c^2/d^2)-2/9*a/d*(d*x^3+c)^(3/2))+a^2/b^2*(2/3*(d*x^3+c)^(1/2)/b+1/3*I/b/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*b/d*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
359,1,458,73,0.244000," ","int(x^5*(d*x^3+c)^(1/2)/(b*x^3+a),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}}\right) a}{b}+\frac{2 \left(d \,x^{3}+c \right)^{\frac{3}{2}}}{9 b d}"," ",0,"2/9*(d*x^3+c)^(3/2)/b/d-a/b*(2/3*(d*x^3+c)^(1/2)/b+1/3*I/b/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
360,1,434,54,0.229000," ","int(x^2*(d*x^3+c)^(1/2)/(b*x^3+a),x)","\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}}"," ",0,"2/3*(d*x^3+c)^(1/2)/b+1/3*I/b/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
361,1,476,65,0.262000," ","int((d*x^3+c)^(1/2)/x/(b*x^3+a),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}}\right) b}{a}+\frac{-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}}{a}"," ",0,"-1/a*b*(2/3*(d*x^3+c)^(1/2)/b+1/3*I/b/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
362,1,518,91,0.249000," ","int((d*x^3+c)^(1/2)/x^4/(b*x^3+a),x)","\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}}\right) b^{2}}{a^{2}}+\frac{-\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 \sqrt{c}}-\frac{\sqrt{d \,x^{3}+c}}{3 x^{3}}}{a}-\frac{\left(-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}\right) b}{a^{2}}"," ",0,"1/a*(-1/3*(d*x^3+c)^(1/2)/x^3-1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2))+1/a^2*b^2*(2/3*(d*x^3+c)^(1/2)/b+1/3*I/b/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-1/a^2*b*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
363,1,1012,52,0.349000," ","int(x^3*(d*x^3+c)^(1/2)/(b*x^3+a),x)","-\frac{\left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) a}{b}+\frac{-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{5 \sqrt{d \,x^{3}+c}\, d}+\frac{2 \sqrt{d \,x^{3}+c}\, x}{5}}{b}"," ",0,"1/b*(2/5*(d*x^3+c)^(1/2)*x-2/5*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-a/b*(-2/3*I/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b/d^2*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
364,1,857,52,0.326000," ","int(x*(d*x^3+c)^(1/2)/(b*x^3+a),x)","-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}"," ",0,"-2/3*I/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/b/d^2*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
365,1,705,49,0.236000," ","int((d*x^3+c)^(1/2)/(b*x^3+a),x)","-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}"," ",0,"-2/3*I/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b/d^2*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
366,1,1314,52,0.269000," ","int((d*x^3+c)^(1/2)/x^2/(b*x^3+a),x)","-\frac{\left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}\right) b}{a}+\frac{-\frac{\sqrt{d \,x^{3}+c}}{x}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{\sqrt{d \,x^{3}+c}}}{a}"," ",0,"-1/a*b*(-2/3*I/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/b/d^2*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a*(-(d*x^3+c)^(1/2)/x-I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
367,1,1010,52,0.333000," ","int((d*x^3+c)^(1/2)/x^3/(b*x^3+a),x)","-\frac{\left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) b}{a}+\frac{-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}}{2 x^{2}}}{a}"," ",0,"-1/a*b*(-2/3*I/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b/d^2*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a*(-1/2*(d*x^3+c)^(1/2)/x^2-1/2*I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))","C"
368,1,605,126,0.359000," ","int(x^8*(d*x^3+c)^(3/2)/(b*x^3+a),x)","\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9 b}+\frac{2 \left(-\frac{2 c d}{3 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}\right) a^{2}}{b^{2}}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{9}}{21}+\frac{16 \sqrt{d \,x^{3}+c}\, c \,x^{6}}{105}+\frac{2 \sqrt{d \,x^{3}+c}\, c^{2} x^{3}}{105 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c^{3}}{105 d^{2}}\right) b -\frac{2 \left(d \,x^{3}+c \right)^{\frac{5}{2}} a}{15 d}}{b^{2}}"," ",0,"1/b^2*(b*(2/21*(d*x^3+c)^(1/2)*d*x^9+16/105*(d*x^3+c)^(1/2)*c*x^6+2/105*(d*x^3+c)^(1/2)*c^2/d*x^3-4/105*(d*x^3+c)^(1/2)*c^3/d^2)-2/15*a/d*(d*x^3+c)^(5/2))+a^2/b^2*(2/9*d/b*x^3*(d*x^3+c)^(1/2)+2/3*(-d*(a*d-2*b*c)/b^2-2/3*d/b*c)/d*(d*x^3+c)^(1/2)+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
369,1,531,96,0.324000," ","int(x^5*(d*x^3+c)^(3/2)/(b*x^3+a),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9 b}+\frac{2 \left(-\frac{2 c d}{3 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}\right) a}{b}+\frac{2 \left(d \,x^{3}+c \right)^{\frac{5}{2}}}{15 b d}"," ",0,"2/15*(d*x^3+c)^(5/2)/b/d-a/b*(2/9*(d*x^3+c)^(1/2)/b*d*x^3+2/3*(-2/3/b*c*d-(a*d-2*b*c)/b^2*d)*(d*x^3+c)^(1/2)/d+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
370,1,507,76,0.246000," ","int(x^2*(d*x^3+c)^(3/2)/(b*x^3+a),x)","\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9 b}+\frac{2 \left(-\frac{2 c d}{3 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}"," ",0,"2/9*(d*x^3+c)^(1/2)/b*d*x^3+2/3*(-2/3/b*c*d-(a*d-2*b*c)/b^2*d)*(d*x^3+c)^(1/2)/d+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
371,1,565,80,0.261000," ","int((d*x^3+c)^(3/2)/x/(b*x^3+a),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9 b}+\frac{2 \left(-\frac{2 c d}{3 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}\right) b}{a}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}}{a}"," ",0,"-1/a*b*(2/9*(d*x^3+c)^(1/2)/b*d*x^3+2/3*(-2/3/b*c*d-(a*d-2*b*c)/b^2*d)*(d*x^3+c)^(1/2)/d+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a*(2/9*d*x^3*(d*x^3+c)^(1/2)+8/9*c*(d*x^3+c)^(1/2)-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
372,1,620,92,0.280000," ","int((d*x^3+c)^(3/2)/x^4/(b*x^3+a),x)","\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9 b}+\frac{2 \left(-\frac{2 c d}{3 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}\right) b^{2}}{a^{2}}+\frac{-\sqrt{c}\, d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)+\frac{2 \sqrt{d \,x^{3}+c}\, d}{3}-\frac{\sqrt{d \,x^{3}+c}\, c}{3 x^{3}}}{a}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}\right) b}{a^{2}}"," ",0,"1/a*(-1/3*c*(d*x^3+c)^(1/2)/x^3+2/3*d*(d*x^3+c)^(1/2)-c^(1/2)*d*arctanh((d*x^3+c)^(1/2)/c^(1/2)))+1/a^2*b^2*(2/9*(d*x^3+c)^(1/2)/b*d*x^3+2/3*(-2/3/b*c*d-(a*d-2*b*c)/b^2*d)*(d*x^3+c)^(1/2)/d+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-1/a^2*b*(2/9*(d*x^3+c)^(1/2)*d*x^3+8/9*(d*x^3+c)^(1/2)*c-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
373,1,1101,53,0.375000," ","int(x^3*(d*x^3+c)^(3/2)/(b*x^3+a),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d x}{5 b}-\frac{2 i \left(-\frac{2 c d}{5 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) a}{b}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{4}}{11}-\frac{18 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, c^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{55 \sqrt{d \,x^{3}+c}\, d}+\frac{28 \sqrt{d \,x^{3}+c}\, c x}{55}}{b}"," ",0,"1/b*(2/11*d*x^4*(d*x^3+c)^(1/2)+28/55*c*x*(d*x^3+c)^(1/2)-18/55*I*c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-a/b*(2/5*d/b*x*(d*x^3+c)^(1/2)-2/3*I*(-(a*d-2*b*c)/b^2*d-2/5/b*c*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
374,1,930,53,0.366000," ","int(x*(d*x^3+c)^(3/2)/(b*x^3+a),x)","\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{2}}{7 b}-\frac{2 i \left(-\frac{4 c d}{7 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}"," ",0,"2/7*d/b*x^2*(d*x^3+c)^(1/2)-2/3*I*(-(a*d-2*b*c)/b^2*d-4/7/b*c*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
375,1,776,50,0.259000," ","int((d*x^3+c)^(3/2)/(b*x^3+a),x)","\frac{2 \sqrt{d \,x^{3}+c}\, d x}{5 b}-\frac{2 i \left(-\frac{2 c d}{5 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}"," ",0,"2/5*(d*x^3+c)^(1/2)/b*d*x-2/3*I*(-2/5/b*c*d-(a*d-2*b*c)/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
376,1,1404,53,0.257000," ","int((d*x^3+c)^(3/2)/x^2/(b*x^3+a),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{2}}{7 b}-\frac{2 i \left(-\frac{4 c d}{7 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}\right) b}{a}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}\, c}{x}}{a}"," ",0,"-1/a*b*(2/7*(d*x^3+c)^(1/2)/b*d*x^2-2/3*I*(-4/7/b*c*d-(a*d-2*b*c)/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a*(-(d*x^3+c)^(1/2)*c/x+2/7*d*x^2*(d*x^3+c)^(1/2)-9/7*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
377,1,1096,53,0.305000," ","int((d*x^3+c)^(3/2)/x^3/(b*x^3+a),x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d x}{5 b}-\frac{2 i \left(-\frac{2 c d}{5 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) b}{a}+\frac{-\frac{9 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{10 \sqrt{d \,x^{3}+c}}+\frac{2 \sqrt{d \,x^{3}+c}\, d x}{5}-\frac{\sqrt{d \,x^{3}+c}\, c}{2 x^{2}}}{a}"," ",0,"-1/a*b*(2/5*(d*x^3+c)^(1/2)/b*d*x-2/3*I*(-2/5/b*c*d-(a*d-2*b*c)/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a*(-1/2*c*(d*x^3+c)^(1/2)/x^2+2/5*d*x*(d*x^3+c)^(1/2)-9/10*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))","C"
378,1,488,84,0.339000," ","int(x^8/(b*x^3+a)/(d*x^3+c)^(1/2),x)","-\frac{i a^{2} \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c}{9 d^{2}}\right) b -\frac{2 \sqrt{d \,x^{3}+c}\, a}{3 d}}{b^{2}}"," ",0,"1/b^2*(b*(2/9*(d*x^3+c)^(1/2)/d*x^3-4/9*(d*x^3+c)^(1/2)*c/d^2)-2/3*a/d*(d*x^3+c)^(1/2))-1/3*I*a^2/b^2/d^2*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
379,1,448,58,0.227000," ","int(x^5/(b*x^3+a)/(d*x^3+c)^(1/2),x)","\frac{i a \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}+\frac{2 \sqrt{d \,x^{3}+c}}{3 b d}"," ",0,"2/3*(d*x^3+c)^(1/2)/b/d+1/3*I*a/b/d^2*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
380,1,426,39,0.275000," ","int(x^2/(b*x^3+a)/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}"," ",0,"-1/3*I/d^2*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
381,1,453,65,0.245000," ","int(1/x/(b*x^3+a)/(d*x^3+c)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 a \sqrt{c}}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 a \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}"," ",0,"1/3*I/a*b/d^2*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/a/c^(1/2)","C"
382,1,498,93,0.253000," ","int(1/x^4/(b*x^3+a)/(d*x^3+c)^(1/2),x)","\frac{2 b \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 a^{2} \sqrt{c}}+\frac{\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}-\frac{\sqrt{d \,x^{3}+c}}{3 c \,x^{3}}}{a}-\frac{i b^{2} \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 a^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}"," ",0,"1/a*(-1/3*(d*x^3+c)^(1/2)/c/x^3+1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))-1/3*I/a^2*b^2/d^2*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))+2/3/a^2*b*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2)","C"
383,1,719,52,0.366000," ","int(x^3/(b*x^3+a)/(d*x^3+c)^(1/2),x)","\frac{i a \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, b d}"," ",0,"-2/3*I/b*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I*a/b/d^2*2^(1/2)*sum(1/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
384,1,429,52,0.316000," ","int(x/(b*x^3+a)/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}"," ",0,"-1/3*I/d^2*2^(1/2)*sum(1/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
385,1,429,49,0.256000," ","int(1/(b*x^3+a)/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}"," ",0,"-1/3*I/d^2*2^(1/2)*sum(1/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
386,1,890,52,0.259000," ","int(1/x^2/(b*x^3+a)/(d*x^3+c)^(1/2),x)","\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 a \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}+\frac{-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{c x}}{a}"," ",0,"1/3*I/a*b/d^2*2^(1/2)*sum(1/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))+1/a*(-(d*x^3+c)^(1/2)/c/x-1/3*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
387,1,738,52,0.249000," ","int(1/x^3/(b*x^3+a)/(d*x^3+c)^(1/2),x)","\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 a \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}+\frac{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{2 c \,x^{2}}}{a}"," ",0,"1/3*I/a*b/d^2*2^(1/2)*sum(1/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))+1/a*(-1/2/c*(d*x^3+c)^(1/2)/x^2+1/6*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))","C"
388,1,527,87,0.341000," ","int(x^8/(b*x^3+a)/(d*x^3+c)^(3/2),x)","\frac{\left(-\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(-a d +b c \right) \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{2}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) a^{2}}{b^{2}}+\frac{\left(\frac{2 c}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, d^{2}}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d^{2}}\right) b +\frac{2 a}{3 \sqrt{d \,x^{3}+c}\, d}}{b^{2}}"," ",0,"1/b^2*(b*(2/3/((x^3+c/d)*d)^(1/2)*c/d^2+2/3*(d*x^3+c)^(1/2)/d^2)+2/3*a/d/(d*x^3+c)^(1/2))+a^2/b^2*(-2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-1/3*I*b/d^2*2^(1/2)*sum(1/(-a*d+b*c)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
389,1,487,66,0.271000," ","int(x^5/(b*x^3+a)/(d*x^3+c)^(3/2),x)","-\frac{\left(-\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(-a d +b c \right) \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{2}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) a}{b}-\frac{2}{3 \sqrt{d \,x^{3}+c}\, b d}"," ",0,"-2/3/b/d/(d*x^3+c)^(1/2)-a/b*(-2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-1/3*I*b/d^2*2^(1/2)*sum(1/(-a*d+b*c)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
390,1,463,61,0.229000," ","int(x^2/(b*x^3+a)/(d*x^3+c)^(3/2),x)","-\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(-a d +b c \right) \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{2}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}"," ",0,"-2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-1/3*I*b/d^2*2^(1/2)*sum(1/(-a*d+b*c)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
391,1,512,90,0.286000," ","int(1/x/(b*x^3+a)/(d*x^3+c)^(3/2),x)","-\frac{\left(-\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(-a d +b c \right) \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{2}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) b}{a}+\frac{-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}}{a}"," ",0,"-1/a*b*(-2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-1/3*I*b/d^2*2^(1/2)*sum(1/(-a*d+b*c)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a*(2/3/((x^3+c/d)*d)^(1/2)/c-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
392,1,575,130,0.408000," ","int(1/x^4/(b*x^3+a)/(d*x^3+c)^(3/2),x)","\frac{\left(-\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(-a d +b c \right) \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{2}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) b^{2}}{a^{2}}+\frac{\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{c^{\frac{5}{2}}}-\frac{2 d}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{3 c^{2} x^{3}}}{a}-\frac{\left(-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}\right) b}{a^{2}}"," ",0,"1/a*(-1/3*(d*x^3+c)^(1/2)/c^2/x^3-2/3/((x^3+c/d)*d)^(1/2)/c^2*d+d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2))+1/a^2*b^2*(-2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-1/3*I*b/d^2*2^(1/2)*sum(1/(-a*d+b*c)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-1/a^2*b*(2/3/((x^3+c/d)*d)^(1/2)/c-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
393,1,1069,55,0.390000," ","int(x^3/(b*x^3+a)/(d*x^3+c)^(3/2),x)","-\frac{\left(\frac{2 d x}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, c}\right) a}{b}+\frac{\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \sqrt{d \,x^{3}+c}\, c d}}{b}"," ",0,"1/b*(2/3/((x^3+c/d)*d)^(1/2)/c*x-2/9*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-a/b*(2/3*d/c*x/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-2/9*I/c/(a*d-b*c)*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I*b/d^2*2^(1/2)*sum(1/(a*d-b*c)^2/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
394,1,907,55,0.365000," ","int(x/(b*x^3+a)/(d*x^3+c)^(3/2),x)","\frac{2 d \,x^{2}}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, c}"," ",0,"2/3*d/c*x^2/(a*d-b*c)/((x^3+c/d)*d)^(1/2)+2/9*I/c/(a*d-b*c)*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I*b/d^2*2^(1/2)*sum(1/(a*d-b*c)^2/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
395,1,753,52,0.263000," ","int(1/(b*x^3+a)/(d*x^3+c)^(3/2),x)","\frac{2 d x}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, c}"," ",0,"2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)/c*d*x-2/9*I/c/(a*d-b*c)*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I*b/d^2*2^(1/2)*sum(1/(a*d-b*c)^2/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
396,1,1392,55,0.252000," ","int(1/x^2/(b*x^3+a)/(d*x^3+c)^(3/2),x)","-\frac{\left(\frac{2 d \,x^{2}}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, c}\right) b}{a}+\frac{-\frac{2 d \,x^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \sqrt{d \,x^{3}+c}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{c^{2} x}}{a}"," ",0,"-1/a*b*(2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)/c*d*x^2+2/9*I/c/(a*d-b*c)*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I*b/d^2*2^(1/2)*sum(1/(a*d-b*c)^2/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a*(-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x^2-(d*x^3+c)^(1/2)/c^2/x-5/9*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
397,1,1084,55,0.233000," ","int(1/x^3/(b*x^3+a)/(d*x^3+c)^(3/2),x)","-\frac{\left(\frac{2 d x}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, c}\right) b}{a}+\frac{-\frac{2 d x}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{7 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 \sqrt{d \,x^{3}+c}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{2 c^{2} x^{2}}}{a}"," ",0,"-1/a*b*(2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)/c*d*x-2/9*I/c/(a*d-b*c)*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I*b/d^2*2^(1/2)*sum(1/(a*d-b*c)^2/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a*(-1/2/c^2*(d*x^3+c)^(1/2)/x^2-2/3*d/c^2*x/((x^3+c/d)*d)^(1/2)+7/18*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))","C"
398,1,952,95,0.276000," ","int(x^11*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x)","\frac{512 \left(-\frac{\sqrt{d \,x^{3}+c}}{3 \left(d \,x^{3}-8 c \right) d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{54 c \,d^{3} \sqrt{d \,x^{3}+c}}\right) c^{3}}{d^{3}}+\frac{192 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{3}}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{6}}{15}+\frac{2 \sqrt{d \,x^{3}+c}\, c \,x^{3}}{45 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c^{2}}{45 d^{2}}\right) d +\frac{32 \left(d \,x^{3}+c \right)^{\frac{3}{2}} c}{9 d}}{d^{3}}"," ",0,"1/d^3*(d*(2/15*(d*x^3+c)^(1/2)*x^6+2/45*(d*x^3+c)^(1/2)*c/d*x^3-4/45*(d*x^3+c)^(1/2)*c^2/d^2)+32/9*c/d*(d*x^3+c)^(3/2))+512*c^3/d^3*(-1/3/d*(d*x^3+c)^(1/2)/(d*x^3-8*c)+1/54*I/d^3/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+192*c^2/d^3*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
399,1,892,80,0.207000," ","int(x^8*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x)","\frac{64 \left(-\frac{\sqrt{d \,x^{3}+c}}{3 \left(d \,x^{3}-8 c \right) d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{54 c \,d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{2}}+\frac{16 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d^{2}}+\frac{2 \left(d \,x^{3}+c \right)^{\frac{3}{2}}}{9 d^{3}}"," ",0,"2/9*(d*x^3+c)^(3/2)/d^3+64*c^2/d^2*(-1/3*(d*x^3+c)^(1/2)/(d*x^3-8*c)/d+1/54*I/d^3/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16*c/d^2*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
400,1,874,64,0.166000," ","int(x^5*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x)","\frac{8 \left(-\frac{\sqrt{d \,x^{3}+c}}{3 \left(d \,x^{3}-8 c \right) d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{54 c \,d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d}+\frac{\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}}{d}"," ",0,"8*c/d*(-1/3*(d*x^3+c)^(1/2)/(d*x^3-8*c)/d+1/54*I/d^3/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/d*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
401,1,439,50,0.179000," ","int(x^2*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x)","-\frac{\sqrt{d \,x^{3}+c}}{3 \left(d \,x^{3}-8 c \right) d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{54 c \,d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"-1/3*(d*x^3+c)^(1/2)/(d*x^3-8*c)/d+1/54*I/d^3/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
402,1,912,66,0.179000," ","int((d*x^3+c)^(1/2)/x/(-d*x^3+8*c)^2,x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{3 \left(d \,x^{3}-8 c \right) d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{54 c \,d^{3} \sqrt{d \,x^{3}+c}}\right) d}{8 c}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) d}{64 c^{2}}+\frac{-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}}{64 c^{2}}"," ",0,"1/8/c*d*(-1/3*(d*x^3+c)^(1/2)/(d*x^3-8*c)/d+1/54*I/d^3/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))-1/64/c^2*d*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
403,1,957,98,0.211000," ","int((d*x^3+c)^(1/2)/x^4/(-d*x^3+8*c)^2,x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{3 \left(d \,x^{3}-8 c \right) d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{54 c \,d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{64 c^{2}}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{256 c^{3}}+\frac{-\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 \sqrt{c}}-\frac{\sqrt{d \,x^{3}+c}}{3 x^{3}}}{64 c^{2}}+\frac{\left(-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}\right) d}{256 c^{3}}"," ",0,"1/64/c^2*d^2*(-1/3*(d*x^3+c)^(1/2)/(d*x^3-8*c)/d+1/54*I/d^3/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/3*(d*x^3+c)^(1/2)/x^3-1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2))-1/256/c^3*d^2*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
404,1,1020,134,0.188000," ","int((d*x^3+c)^(1/2)/x^7/(-d*x^3+8*c)^2,x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{3 \left(d \,x^{3}-8 c \right) d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{54 c \,d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{512 c^{3}}-\frac{3 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{4096 c^{4}}+\frac{\frac{d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{12 c^{\frac{3}{2}}}-\frac{\sqrt{d \,x^{3}+c}\, d}{12 c \,x^{3}}-\frac{\sqrt{d \,x^{3}+c}}{6 x^{6}}}{64 c^{2}}+\frac{\left(-\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 \sqrt{c}}-\frac{\sqrt{d \,x^{3}+c}}{3 x^{3}}\right) d}{256 c^{3}}+\frac{3 \left(-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}\right) d^{2}}{4096 c^{4}}"," ",0,"1/512/c^3*d^3*(-1/3*(d*x^3+c)^(1/2)/(d*x^3-8*c)/d+1/54*I/d^3/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-1/3*(d*x^3+c)^(1/2)/x^3-1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2))+1/64/c^2*(-1/6*(d*x^3+c)^(1/2)/x^6-1/12*(d*x^3+c)^(1/2)/c*d/x^3+1/12*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))-3/4096/c^4*d^3*(2/3*(d*x^3+c)^(1/2)/d+1/3*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+3/4096/c^4*d^2*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
405,1,2198,479,0.252000," ","int(x^7*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x)","\text{Expression too large to display}"," ",0,"1/d^2*(2/7*(d*x^3+c)^(1/2)*x^2-2/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+64*c^2/d^2*(-1/24/c*x^2*(d*x^3+c)^(1/2)/(d*x^3-8*c)-1/72*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/216*I/d^3/c*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16*c/d^2*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
406,1,1740,461,0.180000," ","int(x^4*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x)","\frac{8 \left(-\frac{\sqrt{d \,x^{3}+c}\, x^{2}}{24 \left(d \,x^{3}-8 c \right) c}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{72 \sqrt{d \,x^{3}+c}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{216 c \,d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c}{d}+\frac{-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}}{d}"," ",0,"8*c/d*(-1/24*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c*x^2-1/72*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/216*I/d^3/c*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/d*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
407,1,882,464,0.162000," ","int(x*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x)","-\frac{\sqrt{d \,x^{3}+c}\, x^{2}}{24 \left(d \,x^{3}-8 c \right) c}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{72 \sqrt{d \,x^{3}+c}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{216 c \,d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"-1/24*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c*x^2-1/72*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/216*I/d^3/c*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
408,1,2193,481,0.206000," ","int((d*x^3+c)^(1/2)/x^2/(-d*x^3+8*c)^2,x)","\text{Expression too large to display}"," ",0,"1/8/c*d*(-1/24*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c*x^2-1/72*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/216*I/d^3/c*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-(d*x^3+c)^(1/2)/x-I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/64/c^2*d*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
409,1,2671,499,0.182000," ","int((d*x^3+c)^(1/2)/x^5/(-d*x^3+8*c)^2,x)","\text{Expression too large to display}"," ",0,"1/64/c^2*(-1/4*(d*x^3+c)^(1/2)/x^4-3/8*(d*x^3+c)^(1/2)/c*d/x-1/8*I*d/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/64/c^2*d^2*(-1/24*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c*x^2-1/72*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/216*I/d^3/c*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-(d*x^3+c)^(1/2)/x-I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/256/c^3*d^2*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
410,1,3169,519,0.187000," ","int((d*x^3+c)^(1/2)/x^8/(-d*x^3+8*c)^2,x)","\text{output too large to display}"," ",0,"1/256/c^3*d*(-1/4*(d*x^3+c)^(1/2)/x^4-3/8*(d*x^3+c)^(1/2)/c*d/x-1/8*I*d/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/512/c^3*d^3*(-1/24*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c*x^2-1/72*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/216*I/d^3/c*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/7*(d*x^3+c)^(1/2)/x^7-3/56*(d*x^3+c)^(1/2)/c*d/x^4+15/112*(d*x^3+c)^(1/2)/c^2*d^2/x+5/112*I*d^2/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+3/4096/c^4*d^2*(-(d*x^3+c)^(1/2)/x-I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-3/4096/c^4*d^3*(-2/3*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
411,1,998,112,0.275000," ","int(x^11*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x)","\frac{512 \left(-\frac{3 \sqrt{d \,x^{3}+c}\, c}{\left(d \,x^{3}-8 c \right) d}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d^{3} \sqrt{d \,x^{3}+c}}\right) c^{3}}{d^{3}}+\frac{192 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{3}}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{9}}{21}+\frac{16 \sqrt{d \,x^{3}+c}\, c \,x^{6}}{105}+\frac{2 \sqrt{d \,x^{3}+c}\, c^{2} x^{3}}{105 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c^{3}}{105 d^{2}}\right) d +\frac{32 \left(d \,x^{3}+c \right)^{\frac{5}{2}} c}{15 d}}{d^{3}}"," ",0,"1/d^3*(d*(2/21*(d*x^3+c)^(1/2)*d*x^9+16/105*(d*x^3+c)^(1/2)*c*x^6+2/105*(d*x^3+c)^(1/2)*c^2/d*x^3-4/105*(d*x^3+c)^(1/2)*c^3/d^2)+32/15*c/d*(d*x^3+c)^(5/2))+512*c^3/d^3*(-3*c/d*(d*x^3+c)^(1/2)/(d*x^3-8*c)+2/3*(d*x^3+c)^(1/2)/d+1/2*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+192*c^2/d^3*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
412,1,920,97,0.189000," ","int(x^8*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x)","\frac{64 \left(-\frac{3 \sqrt{d \,x^{3}+c}\, c}{\left(d \,x^{3}-8 c \right) d}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{2}}+\frac{16 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d^{2}}+\frac{2 \left(d \,x^{3}+c \right)^{\frac{5}{2}}}{15 d^{3}}"," ",0,"2/15*(d*x^3+c)^(5/2)/d^3+64*c^2/d^2*(-3*(d*x^3+c)^(1/2)/(d*x^3-8*c)*c/d+2/3*(d*x^3+c)^(1/2)/d+1/2*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16*c/d^2*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
413,1,902,79,0.166000," ","int(x^5*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x)","\frac{8 \left(-\frac{3 \sqrt{d \,x^{3}+c}\, c}{\left(d \,x^{3}-8 c \right) d}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}}{d}"," ",0,"8*c/d*(-3*(d*x^3+c)^(1/2)/(d*x^3-8*c)*c/d+2/3*(d*x^3+c)^(1/2)/d+1/2*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/d*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
414,1,451,63,0.177000," ","int(x^2*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x)","-\frac{3 \sqrt{d \,x^{3}+c}\, c}{\left(d \,x^{3}-8 c \right) d}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"-3*(d*x^3+c)^(1/2)/(d*x^3-8*c)*c/d+2/3*(d*x^3+c)^(1/2)/d+1/2*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
415,1,956,63,0.174000," ","int((d*x^3+c)^(3/2)/x/(-d*x^3+8*c)^2,x)","\frac{\left(-\frac{3 \sqrt{d \,x^{3}+c}\, c}{\left(d \,x^{3}-8 c \right) d}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d^{3} \sqrt{d \,x^{3}+c}}\right) d}{8 c}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) d}{64 c^{2}}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}}{64 c^{2}}"," ",0,"1/8/c*d*(-3*(d*x^3+c)^(1/2)/(d*x^3-8*c)*c/d+2/3*(d*x^3+c)^(1/2)/d+1/2*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))-1/64/c^2*d*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(2/9*(d*x^3+c)^(1/2)*d*x^3+8/9*(d*x^3+c)^(1/2)*c-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
416,1,1014,95,0.189000," ","int((d*x^3+c)^(3/2)/x^4/(-d*x^3+8*c)^2,x)","\frac{\left(-\frac{3 \sqrt{d \,x^{3}+c}\, c}{\left(d \,x^{3}-8 c \right) d}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{64 c^{2}}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{256 c^{3}}+\frac{-\sqrt{c}\, d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)+\frac{2 \sqrt{d \,x^{3}+c}\, d}{3}-\frac{\sqrt{d \,x^{3}+c}\, c}{3 x^{3}}}{64 c^{2}}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}\right) d}{256 c^{3}}"," ",0,"1/64/c^2*d^2*(-3*(d*x^3+c)^(1/2)/(d*x^3-8*c)*c/d+2/3*(d*x^3+c)^(1/2)/d+1/2*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/3*(d*x^3+c)^(1/2)*c/x^3+2/3*(d*x^3+c)^(1/2)*d-c^(1/2)*d*arctanh((d*x^3+c)^(1/2)/c^(1/2)))-1/256/c^3*d^2*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(2/9*(d*x^3+c)^(1/2)*d*x^3+8/9*(d*x^3+c)^(1/2)*c-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
417,1,1075,131,0.189000," ","int((d*x^3+c)^(3/2)/x^7/(-d*x^3+8*c)^2,x)","\frac{\left(-\frac{3 \sqrt{d \,x^{3}+c}\, c}{\left(d \,x^{3}-8 c \right) d}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{512 c^{3}}-\frac{3 \left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9}+\frac{56 \sqrt{d \,x^{3}+c}\, c}{9 d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{4096 c^{4}}+\frac{-\frac{d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{4 \sqrt{c}}-\frac{5 \sqrt{d \,x^{3}+c}\, d}{12 x^{3}}-\frac{\sqrt{d \,x^{3}+c}\, c}{6 x^{6}}}{64 c^{2}}+\frac{\left(-\sqrt{c}\, d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)+\frac{2 \sqrt{d \,x^{3}+c}\, d}{3}-\frac{\sqrt{d \,x^{3}+c}\, c}{3 x^{3}}\right) d}{256 c^{3}}+\frac{3 \left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}\right) d^{2}}{4096 c^{4}}"," ",0,"1/512/c^3*d^3*(-3*(d*x^3+c)^(1/2)/(d*x^3-8*c)*c/d+2/3*(d*x^3+c)^(1/2)/d+1/2*I/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-1/3*(d*x^3+c)^(1/2)*c/x^3+2/3*(d*x^3+c)^(1/2)*d-c^(1/2)*d*arctanh((d*x^3+c)^(1/2)/c^(1/2)))+1/64/c^2*(-1/6*c*(d*x^3+c)^(1/2)/x^6-5/12*d*(d*x^3+c)^(1/2)/x^3-1/4*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2))-3/4096/c^4*d^3*(2/9*(d*x^3+c)^(1/2)*x^3+56/9*(d*x^3+c)^(1/2)*c/d+3*I*c/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+3/4096/c^4*d^2*(2/9*(d*x^3+c)^(1/2)*d*x^3+8/9*(d*x^3+c)^(1/2)*c-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
418,1,2223,499,0.243000," ","int(x^7*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x)","\text{Expression too large to display}"," ",0,"1/d^2*(2/13*(d*x^3+c)^(1/2)*d*x^5+32/91*c*x^2*(d*x^3+c)^(1/2)-18/91*I*c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+64*c^2/d^2*(-3/8*x^2*(d*x^3+c)^(1/2)/(d*x^3-8*c)-19/24*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3/8*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16*c/d^2*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
419,1,1747,479,0.180000," ","int(x^4*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x)","\frac{8 \left(-\frac{3 \sqrt{d \,x^{3}+c}\, x^{2}}{8 \left(d \,x^{3}-8 c \right)}-\frac{19 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{24 \sqrt{d \,x^{3}+c}\, d}+\frac{3 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{8 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c}{d}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, x^{2}}{7}-\frac{44 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) c}{7 \sqrt{d \,x^{3}+c}\, d}+\frac{3 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}}{d}"," ",0,"8*c/d*(-3/8*(d*x^3+c)^(1/2)/(d*x^3-8*c)*x^2-19/24*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3/8*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/d*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
420,1,873,458,0.191000," ","int(x*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x)","-\frac{3 \sqrt{d \,x^{3}+c}\, x^{2}}{8 \left(d \,x^{3}-8 c \right)}-\frac{19 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{24 \sqrt{d \,x^{3}+c}\, d}+\frac{3 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{8 d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"-3/8*(d*x^3+c)^(1/2)/(d*x^3-8*c)*x^2-19/24*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3/8*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
421,1,2217,384,0.189000," ","int((d*x^3+c)^(3/2)/x^2/(-d*x^3+8*c)^2,x)","\text{Expression too large to display}"," ",0,"1/8/c*d*(-3/8*(d*x^3+c)^(1/2)/(d*x^3-8*c)*x^2-19/24*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3/8*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-(d*x^3+c)^(1/2)*c/x+2/7*(d*x^3+c)^(1/2)*d*x^2-9/7*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/64/c^2*d*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
422,1,2690,496,0.204000," ","int((d*x^3+c)^(3/2)/x^5/(-d*x^3+8*c)^2,x)","\text{Expression too large to display}"," ",0,"1/64/c^2*(-1/4*c*(d*x^3+c)^(1/2)/x^4-11/8*(d*x^3+c)^(1/2)*d/x-9/8*I*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/64/c^2*d^2*(-3/8*(d*x^3+c)^(1/2)/(d*x^3-8*c)*x^2-19/24*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3/8*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-(d*x^3+c)^(1/2)*c/x+2/7*(d*x^3+c)^(1/2)*d*x^2-9/7*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/256/c^3*d^2*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
423,1,3186,516,0.184000," ","int((d*x^3+c)^(3/2)/x^8/(-d*x^3+8*c)^2,x)","\text{output too large to display}"," ",0,"1/256/c^3*d*(-1/4*(d*x^3+c)^(1/2)*c/x^4-11/8*(d*x^3+c)^(1/2)*d/x-9/8*I*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/512/c^3*d^3*(-3/8*(d*x^3+c)^(1/2)/(d*x^3-8*c)*x^2-19/24*I*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3/8*I/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/7*(d*x^3+c)^(1/2)*c/x^7-17/56*d*(d*x^3+c)^(1/2)/x^4-27/112*d^2/c*(d*x^3+c)^(1/2)/x-9/112*I/c*d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+3/4096/c^4*d^2*(-(d*x^3+c)^(1/2)*c/x+2/7*(d*x^3+c)^(1/2)*d*x^2-9/7*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-3/4096/c^4*d^3*(2/7*(d*x^3+c)^(1/2)*x^2-44/7*I*c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+3*I*c/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
424,1,916,77,0.296000," ","int(x^11/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{512 \left(-\frac{\sqrt{d \,x^{3}+c}}{27 \left(d \,x^{3}-8 c \right) c d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{486 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) c^{3}}{d^{3}}+\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, x^{3}}{9 d}-\frac{4 \sqrt{d \,x^{3}+c}\, c}{9 d^{2}}\right) d +\frac{32 \sqrt{d \,x^{3}+c}\, c}{3 d}}{d^{3}}+\frac{64 i c \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 d^{6} \sqrt{d \,x^{3}+c}}"," ",0,"1/d^3*((2/9*(d*x^3+c)^(1/2)/d*x^3-4/9*(d*x^3+c)^(1/2)*c/d^2)*d+32/3*(d*x^3+c)^(1/2)*c/d)+512*c^3/d^3*(-1/27/c/d*(d*x^3+c)^(1/2)/(d*x^3-8*c)-1/486*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+64/9*I*c/d^6*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
425,1,874,65,0.199000," ","int(x^8/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{64 \left(-\frac{\sqrt{d \,x^{3}+c}}{27 \left(d \,x^{3}-8 c \right) c d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{486 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{2}}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d^{3}}+\frac{16 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 d^{5} \sqrt{d \,x^{3}+c}}"," ",0,"2/3*(d*x^3+c)^(1/2)/d^3+64*c^2/d^2*(-1/27*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c/d-1/486*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16/27*I/d^5*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
426,1,861,50,0.174000," ","int(x^5/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{8 \left(-\frac{\sqrt{d \,x^{3}+c}}{27 \left(d \,x^{3}-8 c \right) c d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{486 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 c \,d^{4} \sqrt{d \,x^{3}+c}}"," ",0,"8*c/d*(-1/27*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c/d-1/486*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/27*I/d^4/c*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
427,1,442,53,0.190000," ","int(x^2/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","-\frac{\sqrt{d \,x^{3}+c}}{27 \left(d \,x^{3}-8 c \right) c d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{486 c^{2} d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"-1/27*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c/d-1/486*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
428,1,880,66,0.186000," ","int(1/x/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{27 \left(d \,x^{3}-8 c \right) c d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{486 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) d}{8 c}-\frac{\arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{96 c^{\frac{5}{2}}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1728 c^{3} d^{2} \sqrt{d \,x^{3}+c}}"," ",0,"1/8/c*d*(-1/27*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c/d-1/486*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))-1/1728*I/c^3/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))-1/96*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2)","C"
429,1,926,98,0.197000," ","int(1/x^4/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{27 \left(d \,x^{3}-8 c \right) c d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{486 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{64 c^{2}}-\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{384 c^{\frac{7}{2}}}+\frac{\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}-\frac{\sqrt{d \,x^{3}+c}}{3 c \,x^{3}}}{64 c^{2}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6912 c^{4} d \sqrt{d \,x^{3}+c}}"," ",0,"1/64/c^2*d^2*(-1/27*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c/d-1/486*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/3*(d*x^3+c)^(1/2)/c/x^3+1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))-1/6912*I/c^4/d*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))-1/384*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(7/2)","C"
430,1,989,134,0.197000," ","int(1/x^7/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{27 \left(d \,x^{3}-8 c \right) c d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{486 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{512 c^{3}}-\frac{d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{2048 c^{\frac{9}{2}}}+\frac{-\frac{d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{4 c^{\frac{5}{2}}}+\frac{\sqrt{d \,x^{3}+c}\, d}{4 c^{2} x^{3}}-\frac{\sqrt{d \,x^{3}+c}}{6 c \,x^{6}}}{64 c^{2}}+\frac{\left(\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}-\frac{\sqrt{d \,x^{3}+c}}{3 c \,x^{3}}\right) d}{256 c^{3}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{36864 c^{5} \sqrt{d \,x^{3}+c}}"," ",0,"1/512/c^3*d^3*(-1/27*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c/d-1/486*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-1/3*(d*x^3+c)^(1/2)/c/x^3+1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))+1/64/c^2*(-1/6*(d*x^3+c)^(1/2)/c/x^6+1/4*(d*x^3+c)^(1/2)/c^2*d/x^3-1/4*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2))-1/36864*I/c^5*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))-1/2048*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(9/2)","C"
431,1,1737,461,0.309000," ","int(x^7/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{64 \left(-\frac{\sqrt{d \,x^{3}+c}\, x^{2}}{216 \left(d \,x^{3}-8 c \right) c^{2}}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{648 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{7 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1944 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c^{2}}{d^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d^{3}}+\frac{16 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 d^{5} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"-2/3*I/d^3*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+64*c^2/d^2*(-1/216/c^2*x^2*(d*x^3+c)^(1/2)/(d*x^3-8*c)-1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-7/1944*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16/27*I/d^5*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
432,1,1304,467,0.184000," ","int(x^4/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{8 \left(-\frac{\sqrt{d \,x^{3}+c}\, x^{2}}{216 \left(d \,x^{3}-8 c \right) c^{2}}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{648 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{7 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1944 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c}{d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 c \,d^{4} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"8*c/d*(-1/216*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2*x^2-1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-7/1944*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/27*I/d^4/c*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
433,1,882,464,0.187000," ","int(x/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","-\frac{\sqrt{d \,x^{3}+c}\, x^{2}}{216 \left(d \,x^{3}-8 c \right) c^{2}}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{648 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{7 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1944 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"-1/216*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2*x^2-1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-7/1944*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
434,1,1761,481,0.217000," ","int(1/x^2/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}\, x^{2}}{216 \left(d \,x^{3}-8 c \right) c^{2}}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{648 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{7 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1944 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) d}{8 c}+\frac{-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{c x}}{64 c^{2}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1728 c^{3} d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"1/8/c*d*(-1/216*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2*x^2-1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-7/1944*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-(d*x^3+c)^(1/2)/c/x-1/3*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/1728*I/c^3/d^2*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
435,1,2240,499,0.239000," ","int(1/x^5/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/64/c^2*(-1/4*(d*x^3+c)^(1/2)/c/x^4+5/8*(d*x^3+c)^(1/2)/c^2*d/x+5/24*I/c^2*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/64/c^2*d^2*(-1/216*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2*x^2-1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-7/1944*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-(d*x^3+c)^(1/2)/c/x-1/3*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/6912*I/c^4/d*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
436,1,2738,519,0.191000," ","int(1/x^8/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/256/c^3*d*(-1/4*(d*x^3+c)^(1/2)/c/x^4+5/8*(d*x^3+c)^(1/2)/c^2*d/x+5/24*I/c^2*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/512/c^3*d^3*(-1/216*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2*x^2-1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-7/1944*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/7*(d*x^3+c)^(1/2)/c/x^7+11/56*(d*x^3+c)^(1/2)/c^2*d/x^4-55/112*(d*x^3+c)^(1/2)/c^3*d^2/x-55/336*I/c^3*d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+3/4096/c^4*d^2*(-(d*x^3+c)^(1/2)/c/x-1/3*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/36864*I/c^5*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
437,1,1431,52,0.285000," ","int(x^6/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{64 \left(-\frac{\sqrt{d \,x^{3}+c}\, x}{216 \left(d \,x^{3}-8 c \right) c^{2}}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{648 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{5 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{972 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) c^{2}}{d^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d^{3}}+\frac{16 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 d^{5} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"-2/3*I/d^3*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+64*c^2/d^2*(-1/216/c^2*x*(d*x^3+c)^(1/2)/(d*x^3-8*c)+1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-5/972*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16/27*I/d^5*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
438,1,1150,52,0.258000," ","int(x^3/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{8 \left(-\frac{\sqrt{d \,x^{3}+c}\, x}{216 \left(d \,x^{3}-8 c \right) c^{2}}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{648 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{5 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{972 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) c}{d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{27 c \,d^{4} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"8*c/d*(-1/216*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2*x+1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-5/972*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/27*I/d^4/c*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
439,1,728,50,0.177000," ","int(1/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","-\frac{\sqrt{d \,x^{3}+c}\, x}{216 \left(d \,x^{3}-8 c \right) c^{2}}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{648 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{5 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{972 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"-1/216*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2*x+1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-5/972*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
440,1,1455,52,0.200000," ","int(1/x^3/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}\, x}{216 \left(d \,x^{3}-8 c \right) c^{2}}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{648 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{5 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{972 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) d}{8 c}+\frac{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{2 c \,x^{2}}}{64 c^{2}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1728 c^{3} d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"1/8/c*d*(-1/216*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2*x+1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-5/972*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/2*(d*x^3+c)^(1/2)/c/x^2+1/6*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/1728*I/c^3/d^2*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
441,1,1782,52,0.179000," ","int(1/x^6/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}\, x}{216 \left(d \,x^{3}-8 c \right) c^{2}}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{648 \sqrt{d \,x^{3}+c}\, c^{2} d}-\frac{5 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{972 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) d^{2}}{64 c^{2}}+\frac{-\frac{7 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{60 \sqrt{d \,x^{3}+c}\, c^{2}}+\frac{7 \sqrt{d \,x^{3}+c}\, d}{20 c^{2} x^{2}}-\frac{\sqrt{d \,x^{3}+c}}{5 c \,x^{5}}}{64 c^{2}}+\frac{\left(\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{2 c \,x^{2}}\right) d}{256 c^{3}}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6912 c^{4} d \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"1/64/c^2*(-1/5/c*(d*x^3+c)^(1/2)/x^5+7/20/c^2*d*(d*x^3+c)^(1/2)/x^2-7/60*I/c^2*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/64/c^2*d^2*(-1/216*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2*x+1/648*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-5/972*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-1/2*(d*x^3+c)^(1/2)/c/x^2+1/6*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/6912*I/c^4/d*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
442,1,970,77,0.288000," ","int(x^11/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{512 \left(-\frac{\sqrt{d \,x^{3}+c}}{243 \left(d \,x^{3}-8 c \right) c^{2} d}-\frac{2}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1458 c^{3} d^{3} \sqrt{d \,x^{3}+c}}\right) c^{3}}{d^{3}}+\frac{192 \left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{3}}+\frac{\left(\frac{2 c}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, d^{2}}+\frac{2 \sqrt{d \,x^{3}+c}}{3 d^{2}}\right) d -\frac{32 c}{3 \sqrt{d \,x^{3}+c}\, d}}{d^{3}}"," ",0,"1/d^3*((2/3/((x^3+c/d)*d)^(1/2)*c/d^2+2/3*(d*x^3+c)^(1/2)/d^2)*d-32/3/(d*x^3+c)^(1/2)*c/d)+512*c^3/d^3*(-1/243/d/c^2*(d*x^3+c)^(1/2)/(d*x^3-8*c)-2/243/d/c^2/((x^3+c/d)*d)^(1/2)-1/1458*I/d^3/c^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+192*c^2/d^3*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
443,1,926,65,0.178000," ","int(x^8/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{64 \left(-\frac{\sqrt{d \,x^{3}+c}}{243 \left(d \,x^{3}-8 c \right) c^{2} d}-\frac{2}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1458 c^{3} d^{3} \sqrt{d \,x^{3}+c}}\right) c^{2}}{d^{2}}+\frac{16 \left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d^{2}}-\frac{2}{3 \sqrt{d \,x^{3}+c}\, d^{3}}"," ",0,"-2/3/d^3/(d*x^3+c)^(1/2)+64*c^2/d^2*(-1/243*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2/d-2/243/((x^3+c/d)*d)^(1/2)/c^2/d-1/1458*I/d^3/c^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16*c/d^2*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
444,1,908,67,0.183000," ","int(x^5/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{8 \left(-\frac{\sqrt{d \,x^{3}+c}}{243 \left(d \,x^{3}-8 c \right) c^{2} d}-\frac{2}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1458 c^{3} d^{3} \sqrt{d \,x^{3}+c}}\right) c}{d}+\frac{\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}}{d}"," ",0,"8*c/d*(-1/243*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2/d-2/243/((x^3+c/d)*d)^(1/2)/c^2/d-1/1458*I/d^3/c^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/d*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
445,1,463,70,0.190000," ","int(x^2/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","-\frac{\sqrt{d \,x^{3}+c}}{243 \left(d \,x^{3}-8 c \right) c^{2} d}-\frac{2}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1458 c^{3} d^{3} \sqrt{d \,x^{3}+c}}"," ",0,"-1/243*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2/d-2/243/((x^3+c/d)*d)^(1/2)/c^2/d-1/1458*I/d^3/c^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
446,1,953,80,0.171000," ","int(1/x/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{243 \left(d \,x^{3}-8 c \right) c^{2} d}-\frac{2}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1458 c^{3} d^{3} \sqrt{d \,x^{3}+c}}\right) d}{8 c}-\frac{\left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) d}{64 c^{2}}+\frac{-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}}{64 c^{2}}"," ",0,"1/8/c*d*(-1/243*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2/d-2/243/((x^3+c/d)*d)^(1/2)/c^2/d-1/1458*I/d^3/c^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))-1/64/c^2*d*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(2/3/((x^3+c/d)*d)^(1/2)/c-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
447,1,1019,113,0.195000," ","int(1/x^4/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{243 \left(d \,x^{3}-8 c \right) c^{2} d}-\frac{2}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1458 c^{3} d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{64 c^{2}}-\frac{\left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) d^{2}}{256 c^{3}}+\frac{\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{c^{\frac{5}{2}}}-\frac{2 d}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{3 c^{2} x^{3}}}{64 c^{2}}+\frac{\left(-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}\right) d}{256 c^{3}}"," ",0,"1/64/c^2*d^2*(-1/243*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2/d-2/243/((x^3+c/d)*d)^(1/2)/c^2/d-1/1458*I/d^3/c^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/3*(d*x^3+c)^(1/2)/c^2/x^3-2/3/((x^3+c/d)*d)^(1/2)/c^2*d+d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2))-1/256/c^3*d^2*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(2/3/((x^3+c/d)*d)^(1/2)/c-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
448,1,1106,151,0.210000," ","int(1/x^7/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}}{243 \left(d \,x^{3}-8 c \right) c^{2} d}-\frac{2}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1458 c^{3} d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{512 c^{3}}-\frac{3 \left(\frac{2}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}}\right) d^{3}}{4096 c^{4}}+\frac{-\frac{5 d^{2} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{4 c^{\frac{7}{2}}}+\frac{2 d^{2}}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}+\frac{7 \sqrt{d \,x^{3}+c}\, d}{12 c^{3} x^{3}}-\frac{\sqrt{d \,x^{3}+c}}{6 c^{2} x^{6}}}{64 c^{2}}+\frac{\left(\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{c^{\frac{5}{2}}}-\frac{2 d}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{3 c^{2} x^{3}}\right) d}{256 c^{3}}+\frac{3 \left(-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}\right) d^{2}}{4096 c^{4}}"," ",0,"1/512/c^3*d^3*(-1/243*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^2/d-2/243/((x^3+c/d)*d)^(1/2)/c^2/d-1/1458*I/d^3/c^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-1/3*(d*x^3+c)^(1/2)/c^2/x^3-2/3/((x^3+c/d)*d)^(1/2)/c^2*d+d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2))+1/64/c^2*(-1/6*(d*x^3+c)^(1/2)/c^2/x^6+7/12*(d*x^3+c)^(1/2)/c^3*d/x^3+2/3/((x^3+c/d)*d)^(1/2)/c^3*d^2-5/4*d^2*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(7/2))-3/4096/c^4*d^3*(2/27/((x^3+c/d)*d)^(1/2)/c/d+1/243*I/c^2/d^3*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+3/4096/c^4*d^2*(2/3/((x^3+c/d)*d)^(1/2)/c-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
449,1,2255,484,0.259000," ","int(x^7/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/d^2*(2/3/((x^3+c/d)*d)^(1/2)/c*x^2+2/9*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+64*c^2/d^2*(-1/1944*x^2/c^3*(d*x^3+c)^(1/2)/(d*x^3-8*c)+2/243*x^2/c^3/((x^3+c/d)*d)^(1/2)+5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-5/5832*I/c^3/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16*c/d^2*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
450,1,1788,487,0.187000," ","int(x^4/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{8 \left(-\frac{\sqrt{d \,x^{3}+c}\, x^{2}}{1944 \left(d \,x^{3}-8 c \right) c^{3}}+\frac{2 x^{2}}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}+\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{1944 \sqrt{d \,x^{3}+c}\, c^{3} d}-\frac{5 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{5832 c^{3} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}\right) c}{d}+\frac{-\frac{2 x^{2}}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}}{d}"," ",0,"8*c/d*(-1/1944*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^3*x^2+2/243/((x^3+c/d)*d)^(1/2)/c^3*x^2+5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-5/5832*I/c^3/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/d*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
451,1,903,481,0.177000," ","int(x/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","-\frac{\sqrt{d \,x^{3}+c}\, x^{2}}{1944 \left(d \,x^{3}-8 c \right) c^{3}}+\frac{2 x^{2}}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}+\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{1944 \sqrt{d \,x^{3}+c}\, c^{3} d}-\frac{5 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{5832 c^{3} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}"," ",0,"-1/1944*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^3*x^2+2/243/((x^3+c/d)*d)^(1/2)/c^3*x^2+5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-5/5832*I/c^3/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
452,1,2269,498,0.197000," ","int(1/x^2/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/8/c*d*(-1/1944*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^3*x^2+2/243/((x^3+c/d)*d)^(1/2)/c^3*x^2+5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-5/5832*I/c^3/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x^2-(d*x^3+c)^(1/2)/c^2/x-5/9*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/64/c^2*d*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
453,1,2774,516,0.194000," ","int(1/x^5/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/64/c^2*(-1/4*(d*x^3+c)^(1/2)/c^2/x^4+13/8*(d*x^3+c)^(1/2)/c^3*d/x+2/3*d^2/c^3*x^2/((x^3+c/d)*d)^(1/2)+55/72*I/c^3*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/64/c^2*d^2*(-1/1944*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^3*x^2+2/243/((x^3+c/d)*d)^(1/2)/c^3*x^2+5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-5/5832*I/c^3/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x^2-(d*x^3+c)^(1/2)/c^2/x-5/9*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-1/256/c^3*d^2*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
454,1,3299,536,0.234000," ","int(1/x^8/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\text{output too large to display}"," ",0,"1/256/c^3*d*(-1/4*(d*x^3+c)^(1/2)/c^2/x^4+13/8*(d*x^3+c)^(1/2)/c^3*d/x+2/3/((x^3+c/d)*d)^(1/2)/c^3*d^2*x^2+55/72*I/c^3*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+1/512/c^3*d^3*(-1/1944*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^3*x^2+2/243/((x^3+c/d)*d)^(1/2)/c^3*x^2+5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-5/5832*I/c^3/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/7*(d*x^3+c)^(1/2)/c^2/x^7+25/56*(d*x^3+c)^(1/2)/c^3*d/x^4-237/112*(d*x^3+c)^(1/2)/c^4*d^2/x-2/3*d^3/c^4*x^2/((x^3+c/d)*d)^(1/2)-935/1008*I/c^4*d^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))+3/4096/c^4*d^2*(-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x^2-(d*x^3+c)^(1/2)/c^2/x-5/9*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))-3/4096/c^4*d^3*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x^2-2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
455,1,1791,197,0.320000," ","int(x^6/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{64 \left(-\frac{\sqrt{d \,x^{3}+c}\, x}{1944 \left(d \,x^{3}-8 c \right) c^{3}}+\frac{2 x}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}-\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1944 \sqrt{d \,x^{3}+c}\, c^{3} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{972 c^{3} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) c^{2}}{d^{2}}+\frac{16 \left(-\frac{2 x}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) c}{d^{2}}+\frac{\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \sqrt{d \,x^{3}+c}\, c d}}{d^{2}}"," ",0,"1/d^2*(2/3/c*x/((x^3+c/d)*d)^(1/2)-2/9*I/c*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+64*c^2/d^2*(-1/1944/c^3*x*(d*x^3+c)^(1/2)/(d*x^3-8*c)+2/243/c^3*x/((x^3+c/d)*d)^(1/2)-5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-1/972*I/c^3/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+16*c/d^2*(-2/27/c^2*x/((x^3+c/d)*d)^(1/2)+2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
456,1,1478,52,0.232000," ","int(x^3/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{8 \left(-\frac{\sqrt{d \,x^{3}+c}\, x}{1944 \left(d \,x^{3}-8 c \right) c^{3}}+\frac{2 x}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}-\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1944 \sqrt{d \,x^{3}+c}\, c^{3} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{972 c^{3} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) c}{d}+\frac{-\frac{2 x}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}}{d}"," ",0,"8*c/d*(-1/1944*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^3*x+2/243/((x^3+c/d)*d)^(1/2)/c^3*x-5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-1/972*I/c^3/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/d*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x+2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
457,1,747,50,0.174000," ","int(1/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","-\frac{\sqrt{d \,x^{3}+c}\, x}{1944 \left(d \,x^{3}-8 c \right) c^{3}}+\frac{2 x}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}-\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1944 \sqrt{d \,x^{3}+c}\, c^{3} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{972 c^{3} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}"," ",0,"-1/1944*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^3*x+2/243/((x^3+c/d)*d)^(1/2)/c^3*x-5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-1/972*I/c^3/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c))","C"
458,1,1805,52,0.167000," ","int(1/x^3/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{3}+c}\, x}{1944 \left(d \,x^{3}-8 c \right) c^{3}}+\frac{2 x}{243 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{3}}-\frac{5 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{1944 \sqrt{d \,x^{3}+c}\, c^{3} d}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{972 c^{3} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) d}{8 c}-\frac{\left(-\frac{2 x}{27 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{81 \sqrt{d \,x^{3}+c}\, c^{2} d}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)}{18 c d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{243 c^{2} d^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(d \,\textit{\_Z}^{3}-8 c \right)^{2}}\right) d}{64 c^{2}}+\frac{-\frac{2 d x}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}+\frac{7 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 \sqrt{d \,x^{3}+c}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{2 c^{2} x^{2}}}{64 c^{2}}"," ",0,"1/8/c*d*(-1/1944*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^3*x+2/243/((x^3+c/d)*d)^(1/2)/c^3*x-5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-1/972*I/c^3/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/64/c^2*(-1/2/c^2*(d*x^3+c)^(1/2)/x^2-2/3*d/c^2*x/((x^3+c/d)*d)^(1/2)+7/18*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/64/c^2*d*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x+2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
459,1,2156,52,0.185000," ","int(1/x^6/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/64/c^2*(-1/5/c^2*(d*x^3+c)^(1/2)/x^5+17/20/c^3*d*(d*x^3+c)^(1/2)/x^2+2/3*d^2/c^3*x/((x^3+c/d)*d)^(1/2)-91/180*I/c^3*d*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/64/c^2*d^2*(-1/1944*(d*x^3+c)^(1/2)/(d*x^3-8*c)/c^3*x+2/243/((x^3+c/d)*d)^(1/2)/c^3*x-5/1944*I/c^3*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))-1/972*I/c^3/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))+1/256/c^3*d*(-1/2*(d*x^3+c)^(1/2)/c^2/x^2-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x+7/18*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/256/c^3*d^2*(-2/27/((x^3+c/d)*d)^(1/2)/c^2*x+2/81*I/c^2*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/243*I/c^2/d^3*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),-1/18*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/c/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*d-8*c)))","C"
460,1,917,137,0.359000," ","int(x^8*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x)","\frac{\left(-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 b d \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b}\right) a^{2}}{b^{2}}-\frac{2 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}}\right) a}{b^{2}}+\frac{2 \left(d \,x^{3}+c \right)^{\frac{3}{2}}}{9 b^{2} d}"," ",0,"2/9*(d*x^3+c)^(3/2)/b^2/d-2*a/b^2*(2/3*(d*x^3+c)^(1/2)/b+1/3*I/b/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+a^2/b^2*(-1/3*(d*x^3+c)^(1/2)/b/(b*x^3+a)-1/6*I/d/b*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
461,1,897,116,0.263000," ","int(x^5*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x)","-\frac{\left(-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 b d \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b}\right) a}{b}+\frac{\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}}}{b}"," ",0,"1/b*(2/3*(d*x^3+c)^(1/2)/b+1/3*I/b/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-a/b*(-1/3*(d*x^3+c)^(1/2)/(b*x^3+a)/b-1/6*I/d/b*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
462,1,453,64,0.270000," ","int(x^2*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 b d \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b}"," ",0,"-1/3*(d*x^3+c)^(1/2)/(b*x^3+a)/b-1/6*I/d/b*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
463,1,934,97,0.285000," ","int((d*x^3+c)^(1/2)/x/(b*x^3+a)^2,x)","-\frac{\left(-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 b d \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b}\right) b}{a}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}}\right) b}{a^{2}}+\frac{-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}}{a^{2}}"," ",0,"-1/a^2*b*(2/3*(d*x^3+c)^(1/2)/b+1/3*I/b/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-1/a*b*(-1/3*(d*x^3+c)^(1/2)/(b*x^3+a)/b-1/6*I/d/b*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
464,1,978,133,0.262000," ","int((d*x^3+c)^(1/2)/x^4/(b*x^3+a)^2,x)","\frac{\left(-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 b d \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b}\right) b^{2}}{a^{2}}+\frac{2 \left(\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}}\right) b^{2}}{a^{3}}+\frac{-\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 \sqrt{c}}-\frac{\sqrt{d \,x^{3}+c}}{3 x^{3}}}{a^{2}}-\frac{2 \left(-\frac{2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{2 \sqrt{d \,x^{3}+c}}{3}\right) b}{a^{3}}"," ",0,"1/a^2*(-1/3*(d*x^3+c)^(1/2)/x^3-1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2))+2/a^3*b^2*(2/3*(d*x^3+c)^(1/2)/b+1/3*I/b/d^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*b^2*(-1/3*(d*x^3+c)^(1/2)/(b*x^3+a)/b-1/6*I/d/b*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-2*b/a^3*(2/3*(d*x^3+c)^(1/2)-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))*c^(1/2))","C"
465,1,1468,52,0.355000," ","int(x^3*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x)","-\frac{\left(\frac{\sqrt{d \,x^{3}+c}\, x}{3 \left(b \,x^{3}+a \right) a}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \sqrt{d \,x^{3}+c}\, a b}+\frac{i \left(a d -4 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a b \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) a}{b}+\frac{-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}}{b}"," ",0,"1/b*(-2/3*I/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b/d^2*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-a/b*(1/3/a*x*(d*x^3+c)^(1/2)/(b*x^3+a)-1/9*I/a/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/b/d^2*2^(1/2)*sum((a*d-4*b*c)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
466,1,908,52,0.361000," ","int(x*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x)","\frac{\sqrt{d \,x^{3}+c}\, x^{2}}{3 \left(b \,x^{3}+a \right) a}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \sqrt{d \,x^{3}+c}\, a b}+\frac{i \left(-a d -2 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a b \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}"," ",0,"1/3/a*x^2*(d*x^3+c)^(1/2)/(b*x^3+a)+1/9*I/a/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/18*I/a/b/d^2*2^(1/2)*sum((-a*d-2*b*c)/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
467,1,753,49,0.266000," ","int((d*x^3+c)^(1/2)/(b*x^3+a)^2,x)","\frac{\sqrt{d \,x^{3}+c}\, x}{3 \left(b \,x^{3}+a \right) a}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \sqrt{d \,x^{3}+c}\, a b}+\frac{i \left(a d -4 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a b \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}"," ",0,"1/3*(d*x^3+c)^(1/2)/(b*x^3+a)/a*x-1/9*I/a/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/b/d^2*2^(1/2)*sum((a*d-4*b*c)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
468,1,2227,52,0.373000," ","int((d*x^3+c)^(1/2)/x^2/(b*x^3+a)^2,x)","\text{Expression too large to display}"," ",0,"-1/a^2*b*(-2/3*I/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/b/d^2*2^(1/2)*sum(1/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-1/a*b*(1/3*(d*x^3+c)^(1/2)/(b*x^3+a)/a*x^2+1/9*I/a/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/18*I/a/b/d^2*2^(1/2)*sum((-a*d-2*b*c)/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(-(d*x^3+c)^(1/2)/x-I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
469,1,1768,52,0.264000," ","int((d*x^3+c)^(1/2)/x^3/(b*x^3+a)^2,x)","-\frac{\left(\frac{\sqrt{d \,x^{3}+c}\, x}{3 \left(b \,x^{3}+a \right) a}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \sqrt{d \,x^{3}+c}\, a b}+\frac{i \left(a d -4 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a b \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) b}{a}-\frac{\left(-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, b}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) b}{a^{2}}+\frac{-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}}{2 x^{2}}}{a^{2}}"," ",0,"-1/a^2*b*(-2/3*I/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b/d^2*2^(1/2)*sum(1/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(-1/2*(d*x^3+c)^(1/2)/x^2-1/2*I*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/a*b*(1/3*(d*x^3+c)^(1/2)/(b*x^3+a)/a*x-1/9*I/a/b*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/b/d^2*2^(1/2)*sum((a*d-4*b*c)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
470,1,1003,161,0.367000," ","int(x^8*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x)","\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d}{3 b^{2}}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 b^{2} d \sqrt{d \,x^{3}+c}}+\frac{\left(a d -b c \right) \sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b^{2}}\right) a^{2}}{b^{2}}-\frac{2 \left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9 b}+\frac{2 \left(-\frac{2 c d}{3 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}\right) a}{b^{2}}+\frac{2 \left(d \,x^{3}+c \right)^{\frac{5}{2}}}{15 b^{2} d}"," ",0,"2/15*(d*x^3+c)^(5/2)/b^2/d-2*a/b^2*(2/9*(d*x^3+c)^(1/2)/b*d*x^3+2/3*(-2/3/b*c*d-(a*d-2*b*c)/b^2*d)*(d*x^3+c)^(1/2)/d+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+a^2/b^2*(1/3*(a*d-b*c)/b^2*(d*x^3+c)^(1/2)/(b*x^3+a)+2/3*d*(d*x^3+c)^(1/2)/b^2+1/2*I/d/b^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
471,1,983,139,0.269000," ","int(x^5*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d}{3 b^{2}}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 b^{2} d \sqrt{d \,x^{3}+c}}+\frac{\left(a d -b c \right) \sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b^{2}}\right) a}{b}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9 b}+\frac{2 \left(-\frac{2 c d}{3 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}}{b}"," ",0,"1/b*(2/9*(d*x^3+c)^(1/2)/b*d*x^3+2/3*(-2/3/b*c*d-(a*d-2*b*c)/b^2*d)*(d*x^3+c)^(1/2)/d+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-a/b*(1/3*(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/b^2+2/3*(d*x^3+c)^(1/2)/b^2*d+1/2*I/d/b^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
472,1,466,78,0.266000," ","int(x^2*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x)","\frac{2 \sqrt{d \,x^{3}+c}\, d}{3 b^{2}}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 b^{2} d \sqrt{d \,x^{3}+c}}+\frac{\left(a d -b c \right) \sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b^{2}}"," ",0,"1/3*(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/b^2+2/3*(d*x^3+c)^(1/2)/b^2*d+1/2*I/d/b^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
473,1,1036,107,0.267000," ","int((d*x^3+c)^(3/2)/x/(b*x^3+a)^2,x)","-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d}{3 b^{2}}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 b^{2} d \sqrt{d \,x^{3}+c}}+\frac{\left(a d -b c \right) \sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b^{2}}\right) b}{a}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9 b}+\frac{2 \left(-\frac{2 c d}{3 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}\right) b}{a^{2}}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}}{a^{2}}"," ",0,"-1/a^2*b*(2/9*(d*x^3+c)^(1/2)/b*d*x^3+2/3*(-2/3/b*c*d-(a*d-2*b*c)/b^2*d)*(d*x^3+c)^(1/2)/d+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-1/a*b*(1/3*(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/b^2+2/3*(d*x^3+c)^(1/2)/b^2*d+1/2*I/d/b^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(2/9*(d*x^3+c)^(1/2)*d*x^3+8/9*(d*x^3+c)^(1/2)*c-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
474,1,1093,142,0.248000," ","int((d*x^3+c)^(3/2)/x^4/(b*x^3+a)^2,x)","\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d}{3 b^{2}}+\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 b^{2} d \sqrt{d \,x^{3}+c}}+\frac{\left(a d -b c \right) \sqrt{d \,x^{3}+c}}{3 \left(b \,x^{3}+a \right) b^{2}}\right) b^{2}}{a^{2}}+\frac{2 \left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9 b}+\frac{2 \left(-\frac{2 c d}{3 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{d \,x^{3}+c}}{3 d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}\right) b^{2}}{a^{3}}+\frac{-\sqrt{c}\, d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)+\frac{2 \sqrt{d \,x^{3}+c}\, d}{3}-\frac{\sqrt{d \,x^{3}+c}\, c}{3 x^{3}}}{a^{2}}-\frac{2 \left(\frac{2 \sqrt{d \,x^{3}+c}\, d \,x^{3}}{9}-\frac{2 c^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3}+\frac{8 \sqrt{d \,x^{3}+c}\, c}{9}\right) b}{a^{3}}"," ",0,"1/a^2*(-1/3*(d*x^3+c)^(1/2)*c/x^3+2/3*(d*x^3+c)^(1/2)*d-c^(1/2)*d*arctanh((d*x^3+c)^(1/2)/c^(1/2)))+2/a^3*b^2*(2/9*(d*x^3+c)^(1/2)/b*d*x^3+2/3*(-2/3/b*c*d-(a*d-2*b*c)/b^2*d)*(d*x^3+c)^(1/2)/d+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*b^2*(1/3*(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/b^2+2/3*(d*x^3+c)^(1/2)/b^2*d+1/2*I/d/b^2*2^(1/2)*sum((-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-2*b/a^3*(2/9*(d*x^3+c)^(1/2)*d*x^3+8/9*(d*x^3+c)^(1/2)*c-2/3*c^(3/2)*arctanh((d*x^3+c)^(1/2)/c^(1/2)))","C"
475,1,1587,53,0.349000," ","int(x^3*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x)","-\frac{\left(-\frac{2 i \left(\frac{d^{2}}{b^{2}}-\frac{\left(a d -b c \right) d}{6 a \,b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}-\frac{\left(a d -b c \right) \sqrt{d \,x^{3}+c}\, x}{3 \left(b \,x^{3}+a \right) a b}+\frac{i \left(5 a^{2} d^{2}-a b c d -4 b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) a}{b}+\frac{\frac{2 \sqrt{d \,x^{3}+c}\, d x}{5 b}-\frac{2 i \left(-\frac{2 c d}{5 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}}{b}"," ",0,"1/b*(2/5*(d*x^3+c)^(1/2)/b*d*x-2/3*I*(-2/5/b*c*d-(a*d-2*b*c)/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-a/b*(-1/3*(a*d-b*c)/a/b*x*(d*x^3+c)^(1/2)/(b*x^3+a)-2/3*I*(d^2/b^2-1/6/b^2*d*(a*d-b*c)/a)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/b^2/d^2*2^(1/2)*sum((5*a^2*d^2-a*b*c*d-4*b^2*c^2)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
476,1,955,53,0.355000," ","int(x*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x)","-\frac{\left(a d -b c \right) \sqrt{d \,x^{3}+c}\, x^{2}}{3 \left(b \,x^{3}+a \right) a b}-\frac{2 i \left(\frac{d^{2}}{b^{2}}+\frac{\left(a d -b c \right) d}{6 a \,b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(7 a^{2} d^{2}-5 a b c d -2 b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}"," ",0,"-1/3*(a*d-b*c)/a/b*x^2*(d*x^3+c)^(1/2)/(b*x^3+a)-2/3*I*(1/b^2*d^2+1/6*(a*d-b*c)/a/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/18*I/a/b^2/d^2*2^(1/2)*sum((7*a^2*d^2-5*a*b*c*d-2*b^2*c^2)/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
477,1,801,50,0.259000," ","int((d*x^3+c)^(3/2)/(b*x^3+a)^2,x)","-\frac{2 i \left(\frac{d^{2}}{b^{2}}-\frac{\left(a d -b c \right) d}{6 a \,b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}-\frac{\left(a d -b c \right) \sqrt{d \,x^{3}+c}\, x}{3 \left(b \,x^{3}+a \right) a b}+\frac{i \left(5 a^{2} d^{2}-a b c d -4 b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}"," ",0,"-1/3*(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/a/b*x-2/3*I*(1/b^2*d^2-1/6*(a*d-b*c)/a/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/b^2/d^2*2^(1/2)*sum((5*a^2*d^2-a*b*c*d-4*b^2*c^2)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
478,1,2364,53,0.265000," ","int((d*x^3+c)^(3/2)/x^2/(b*x^3+a)^2,x)","\text{Expression too large to display}"," ",0,"-1/a^2*b*(2/7*(d*x^3+c)^(1/2)/b*d*x^2-2/3*I*(-4/7/b*c*d-(a*d-2*b*c)/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-1/a*b*(-1/3*(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/a/b*x^2-2/3*I*(1/b^2*d^2+1/6*(a*d-b*c)/a/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/18*I/a/b^2/d^2*2^(1/2)*sum((7*a^2*d^2-5*a*b*c*d-2*b^2*c^2)/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(-(d*x^3+c)^(1/2)*c/x+2/7*(d*x^3+c)^(1/2)*d*x^2-9/7*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
479,1,1902,53,0.245000," ","int((d*x^3+c)^(3/2)/x^3/(b*x^3+a)^2,x)","-\frac{\left(-\frac{2 i \left(\frac{d^{2}}{b^{2}}-\frac{\left(a d -b c \right) d}{6 a \,b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}-\frac{\left(a d -b c \right) \sqrt{d \,x^{3}+c}\, x}{3 \left(b \,x^{3}+a \right) a b}+\frac{i \left(5 a^{2} d^{2}-a b c d -4 b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) b}{a}-\frac{\left(\frac{2 \sqrt{d \,x^{3}+c}\, d x}{5 b}-\frac{2 i \left(-\frac{2 c d}{5 b}-\frac{\left(a d -2 b c \right) d}{b^{2}}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i \left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) b}{a^{2}}+\frac{-\frac{9 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{10 \sqrt{d \,x^{3}+c}}+\frac{2 \sqrt{d \,x^{3}+c}\, d x}{5}-\frac{\sqrt{d \,x^{3}+c}\, c}{2 x^{2}}}{a^{2}}"," ",0,"-1/a^2*b*(2/5*(d*x^3+c)^(1/2)/b*d*x-2/3*I*(-2/5/b*c*d-(a*d-2*b*c)/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I/b^2/d^2*2^(1/2)*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(-1/2*(d*x^3+c)^(1/2)*c/x^2+2/5*(d*x^3+c)^(1/2)*d*x-9/10*I*c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/a*b*(-1/3*(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/a/b*x-2/3*I*(1/b^2*d^2-1/6*(a*d-b*c)/a/b^2*d)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/b^2/d^2*2^(1/2)*sum((5*a^2*d^2-a*b*c*d-4*b^2*c^2)/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
480,1,911,103,0.424000," ","int(x^8/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","\frac{\left(-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 d \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}}+\frac{\sqrt{d \,x^{3}+c}}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right)}\right) a^{2}}{b^{2}}+\frac{2 i a \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}+\frac{2 \sqrt{d \,x^{3}+c}}{3 b^{2} d}"," ",0,"2/3*(d*x^3+c)^(1/2)/b^2/d+2/3*I*a/b^2/d^2*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))+a^2/b^2*(1/3/(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)-1/6*I/d*2^(1/2)*sum(1/(a*d-b*c)^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
481,1,892,83,0.272000," ","int(x^5/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","-\frac{\left(-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 d \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}}+\frac{\sqrt{d \,x^{3}+c}}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right)}\right) a}{b}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}"," ",0,"-1/3*I/b/d^2*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))-a/b*(1/3/(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)-1/6*I/d*2^(1/2)*sum(1/(a*d-b*c)^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
482,1,457,71,0.256000," ","int(x^2/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 d \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}}+\frac{\sqrt{d \,x^{3}+c}}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right)}"," ",0,"1/3/(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)-1/6*I/d*2^(1/2)*sum(1/(a*d-b*c)^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
483,1,915,108,0.276000," ","int(1/x/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","-\frac{\left(-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 d \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}}+\frac{\sqrt{d \,x^{3}+c}}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right)}\right) b}{a}-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 a^{2} \sqrt{c}}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 a^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}"," ",0,"1/3*I/a^2*b/d^2*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))-1/a*b*(1/3/(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)-1/6*I/d*2^(1/2)*sum(1/(a*d-b*c)^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/a^2/c^(1/2)","C"
484,1,961,157,0.287000," ","int(1/x^4/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","\frac{\left(-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 d \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}}+\frac{\sqrt{d \,x^{3}+c}}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right)}\right) b^{2}}{a^{2}}+\frac{4 b \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 a^{3} \sqrt{c}}+\frac{\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}-\frac{\sqrt{d \,x^{3}+c}}{3 c \,x^{3}}}{a^{2}}-\frac{2 i b^{2} \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 a^{3} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}}"," ",0,"1/a^2*(-1/3*(d*x^3+c)^(1/2)/c/x^3+1/3*d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))-2/3*I/a^3*b^2/d^2*2^(1/2)*sum(1/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))+1/a^2*b^2*(1/3/(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)-1/6*I/d*2^(1/2)*sum(1/(a*d-b*c)^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+4/3*b/a^3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(1/2)","C"
485,1,1207,52,0.370000," ","int(x^3/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","-\frac{\left(-\frac{\sqrt{d \,x^{3}+c}\, b x}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right) a}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, a}+\frac{i \left(-7 a d +4 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) a}{b}-\frac{i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 b \,d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}"," ",0,"-1/3*I/b/d^2*2^(1/2)*sum(1/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))-a/b*(-1/3/a*b/(a*d-b*c)*x*(d*x^3+c)^(1/2)/(b*x^3+a)+1/9*I/(a*d-b*c)/a*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/d^2*2^(1/2)*sum((-7*a*d+4*b*c)/(a*d-b*c)^2/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
486,1,923,52,0.398000," ","int(x/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","-\frac{\sqrt{d \,x^{3}+c}\, b \,x^{2}}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right) a}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, a}+\frac{i \left(-5 a d +2 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}"," ",0,"-1/3/a*b/(a*d-b*c)*x^2*(d*x^3+c)^(1/2)/(b*x^3+a)-1/9*I/(a*d-b*c)/a*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/18*I/a/d^2*2^(1/2)*sum((-5*a*d+2*b*c)/(a*d-b*c)^2/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
487,1,769,49,0.279000," ","int(1/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","-\frac{\sqrt{d \,x^{3}+c}\, b x}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right) a}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, a}+\frac{i \left(-7 a d +4 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}"," ",0,"-1/3/(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/a*b*x+1/9*I/(a*d-b*c)/a*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/d^2*2^(1/2)*sum((-7*a*d+4*b*c)/(a*d-b*c)^2/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
488,1,1818,52,0.267000," ","int(1/x^2/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","-\frac{\left(-\frac{\sqrt{d \,x^{3}+c}\, b \,x^{2}}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right) a}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, a}+\frac{i \left(-5 a d +2 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}\right) b}{a}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 a^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}+\frac{-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{c x}}{a^{2}}"," ",0,"1/3*I/a^2*b/d^2*2^(1/2)*sum(1/_alpha/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))-1/a*b*(-1/3/(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/a*b*x^2-1/9*I/(a*d-b*c)/a*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/18*I/a/d^2*2^(1/2)*sum((-5*a*d+2*b*c)/(a*d-b*c)^2/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(-(d*x^3+c)^(1/2)/c/x-1/3*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
489,1,1512,52,0.265000," ","int(1/x^3/(b*x^3+a)^2/(d*x^3+c)^(1/2),x)","-\frac{\left(-\frac{\sqrt{d \,x^{3}+c}\, b x}{3 \left(a d -b c \right) \left(b \,x^{3}+a \right) a}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, a}+\frac{i \left(-7 a d +4 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) b}{a}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 a^{2} d^{2} \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}+\frac{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{6 \sqrt{d \,x^{3}+c}\, c}-\frac{\sqrt{d \,x^{3}+c}}{2 c \,x^{2}}}{a^{2}}"," ",0,"1/3*I/a^2*b/d^2*2^(1/2)*sum(1/_alpha^2/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))+1/a^2*(-1/2*(d*x^3+c)^(1/2)/c/x^2+1/6*I/c*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/a*b*(-1/3/(a*d-b*c)*(d*x^3+c)^(1/2)/(b*x^3+a)/a*b*x+1/9*I/(a*d-b*c)/a*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/d^2*2^(1/2)*sum((-7*a*d+4*b*c)/(a*d-b*c)^2/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
490,1,978,130,0.364000," ","int(x^8/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","\frac{\left(\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d \left(a d -b c \right)^{3} \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}\, b}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right)}-\frac{2 d}{3 \left(a d -b c \right)^{2} \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) a^{2}}{b^{2}}-\frac{2 \left(-\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(-a d +b c \right) \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{2}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) a}{b^{2}}-\frac{2}{3 \sqrt{d \,x^{3}+c}\, b^{2} d}"," ",0,"-2/3/b^2/d/(d*x^3+c)^(1/2)-2*a/b^2*(-2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-1/3*I*b/d^2*2^(1/2)*sum(1/(-a*d+b*c)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+a^2/b^2*(-1/3*b/(a*d-b*c)^2*(d*x^3+c)^(1/2)/(b*x^3+a)-2/3*d/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)+1/2*I*b/d*2^(1/2)*sum(1/(a*d-b*c)^3*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
491,1,958,114,0.274000," ","int(x^5/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","-\frac{\left(\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d \left(a d -b c \right)^{3} \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}\, b}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right)}-\frac{2 d}{3 \left(a d -b c \right)^{2} \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) a}{b}+\frac{-\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(-a d +b c \right) \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{2}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}}{b}"," ",0,"1/b*(-2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-1/3*I*b/d^2*2^(1/2)*sum(1/(-a*d+b*c)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-a/b*(-1/3/(a*d-b*c)^2*(d*x^3+c)^(1/2)/(b*x^3+a)*b-2/3/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)*d+1/2*I*b/d*2^(1/2)*sum(1/(a*d-b*c)^3*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
492,1,485,92,0.249000," ","int(x^2/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d \left(a d -b c \right)^{3} \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}\, b}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right)}-\frac{2 d}{3 \left(a d -b c \right)^{2} \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}"," ",0,"-1/3/(a*d-b*c)^2*(d*x^3+c)^(1/2)/(b*x^3+a)*b-2/3/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)*d+1/2*I*b/d*2^(1/2)*sum(1/(a*d-b*c)^3*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
493,1,1002,144,0.273000," ","int(1/x/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","-\frac{\left(\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d \left(a d -b c \right)^{3} \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}\, b}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right)}-\frac{2 d}{3 \left(a d -b c \right)^{2} \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) b}{a}-\frac{\left(-\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(-a d +b c \right) \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{2}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) b}{a^{2}}+\frac{-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}}{a^{2}}"," ",0,"-1/a^2*b*(-2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-1/3*I*b/d^2*2^(1/2)*sum(1/(-a*d+b*c)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-1/a*b*(-1/3/(a*d-b*c)^2*(d*x^3+c)^(1/2)/(b*x^3+a)*b-2/3/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)*d+1/2*I*b/d*2^(1/2)*sum(1/(a*d-b*c)^3*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(2/3/((x^3+c/d)*d)^(1/2)/c-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
494,1,1067,209,0.246000," ","int(1/x^4/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","\frac{\left(\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{2 d \left(a d -b c \right)^{3} \sqrt{d \,x^{3}+c}}-\frac{\sqrt{d \,x^{3}+c}\, b}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right)}-\frac{2 d}{3 \left(a d -b c \right)^{2} \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) b^{2}}{a^{2}}+\frac{2 \left(-\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(-a d +b c \right) \left(a d -b c \right) \sqrt{d \,x^{3}+c}}-\frac{2}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}}\right) b^{2}}{a^{3}}+\frac{\frac{d \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{c^{\frac{5}{2}}}-\frac{2 d}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c^{2}}-\frac{\sqrt{d \,x^{3}+c}}{3 c^{2} x^{3}}}{a^{2}}-\frac{2 \left(-\frac{2 \arctanh \left(\frac{\sqrt{d \,x^{3}+c}}{\sqrt{c}}\right)}{3 c^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}\right) b}{a^{3}}"," ",0,"1/a^2*(-1/3*(d*x^3+c)^(1/2)/c^2/x^3-2/3/((x^3+c/d)*d)^(1/2)/c^2*d+d*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(5/2))+2/a^3*b^2*(-2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-1/3*I*b/d^2*2^(1/2)*sum(1/(-a*d+b*c)/(a*d-b*c)*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*b^2*(-1/3/(a*d-b*c)^2*(d*x^3+c)^(1/2)/(b*x^3+a)*b-2/3/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)*d+1/2*I*b/d*2^(1/2)*sum(1/(a*d-b*c)^3*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-2*b/a^3*(2/3/((x^3+c/d)*d)^(1/2)/c-2/3*arctanh((d*x^3+c)^(1/2)/c^(1/2))/c^(3/2))","C"
495,1,1593,55,0.337000," ","int(x^3/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","-\frac{\left(\frac{\sqrt{d \,x^{3}+c}\, b^{2} x}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right) a}+\frac{2 d^{2} x}{3 \left(a d -b c \right)^{2} \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}-\frac{2 i \left(\frac{b d}{6 \left(a d -b c \right)^{2} a}+\frac{d^{2}}{3 \left(a d -b c \right)^{2} c}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i b \left(13 a d -4 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,d^{2} \left(a d -b c \right)^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}\right) a}{b}+\frac{\frac{2 d x}{3 \left(a d -b c \right) \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}+\frac{i b \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 d^{2} \left(a d -b c \right)^{2} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{9 \left(a d -b c \right) \sqrt{d \,x^{3}+c}\, c}}{b}"," ",0,"1/b*(2/3*d/c*x/(a*d-b*c)/((x^3+c/d)*d)^(1/2)-2/9*I/c/(a*d-b*c)*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I*b/d^2*2^(1/2)*sum(1/(a*d-b*c)^2/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-a/b*(1/3/a*b^2/(a*d-b*c)^2*x*(d*x^3+c)^(1/2)/(b*x^3+a)+2/3*d^2/c*x/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)-2/3*I*(1/6*b*d/(a*d-b*c)^2/a+1/3/c*d^2/(a*d-b*c)^2)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/d^2*b*2^(1/2)*sum((13*a*d-4*b*c)/(a*d-b*c)^3/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
496,1,986,55,0.346000," ","int(x/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","\frac{\sqrt{d \,x^{3}+c}\, b^{2} x^{2}}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right) a}+\frac{2 d^{2} x^{2}}{3 \left(a d -b c \right)^{2} \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}+\frac{i b \left(11 a d -2 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,d^{2} \left(a d -b c \right)^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)}-\frac{2 i \left(-\frac{b d}{6 \left(a d -b c \right)^{2} a}-\frac{d^{2}}{3 \left(a d -b c \right)^{2} c}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right)}{3 \sqrt{d \,x^{3}+c}\, d}"," ",0,"1/3/a*b^2/(a*d-b*c)^2*x^2*(d*x^3+c)^(1/2)/(b*x^3+a)+2/3*d^2/c*x^2/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)-2/3*I*(-1/6/(a*d-b*c)^2/a*b*d-1/3/(a*d-b*c)^2/c*d^2)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/18*I/a/d^2*b*2^(1/2)*sum((11*a*d-2*b*c)/(a*d-b*c)^3/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
497,1,830,52,0.265000," ","int(1/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","\frac{\sqrt{d \,x^{3}+c}\, b^{2} x}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right) a}+\frac{2 d^{2} x}{3 \left(a d -b c \right)^{2} \sqrt{\left(x^{3}+\frac{c}{d}\right) d}\, c}-\frac{2 i \left(\frac{b d}{6 \left(a d -b c \right)^{2} a}+\frac{d^{2}}{3 \left(a d -b c \right)^{2} c}\right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, d}+\frac{i b \left(13 a d -4 b c \right) \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{-i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{-3 \left(-c \,d^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}+\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}\right) d}{2 \left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d^{2}+i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right) d -\left(-c \,d^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right) d -i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{2}{3}}-\left(-c \,d^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{\left(2 i \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2} d +i \sqrt{3}\, c d -3 c d -i \left(-c \,d^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)-3 \left(-c \,d^{2}\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3} b +a \right)\right) b}{2 \left(a d -b c \right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{18 a \,d^{2} \left(a d -b c \right)^{3} \sqrt{d \,x^{3}+c}\, \RootOf \left(\textit{\_Z}^{3} b +a \right)^{2}}"," ",0,"1/3/(a*d-b*c)^2*(d*x^3+c)^(1/2)/(b*x^3+a)/a*b^2*x+2/3/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)/c*d^2*x-2/3*I*(1/6/(a*d-b*c)^2/a*b*d+1/3/(a*d-b*c)^2/c*d^2)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/d^2*b*2^(1/2)*sum((13*a*d-4*b*c)/(a*d-b*c)^3/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a))","C"
498,1,2383,55,0.297000," ","int(1/x^2/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/a^2*b*(2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)/c*d*x^2+2/9*I/c/(a*d-b*c)*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/3*I*b/d^2*2^(1/2)*sum(1/(a*d-b*c)^2/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))-1/a*b*(1/3/(a*d-b*c)^2*(d*x^3+c)^(1/2)/(b*x^3+a)/a*b^2*x^2+2/3/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)/c*d^2*x^2-2/3*I*(-1/6/(a*d-b*c)^2/a*b*d-1/3/(a*d-b*c)^2/c*d^2)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))+1/18*I/a/d^2*b*2^(1/2)*sum((11*a*d-2*b*c)/(a*d-b*c)^3/_alpha*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x^2-(d*x^3+c)^(1/2)/c^2/x-5/9*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*((-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+(-c*d^2)^(1/3)/d*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))))","C"
499,1,1919,55,0.258000," ","int(1/x^3/(b*x^3+a)^2/(d*x^3+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/a^2*b*(2/3/(a*d-b*c)/((x^3+c/d)*d)^(1/2)/c*d*x-2/9*I/c/(a*d-b*c)*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/3*I*b/d^2*2^(1/2)*sum(1/(a*d-b*c)^2/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))+1/a^2*(-1/2*(d*x^3+c)^(1/2)/c^2/x^2-2/3/((x^3+c/d)*d)^(1/2)/c^2*d*x+7/18*I/c^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)))-1/a*b*(1/3/(a*d-b*c)^2*(d*x^3+c)^(1/2)/(b*x^3+a)/a*b^2*x+2/3/(a*d-b*c)^2/((x^3+c/d)*d)^(1/2)/c*d^2*x-2/3*I*(1/6/(a*d-b*c)^2/a*b*d+1/3/(a*d-b*c)^2/c*d^2)*3^(1/2)*(-c*d^2)^(1/3)/d*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d))^(1/2)*(-I*(x+1/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2))+1/18*I/a/d^2*b*2^(1/2)*sum((13*a*d-4*b*c)/(a*d-b*c)^3/_alpha^2*(-c*d^2)^(1/3)*(1/2*I*(2*x+(-I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)*((x-(-c*d^2)^(1/3)/d)/(-3*(-c*d^2)^(1/3)+I*3^(1/2)*(-c*d^2)^(1/3))*d)^(1/2)*(-1/2*I*(2*x+(I*3^(1/2)*(-c*d^2)^(1/3)+(-c*d^2)^(1/3))/d)/(-c*d^2)^(1/3)*d)^(1/2)/(d*x^3+c)^(1/2)*(2*_alpha^2*d^2+I*(-c*d^2)^(1/3)*3^(1/2)*_alpha*d-(-c*d^2)^(1/3)*_alpha*d-I*3^(1/2)*(-c*d^2)^(2/3)-(-c*d^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-c*d^2)^(1/3)/d-1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)*3^(1/2)/(-c*d^2)^(1/3)*d)^(1/2),1/2*(2*I*(-c*d^2)^(1/3)*3^(1/2)*_alpha^2*d+I*3^(1/2)*c*d-3*c*d-I*(-c*d^2)^(2/3)*3^(1/2)*_alpha-3*(-c*d^2)^(2/3)*_alpha)/(a*d-b*c)*b/d,(I*3^(1/2)*(-c*d^2)^(1/3)/(-3/2*(-c*d^2)^(1/3)/d+1/2*I*3^(1/2)*(-c*d^2)^(1/3)/d)/d)^(1/2)),_alpha=RootOf(_Z^3*b+a)))","C"
500,0,0,124,0.451000," ","int((e*x)^m*(b*x^3+a)^(5/2)*(B*x^3+A),x)","\int \left(b \,x^{3}+a \right)^{\frac{5}{2}} \left(B \,x^{3}+A \right) \left(e x \right)^{m}\, dx"," ",0,"int((e*x)^m*(b*x^3+a)^(5/2)*(B*x^3+A),x)","F"
501,0,0,122,0.413000," ","int((e*x)^m*(b*x^3+a)^(3/2)*(B*x^3+A),x)","\int \left(b \,x^{3}+a \right)^{\frac{3}{2}} \left(B \,x^{3}+A \right) \left(e x \right)^{m}\, dx"," ",0,"int((e*x)^m*(b*x^3+a)^(3/2)*(B*x^3+A),x)","F"
502,0,0,121,0.410000," ","int((e*x)^m*(b*x^3+a)^(1/2)*(B*x^3+A),x)","\int \sqrt{b \,x^{3}+a}\, \left(B \,x^{3}+A \right) \left(e x \right)^{m}\, dx"," ",0,"int((e*x)^m*(b*x^3+a)^(1/2)*(B*x^3+A),x)","F"
503,0,0,121,0.427000," ","int((e*x)^m*(B*x^3+A)/(b*x^3+a)^(1/2),x)","\int \frac{\left(B \,x^{3}+A \right) \left(e x \right)^{m}}{\sqrt{b \,x^{3}+a}}\, dx"," ",0,"int((e*x)^m*(B*x^3+A)/(b*x^3+a)^(1/2),x)","F"
504,0,0,119,0.381000," ","int((e*x)^m*(B*x^3+A)/(b*x^3+a)^(3/2),x)","\int \frac{\left(B \,x^{3}+A \right) \left(e x \right)^{m}}{\left(b \,x^{3}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x)^m*(B*x^3+A)/(b*x^3+a)^(3/2),x)","F"
505,0,0,119,0.398000," ","int((e*x)^m*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\int \frac{\left(B \,x^{3}+A \right) \left(e x \right)^{m}}{\left(b \,x^{3}+a \right)^{\frac{5}{2}}}\, dx"," ",0,"int((e*x)^m*(B*x^3+A)/(b*x^3+a)^(5/2),x)","F"
506,0,0,68,0.177000," ","int(x^5/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{x^{5}}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}}\, dx"," ",0,"int(x^5/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
507,0,0,34,0.652000," ","int(x^2/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{x^{2}}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}}\, dx"," ",0,"int(x^2/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
508,0,0,34,0.585000," ","int(1/x/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}\, x}\, dx"," ",0,"int(1/x/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
509,0,0,71,0.122000," ","int(1/x^4/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}\, x^{4}}\, dx"," ",0,"int(1/x^4/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
510,0,0,70,0.714000," ","int(x^4/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{x^{4}}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}}\, dx"," ",0,"int(x^4/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
511,0,0,70,0.612000," ","int(x^3/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{x^{3}}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}}\, dx"," ",0,"int(x^3/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
512,0,0,70,0.603000," ","int(x/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{x}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}}\, dx"," ",0,"int(x/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
513,0,0,67,0.592000," ","int(1/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}}\, dx"," ",0,"int(1/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
514,0,0,70,0.180000," ","int(1/x^2/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}\, x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
515,0,0,70,0.195000," ","int(1/x^3/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{3}+a}\, \sqrt{d \,x^{3}+c}\, x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x)","F"
516,1,7293,129,8.015000," ","int((e*x)^(7/2)*(B*x^3+A)*(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
517,1,4175,325,1.116000," ","int((e*x)^(5/2)*(B*x^3+A)*(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"1/320*e^2*(e*x)^(1/2)*(b*x^3+a)^(1/2)/b^3/(-a*b^2)^(1/3)*(-42*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^3*e+64*I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*b^3+96*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^2*b*e+40*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^6*b^3+84*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^3*b*e+96*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^2*b^3*e-96*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^2*b^3*e+12*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*a*b^2+42*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^3*b^2*e-120*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^6*b^3+48*I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*a*b^2+192*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^2*b^2*e-192*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^2*b^2*e-84*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^3*b*e-96*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^2*b*e+42*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^3*e-192*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*b^3-36*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*a*b^2-21*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*a^2*b-42*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^3*b^2*e-144*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*a*b^2+63*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*a^2*b)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
518,1,5358,585,1.057000," ","int((e*x)^(3/2)*(B*x^3+A)*(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
519,1,6858,95,1.092000," ","int((B*x^3+A)*(e*x)^(1/2)*(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
520,1,3721,293,1.214000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/(e*x)^(1/2),x)","\text{output too large to display}"," ",0,"-1/20*(b*x^3+a)^(1/2)*x/b^2/(-a*b^2)^(1/3)*(60*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^3*e-6*I*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*x^2*a^2*b^2*e-4*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*b^2-3*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a*b-6*I*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*(-a*b^2)^(2/3)*a^2*e-60*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^3*e-10*I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*b^2+6*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^2*b^2*e+120*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a*b^2*e+12*I*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*(-a*b^2)^(1/3)*x*a^2*b*e-12*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^2*b*e-60*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a*b*e+6*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^2*e+12*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*b^2+60*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a*b*e-120*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a*b^2*e+30*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*b^2+9*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a*b)/(e*x)^(1/2)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
521,1,5736,586,1.019000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/(e*x)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
522,1,6668,92,1.040000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/(e*x)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
523,1,3512,290,1.016000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/(e*x)^(7/2),x)","\text{output too large to display}"," ",0,"-1/10*(b*x^3+a)^(1/2)/x^2/(-a*b^2)^(1/3)/b*(-60*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^4*a*b*e-5*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*b+24*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*b^3*e-24*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*b^3*e+48*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^4*b^2*e-24*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^3*b*e+30*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^3*a*e-12*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*b+24*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^3*b*e-48*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^4*b^2*e+30*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a*b^2*e-30*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a*b^2*e+60*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^4*a*b*e-30*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^3*a*e+4*I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*b+15*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*b)/e^3/(e*x)^(1/2)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
524,1,5911,568,1.729000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
525,1,3759,57,0.999000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^(11/2),x)","\text{output too large to display}"," ",0,"-2/9*(b*x^3+a)^(1/2)/x^(9/2)/b*(18*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^5*a-3*A*(x*(b*x^3+a))^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*b^2+I*A*(x*(b*x^3+a))^(1/2)*3^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*b^2-3*A*(x*(b*x^3+a))^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*a*b-36*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^6*a*b-18*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^5*a+I*A*(x*(b*x^3+a))^(1/2)*3^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*a*b-18*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^7*a*b^2+3*I*B*(x*(b*x^3+a))^(1/2)*3^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*a*b+36*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^6*a*b-18*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^7*a*b^2+18*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^7*a*b^2+36*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^6*a*b-36*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^6*a*b-18*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^5*a+18*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^5*a+18*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^7*a*b^2-9*B*(x*(b*x^3+a))^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*a*b)/(x*(b*x^3+a))^(1/2)/a/(I*3^(1/2)-3)/(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
526,1,3690,276,1.100000," ","int((B*x^3+A)*(b*x^3+a)^(1/2)/x^(13/2),x)","\text{output too large to display}"," ",0,"2/55*(b*x^3+a)^(1/2)/x^(11/2)/(-a*b^2)^(1/3)*(12*I*A*3^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^8*b^3+12*I*A*3^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(2/3)*x^6*b-11*I*B*3^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*a-24*I*A*3^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x^7*b^2-5*I*A*3^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*a-12*A*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^8*b^3+132*I*B*3^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x^7*a*b+66*B*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^8*a*b^2+24*A*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x^7*b^2-132*B*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x^7*a*b-12*A*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(2/3)*x^6*b+66*B*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(2/3)*x^6*a-66*I*B*3^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^8*a*b^2-66*I*B*3^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(2/3)*x^6*a+9*A*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*b+33*B*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*a-3*I*A*3^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*b+15*A*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*a)/(x*(b*x^3+a))^(1/2)/a/(I*3^(1/2)-3)/(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
527,1,7705,163,1.142000," ","int((e*x)^(7/2)*(b*x^3+a)^(3/2)*(B*x^3+A),x)","\text{output too large to display}"," ",0,"result too large to display","C"
528,1,4619,359,1.316000," ","int((e*x)^(5/2)*(b*x^3+a)^(3/2)*(B*x^3+A),x)","\text{output too large to display}"," ",0,"1/7040*e^2*(e*x)^(1/2)*(b*x^3+a)^(1/2)/(-a*b^2)^(1/3)/b^3*(378*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^4*e-1782*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a^2*b^2+567*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a^3*b-1920*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^9*b^4-2640*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^6*b^4+880*I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^6*b^4+594*I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a^2*b^2-189*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a^3*b-2376*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^3*b^2*e+756*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^4*b*e+1188*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^3*b^3*e-378*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^4*b^2*e+1188*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^3*b*e-1188*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^3*b*e+378*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^4*b^2*e-1188*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^3*b^3*e+1672*I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*a*b^3+108*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*a^2*b^2+1000*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^6*a*b^3-3000*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^6*a*b^3-5016*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*a*b^3-324*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*a^2*b^2+640*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^9*b^4-756*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^4*b*e+2376*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^3*b^2*e-378*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^4*e)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
529,1,5790,619,0.958000," ","int((e*x)^(3/2)*(b*x^3+a)^(3/2)*(B*x^3+A),x)","\text{output too large to display}"," ",0,"result too large to display","C"
530,1,7290,129,1.064000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)*(e*x)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
531,1,4173,325,1.171000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/(e*x)^(1/2),x)","\text{output too large to display}"," ",0,"-1/320*(b*x^3+a)^(1/2)*x/(-a*b^2)^(1/3)/b^2*(-40*I*B*3^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^6*b^3-54*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^3*b^2*e+108*I*B*3^(1/2)*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a^3*b*e+864*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^2*b^3*e-76*I*B*3^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^3*a*b^2+864*I*A*3^(1/2)*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^2*b*e-864*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^2*b^3*e-27*I*B*3^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*a^2*b+120*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^6*b^3+54*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^3*b^2*e-208*I*A*3^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*a*b^2+1728*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^2*b^2*e-54*I*B*3^(1/2)*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^3*e-108*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^3*b*e-864*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^2*b*e+54*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^3*e+192*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*b^3+228*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*a*b^2-1728*I*A*3^(1/2)*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a^2*b^2*e-64*I*A*3^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^3*b^3+624*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*a*b^2+81*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*a^2*b)/(e*x)^(1/2)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
532,1,6142,614,1.142000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/(e*x)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
533,1,7108,120,1.183000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/(e*x)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
534,1,3966,315,0.975000," ","int((b*x^3+a)^(3/2)*(B*x^3+A)/(e*x)^(7/2),x)","\text{output too large to display}"," ",0,"-1/20*(b*x^3+a)^(1/2)*(-108*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a*b^3*e-54*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a^2*b^2*e-54*B*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a^2*e-13*I*B*3^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^3*a*b+30*A*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^3*b^2+12*B*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^6*b^2-24*A*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*a*b+216*A*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a*b^2*e+108*B*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a^2*b*e-108*A*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a*b*e+108*I*A*3^(1/2)*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a*b*e+108*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a*b^3*e-108*I*B*3^(1/2)*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a^2*b*e-4*I*B*3^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^6*b^2+54*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a^2*b^2*e-10*I*A*3^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^3*b^2+54*I*B*3^(1/2)*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a^2*e-216*I*A*3^(1/2)*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a*b^2*e+8*I*A*3^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*a*b+39*B*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^3*a*b)/x^2/(-a*b^2)^(1/3)/b/e^3/(e*x)^(1/2)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
535,1,8117,197,1.065000," ","int((e*x)^(7/2)*(b*x^3+a)^(5/2)*(B*x^3+A),x)","\text{output too large to display}"," ",0,"result too large to display","C"
536,1,5063,393,1.094000," ","int((e*x)^(5/2)*(b*x^3+a)^(5/2)*(B*x^3+A),x)","\text{output too large to display}"," ",0,"result too large to display","C"
537,1,6202,653,1.036000," ","int((e*x)^(3/2)*(b*x^3+a)^(5/2)*(B*x^3+A),x)","\text{output too large to display}"," ",0,"result too large to display","C"
538,1,7702,163,1.104000," ","int((b*x^3+a)^(5/2)*(B*x^3+A)*(e*x)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
539,1,4617,359,1.064000," ","int((b*x^3+a)^(5/2)*(B*x^3+A)/(e*x)^(1/2),x)","\text{output too large to display}"," ",0,"-1/1408*(b*x^3+a)^(1/2)*x/b^2/(-a*b^2)^(1/3)*(162*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^4*e+3102*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a^2*b^2+243*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a^3*b+384*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^9*b^4+528*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^6*b^4-162*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^4*b^2*e+3564*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^3*b^3*e-3564*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^3*b*e+162*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^4*b^2*e-3564*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^3*b^3*e-162*I*B*(-a*b^2)^(2/3)*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^4*e+1128*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^6*a*b^3+1848*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*a*b^3+1068*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*a^2*b^2-324*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^4*b*e+7128*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^3*b^2*e-616*I*A*(-a*b^2)^(1/3)*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*a*b^3-376*I*B*(-a*b^2)^(1/3)*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^6*a*b^3-356*I*B*(-a*b^2)^(1/3)*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*a^2*b^2+3564*I*A*(-a*b^2)^(2/3)*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^3*b*e-81*I*B*(-a*b^2)^(1/3)*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*a^3*b-176*I*A*(-a*b^2)^(1/3)*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^6*b^4-1034*I*A*(-a*b^2)^(1/3)*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*a^2*b^2-128*I*B*(-a*b^2)^(1/3)*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^9*b^4+324*I*B*(-a*b^2)^(1/3)*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a^4*b*e-7128*I*A*(-a*b^2)^(1/3)*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a^3*b^2*e)/(e*x)^(1/2)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
540,1,6530,644,1.147000," ","int((b*x^3+a)^(5/2)*(B*x^3+A)/(e*x)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
541,1,7544,150,1.157000," ","int((b*x^3+a)^(5/2)*(B*x^3+A)/(e*x)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
542,1,4422,347,1.102000," ","int((b*x^3+a)^(5/2)*(B*x^3+A)/(e*x)^(7/2),x)","\text{output too large to display}"," ",0,"-1/320*(b*x^3+a)^(1/2)*(2592*I*A*3^(1/2)*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a^2*b*e-64*I*A*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^6*b^3-810*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a^3*b^2*e-810*B*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a^3*e+810*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a^3*b^2*e-2592*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a^2*b^3*e+120*B*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^9*b^3+192*A*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^6*b^3-384*A*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*a^2*b+5184*A*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a^2*b^2*e+1620*B*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a^3*b*e-2592*A*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a^2*b*e+810*I*B*3^(1/2)*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a^3*e+128*I*A*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*a^2*b-1620*I*B*3^(1/2)*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a^3*b*e+1104*A*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*a*b^2+705*B*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*a^2*b+420*B*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^6*a*b^2-40*I*B*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^9*b^3-5184*I*A*3^(1/2)*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a^2*b^2*e-235*I*B*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*a^2*b-368*I*A*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^3*a*b^2+2592*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a^2*b^3*e-140*I*B*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^6*a*b^2)/x^2/b/(-a*b^2)^(1/3)/e^3/(e*x)^(1/2)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
543,1,6861,95,1.010000," ","int((e*x)^(7/2)*(B*x^3+A)/(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
544,1,3723,293,1.030000," ","int((e*x)^(5/2)*(B*x^3+A)/(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"1/20*e^2*(e*x)^(1/2)*(b*x^3+a)^(1/2)/b^3/(-a*b^2)^(1/3)*(-40*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a*b^2*e+4*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*b^2+20*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^3*e-7*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a*b-14*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^2*b^2*e-20*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^3*e+28*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^2*b*e+14*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^2*b^2*e+40*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a*b^2*e+10*I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*b^2-28*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a^2*b*e-20*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a*b*e+14*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^2*e-12*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*x^3*b^2-14*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a^2*e+20*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a*b*e-30*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*b^2+21*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*a*b)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
545,1,4914,553,1.093000," ","int((e*x)^(3/2)*(B*x^3+A)/(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"1/4*e*(e*x)^(1/2)*(b*x^3+a)^(1/2)*(15*B*(-a*b^2)^(1/3)*x^2*a*b*e+8*I*A*3^(1/2)*x^3*b^3*e+8*I*A*3^(1/2)*(-a*b^2)^(1/3)*x^2*b^2*e+8*I*A*3^(1/2)*(-a*b^2)^(2/3)*x*b*e-5*I*B*3^(1/2)*(-a*b^2)^(2/3)*x*a*e+I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^2*b^2-5*I*B*3^(1/2)*x^3*a*b^2*e-24*A*x^3*b^3*e+48*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x*b*e+20*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x*a*e-30*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x*a*e+16*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^2*b^2*e-24*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^2*b^2*e-32*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x*b*e+8*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^2*b^2*e-16*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x*b*e+10*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x*a*e-10*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^2*a*b*e+15*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^2*a*b*e-8*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a*b^2*e+5*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^2*b*e+10*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^2*b*e-15*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^2*b*e-16*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a*b^2*e+24*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a*b^2*e-5*I*B*3^(1/2)*(-a*b^2)^(1/3)*x^2*a*b*e-5*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^2*a*b*e+15*B*x^3*a*b^2*e-24*A*(-a*b^2)^(1/3)*x^2*b^2*e-24*A*(-a*b^2)^(2/3)*x*b*e+15*B*(-a*b^2)^(2/3)*x*a*e-3*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*x^2*b^2)/b^3/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
546,1,6424,63,1.148000," ","int((B*x^3+A)*(e*x)^(1/2)/(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
547,1,3275,262,1.093000," ","int((B*x^3+A)/(e*x)^(1/2)/(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"-1/2*(b*x^3+a)^(1/2)*x/b^2/(-a*b^2)^(1/3)*(8*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*b^3*e-2*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^2*e-16*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*b^2*e+4*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x*a*b*e+8*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*b*e-8*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*b^3*e-2*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*a*e+2*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^2*e+16*A*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*b^2*e-4*B*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a*b*e-8*A*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*b*e+2*B*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a*e-I*B*3^(1/2)*(e*x*(b*x^3+a))^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*b+3*B*(e*x*(b*x^3+a))^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*b)/(e*x)^(1/2)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
548,1,5385,558,1.022000," ","int((B*x^3+A)/(e*x)^(3/2)/(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
549,1,3397,55,1.003000," ","int((B*x^3+A)/(e*x)^(5/2)/(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"-2/3*(b*x^3+a)^(1/2)/x/b^2*(6*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a*b^2*e-6*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a*b^2*e-12*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^3*a*b*e+12*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^3*a*b*e+6*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^2*a*e-6*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^2*a*e-6*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a*b^2*e+6*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4*a*b^2*e+12*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^3*a*b*e-12*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^3*a*b*e-6*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^2*a*e+6*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^2*a*e+I*A*(e*x*(b*x^3+a))^(1/2)*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*b^2-3*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*b^2)/e^2/(e*x)^(1/2)/(e*x*(b*x^3+a))^(1/2)/a/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
550,1,3303,259,1.072000," ","int((B*x^3+A)/(e*x)^(7/2)/(b*x^3+a)^(1/2),x)","\text{output too large to display}"," ",0,"2/5*(b*x^3+a)^(1/2)/x^2/(-a*b^2)^(1/3)/b/a*(10*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a*b^2*e+10*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^3*a*e-4*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*b^3*e+3*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*(e*x*(b*x^3+a))^(1/2)*b-4*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^3*b*e+8*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^4*b^2*e-20*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^4*a*b*e+4*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*b^3*e-10*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*a*b^2*e-8*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^4*b^2*e+20*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^4*a*b*e+4*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^3*b*e-10*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^3*a*e-I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*b)/e^3/(e*x)^(1/2)/(e*x*(b*x^3+a))^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
551,1,7016,94,1.132000," ","int((e*x)^(7/2)*(B*x^3+A)/(b*x^3+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
552,1,3760,293,1.079000," ","int((e*x)^(5/2)*(B*x^3+A)/(b*x^3+a)^(3/2),x)","\text{output too large to display}"," ",0,"-1/6*e^2/x*(e*x)^(1/2)*(-14*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*a*b^2-3*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x^4*b^2+8*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(2/3)*b-7*I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x*a*b+8*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*b^3-8*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*b^3-14*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(2/3)*a+4*I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x*b^2+14*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*a*b^2+16*A*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x*b^2-28*B*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x*a*b-8*A*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*b+14*B*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*a+9*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x^4*b^2+28*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x*a*b-16*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x*b^2-12*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x*b^2+21*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x*a*b)/(b*x^3+a)^(1/2)/b^3/(-a*b^2)^(1/3)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
553,1,5392,566,1.032000," ","int((e*x)^(3/2)*(B*x^3+A)/(b*x^3+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
554,1,3654,65,1.000000," ","int((B*x^3+A)*(e*x)^(1/2)/(b*x^3+a)^(3/2),x)","\text{output too large to display}"," ",0,"2/3*(e*x)^(1/2)/(b*x^3+a)^(1/2)/b^3*(-6*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*a*b^2-12*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x*a*b+12*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x*a*b-6*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(2/3)*a+6*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*a*b^2+I*A*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^2*b^3+6*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*a*b^2-6*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*a*b^2-12*B*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x*a*b+12*B*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x*a*b-I*B*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^2*a*b^2+6*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(2/3)*a+6*B*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*a-6*B*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*a-3*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^2*b^3+3*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x^2*a*b^2)/x/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)/a","C"
555,1,3565,271,1.034000," ","int((B*x^3+A)/(b*x^3+a)^(3/2)/(e*x)^(1/2),x)","\text{output too large to display}"," ",0,"-2/3/(b*x^3+a)^(1/2)/b^2/(-a*b^2)^(1/3)/a*(4*I*A*(-a*b^2)^(2/3)*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*b+2*I*B*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*a*b^2-4*I*B*(-a*b^2)^(1/3)*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x*a*b+I*B*(-a*b^2)^(1/3)*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x*a*b+4*I*A*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*b^3-4*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*b^3-8*I*A*(-a*b^2)^(1/3)*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x*b^2-2*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^2*a*b^2+8*A*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x*b^2+4*B*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x*a*b-4*A*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*b-2*B*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*a+2*I*B*(-a*b^2)^(2/3)*3^(1/2)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*a-I*A*(-a*b^2)^(1/3)*3^(1/2)*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*x*b^2+3*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x*b^2-3*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x*a*b)/(e*x)^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
556,1,5563,593,1.077000," ","int((B*x^3+A)/(e*x)^(3/2)/(b*x^3+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
557,1,39,55,0.047000," ","int((B*x^3+A)/(e*x)^(5/2)/(b*x^3+a)^(3/2),x)","-\frac{2 \left(2 A \,x^{3} b -B a \,x^{3}+A a \right) x}{3 \sqrt{b \,x^{3}+a}\, \left(e x \right)^{\frac{5}{2}} a^{2}}"," ",0,"-2/3*x*(2*A*b*x^3-B*a*x^3+A*a)/(b*x^3+a)^(1/2)/a^2/(e*x)^(5/2)","A"
558,1,3783,290,1.092000," ","int((B*x^3+A)/(e*x)^(7/2)/(b*x^3+a)^(3/2),x)","\text{output too large to display}"," ",0,"2/15/x^2*(32*I*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*3^(1/2)*x^4*b^3-3*I*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*3^(1/2)*(-a*b^2)^(1/3)*a*b-8*I*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*3^(1/2)*(-a*b^2)^(1/3)*x^3*b^2-20*I*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*3^(1/2)*(-a*b^2)^(2/3)*x^2*a+32*I*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*3^(1/2)*(-a*b^2)^(2/3)*x^2*b-32*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^4*b^3-20*I*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*3^(1/2)*x^4*a*b^2+20*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*x^4*a*b^2+64*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*b^2-40*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(1/3)*x^3*a*b-32*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(2/3)*x^2*b+20*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*(-a*b^2)^(2/3)*x^2*a+40*I*B*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*3^(1/2)*(-a*b^2)^(1/3)*x^3*a*b+5*I*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*3^(1/2)*(-a*b^2)^(1/3)*x^3*a*b+24*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x^3*b^2-15*B*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*x^3*a*b-64*I*A*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(e*x*(b*x^3+a))^(1/2)*3^(1/2)*(-a*b^2)^(1/3)*x^3*b^2+9*A*(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)*(-a*b^2)^(1/3)*a*b)/(b*x^3+a)^(1/2)/(-a*b^2)^(1/3)/b/a^2/e^3/(e*x)^(1/2)/(I*3^(1/2)-3)/(1/b^2*e*x*(-b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3)))^(1/2)","C"
559,1,7081,88,1.053000," ","int((e*x)^(7/2)*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
560,1,7083,306,0.997000," ","int((e*x)^(5/2)*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
561,1,10786,600,1.068000," ","int((e*x)^(3/2)*(B*x^3+A)/(b*x^3+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
562,1,39,67,0.049000," ","int((B*x^3+A)*(e*x)^(1/2)/(b*x^3+a)^(5/2),x)","\frac{2 \left(2 A \,x^{3} b +B a \,x^{3}+3 A a \right) \sqrt{e x}\, x}{9 \left(b \,x^{3}+a \right)^{\frac{3}{2}} a^{2}}"," ",0,"2/9*x*(2*A*b*x^3+B*a*x^3+3*A*a)*(e*x)^(1/2)/(b*x^3+a)^(3/2)/a^2","A"
563,1,7077,304,1.114000," ","int((B*x^3+A)/(b*x^3+a)^(5/2)/(e*x)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
564,1,10961,624,1.141000," ","int((B*x^3+A)/(e*x)^(3/2)/(b*x^3+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
565,1,62,86,0.049000," ","int((B*x^3+A)/(e*x)^(5/2)/(b*x^3+a)^(5/2),x)","-\frac{2 \left(8 A \,b^{2} x^{6}-2 B a b \,x^{6}+12 A a b \,x^{3}-3 B \,a^{2} x^{3}+3 A \,a^{2}\right) x}{9 \left(b \,x^{3}+a \right)^{\frac{3}{2}} \left(e x \right)^{\frac{5}{2}} a^{3}}"," ",0,"-2/9*x*(8*A*b^2*x^6-2*B*a*b*x^6+12*A*a*b*x^3-3*B*a^2*x^3+3*A*a^2)/(b*x^3+a)^(3/2)/a^3/(e*x)^(5/2)","A"
566,1,7299,321,1.056000," ","int((B*x^3+A)/(e*x)^(7/2)/(b*x^3+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
567,0,0,176,0.654000," ","int(x^11*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{11}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^11*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
568,0,0,138,0.631000," ","int(x^8*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{8}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^8*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
569,0,0,136,0.636000," ","int(x^5*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{5}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^5*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
570,0,0,118,0.636000," ","int(x^2*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{2}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^2*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
571,0,0,161,0.598000," ","int((b*x^3+a)^(1/3)/x/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(-b d \,x^{3}+a d \right) x}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x/(-b*d*x^3+a*d),x)","F"
572,0,0,205,0.615000," ","int((b*x^3+a)^(1/3)/x^4/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(-b d \,x^{3}+a d \right) x^{4}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^4/(-b*d*x^3+a*d),x)","F"
573,0,0,220,0.652000," ","int((b*x^3+a)^(1/3)/x^7/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(-b d \,x^{3}+a d \right) x^{7}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^7/(-b*d*x^3+a*d),x)","F"
574,0,0,212,0.649000," ","int(x^7*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{7}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^7*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
575,0,0,181,0.737000," ","int(x^4*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{4}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^4*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
576,0,0,156,0.710000," ","int(x*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
577,0,0,125,0.842000," ","int((b*x^3+a)^(1/3)/x^2/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(-b d \,x^{3}+a d \right) x^{2}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^2/(-b*d*x^3+a*d),x)","F"
578,0,0,146,0.622000," ","int((b*x^3+a)^(1/3)/x^5/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(-b d \,x^{3}+a d \right) x^{5}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^5/(-b*d*x^3+a*d),x)","F"
579,0,0,169,0.612000," ","int((b*x^3+a)^(1/3)/x^8/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(-b d \,x^{3}+a d \right) x^{8}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^8/(-b*d*x^3+a*d),x)","F"
580,0,0,192,0.625000," ","int((b*x^3+a)^(1/3)/x^11/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(-b d \,x^{3}+a d \right) x^{11}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^11/(-b*d*x^3+a*d),x)","F"
581,0,0,391,0.584000," ","int(x^6*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{6}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^6*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
582,0,0,368,0.609000," ","int(x^3*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{3}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^3*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
583,0,0,304,0.631000," ","int((b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{-b d \,x^{3}+a d}\, dx"," ",0,"int((b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x)","F"
584,0,0,370,0.614000," ","int((b*x^3+a)^(1/3)/x^3/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(-b d \,x^{3}+a d \right) x^{3}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^3/(-b*d*x^3+a*d),x)","F"
585,0,0,393,0.645000," ","int((b*x^3+a)^(1/3)/x^6/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(-b d \,x^{3}+a d \right) x^{6}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^6/(-b*d*x^3+a*d),x)","F"
586,0,0,176,0.576000," ","int(x^11*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{11}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^11*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
587,0,0,138,0.575000," ","int(x^8*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{8}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^8*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
588,0,0,136,0.605000," ","int(x^5*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{5}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^5*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
589,0,0,118,0.622000," ","int(x^2*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{2}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^2*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
590,0,0,161,0.682000," ","int((b*x^3+a)^(2/3)/x/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(-b d \,x^{3}+a d \right) x}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x/(-b*d*x^3+a*d),x)","F"
591,0,0,205,0.624000," ","int((b*x^3+a)^(2/3)/x^4/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(-b d \,x^{3}+a d \right) x^{4}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^4/(-b*d*x^3+a*d),x)","F"
592,0,0,220,0.574000," ","int((b*x^3+a)^(2/3)/x^7/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(-b d \,x^{3}+a d \right) x^{7}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^7/(-b*d*x^3+a*d),x)","F"
593,0,0,209,0.595000," ","int(x^6*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{6}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^6*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
594,0,0,178,0.583000," ","int(x^3*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{3}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^3*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
595,0,0,155,0.630000," ","int((b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{-b d \,x^{3}+a d}\, dx"," ",0,"int((b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
596,0,0,125,0.635000," ","int((b*x^3+a)^(2/3)/x^3/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(-b d \,x^{3}+a d \right) x^{3}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^3/(-b*d*x^3+a*d),x)","F"
597,0,0,146,0.635000," ","int((b*x^3+a)^(2/3)/x^6/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(-b d \,x^{3}+a d \right) x^{6}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^6/(-b*d*x^3+a*d),x)","F"
598,0,0,169,0.640000," ","int((b*x^3+a)^(2/3)/x^9/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(-b d \,x^{3}+a d \right) x^{9}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^9/(-b*d*x^3+a*d),x)","F"
599,0,0,192,0.580000," ","int((b*x^3+a)^(2/3)/x^12/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(-b d \,x^{3}+a d \right) x^{12}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^12/(-b*d*x^3+a*d),x)","F"
600,0,0,382,0.595000," ","int(x^7*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{7}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^7*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
601,0,0,359,0.637000," ","int(x^4*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{4}}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x^4*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
602,0,0,335,0.608000," ","int(x*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x}{-b d \,x^{3}+a d}\, dx"," ",0,"int(x*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x)","F"
603,0,0,359,0.650000," ","int((b*x^3+a)^(2/3)/x^2/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(-b d \,x^{3}+a d \right) x^{2}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^2/(-b*d*x^3+a*d),x)","F"
604,0,0,382,0.572000," ","int((b*x^3+a)^(2/3)/x^5/(-b*d*x^3+a*d),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(-b d \,x^{3}+a d \right) x^{5}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^5/(-b*d*x^3+a*d),x)","F"
605,1,792,95,9.325000," ","int(x^14/(-x^3+1)^(1/3)/(x^3+1),x)","-\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{72 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-24 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-126 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+168 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-7 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{-90 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-90 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-3 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-126 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+210 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+7 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{72 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-24 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-126 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+168 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-7 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}+\frac{\left(20 x^{9}-5 x^{6}+38 x^{3}-53\right) \left(x^{3}-1\right)}{220 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"1/220*(20*x^9-5*x^6+38*x^3-53)*(x^3-1)/(-x^3+1)^(1/3)+1/6*RootOf(_Z^3-4)*ln((-3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-90*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-3*RootOf(_Z^3-4)*x^3-90*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)-126*RootOf(_Z^3-4)*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+42*(-x^3+1)^(2/3)+7*RootOf(_Z^3-4)+210*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/6*ln((-3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+72*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+RootOf(_Z^3-4)*x^3-24*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)-126*RootOf(_Z^3-4)*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+42*(-x^3+1)^(2/3)-7*RootOf(_Z^3-4)+168*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)-ln((-3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+72*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+RootOf(_Z^3-4)*x^3-24*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)-126*RootOf(_Z^3-4)*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+42*(-x^3+1)^(2/3)-7*RootOf(_Z^3-4)+168*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
606,1,683,95,8.409000," ","int(x^11/(-x^3+1)^(1/3)/(x^3+1),x)","-\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+12 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-28 \RootOf \left(\textit{\_Z}^{3}+4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)+\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+5 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-35 \RootOf \left(\textit{\_Z}^{3}+4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)-\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+12 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-28 \RootOf \left(\textit{\_Z}^{3}+4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}+\frac{\left(5 x^{6}-2 x^{3}+17\right) \left(x^{3}-1\right)}{40 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"1/40*(5*x^6-2*x^3+17)*(x^3-1)/(-x^3+1)^(1/3)+RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*ln((15*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+5*RootOf(_Z^3+4)*x^3+6*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3+21*RootOf(_Z^3+4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-35*RootOf(_Z^3+4)-42*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/6*ln((-12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+12*RootOf(_Z^3+4)*x^3-18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3+21*RootOf(_Z^3+4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-28*RootOf(_Z^3+4)+42*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(_Z^3+4)-ln((-12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+12*RootOf(_Z^3+4)*x^3-18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3+21*RootOf(_Z^3+4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-28*RootOf(_Z^3+4)+42*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)","C"
607,1,673,73,6.727000," ","int(x^8/(-x^3+1)^(1/3)/(x^3+1),x)","-\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)+\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-5 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+35 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}+\frac{\left(x^{3}-1\right)^{2}}{5 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"1/5*(x^3-1)^2/(-x^3+1)^(1/3)+RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+15*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-5*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)+42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+35*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))-1/6*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)-ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
608,1,671,73,3.820000," ","int(x^5/(-x^3+1)^(1/3)/(x^3+1),x)","-\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+12 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-28 \RootOf \left(\textit{\_Z}^{3}+4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)+\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+5 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-35 \RootOf \left(\textit{\_Z}^{3}+4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)-\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+12 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-28 \RootOf \left(\textit{\_Z}^{3}+4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}+\frac{x^{3}-1}{2 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"1/2*(x^3-1)/(-x^3+1)^(1/3)+RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*ln((15*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+5*RootOf(_Z^3+4)*x^3+6*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3+21*RootOf(_Z^3+4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-35*RootOf(_Z^3+4)-42*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/6*ln((-12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+12*RootOf(_Z^3+4)*x^3-18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3+21*RootOf(_Z^3+4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-28*RootOf(_Z^3+4)+42*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(_Z^3+4)-ln((-12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+12*RootOf(_Z^3+4)*x^3-18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3+21*RootOf(_Z^3+4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-28*RootOf(_Z^3+4)+42*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)","C"
609,1,476,62,5.594000," ","int(x^2/(-x^3+1)^(1/3)/(x^3+1),x)","\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{72 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+72 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+15 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+126 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-168 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-35 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{45 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-2 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-63 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+105 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+14 \RootOf \left(\textit{\_Z}^{3}-4\right)-21 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}"," ",0,"RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((15*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+72*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+15*RootOf(_Z^3-4)*x^3+72*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+126*RootOf(_Z^3-4)*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+42*(-x^3+1)^(2/3)-35*RootOf(_Z^3-4)-168*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))+1/6*RootOf(_Z^3-4)*ln(-(6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+45*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-2*RootOf(_Z^3-4)*x^3-15*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-63*RootOf(_Z^3-4)*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)-21*(-x^3+1)^(2/3)+14*RootOf(_Z^3-4)+105*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))","C"
610,0,0,106,2.438000," ","int(1/x/(-x^3+1)^(1/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+1\right) x}\, dx"," ",0,"int(1/x/(-x^3+1)^(1/3)/(x^3+1),x)","F"
611,0,0,120,2.822000," ","int(1/x^4/(-x^3+1)^(1/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+1\right) x^{4}}\, dx"," ",0,"int(1/x^4/(-x^3+1)^(1/3)/(x^3+1),x)","F"
612,0,0,118,1.916000," ","int(x^6/(-x^3+1)^(1/3)/(x^3+1),x)","\int \frac{x^{6}}{\left(-x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^6/(-x^3+1)^(1/3)/(x^3+1),x)","F"
613,0,0,106,1.737000," ","int(x^3/(-x^3+1)^(1/3)/(x^3+1),x)","\int \frac{x^{3}}{\left(-x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^3/(-x^3+1)^(1/3)/(x^3+1),x)","F"
614,1,931,67,4.935000," ","int(1/(-x^3+1)^(1/3)/(x^3+1),x)","\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+9 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+9 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-5 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+10 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-3 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)-\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(-\frac{-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-2 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-2 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}"," ",0,"RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x-5*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-24*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+9*RootOf(_Z^3-4)*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+10*x*(-x^3+1)^(2/3)-3*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/6*ln(-(6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-24*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-2*RootOf(_Z^3-4)*x^3+6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*x*(-x^3+1)^(2/3)+2*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)-ln(-(6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-24*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-2*RootOf(_Z^3-4)*x^3+6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*x*(-x^3+1)^(2/3)+2*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
615,1,929,81,4.490000," ","int(1/x^3/(-x^3+1)^(1/3)/(x^3+1),x)","-\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \ln \left(-\frac{-36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}+36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-3 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)-30 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)-\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-10 \left(-x^{3}+1\right)^{\frac{2}{3}} x -12 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(\frac{-54 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+6 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)+5 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \left(-x^{3}+1\right)^{\frac{2}{3}} x +18 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}-\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(-\frac{-36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}+36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-3 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)-30 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)-\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-10 \left(-x^{3}+1\right)^{\frac{2}{3}} x -12 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}+\frac{x^{3}-1}{2 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}}"," ",0,"1/2*(x^3-1)/x^2/(-x^3+1)^(1/3)-1/6*ln(-(-36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+3*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x-30*(-x^3+1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2-(-x^3+1)^(1/3)*RootOf(_Z^3+4)^2*x^2+36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-3*RootOf(_Z^3+4)*x^3-10*(-x^3+1)^(2/3)*x-12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)+RootOf(_Z^3+4))/(x+1)/(x^2-x+1))*RootOf(_Z^3+4)-ln(-(-36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+3*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x-30*(-x^3+1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2-(-x^3+1)^(1/3)*RootOf(_Z^3+4)^2*x^2+36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-3*RootOf(_Z^3+4)*x^3-10*(-x^3+1)^(2/3)*x-12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)+RootOf(_Z^3+4))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)+1/6*RootOf(_Z^3+4)*ln((-54*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3-3*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+6*(-x^3+1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2+5*(-x^3+1)^(1/3)*RootOf(_Z^3+4)^2*x^2-18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-RootOf(_Z^3+4)*x^3+2*(-x^3+1)^(2/3)*x+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)+RootOf(_Z^3+4))/(x+1)/(x^2-x+1))","C"
616,1,955,95,2.747000," ","int(1/x^6/(-x^3+1)^(1/3)/(x^3+1),x)","\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+9 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+9 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-5 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+10 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-3 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)-\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(-\frac{-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-2 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-2 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}-\frac{x^{6}-2 x^{3}+1}{5 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{5}}"," ",0,"-1/5*(x^6-2*x^3+1)/x^5/(-x^3+1)^(1/3)+RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x-5*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-24*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+9*RootOf(_Z^3-4)*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+10*(-x^3+1)^(2/3)*x-3*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/6*ln(-(6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-24*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-2*RootOf(_Z^3-4)*x^3+6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*(-x^3+1)^(2/3)*x+2*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)-ln(-(6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-24*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-2*RootOf(_Z^3-4)*x^3+6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*(-x^3+1)^(2/3)*x+2*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
617,1,963,109,4.067000," ","int(1/x^9/(-x^3+1)^(1/3)/(x^3+1),x)","-\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-2 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)-\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)+\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \ln \left(-\frac{-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-9 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+9 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)+5 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-10 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-3 \RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)-\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)-2 x^{3} \RootOf \left(\textit{\_Z}^{3}+4\right)+24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)-\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}+\frac{17 x^{9}-19 x^{6}+7 x^{3}-5}{40 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{8}}"," ",0,"1/40*(17*x^9-19*x^6+7*x^3-5)/x^8/(-x^3+1)^(1/3)+RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*ln(-(-18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3-9*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+24*(-x^3+1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2+5*(-x^3+1)^(1/3)*RootOf(_Z^3+4)^2*x^2+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3+9*RootOf(_Z^3+4)*x^3-10*(-x^3+1)^(2/3)*x-6*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)-3*RootOf(_Z^3+4))/(x+1)/(x^2-x+1))-1/6*ln((18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3-6*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+24*(-x^3+1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2-(-x^3+1)^(1/3)*RootOf(_Z^3+4)^2*x^2+6*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-2*RootOf(_Z^3+4)*x^3+2*(-x^3+1)^(2/3)*x-6*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)+2*RootOf(_Z^3+4))/(x+1)/(x^2-x+1))*RootOf(_Z^3+4)-ln((18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3-6*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+24*(-x^3+1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2-(-x^3+1)^(1/3)*RootOf(_Z^3+4)^2*x^2+6*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-2*RootOf(_Z^3+4)*x^3+2*(-x^3+1)^(2/3)*x-6*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)+2*RootOf(_Z^3+4))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)","C"
618,0,0,210,0.593000," ","int(x^7/(-x^3+1)^(1/3)/(x^3+1),x)","\int \frac{x^{7}}{\left(-x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^7/(-x^3+1)^(1/3)/(x^3+1),x)","F"
619,0,0,196,0.573000," ","int(x^4/(-x^3+1)^(1/3)/(x^3+1),x)","\int \frac{x^{4}}{\left(-x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^4/(-x^3+1)^(1/3)/(x^3+1),x)","F"
620,0,0,182,3.084000," ","int(x/(-x^3+1)^(1/3)/(x^3+1),x)","\int \frac{x}{\left(-x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x/(-x^3+1)^(1/3)/(x^3+1),x)","F"
621,0,0,210,0.568000," ","int(1/x^2/(-x^3+1)^(1/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+1\right) x^{2}}\, dx"," ",0,"int(1/x^2/(-x^3+1)^(1/3)/(x^3+1),x)","F"
622,0,0,224,0.551000," ","int(1/x^5/(-x^3+1)^(1/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+1\right) x^{5}}\, dx"," ",0,"int(1/x^5/(-x^3+1)^(1/3)/(x^3+1),x)","F"
623,1,1579,95,7.448000," ","int(x^11/(-x^3+1)^(2/3)/(x^3+1),x)","\text{Expression too large to display}"," ",0,"1/28*(4*x^6-x^3+25)*(x^3-1)/(-x^3+1)^(2/3)+(1/6*RootOf(_Z^3+2)*ln((36*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6-24*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6-36*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+24*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3+6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6-4*RootOf(_Z^3+2)*x^6-144*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3-9*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)*x^3+90*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)-48*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3+32*RootOf(_Z^3+2)*x^3+144*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)+9*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)-48*(x^6-2*x^3+1)^(2/3)+42*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)-28*RootOf(_Z^3+2))/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1))-1/6*ln(-(90*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6+12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6-90*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-45*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6-6*RootOf(_Z^3+2)*x^6+27*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3+12*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)*x^3+45*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+150*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3+20*RootOf(_Z^3+2)*x^3-27*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)-12*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)+9*(x^6-2*x^3+1)^(2/3)-105*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)-14*RootOf(_Z^3+2))/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1))*RootOf(_Z^3+2)-ln(-(90*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6+12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6-90*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-45*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6-6*RootOf(_Z^3+2)*x^6+27*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3+12*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)*x^3+45*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+150*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3+20*RootOf(_Z^3+2)*x^3-27*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)-12*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)+9*(x^6-2*x^3+1)^(2/3)-105*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)-14*RootOf(_Z^3+2))/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2))/(-x^3+1)^(2/3)*((x^3-1)^2)^(1/3)","C"
624,1,1584,73,7.461000," ","int(x^8/(-x^3+1)^(2/3)/(x^3+1),x)","\text{Expression too large to display}"," ",0,"1/4*(x^3-1)^2/(-x^3+1)^(2/3)+(RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*ln((144*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^6-6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^6-144*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+72*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^6-3*RootOf(_Z^3-2)*x^6-90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^3+9*RootOf(_Z^3-2)^2*(x^6-2*x^3+1)^(1/3)*x^3+90*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)-240*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+10*RootOf(_Z^3-2)*x^3+90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)-9*RootOf(_Z^3-2)^2*(x^6-2*x^3+1)^(1/3)-18*(x^6-2*x^3+1)^(2/3)+168*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)-7*RootOf(_Z^3-2))/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1))-1/6*ln((144*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^6+30*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^6-144*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-30*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3-24*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^6-5*RootOf(_Z^3-2)*x^6+90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^3+24*RootOf(_Z^3-2)^2*(x^6-2*x^3+1)^(1/3)*x^3-90*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)+192*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+40*RootOf(_Z^3-2)*x^3-90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)-24*RootOf(_Z^3-2)^2*(x^6-2*x^3+1)^(1/3)-48*(x^6-2*x^3+1)^(2/3)-168*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)-35*RootOf(_Z^3-2))/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1))*RootOf(_Z^3-2)-ln((144*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^6+30*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^6-144*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-30*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3-24*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^6-5*RootOf(_Z^3-2)*x^6+90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^3+24*RootOf(_Z^3-2)^2*(x^6-2*x^3+1)^(1/3)*x^3-90*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)+192*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+40*RootOf(_Z^3-2)*x^3-90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)-24*RootOf(_Z^3-2)^2*(x^6-2*x^3+1)^(1/3)-48*(x^6-2*x^3+1)^(2/3)-168*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)-35*RootOf(_Z^3-2))/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(-x^3+1)^(2/3)*((x^3-1)^2)^(1/3)","C"
625,1,1582,73,5.099000," ","int(x^5/(-x^3+1)^(2/3)/(x^3+1),x)","\text{Expression too large to display}"," ",0,"(x^3-1)/(-x^3+1)^(2/3)+(-1/6*ln((30*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6+144*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6-30*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-144*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+5*RootOf(_Z^3+2)*x^6+24*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+24*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)*x^3+90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3+90*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)-40*RootOf(_Z^3+2)*x^3-192*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3-24*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)-90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)-48*(x^6-2*x^3+1)^(2/3)+35*RootOf(_Z^3+2)+168*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2))/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1))*RootOf(_Z^3+2)-ln((30*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6+144*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6-30*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-144*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+5*RootOf(_Z^3+2)*x^6+24*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+24*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)*x^3+90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3+90*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)-40*RootOf(_Z^3+2)*x^3-192*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3-24*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)-90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)-48*(x^6-2*x^3+1)^(2/3)+35*RootOf(_Z^3+2)+168*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2))/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*ln(-(6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6-144*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6-6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3+144*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-3*RootOf(_Z^3+2)*x^6+72*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6-9*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)*x^3+90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3+90*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+10*RootOf(_Z^3+2)*x^3-240*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3+9*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)-90*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)+18*(x^6-2*x^3+1)^(2/3)-7*RootOf(_Z^3+2)+168*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2))/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)))/(-x^3+1)^(2/3)*((x^3-1)^2)^(1/3)","C"
626,1,529,62,6.280000," ","int(x^2/(-x^3+1)^(2/3)/(x^3+1),x)","\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(\frac{144 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{3}-6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{4}-24 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)+x^{3} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+168 \RootOf \left(36 \textit{\_Z}^{2}+6 \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)-7 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-252 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-42 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(-\frac{180 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{4}+90 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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 x^{3} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-210 \RootOf \left(36 \textit{\_Z}^{2}+6 \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)-7 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+252 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+42 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)-42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}"," ",0,"RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*ln((144*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^3*x^3-6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^4*x^3-24*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^3+RootOf(_Z^3-2)^2*x^3+168*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)-252*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*(-x^3+1)^(1/3)-7*RootOf(_Z^3-2)^2-42*RootOf(_Z^3-2)*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3))/(x+1)/(x^2-x+1))+1/6*RootOf(_Z^3-2)*ln(-(180*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^3*x^3+6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^4*x^3+90*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^3+3*RootOf(_Z^3-2)^2*x^3-210*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)+252*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*(-x^3+1)^(1/3)-7*RootOf(_Z^3-2)^2+42*RootOf(_Z^3-2)*(-x^3+1)^(1/3)-42*(-x^3+1)^(2/3))/(x+1)/(x^2-x+1))","C"
627,0,0,106,2.376000," ","int(1/x/(-x^3+1)^(2/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{2}{3}} \left(x^{3}+1\right) x}\, dx"," ",0,"int(1/x/(-x^3+1)^(2/3)/(x^3+1),x)","F"
628,0,0,120,3.079000," ","int(1/x^4/(-x^3+1)^(2/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{2}{3}} \left(x^{3}+1\right) x^{4}}\, dx"," ",0,"int(1/x^4/(-x^3+1)^(2/3)/(x^3+1),x)","F"
629,0,0,124,2.045000," ","int(x^7/(-x^3+1)^(2/3)/(x^3+1),x)","\int \frac{x^{7}}{\left(-x^{3}+1\right)^{\frac{2}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^7/(-x^3+1)^(2/3)/(x^3+1),x)","F"
630,0,0,110,1.759000," ","int(x^4/(-x^3+1)^(2/3)/(x^3+1),x)","\int \frac{x^{4}}{\left(-x^{3}+1\right)^{\frac{2}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^4/(-x^3+1)^(2/3)/(x^3+1),x)","F"
631,1,938,67,4.243000," ","int(x/(-x^3+1)^(2/3)/(x^3+1),x)","-\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \ln \left(-\frac{72 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{4}+12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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 x^{3} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-24 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{2}-60 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-8 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)-12 \RootOf \left(36 \textit{\_Z}^{2}+6 \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 \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}+2\right) \ln \left(\frac{54 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{4}-27 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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 x^{3} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{2}+6 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-4 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)+9 \RootOf \left(36 \textit{\_Z}^{2}+6 \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)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+5 \left(-x^{3}+1\right)^{\frac{2}{3}} x}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}-\frac{\RootOf \left(\textit{\_Z}^{3}+2\right) \ln \left(-\frac{72 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{4}+12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \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 x^{3} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-24 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \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)^{2}-60 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-8 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)-12 \RootOf \left(36 \textit{\_Z}^{2}+6 \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 \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{6}"," ",0,"1/6*RootOf(_Z^3+2)*ln((54*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^3*x^3+6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^4*x^3-12*(-x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x-27*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3-3*x^3*RootOf(_Z^3+2)^2+6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*(-x^3+1)^(1/3)*x^2-4*RootOf(_Z^3+2)*(-x^3+1)^(1/3)*x^2+5*(-x^3+1)^(2/3)*x+9*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)+RootOf(_Z^3+2)^2)/(x+1)/(x^2-x+1))-1/6*ln(-(72*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^3*x^3+18*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^4*x^3-24*(-x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x+12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3+3*x^3*RootOf(_Z^3+2)^2-60*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*(-x^3+1)^(1/3)*x^2-8*RootOf(_Z^3+2)*(-x^3+1)^(1/3)*x^2-2*(-x^3+1)^(2/3)*x-12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)-3*RootOf(_Z^3+2)^2)/(x+1)/(x^2-x+1))*RootOf(_Z^3+2)-ln(-(72*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^3*x^3+18*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^4*x^3-24*(-x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x+12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3+3*x^3*RootOf(_Z^3+2)^2-60*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*(-x^3+1)^(1/3)*x^2-8*RootOf(_Z^3+2)*(-x^3+1)^(1/3)*x^2-2*(-x^3+1)^(2/3)*x-12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)-3*RootOf(_Z^3+2)^2)/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)","C"
632,1,1387,81,4.057000," ","int(1/x^2/(-x^3+1)^(2/3)/(x^3+1),x)","\text{Expression too large to display}"," ",0,"(x^3-1)/x/(-x^3+1)^(2/3)+(-1/6*ln((18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^6+6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^6+9*(x^6-2*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x^2-9*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^4-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3-3*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^6-RootOf(_Z^3-2)*x^6+3*(x^6-2*x^3+1)^(2/3)*x^2+9*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x+6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+2*RootOf(_Z^3-2)*x^3-3*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)-RootOf(_Z^3-2))/(x-1)/(x^2+x+1)/(x+1)/(x^2-x+1))*RootOf(_Z^3-2)-ln((18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^6+6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^6+9*(x^6-2*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x^2-9*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^4-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3-3*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^6-RootOf(_Z^3-2)*x^6+3*(x^6-2*x^3+1)^(2/3)*x^2+9*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x+6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+2*RootOf(_Z^3-2)*x^3-3*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)-RootOf(_Z^3-2))/(x-1)/(x^2+x+1)/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)+1/6*RootOf(_Z^3-2)*ln(-(-36*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^6-12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^6+18*(x^6-2*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x^2+3*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x^4+36*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^6-6*RootOf(_Z^3-2)*x^6-3*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x+24*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+8*RootOf(_Z^3-2)*x^3-6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)-2*RootOf(_Z^3-2))/(x-1)/(x^2+x+1)/(x+1)/(x^2-x+1)))/(-x^3+1)^(2/3)*((x^3-1)^2)^(1/3)","C"
633,1,1386,95,3.514000," ","int(1/x^5/(-x^3+1)^(2/3)/(x^3+1),x)","\text{Expression too large to display}"," ",0,"-1/4*(x^6-2*x^3+1)/x^4/(-x^3+1)^(2/3)+(-1/6*ln((18*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6+6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6-18*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-9*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^2-9*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^4+3*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+RootOf(_Z^3+2)*x^6+9*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x-6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3-2*RootOf(_Z^3+2)*x^3+3*(x^6-2*x^3+1)^(2/3)*x^2+3*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+RootOf(_Z^3+2))/(x-1)/(x^2+x+1)/(x+1)/(x^2-x+1))*RootOf(_Z^3+2)-ln((18*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6+6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6-18*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-9*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^2-9*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^4+3*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+RootOf(_Z^3+2)*x^6+9*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x-6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3-2*RootOf(_Z^3+2)*x^3+3*(x^6-2*x^3+1)^(2/3)*x^2+3*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+RootOf(_Z^3+2))/(x-1)/(x^2+x+1)/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+1/6*RootOf(_Z^3+2)*ln((36*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6+12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6-36*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-12*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3+18*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^2-18*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6-3*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3+2)^2*x^4-6*RootOf(_Z^3+2)*x^6+24*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3+3*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3+2)^2*x+8*RootOf(_Z^3+2)*x^3-6*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)-2*RootOf(_Z^3+2))/(x-1)/(x^2+x+1)/(x+1)/(x^2-x+1)))/(-x^3+1)^(2/3)*((x^3-1)^2)^(1/3)","C"
634,1,696,225,14.511000," ","int(x^6/(-x^3+1)^(2/3)/(x^3+1),x)","\frac{\left(x^{3}-1\right) x}{2 \left(-x^{3}+1\right)^{\frac{2}{3}}}+\frac{\left(\frac{\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(-\frac{3 x^{6} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+2 x^{6} \RootOf \left(\textit{\_Z}^{3}-2\right)+18 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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}+12 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-4 x^{3} \RootOf \left(\textit{\_Z}^{3}-2\right)-18 \left(x^{6}-2 x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(9 \textit{\_Z}^{2}+3 \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)-6 \left(x^{6}-2 x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-9 \left(x^{6}-2 x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(9 \textit{\_Z}^{2}+3 \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)^{2}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \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)}{\left(x +1\right)^{2} \left(x^{2}-x +1\right)^{2}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{-6 x^{6} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-x^{6} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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}+6 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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}+36 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+6 x^{3} \RootOf \left(\textit{\_Z}^{3}-2\right)-6 \left(x^{6}-2 x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-9 \left(x^{6}-2 x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(9 \textit{\_Z}^{2}+3 \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)^{2}-6 \left(x^{6}-2 x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(9 \textit{\_Z}^{2}+3 \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)}{\left(x +1\right)^{2} \left(x^{2}-x +1\right)^{2}}\right)}{12}\right) \left(\left(x^{3}-1\right)^{2}\right)^{\frac{1}{3}}}{\left(-x^{3}+1\right)^{\frac{2}{3}}}"," ",0,"1/2*x*(x^3-1)/(-x^3+1)^(2/3)+(1/12*RootOf(_Z^3-2)*ln((6*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*RootOf(_Z^3-2)^3*x^3+36*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-RootOf(_Z^3-2)*x^6-6*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*x^6-9*(x^6-2*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*RootOf(_Z^3-2)^2*x-6*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x^2+6*RootOf(_Z^3-2)*x^3+36*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*x^3-6*(x^6-2*x^3+1)^(2/3)*x-RootOf(_Z^3-2)-6*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2))/(x+1)^2/(x^2-x+1)^2)+1/4*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*ln(-(12*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*RootOf(_Z^3-2)^3*x^3+18*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+2*RootOf(_Z^3-2)*x^6+3*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*x^6-9*(x^6-2*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*RootOf(_Z^3-2)^2*x-6*(x^6-2*x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x^2-18*RootOf(_Z^3-2)*(x^6-2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*x^2-4*RootOf(_Z^3-2)*x^3-6*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2)*x^3+2*RootOf(_Z^3-2)+3*RootOf(RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+9*_Z^2))/(x+1)^2/(x^2-x+1)^2))/(-x^3+1)^(2/3)*((x^3-1)^2)^(1/3)","C"
635,0,0,225,1.784000," ","int(x^3/(-x^3+1)^(2/3)/(x^3+1),x)","\int \frac{x^{3}}{\left(-x^{3}+1\right)^{\frac{2}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^3/(-x^3+1)^(2/3)/(x^3+1),x)","F"
636,0,0,225,1.941000," ","int(1/(-x^3+1)^(2/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{2}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(1/(-x^3+1)^(2/3)/(x^3+1),x)","F"
637,1,991,227,14.426000," ","int(1/x^3/(-x^3+1)^(2/3)/(x^3+1),x)","\frac{x^{3}-1}{2 \left(-x^{3}+1\right)^{\frac{2}{3}} x^{2}}+\frac{\left(-\frac{\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right) \ln \left(\frac{-3 x^{6} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)+x^{6} \RootOf \left(\textit{\_Z}^{3}+2\right)-18 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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}+6 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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}+18 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-6 x^{3} \RootOf \left(\textit{\_Z}^{3}+2\right)-18 \left(x^{6}-2 x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(9 \textit{\_Z}^{2}+3 \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)+9 \left(x^{6}-2 x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(9 \textit{\_Z}^{2}+3 \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)^{2}-6 \left(x^{6}-2 x^{3}+1\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \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)}{\left(x +1\right)^{2} \left(x^{2}-x +1\right)^{2}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{3}+2\right) \ln \left(\frac{-6 x^{6} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-x^{6} \RootOf \left(\textit{\_Z}^{3}+2\right)+36 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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}+6 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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}+12 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)+2 x^{3} \RootOf \left(\textit{\_Z}^{3}+2\right)-6 \left(x^{6}-2 x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-9 \left(x^{6}-2 x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(9 \textit{\_Z}^{2}+3 \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)^{2}-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \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)}{\left(x +1\right)^{2} \left(x^{2}-x +1\right)^{2}}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{3}+2\right) \ln \left(\frac{-3 x^{6} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)+x^{6} \RootOf \left(\textit{\_Z}^{3}+2\right)-18 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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}+6 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \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}+18 x^{3} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}\right)-6 x^{3} \RootOf \left(\textit{\_Z}^{3}+2\right)-18 \left(x^{6}-2 x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(9 \textit{\_Z}^{2}+3 \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)+9 \left(x^{6}-2 x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(9 \textit{\_Z}^{2}+3 \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)^{2}-6 \left(x^{6}-2 x^{3}+1\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \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)}{\left(x +1\right)^{2} \left(x^{2}-x +1\right)^{2}}\right)}{12}\right) \left(\left(x^{3}-1\right)^{2}\right)^{\frac{1}{3}}}{\left(-x^{3}+1\right)^{\frac{2}{3}}}"," ",0,"1/2*(x^3-1)/x^2/(-x^3+1)^(2/3)+(-1/12*ln((6*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*RootOf(_Z^3+2)^3*x^3-18*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+RootOf(_Z^3+2)*x^6-3*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*x^6+9*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*x-18*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*RootOf(_Z^3+2)*(x^6-2*x^3+1)^(1/3)*x^2-6*RootOf(_Z^3+2)*x^3+18*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*x^3-6*(x^6-2*x^3+1)^(2/3)*x+RootOf(_Z^3+2)-3*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2))/(x+1)^2/(x^2-x+1)^2)*RootOf(_Z^3+2)-1/4*ln((6*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*RootOf(_Z^3+2)^3*x^3-18*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+RootOf(_Z^3+2)*x^6-3*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*x^6+9*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*x-18*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*RootOf(_Z^3+2)*(x^6-2*x^3+1)^(1/3)*x^2-6*RootOf(_Z^3+2)*x^3+18*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*x^3-6*(x^6-2*x^3+1)^(2/3)*x+RootOf(_Z^3+2)-3*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2))/(x+1)^2/(x^2-x+1)^2)*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)+1/12*RootOf(_Z^3+2)*ln((6*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*RootOf(_Z^3+2)^3*x^3+36*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-RootOf(_Z^3+2)*x^6-6*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*x^6-9*(x^6-2*x^3+1)^(2/3)*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*x-6*RootOf(_Z^3+2)^2*(x^6-2*x^3+1)^(1/3)*x^2+2*RootOf(_Z^3+2)*x^3+12*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2)*x^3-RootOf(_Z^3+2)-6*RootOf(RootOf(_Z^3+2)^2+3*_Z*RootOf(_Z^3+2)+9*_Z^2))/(x+1)^2/(x^2-x+1)^2))/(-x^3+1)^(2/3)*((x^3-1)^2)^(1/3)","C"
638,1,682,104,3.784000," ","int(x^14/(-x^3+1)^(4/3)/(x^3+1),x)","-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}+\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-5 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+35 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}-\frac{5 x^{9}+x^{6}+23 x^{3}-49}{40 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"-1/40*(5*x^9+x^6+23*x^3-49)/(-x^3+1)^(1/3)-1/12*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)-1/2*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+1/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+15*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-5*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)+42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+35*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))","C"
639,1,497,95,3.791000," ","int(x^11/(-x^3+1)^(4/3)/(x^3+1),x)","-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{72 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+72 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+15 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+126 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-168 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-35 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{-45 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+2 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+63 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-105 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-14 \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}-\frac{2 x^{6}+x^{3}-8}{10 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"-1/10*(2*x^6+x^3-8)/(-x^3+1)^(1/3)-1/12*RootOf(_Z^3-4)*ln((-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-45*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+2*RootOf(_Z^3-4)*x^3+15*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+63*RootOf(_Z^3-4)*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+21*(-x^3+1)^(2/3)-14*RootOf(_Z^3-4)-105*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((15*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+72*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+15*RootOf(_Z^3-4)*x^3+72*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+126*RootOf(_Z^3-4)*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+42*(-x^3+1)^(2/3)-35*RootOf(_Z^3-4)-168*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))","C"
640,1,672,84,3.782000," ","int(x^8/(-x^3+1)^(4/3)/(x^3+1),x)","-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}+\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-5 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+35 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}-\frac{x^{3}-2}{2 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"-1/2*(x^3-2)/(-x^3+1)^(1/3)+1/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+15*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-5*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)+42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+35*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))-1/12*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)-1/2*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
641,1,667,73,3.763000," ","int(x^5/(-x^3+1)^(4/3)/(x^3+1),x)","\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-5 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+35 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}+\frac{1}{2 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"1/2/(-x^3+1)^(1/3)-1/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+15*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-5*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)+42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+35*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))+1/12*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)+1/2*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
642,1,667,73,3.867000," ","int(x^2/(-x^3+1)^(4/3)/(x^3+1),x)","-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}+\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+15 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-5 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+35 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-12 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+21 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-42 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}-4\right)+42 \left(-x^{3}+1\right)^{\frac{2}{3}}}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}+\frac{1}{2 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"1/2/(-x^3+1)^(1/3)+1/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+15*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-5*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)+42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+35*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))-1/12*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)-1/2*ln((18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-12*RootOf(_Z^3-4)*x^3+21*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)+42*(-x^3+1)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)+28*RootOf(_Z^3-4))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
643,0,0,117,2.719000," ","int(1/x/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right) x}\, dx"," ",0,"int(1/x/(-x^3+1)^(4/3)/(x^3+1),x)","F"
644,0,0,131,2.293000," ","int(1/x^4/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right) x^{4}}\, dx"," ",0,"int(1/x^4/(-x^3+1)^(4/3)/(x^3+1),x)","F"
645,0,0,132,1.457000," ","int(x^9/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{x^{9}}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^9/(-x^3+1)^(4/3)/(x^3+1),x)","F"
646,0,0,118,1.685000," ","int(x^6/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{x^{6}}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^6/(-x^3+1)^(4/3)/(x^3+1),x)","F"
647,1,627,79,4.228000," ","int(x^3/(-x^3+1)^(4/3)/(x^3+1),x)","-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(-\frac{-36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-9 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+3 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+30 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -12 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-3 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{-27 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-27 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-3 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-3 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+2 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+5 \left(-x^{3}+1\right)^{\frac{2}{3}} x +9 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}+\frac{x}{2 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"1/2*x/(-x^3+1)^(1/3)-1/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln(-(-9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-36*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+4*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2+30*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+3*RootOf(_Z^3-4)*x^3+12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*(-x^3+1)^(2/3)*x-3*RootOf(_Z^3-4)-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/12*RootOf(_Z^3-4)*ln((-3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-27*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+6*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+2*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-3*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-3*RootOf(_Z^3-4)*x^3-27*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+5*(-x^3+1)^(2/3)*x+RootOf(_Z^3-4)+9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))","C"
648,1,944,79,3.009000," ","int(1/(-x^3+1)^(4/3)/(x^3+1),x)","\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+9 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+9 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-5 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+10 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-3 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(-\frac{-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-2 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+6 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-2 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-24 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}+\frac{x}{2 \left(-x^{3}+1\right)^{\frac{1}{3}}}"," ",0,"1/2/(-x^3+1)^(1/3)*x+1/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x-5*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-24*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+9*RootOf(_Z^3-4)*x^3+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+10*(-x^3+1)^(2/3)*x-3*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/12*ln(-(6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-24*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-2*RootOf(_Z^3-4)*x^3+6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*(-x^3+1)^(2/3)*x+2*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)-1/2*ln(-(6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-24*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-2*RootOf(_Z^3-4)*x^3+6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*(-x^3+1)^(2/3)*x+2*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
649,1,570,95,2.916000," ","int(1/x^3/(-x^3+1)^(4/3)/(x^3+1),x)","-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(-\frac{-36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-9 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+3 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+30 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -12 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-3 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{-9 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-9 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-3 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-9 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+3 \left(-x^{3}+1\right)^{\frac{2}{3}} x +3 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}+\frac{2 x^{3}-1}{2 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}}"," ",0,"1/2*(2*x^3-1)/x^2/(-x^3+1)^(1/3)-1/12*RootOf(_Z^3-4)*ln((-3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-9*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-3*RootOf(_Z^3-4)*x^3-9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+3*(-x^3+1)^(2/3)*x+RootOf(_Z^3-4)+3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln(-(-9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-36*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+4*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2+30*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+3*RootOf(_Z^3-4)*x^3+12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*(-x^3+1)^(2/3)*x-3*RootOf(_Z^3-4)-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))","C"
650,1,851,109,4.018000," ","int(1/x^6/(-x^3+1)^(4/3)/(x^3+1),x)","-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(\frac{36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+3 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+18 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+3 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \left(-x^{3}+1\right)^{\frac{2}{3}} x -12 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-\RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+3 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+18 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+3 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \left(-x^{3}+1\right)^{\frac{2}{3}} x -12 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-\RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{54 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-18 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)-6 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-5 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x +18 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}+\frac{8 x^{6}-x^{3}-2}{10 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{5}}"," ",0,"1/10*(8*x^6-x^3-2)/x^5/(-x^3+1)^(1/3)+1/12*RootOf(_Z^3-4)*ln(-(3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+54*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x-5*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2-6*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-RootOf(_Z^3-4)*x^3-18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*(-x^3+1)^(2/3)*x+RootOf(_Z^3-4)+18*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/12*ln((3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+36*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+3*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2+18*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+3*RootOf(_Z^3-4)*x^3+36*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+6*(-x^3+1)^(2/3)*x-RootOf(_Z^3-4)-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(_Z^3-4)-1/2*ln((3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+36*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+3*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2+18*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+3*RootOf(_Z^3-4)*x^3+36*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3+6*(-x^3+1)^(2/3)*x-RootOf(_Z^3-4)-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
651,1,649,123,2.684000," ","int(1/x^9/(-x^3+1)^(4/3)/(x^3+1),x)","-\frac{\RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \ln \left(-\frac{-36 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-9 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+12 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+3 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+30 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -12 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-3 \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{27 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}+27 x^{3} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)+3 x^{3} \RootOf \left(\textit{\_Z}^{3}-4\right)+3 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-2 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-6 \left(-x^{3}+1\right)^{\frac{2}{3}} x \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-5 \left(-x^{3}+1\right)^{\frac{2}{3}} x -9 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}\right)-\RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(x +1\right) \left(x^{2}-x +1\right)}\right)}{12}+\frac{49 x^{9}-23 x^{6}-x^{3}-5}{40 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{8}}"," ",0,"1/40*(49*x^9-23*x^6-x^3-5)/x^8/(-x^3+1)^(1/3)-1/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln(-(-9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3-36*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+12*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+4*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2+30*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+3*RootOf(_Z^3-4)*x^3+12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-2*(-x^3+1)^(2/3)*x-3*RootOf(_Z^3-4)-12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))-1/12*RootOf(_Z^3-4)*ln(-(3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+27*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-6*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x-2*RootOf(_Z^3-4)^2*(-x^3+1)^(1/3)*x^2+3*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+3*RootOf(_Z^3-4)*x^3+27*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-5*(-x^3+1)^(2/3)*x-RootOf(_Z^3-4)-9*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x+1)/(x^2-x+1))","C"
652,0,0,224,0.579000," ","int(x^10/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{x^{10}}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^10/(-x^3+1)^(4/3)/(x^3+1),x)","F"
653,0,0,210,0.655000," ","int(x^7/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{x^{7}}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^7/(-x^3+1)^(4/3)/(x^3+1),x)","F"
654,0,0,210,0.601000," ","int(x^4/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{x^{4}}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x^4/(-x^3+1)^(4/3)/(x^3+1),x)","F"
655,0,0,210,0.611000," ","int(x/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{x}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right)}\, dx"," ",0,"int(x/(-x^3+1)^(4/3)/(x^3+1),x)","F"
656,0,0,224,0.572000," ","int(1/x^2/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right) x^{2}}\, dx"," ",0,"int(1/x^2/(-x^3+1)^(4/3)/(x^3+1),x)","F"
657,0,0,238,0.590000," ","int(1/x^5/(-x^3+1)^(4/3)/(x^3+1),x)","\int \frac{1}{\left(-x^{3}+1\right)^{\frac{4}{3}} \left(x^{3}+1\right) x^{5}}\, dx"," ",0,"int(1/x^5/(-x^3+1)^(4/3)/(x^3+1),x)","F"
658,0,0,219,0.652000," ","int(x^11*(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{11}}{d \,x^{3}+c}\, dx"," ",0,"int(x^11*(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
659,0,0,180,0.629000," ","int(x^8*(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{8}}{d \,x^{3}+c}\, dx"," ",0,"int(x^8*(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
660,0,0,149,0.620000," ","int(x^5*(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{5}}{d \,x^{3}+c}\, dx"," ",0,"int(x^5*(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
661,0,0,127,0.607000," ","int(x^2*(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{2}}{d \,x^{3}+c}\, dx"," ",0,"int(x^2*(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
662,0,0,192,0.566000," ","int((b*x^3+a)^(1/3)/x/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right) x}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x/(d*x^3+c),x)","F"
663,0,0,275,0.617000," ","int((b*x^3+a)^(1/3)/x^4/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right) x^{4}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^4/(d*x^3+c),x)","F"
664,0,0,306,0.633000," ","int((b*x^3+a)^(1/3)/x^7/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right) x^{7}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^7/(d*x^3+c),x)","F"
665,0,0,279,0.628000," ","int(x^7*(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{7}}{d \,x^{3}+c}\, dx"," ",0,"int(x^7*(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
666,0,0,222,0.595000," ","int(x^4*(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{4}}{d \,x^{3}+c}\, dx"," ",0,"int(x^4*(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
667,0,0,187,0.579000," ","int(x*(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x}{d \,x^{3}+c}\, dx"," ",0,"int(x*(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
668,0,0,135,0.602000," ","int((b*x^3+a)^(1/3)/x^2/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right) x^{2}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^2/(d*x^3+c),x)","F"
669,0,0,166,0.621000," ","int((b*x^3+a)^(1/3)/x^5/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right) x^{5}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^5/(d*x^3+c),x)","F"
670,0,0,215,0.602000," ","int((b*x^3+a)^(1/3)/x^8/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right) x^{8}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^8/(d*x^3+c),x)","F"
671,0,0,272,0.634000," ","int((b*x^3+a)^(1/3)/x^11/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right) x^{11}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^11/(d*x^3+c),x)","F"
672,0,0,52,0.623000," ","int(x^6*(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{6}}{d \,x^{3}+c}\, dx"," ",0,"int(x^6*(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
673,0,0,52,0.628000," ","int(x^3*(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}} x^{3}}{d \,x^{3}+c}\, dx"," ",0,"int(x^3*(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
674,0,0,49,0.039000," ","int((b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{d \,x^{3}+c}\, dx"," ",0,"int((b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
675,0,0,52,0.612000," ","int((b*x^3+a)^(1/3)/x^3/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right) x^{3}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^3/(d*x^3+c),x)","F"
676,0,0,52,0.617000," ","int((b*x^3+a)^(1/3)/x^6/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right) x^{6}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/x^6/(d*x^3+c),x)","F"
677,0,0,219,0.605000," ","int(x^11*(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{11}}{d \,x^{3}+c}\, dx"," ",0,"int(x^11*(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
678,0,0,181,0.714000," ","int(x^8*(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{8}}{d \,x^{3}+c}\, dx"," ",0,"int(x^8*(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
679,0,0,149,0.682000," ","int(x^5*(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{5}}{d \,x^{3}+c}\, dx"," ",0,"int(x^5*(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
680,0,0,128,0.578000," ","int(x^2*(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{2}}{d \,x^{3}+c}\, dx"," ",0,"int(x^2*(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
681,0,0,192,0.622000," ","int((b*x^3+a)^(2/3)/x/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right) x}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x/(d*x^3+c),x)","F"
682,0,0,280,0.608000," ","int((b*x^3+a)^(2/3)/x^4/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right) x^{4}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^4/(d*x^3+c),x)","F"
683,0,0,306,0.669000," ","int((b*x^3+a)^(2/3)/x^7/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right) x^{7}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^7/(d*x^3+c),x)","F"
684,0,0,276,0.584000," ","int(x^6*(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{6}}{d \,x^{3}+c}\, dx"," ",0,"int(x^6*(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
685,0,0,219,0.620000," ","int(x^3*(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{3}}{d \,x^{3}+c}\, dx"," ",0,"int(x^3*(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
686,0,0,186,0.046000," ","int((b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{d \,x^{3}+c}\, dx"," ",0,"int((b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
687,0,0,135,0.609000," ","int((b*x^3+a)^(2/3)/x^3/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right) x^{3}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^3/(d*x^3+c),x)","F"
688,0,0,167,0.598000," ","int((b*x^3+a)^(2/3)/x^6/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right) x^{6}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^6/(d*x^3+c),x)","F"
689,0,0,215,0.598000," ","int((b*x^3+a)^(2/3)/x^9/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right) x^{9}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^9/(d*x^3+c),x)","F"
690,0,0,273,0.608000," ","int((b*x^3+a)^(2/3)/x^12/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right) x^{12}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^12/(d*x^3+c),x)","F"
691,0,0,52,0.607000," ","int(x^7*(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{7}}{d \,x^{3}+c}\, dx"," ",0,"int(x^7*(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
692,0,0,52,0.624000," ","int(x^4*(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x^{4}}{d \,x^{3}+c}\, dx"," ",0,"int(x^4*(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
693,0,0,52,0.574000," ","int(x*(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}} x}{d \,x^{3}+c}\, dx"," ",0,"int(x*(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
694,0,0,52,0.687000," ","int((b*x^3+a)^(2/3)/x^2/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right) x^{2}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^2/(d*x^3+c),x)","F"
695,0,0,52,0.608000," ","int((b*x^3+a)^(2/3)/x^5/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right) x^{5}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/x^5/(d*x^3+c),x)","F"
696,0,0,206,0.622000," ","int(x^8*(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}} x^{8}}{d \,x^{3}+c}\, dx"," ",0,"int(x^8*(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
697,0,0,171,0.745000," ","int(x^5*(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}} x^{5}}{d \,x^{3}+c}\, dx"," ",0,"int(x^5*(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
698,0,0,150,0.647000," ","int(x^2*(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}} x^{2}}{d \,x^{3}+c}\, dx"," ",0,"int(x^2*(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
699,0,0,206,0.779000," ","int((b*x^3+a)^(4/3)/x/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x/(d*x^3+c),x)","F"
700,0,0,325,0.651000," ","int((b*x^3+a)^(4/3)/x^4/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x^{4}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x^4/(d*x^3+c),x)","F"
701,0,0,371,0.678000," ","int((b*x^3+a)^(4/3)/x^7/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x^{7}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x^7/(d*x^3+c),x)","F"
702,0,0,277,0.590000," ","int(x^4*(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}} x^{4}}{d \,x^{3}+c}\, dx"," ",0,"int(x^4*(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
703,0,0,223,0.598000," ","int(x*(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}} x}{d \,x^{3}+c}\, dx"," ",0,"int(x*(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
704,0,0,205,0.635000," ","int((b*x^3+a)^(4/3)/x^2/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x^{2}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x^2/(d*x^3+c),x)","F"
705,0,0,162,0.626000," ","int((b*x^3+a)^(4/3)/x^5/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x^{5}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x^5/(d*x^3+c),x)","F"
706,0,0,208,0.644000," ","int((b*x^3+a)^(4/3)/x^8/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x^{8}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x^8/(d*x^3+c),x)","F"
707,0,0,271,0.638000," ","int((b*x^3+a)^(4/3)/x^11/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x^{11}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x^11/(d*x^3+c),x)","F"
708,0,0,342,0.621000," ","int((b*x^3+a)^(4/3)/x^14/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x^{14}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x^14/(d*x^3+c),x)","F"
709,0,0,53,0.643000," ","int(x^6*(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}} x^{6}}{d \,x^{3}+c}\, dx"," ",0,"int(x^6*(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
710,0,0,53,0.645000," ","int(x^3*(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}} x^{3}}{d \,x^{3}+c}\, dx"," ",0,"int(x^3*(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
711,0,0,50,0.036000," ","int((b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{d \,x^{3}+c}\, dx"," ",0,"int((b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
712,0,0,53,0.642000," ","int((b*x^3+a)^(4/3)/x^3/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x^{3}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x^3/(d*x^3+c),x)","F"
713,0,0,53,0.615000," ","int((b*x^3+a)^(4/3)/x^6/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right) x^{6}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/x^6/(d*x^3+c),x)","F"
714,0,0,243,0.601000," ","int(x^14/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x^{14}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^14/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
715,0,0,202,0.596000," ","int(x^11/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x^{11}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^11/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
716,0,0,164,0.592000," ","int(x^8/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x^{8}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^8/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
717,0,0,134,0.612000," ","int(x^5/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x^{5}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^5/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
718,0,0,114,0.605000," ","int(x^2/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x^{2}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^2/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
719,0,0,192,0.613000," ","int(1/x/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right) x}\, dx"," ",0,"int(1/x/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
720,0,0,236,0.593000," ","int(1/x^4/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right) x^{4}}\, dx"," ",0,"int(1/x^4/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
721,0,0,220,0.709000," ","int(x^6/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x^{6}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^6/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
722,0,0,186,0.668000," ","int(x^3/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x^{3}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^3/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
723,0,0,118,0.040000," ","int(1/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
724,0,0,141,0.621000," ","int(1/x^3/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right) x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
725,0,0,176,0.586000," ","int(1/x^6/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right) x^{6}}\, dx"," ",0,"int(1/x^6/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
726,0,0,219,0.585000," ","int(1/x^9/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right) x^{9}}\, dx"," ",0,"int(1/x^9/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
727,0,0,52,0.622000," ","int(x^7/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x^{7}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^7/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
728,0,0,52,0.619000," ","int(x^4/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x^{4}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^4/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
729,0,0,52,0.612000," ","int(x/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{x}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
730,0,0,52,0.581000," ","int(1/x^2/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right) x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
731,0,0,52,0.586000," ","int(1/x^5/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right) x^{5}}\, dx"," ",0,"int(1/x^5/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
732,0,0,201,0.612000," ","int(x^11/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{x^{11}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^11/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
733,0,0,164,0.610000," ","int(x^8/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{x^{8}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^8/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
734,0,0,133,0.643000," ","int(x^5/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{x^{5}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^5/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
735,0,0,114,0.599000," ","int(x^2/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{x^{2}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^2/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
736,0,0,192,0.611000," ","int(1/x/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right) x}\, dx"," ",0,"int(1/x/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
737,0,0,239,0.635000," ","int(1/x^4/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right) x^{4}}\, dx"," ",0,"int(1/x^4/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
738,0,0,225,0.639000," ","int(x^7/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{x^{7}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^7/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
739,0,0,187,0.636000," ","int(x^4/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{x^{4}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^4/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
740,0,0,118,0.584000," ","int(x/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{x}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
741,0,0,141,0.653000," ","int(1/x^2/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right) x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
742,0,0,176,0.612000," ","int(1/x^5/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right) x^{5}}\, dx"," ",0,"int(1/x^5/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
743,0,0,52,0.613000," ","int(x^6/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{x^{6}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^6/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
744,0,0,52,0.581000," ","int(x^3/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{x^{3}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^3/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
745,0,0,49,0.042000," ","int(1/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
746,0,0,52,0.621000," ","int(1/x^3/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right) x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
747,0,0,291,0.458000," ","int(x^14/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{14}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^14/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
748,0,0,208,0.464000," ","int(x^11/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{11}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^11/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
749,0,0,167,0.428000," ","int(x^8/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{8}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^8/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
750,0,0,141,0.674000," ","int(x^5/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{5}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^5/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
751,0,0,135,0.612000," ","int(x^2/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{2}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^2/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
752,0,0,216,0.708000," ","int(1/x/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right) x}\, dx"," ",0,"int(1/x/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
753,0,0,292,0.477000," ","int(1/x^4/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right) x^{4}}\, dx"," ",0,"int(1/x^4/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
754,0,0,267,0.447000," ","int(x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{9}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
755,0,0,211,0.656000," ","int(x^6/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{6}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^6/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
756,0,0,140,0.609000," ","int(x^3/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{3}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^3/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
757,0,0,146,0.046000," ","int(1/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
758,0,0,193,0.444000," ","int(1/x^3/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right) x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
759,0,0,246,0.452000," ","int(1/x^6/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right) x^{6}}\, dx"," ",0,"int(1/x^6/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
760,0,0,307,0.460000," ","int(1/x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right) x^{9}}\, dx"," ",0,"int(1/x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
761,0,0,55,0.546000," ","int(x^10/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{10}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^10/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
762,0,0,55,0.681000," ","int(x^7/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{7}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^7/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
763,0,0,55,0.990000," ","int(x^4/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x^{4}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x^4/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
764,0,0,55,0.862000," ","int(x/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{x}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(x/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
765,0,0,55,0.493000," ","int(1/x^2/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right) x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
766,0,0,55,0.496000," ","int(1/x^5/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right) x^{5}}\, dx"," ",0,"int(1/x^5/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
767,1,89,82,0.059000," ","int(x^15/(b*x^4+a)/(d*x^4+c),x)","\frac{x^{8}}{8 b d}-\frac{a \,x^{4}}{4 b^{2} d}-\frac{c \,x^{4}}{4 b \,d^{2}}+\frac{a^{3} \ln \left(b \,x^{4}+a \right)}{4 \left(a d -b c \right) b^{3}}-\frac{c^{3} \ln \left(d \,x^{4}+c \right)}{4 \left(a d -b c \right) d^{3}}"," ",0,"1/8*x^8/b/d-1/4/b^2/d*x^4*a-1/4/b/d^2*x^4*c-1/4*c^3/d^3/(a*d-b*c)*ln(d*x^4+c)+1/4*a^3/b^3/(a*d-b*c)*ln(b*x^4+a)","A"
768,1,65,64,0.053000," ","int(x^11/(b*x^4+a)/(d*x^4+c),x)","\frac{x^{4}}{4 b d}-\frac{a^{2} \ln \left(b \,x^{4}+a \right)}{4 \left(a d -b c \right) b^{2}}+\frac{c^{2} \ln \left(d \,x^{4}+c \right)}{4 \left(a d -b c \right) d^{2}}"," ",0,"1/4*x^4/b/d+1/4*c^2/d^2/(a*d-b*c)*ln(d*x^4+c)-1/4*a^2/b^2/(a*d-b*c)*ln(b*x^4+a)","A"
769,1,50,49,0.052000," ","int(x^7/(b*x^4+a)/(d*x^4+c),x)","\frac{a \ln \left(b \,x^{4}+a \right)}{4 \left(a d -b c \right) b}-\frac{c \ln \left(d \,x^{4}+c \right)}{4 \left(a d -b c \right) d}"," ",0,"-1/4*c/(a*d-b*c)/d*ln(d*x^4+c)+1/4*a/(a*d-b*c)/b*ln(b*x^4+a)","A"
770,1,42,41,0.051000," ","int(x^3/(b*x^4+a)/(d*x^4+c),x)","-\frac{\ln \left(b \,x^{4}+a \right)}{4 \left(a d -b c \right)}+\frac{\ln \left(d \,x^{4}+c \right)}{4 a d -4 b c}"," ",0,"1/4/(a*d-b*c)*ln(d*x^4+c)-1/4/(a*d-b*c)*ln(b*x^4+a)","A"
771,1,59,58,0.057000," ","int(1/x/(b*x^4+a)/(d*x^4+c),x)","\frac{b \ln \left(b \,x^{4}+a \right)}{4 \left(a d -b c \right) a}-\frac{d \ln \left(d \,x^{4}+c \right)}{4 \left(a d -b c \right) c}+\frac{\ln \left(x \right)}{a c}"," ",0,"-1/4*d/c/(a*d-b*c)*ln(d*x^4+c)+1/4*b/a/(a*d-b*c)*ln(b*x^4+a)+1/a/c*ln(x)","A"
772,1,87,81,0.059000," ","int(1/x^5/(b*x^4+a)/(d*x^4+c),x)","-\frac{b^{2} \ln \left(b \,x^{4}+a \right)}{4 \left(a d -b c \right) a^{2}}+\frac{d^{2} \ln \left(d \,x^{4}+c \right)}{4 \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}{4 a c \,x^{4}}"," ",0,"1/4*d^2/c^2/(a*d-b*c)*ln(d*x^4+c)-1/4*b^2/a^2/(a*d-b*c)*ln(b*x^4+a)-1/4/a/c/x^4-1/a/c^2*ln(x)*d-1/a^2/c*ln(x)*b","A"
773,1,105,88,0.061000," ","int(x^13/(b*x^4+a)/(d*x^4+c),x)","\frac{x^{6}}{6 b d}+\frac{a^{3} \arctan \left(\frac{b \,x^{2}}{\sqrt{a b}}\right)}{2 \left(a d -b c \right) \sqrt{a b}\, b^{2}}-\frac{c^{3} \arctan \left(\frac{d \,x^{2}}{\sqrt{c d}}\right)}{2 \left(a d -b c \right) \sqrt{c d}\, d^{2}}-\frac{a \,x^{2}}{2 b^{2} d}-\frac{c \,x^{2}}{2 b \,d^{2}}"," ",0,"1/6*x^6/b/d-1/2/b^2/d*x^2*a-1/2/b/d^2*x^2*c-1/2*c^3/d^2/(a*d-b*c)/(c*d)^(1/2)*arctan(d*x^2/(c*d)^(1/2))+1/2*a^3/b^2/(a*d-b*c)/(a*b)^(1/2)*arctan(x^2*b/(a*b)^(1/2))","A"
774,1,81,70,0.056000," ","int(x^9/(b*x^4+a)/(d*x^4+c),x)","-\frac{a^{2} \arctan \left(\frac{b \,x^{2}}{\sqrt{a b}}\right)}{2 \left(a d -b c \right) \sqrt{a b}\, b}+\frac{c^{2} \arctan \left(\frac{d \,x^{2}}{\sqrt{c d}}\right)}{2 \left(a d -b c \right) \sqrt{c d}\, d}+\frac{x^{2}}{2 b d}"," ",0,"1/2/b/d*x^2+1/2*c^2/d/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x^2)-1/2*a^2/b/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^2)","A"
775,1,60,59,0.056000," ","int(x^5/(b*x^4+a)/(d*x^4+c),x)","\frac{a \arctan \left(\frac{b \,x^{2}}{\sqrt{a b}}\right)}{2 \left(a d -b c \right) \sqrt{a b}}-\frac{c \arctan \left(\frac{d \,x^{2}}{\sqrt{c d}}\right)}{2 \left(a d -b c \right) \sqrt{c d}}"," ",0,"-1/2*c/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x^2)+1/2*a/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^2)","A"
776,1,60,59,0.058000," ","int(x/(b*x^4+a)/(d*x^4+c),x)","-\frac{b \arctan \left(\frac{b \,x^{2}}{\sqrt{a b}}\right)}{2 \left(a d -b c \right) \sqrt{a b}}+\frac{d \arctan \left(\frac{d \,x^{2}}{\sqrt{c d}}\right)}{2 \left(a d -b c \right) \sqrt{c d}}"," ",0,"1/2*d/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x^2)-1/2*b/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^2)","A"
777,1,81,70,0.056000," ","int(1/x^3/(b*x^4+a)/(d*x^4+c),x)","\frac{b^{2} \arctan \left(\frac{b \,x^{2}}{\sqrt{a b}}\right)}{2 \left(a d -b c \right) \sqrt{a b}\, a}-\frac{d^{2} \arctan \left(\frac{d \,x^{2}}{\sqrt{c d}}\right)}{2 \left(a d -b c \right) \sqrt{c d}\, c}-\frac{1}{2 a c \,x^{2}}"," ",0,"-1/2*d^2/c/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x^2)-1/2/a/c/x^2+1/2*b^2/a/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^2)","A"
778,1,105,88,0.062000," ","int(1/x^7/(b*x^4+a)/(d*x^4+c),x)","-\frac{b^{3} \arctan \left(\frac{b \,x^{2}}{\sqrt{a b}}\right)}{2 \left(a d -b c \right) \sqrt{a b}\, a^{2}}+\frac{d^{3} \arctan \left(\frac{d \,x^{2}}{\sqrt{c d}}\right)}{2 \left(a d -b c \right) \sqrt{c d}\, c^{2}}+\frac{d}{2 a \,c^{2} x^{2}}+\frac{b}{2 a^{2} c \,x^{2}}-\frac{1}{6 a c \,x^{6}}"," ",0,"1/2*d^3/c^2/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x^2)-1/2*b^3/a^2/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x^2)-1/6/a/c/x^6+1/2/a/c^2/x^2*d+1/2/a^2/c/x^2*b","A"
779,1,328,327,0.059000," ","int(x^8/(b*x^4+a)/(d*x^4+c),x)","-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(a d -b c \right) b}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right) d}+\frac{x}{b d}"," ",0,"1/b/d*x+1/8/d*c/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*x*2^(1/2)+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*x*2^(1/2)+(c/d)^(1/2)))+1/4/d*c/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)+1/4/d*c/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)-1/8/b*a/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4/b*a/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/4/b*a/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
780,1,320,319,0.053000," ","int(x^6/(b*x^4+a)/(d*x^4+c),x)","\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, a \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} d}-\frac{\sqrt{2}\, c \ln \left(\frac{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} d}"," ",0,"-1/8*c/(a*d-b*c)/d/(c/d)^(1/4)*2^(1/2)*ln((x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))-1/4*c/(a*d-b*c)/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)-1/4*c/(a*d-b*c)/d/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)+1/8*a/(a*d-b*c)/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*a/(a*d-b*c)/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*a/(a*d-b*c)/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
781,1,296,319,0.059000," ","int(x^4/(b*x^4+a)/(d*x^4+c),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a d -4 b c}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a d -4 b c}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right)}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right)}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a d -8 b c}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right)}"," ",0,"-1/8/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))-1/4/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)-1/4/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)+1/8/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
782,1,296,319,0.057000," ","int(x^2/(b*x^4+a)/(d*x^4+c),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}}}"," ",0,"1/8/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*ln((x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))+1/4/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)+1/4/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)-1/8/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/4/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
783,1,320,319,0.056000," ","int(1/(b*x^4+a)/(d*x^4+c),x)","-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(a d -b c \right) a}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right) c}"," ",0,"1/8*d/(a*d-b*c)*(c/d)^(1/4)/c*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))+1/4*d/(a*d-b*c)*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)+1/4*d/(a*d-b*c)*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)-1/8*b/(a*d-b*c)*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4*b/(a*d-b*c)*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/4*b/(a*d-b*c)*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
784,1,331,330,0.058000," ","int(1/x^2/(b*x^4+a)/(d*x^4+c),x)","\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, b \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, d \ln \left(\frac{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c}-\frac{1}{a c x}"," ",0,"-1/8*d/c/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*ln((x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))-1/4*d/c/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)-1/4*d/c/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)+1/8*b/a/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*b/a/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*b/a/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)-1/a/c/x","A"
785,1,343,330,0.059000," ","int(1/x^4/(b*x^4+a)/(d*x^4+c),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \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}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \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^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \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}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \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}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \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^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right) c^{2}}-\frac{1}{3 a c \,x^{3}}"," ",0,"-1/8/c^2*d^2/(a*d-b*c)*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))-1/4/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)-1/4/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)-1/3/a/c/x^3+1/8/a^2*b^2/(a*d-b*c)*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4/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)+1/4/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)","A"
786,1,365,347,0.066000," ","int(1/x^6/(b*x^4+a)/(d*x^4+c),x)","-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \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}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \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^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \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}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \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}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \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^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{1}{4}} c^{2}}+\frac{d}{a \,c^{2} x}+\frac{b}{a^{2} c x}-\frac{1}{5 a c \,x^{5}}"," ",0,"1/8*d^2/c^2/(a*d-b*c)/(c/d)^(1/4)*2^(1/2)*ln((x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))+1/4*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)+1/4*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)-1/8*b^2/a^2/(a*d-b*c)/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4*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)-1/4*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)-1/5/a/c/x^5+1/a/c^2/x*d+1/a^2/c/x*b","A"
787,1,1015,73,0.272000," ","int(x^7*(d*x^4+c)^(1/2)/(b*x^4+a),x)","-\frac{a^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{a c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{-a b}\, a \sqrt{d}\, \ln \left(\frac{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{3}}-\frac{\sqrt{-a b}\, a \sqrt{d}\, \ln \left(\frac{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{3}}-\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{4 b^{2}}-\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{4 b^{2}}+\frac{\left(d \,x^{4}+c \right)^{\frac{3}{2}}}{6 b d}"," ",0,"1/6*(d*x^4+c)^(3/2)/b/d-1/4*a/b^2*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)/b*d*(x^2+(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2)+1/4*a/b^3*(-a*b)^(1/2)*d^(1/2)*ln((-(-a*b)^(1/2)/b*d+d*(x^2+(-a*b)^(1/2)/b))/d^(1/2)+((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)/b*d*(x^2+(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))-1/4*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b-2*(-a*b)^(1/2)/b*d*(x^2+(-a*b)^(1/2)/b)+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)/b*d*(x^2+(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*d+1/4*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b-2*(-a*b)^(1/2)/b*d*(x^2+(-a*b)^(1/2)/b)+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)/b*d*(x^2+(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*c-1/4*a/b^2*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)/b*d*(x^2-(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2)-1/4*a/b^3*(-a*b)^(1/2)*d^(1/2)*ln(((-a*b)^(1/2)/b*d+d*(x^2-(-a*b)^(1/2)/b))/d^(1/2)+((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)/b*d*(x^2-(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))-1/4*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b+2*(-a*b)^(1/2)/b*d*(x^2-(-a*b)^(1/2)/b)+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)/b*d*(x^2-(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*d+1/4*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b+2*(-a*b)^(1/2)/b*d*(x^2-(-a*b)^(1/2)/b)+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)/b*d*(x^2-(-a*b)^(1/2)/b)-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*c","B"
788,1,1066,96,0.278000," ","int(x^5*(d*x^4+c)^(1/2)/(b*x^4+a),x)","-\frac{a^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\sqrt{d \,x^{4}+c}\, x^{2}}{4 b}-\frac{a \sqrt{d}\, \ln \left(\frac{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}-\frac{a \sqrt{d}\, \ln \left(\frac{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}+\frac{c \ln \left(\sqrt{d}\, x^{2}+\sqrt{d \,x^{4}+c}\right)}{4 b \sqrt{d}}+\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{4 \sqrt{-a b}\, b}-\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{4 \sqrt{-a b}\, b}"," ",0,"1/4*x^2*(d*x^4+c)^(1/2)/b+1/4/b*c/d^(1/2)*ln(x^2*d^(1/2)+(d*x^4+c)^(1/2))+1/4*a/b/(-a*b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*a/b^2*d^(1/2)*ln(((x^2+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4*a^2/b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*d-1/4*a/b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*c-1/4*a/b/(-a*b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4*a/b^2*d^(1/2)*ln(((x^2-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4*a^2/b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*d+1/4*a/b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*c","B"
789,1,988,54,0.204000," ","int(x^3*(d*x^4+c)^(1/2)/(b*x^4+a),x)","\frac{a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}+\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b^{2}}+\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 b}+\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 b}"," ",0,"1/4/b*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/b^2*(-a*b)^(1/2)*d^(1/2)*ln(((x^2+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*a*d-1/4/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*c+1/4/b*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b^2*(-a*b)^(1/2)*d^(1/2)*ln(((x^2-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*a*d-1/4/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*c","B"
790,1,1000,71,0.196000," ","int(x*(d*x^4+c)^(1/2)/(b*x^4+a),x)","\frac{a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{\sqrt{d}\, \ln \left(\frac{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b}+\frac{\sqrt{d}\, \ln \left(\frac{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 b}-\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \sqrt{-a b}}+\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \sqrt{-a b}}"," ",0,"-1/4/(-a*b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b*d^(1/2)*ln(((x^2+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-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^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*a*d+1/4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*c+1/4/(-a*b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b*d^(1/2)*ln(((x^2-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-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^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*a*d-1/4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*c","B"
791,1,1037,65,0.262000," ","int((d*x^4+c)^(1/2)/x/(b*x^4+a),x)","\frac{c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{4}+c}\, \sqrt{c}}{x^{2}}\right)}{2 a}+\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a b}-\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a b}-\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 a}-\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 a}+\frac{\sqrt{d \,x^{4}+c}}{2 a}"," ",0,"-1/4/a*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a/b*(-a*b)^(1/2)*d^(1/2)*ln(((x^2+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*d+1/4/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*c-1/4/a*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a/b*(-a*b)^(1/2)*d^(1/2)*ln(((x^2-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*d+1/4/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*c+1/2/a*(d*x^4+c)^(1/2)-1/2/a*c^(1/2)*ln((2*c+2*c^(1/2)*(d*x^4+c)^(1/2))/x^2)","B"
792,1,1075,60,0.259000," ","int((d*x^4+c)^(1/2)/x^3/(b*x^4+a),x)","\frac{b c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{\sqrt{d \,x^{4}+c}\, d \,x^{2}}{2 a c}+\frac{\sqrt{d}\, \ln \left(\sqrt{d}\, x^{2}+\sqrt{d \,x^{4}+c}\right)}{2 a}-\frac{\sqrt{d}\, \ln \left(\frac{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a}-\frac{\sqrt{d}\, \ln \left(\frac{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a}+\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 \sqrt{-a b}\, a}-\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 \sqrt{-a b}\, a}-\frac{\left(d \,x^{4}+c \right)^{\frac{3}{2}}}{2 a c \,x^{2}}"," ",0,"-1/2/a/c/x^2*(d*x^4+c)^(3/2)+1/2/a/c*d*x^2*(d*x^4+c)^(1/2)+1/2/a*d^(1/2)*ln(d^(1/2)*x^2+(d*x^4+c)^(1/2))+1/4/a*b/(-a*b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a*d^(1/2)*ln(((x^2+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*d-1/4/a*b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*c-1/4/a*b/(-a*b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a*d^(1/2)*ln(((x^2-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*d+1/4/a*b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*c","B"
793,1,1107,91,0.270000," ","int((d*x^4+c)^(1/2)/x^5/(b*x^4+a),x)","\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b c \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b c \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{d \ln \left(\frac{2 c +2 \sqrt{d \,x^{4}+c}\, \sqrt{c}}{x^{2}}\right)}{4 a \sqrt{c}}+\frac{b \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{4}+c}\, \sqrt{c}}{x^{2}}\right)}{2 a^{2}}-\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}+\frac{\sqrt{-a b}\, \sqrt{d}\, \ln \left(\frac{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}+\frac{\sqrt{d \,x^{4}+c}\, d}{4 a c}+\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 a^{2}}+\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{4 a^{2}}-\frac{\sqrt{d \,x^{4}+c}\, b}{2 a^{2}}-\frac{\left(d \,x^{4}+c \right)^{\frac{3}{2}}}{4 a c \,x^{4}}"," ",0,"-1/4/a/c/x^4*(d*x^4+c)^(3/2)-1/4/a/c^(1/2)*d*ln((2*c+2*(d*x^4+c)^(1/2)*c^(1/2))/x^2)+1/4/a/c*d*(d*x^4+c)^(1/2)+1/4/a^2*b*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/a^2*(-a*b)^(1/2)*d^(1/2)*ln(((x^2+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*d-1/4/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*c+1/4/a^2*b*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a^2*(-a*b)^(1/2)*d^(1/2)*ln(((x^2-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*d-1/4/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*c-1/2/a^2*b*(d*x^4+c)^(1/2)+1/2/a^2*b*c^(1/2)*ln((2*c+2*(d*x^4+c)^(1/2)*c^(1/2))/x^2)","B"
794,1,1116,90,0.263000," ","int((d*x^4+c)^(1/2)/x^7/(b*x^4+a),x)","\frac{b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\sqrt{d \,x^{4}+c}\, b d \,x^{2}}{2 a^{2} c}-\frac{b \sqrt{d}\, \ln \left(\sqrt{d}\, x^{2}+\sqrt{d \,x^{4}+c}\right)}{2 a^{2}}+\frac{b \sqrt{d}\, \ln \left(\frac{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d -\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}+\frac{b \sqrt{d}\, \ln \left(\frac{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d +\frac{\sqrt{-a b}\, d}{b}}{\sqrt{d}}+\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\right)}{4 a^{2}}-\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{4 \sqrt{-a b}\, a^{2}}+\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{4 \sqrt{-a b}\, a^{2}}+\frac{\left(d \,x^{4}+c \right)^{\frac{3}{2}} b}{2 a^{2} c \,x^{2}}-\frac{\left(d \,x^{4}+c \right)^{\frac{3}{2}}}{6 a c \,x^{6}}"," ",0,"1/2/a^2*b/c/x^2*(d*x^4+c)^(3/2)-1/2/a^2*b/c*d*x^2*(d*x^4+c)^(1/2)-1/2/a^2*b*d^(1/2)*ln(d^(1/2)*x^2+(d*x^4+c)^(1/2))-1/4/a^2*b^2/(-a*b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a^2*b*d^(1/2)*ln(((x^2+(-a*b)^(1/2)/b)*d-(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))-1/4/a*b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*d+1/4/a^2*b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))*c+1/4/a^2*b^2/(-a*b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/a^2*b*d^(1/2)*ln(((x^2-(-a*b)^(1/2)/b)*d+(-a*b)^(1/2)/b*d)/d^(1/2)+((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))+1/4/a*b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*d-1/4/a^2*b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))*c-1/6/a/x^6*(d*x^4+c)^(3/2)/c","B"
795,1,421,781,0.767000," ","int(x^6*(d*x^4+c)^(1/2)/(b*x^4+a),x)","-\frac{\left(\frac{i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{c}\, \sqrt{d}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, b}-\frac{\left(a d -b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}\right) a}{b}+\frac{\frac{\sqrt{d \,x^{4}+c}\, x^{3}}{5}+\frac{2 i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) c^{\frac{3}{2}}}{5 \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, \sqrt{d}}}{b}"," ",0,"1/b*(1/5*x^3*(d*x^4+c)^(1/2)+2/5*I*c^(3/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(1-I/c^(1/2)*d^(1/2)*x^2)^(1/2)*(1+I/c^(1/2)*d^(1/2)*x^2)^(1/2)/(d*x^4+c)^(1/2)/d^(1/2)*(EllipticF(x*(I/c^(1/2)*d^(1/2))^(1/2),I)-EllipticE(x*(I/c^(1/2)*d^(1/2))^(1/2),I)))-a/b*(I*d^(1/2)/b*c^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(1-I/c^(1/2)*d^(1/2)*x^2)^(1/2)*(1+I/c^(1/2)*d^(1/2)*x^2)^(1/2)/(d*x^4+c)^(1/2)*(EllipticF(x*(I/c^(1/2)*d^(1/2))^(1/2),I)-EllipticE(x*(I/c^(1/2)*d^(1/2))^(1/2),I))-1/8/b^2*sum((a*d-b*c)/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(1-I/c^(1/2)*d^(1/2)*x^2)^(1/2)*(1+I/c^(1/2)*d^(1/2)*x^2)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi(x*(I/c^(1/2)*d^(1/2))^(1/2),I*c^(1/2)/d^(1/2)*_alpha^2/a*b,(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a)))","C"
796,1,368,628,0.352000," ","int(x^4*(d*x^4+c)^(1/2)/(b*x^4+a),x)","-\frac{\left(\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, b}-\frac{\left(a d -b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}\right) a}{b}+\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}}+\frac{\sqrt{d \,x^{4}+c}\, x}{3}}{b}"," ",0,"1/b*(1/3*x*(d*x^4+c)^(1/2)+2/3*c/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-a/b*(d/b/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-1/8/b^2*sum((a*d-b*c)/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a)))","C"
797,1,299,720,0.293000," ","int(x^2*(d*x^4+c)^(1/2)/(b*x^4+a),x)","\frac{i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{c}\, \sqrt{d}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, b}-\frac{\left(a d -b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}"," ",0,"I*d^(1/2)/b*c^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*(EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-EllipticE((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-1/8/b^2*sum((a*d-b*c)/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
798,1,273,613,0.268000," ","int((d*x^4+c)^(1/2)/(b*x^4+a),x)","\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, b}-\frac{\left(a d -b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}"," ",0,"d/b/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-1/8/b^2*sum((a*d-b*c)/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
799,1,421,741,0.289000," ","int((d*x^4+c)^(1/2)/x^2/(b*x^4+a),x)","-\frac{\left(\frac{i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{c}\, \sqrt{d}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, b}-\frac{\left(a d -b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}\right) b}{a}+\frac{\frac{2 i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{c}\, \sqrt{d}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}}-\frac{\sqrt{d \,x^{4}+c}}{x}}{a}"," ",0,"-1/a*b*(I*d^(1/2)/b*c^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*(EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-EllipticE((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-1/8/b^2*sum((a*d-b*c)/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a)))+1/a*(-(d*x^4+c)^(1/2)/x+2*I*d^(1/2)*c^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*(EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-EllipticE((I/c^(1/2)*d^(1/2))^(1/2)*x,I)))","C"
800,1,370,631,0.298000," ","int((d*x^4+c)^(1/2)/x^4/(b*x^4+a),x)","-\frac{\left(\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, b}-\frac{\left(a d -b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}\right) b}{a}+\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}}-\frac{\sqrt{d \,x^{4}+c}}{3 x^{3}}}{a}"," ",0,"1/a*(-1/3*(d*x^4+c)^(1/2)/x^3+2/3*d/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-1/a*b*(d/b/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-1/8/b^2*sum((a*d-b*c)/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a)))","C"
801,0,0,57,0.607000," ","int((e*x)^(3/2)*(d*x^4+c)^(1/2)/(b*x^4+a),x)","\int \frac{\left(e x \right)^{\frac{3}{2}} \sqrt{d \,x^{4}+c}}{b \,x^{4}+a}\, dx"," ",0,"int((e*x)^(3/2)*(d*x^4+c)^(1/2)/(b*x^4+a),x)","F"
802,0,0,57,0.649000," ","int((e*x)^(1/2)*(d*x^4+c)^(1/2)/(b*x^4+a),x)","\int \frac{\sqrt{e x}\, \sqrt{d \,x^{4}+c}}{b \,x^{4}+a}\, dx"," ",0,"int((e*x)^(1/2)*(d*x^4+c)^(1/2)/(b*x^4+a),x)","F"
803,0,0,57,0.637000," ","int((d*x^4+c)^(1/2)/(e*x)^(1/2)/(b*x^4+a),x)","\int \frac{\sqrt{d \,x^{4}+c}}{\sqrt{e x}\, \left(b \,x^{4}+a \right)}\, dx"," ",0,"int((d*x^4+c)^(1/2)/(e*x)^(1/2)/(b*x^4+a),x)","F"
804,0,0,57,0.699000," ","int((d*x^4+c)^(1/2)/(e*x)^(3/2)/(b*x^4+a),x)","\int \frac{\sqrt{d \,x^{4}+c}}{\left(e x \right)^{\frac{3}{2}} \left(b \,x^{4}+a \right)}\, dx"," ",0,"int((d*x^4+c)^(1/2)/(e*x)^(3/2)/(b*x^4+a),x)","F"
805,1,378,84,0.283000," ","int(x^11/(b*x^4+a)/(d*x^4+c)^(1/2),x)","\frac{\sqrt{d \,x^{4}+c}\, x^{4}}{6 b d}-\frac{a^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{\sqrt{d \,x^{4}+c}\, a}{2 b^{2} d}-\frac{\sqrt{d \,x^{4}+c}\, c}{3 b \,d^{2}}"," ",0,"1/6/b*(d*x^4+c)^(1/2)/d*x^4-1/3/b*(d*x^4+c)^(1/2)/d^2*c-1/2/b^2*a/d*(d*x^4+c)^(1/2)-1/4*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/4*a^2/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
806,1,335,58,0.209000," ","int(x^7/(b*x^4+a)/(d*x^4+c)^(1/2),x)","\frac{a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{d \,x^{4}+c}}{2 b d}"," ",0,"1/2*(d*x^4+c)^(1/2)/b/d+1/4*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+1/4*a/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
807,1,316,39,0.213000," ","int(x^3/(b*x^4+a)/(d*x^4+c)^(1/2),x)","-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b}"," ",0,"-1/4/b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/4/b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
808,1,347,65,0.287000," ","int(1/x/(b*x^4+a)/(d*x^4+c)^(1/2),x)","\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{\ln \left(\frac{2 c +2 \sqrt{d \,x^{4}+c}\, \sqrt{c}}{x^{2}}\right)}{2 a \sqrt{c}}"," ",0,"1/4/a/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+1/4/a/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/2/a/c^(1/2)*ln((2*c+2*(d*x^4+c)^(1/2)*c^(1/2))/x^2)","B"
809,1,402,93,0.292000," ","int(1/x^5/(b*x^4+a)/(d*x^4+c)^(1/2),x)","-\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{d \ln \left(\frac{2 c +2 \sqrt{d \,x^{4}+c}\, \sqrt{c}}{x^{2}}\right)}{4 a \,c^{\frac{3}{2}}}+\frac{b \ln \left(\frac{2 c +2 \sqrt{d \,x^{4}+c}\, \sqrt{c}}{x^{2}}\right)}{2 a^{2} \sqrt{c}}-\frac{\sqrt{d \,x^{4}+c}}{4 a c \,x^{4}}"," ",0,"-1/4*(d*x^4+c)^(1/2)/a/c/x^4+1/4/a*d/c^(3/2)*ln((2*c+2*(d*x^4+c)^(1/2)*c^(1/2))/x^2)-1/4/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/4/a^2*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/2/a^2*b/c^(1/2)*ln((2*c+2*(d*x^4+c)^(1/2)*c^(1/2))/x^2)","B"
810,1,408,99,0.316000," ","int(x^9/(b*x^4+a)/(d*x^4+c)^(1/2),x)","-\frac{a^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{d \,x^{4}+c}\, x^{2}}{4 b d}-\frac{a \ln \left(\sqrt{d}\, x^{2}+\sqrt{d \,x^{4}+c}\right)}{2 b^{2} \sqrt{d}}-\frac{c \ln \left(\sqrt{d}\, x^{2}+\sqrt{d \,x^{4}+c}\right)}{4 b \,d^{\frac{3}{2}}}"," ",0,"1/4*x^2*(d*x^4+c)^(1/2)/b/d-1/4/b*c/d^(3/2)*ln(d^(1/2)*x^2+(d*x^4+c)^(1/2))-1/2/b^2*a*ln(d^(1/2)*x^2+(d*x^4+c)^(1/2))/d^(1/2)+1/4*a^2/b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/4*a^2/b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
811,1,356,71,0.333000," ","int(x^5/(b*x^4+a)/(d*x^4+c)^(1/2),x)","\frac{a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}-\frac{a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\ln \left(\sqrt{d}\, x^{2}+\sqrt{d \,x^{4}+c}\right)}{2 b \sqrt{d}}"," ",0,"1/2/b*ln(d^(1/2)*x^2+(d*x^4+c)^(1/2))/d^(1/2)-1/4*a/b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+1/4*a/b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
812,1,322,42,0.324000," ","int(x/(b*x^4+a)/(d*x^4+c)^(1/2),x)","-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}"," ",0,"1/4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/4/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
813,1,350,64,0.297000," ","int(1/x^3/(b*x^4+a)/(d*x^4+c)^(1/2),x)","\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{\sqrt{d \,x^{4}+c}}{2 a c \,x^{2}}"," ",0,"-1/2*(d*x^4+c)^(1/2)/a/c/x^2-1/4/a*b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+1/4/a*b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
814,1,383,95,0.270000," ","int(1/x^7/(b*x^4+a)/(d*x^4+c)^(1/2),x)","-\frac{b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{\sqrt{d \,x^{4}+c}\, b}{2 a^{2} c \,x^{2}}-\frac{\sqrt{d \,x^{4}+c}\, \left(-2 d \,x^{4}+c \right)}{6 a \,c^{2} x^{6}}"," ",0,"1/2/a^2*b/x^2*(d*x^4+c)^(1/2)/c+1/4/a^2*b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/4/a^2*b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/6/a*(d*x^4+c)^(1/2)*(-2*d*x^4+c)/x^6/c^2","B"
815,1,363,823,0.317000," ","int(x^8/(b*x^4+a)/(d*x^4+c)^(1/2),x)","\frac{a^{2} \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{8 b^{3} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}+\frac{-\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, a \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}}+\left(-\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, d}+\frac{\sqrt{d \,x^{4}+c}\, x}{3 d}\right) b}{b^{2}}"," ",0,"1/b^2*(b*(1/3/d*x*(d*x^4+c)^(1/2)-1/3*c/d/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-a/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I))+1/8*a^2/b^3*sum(1/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
816,1,265,570,0.230000," ","int(x^4/(b*x^4+a)/(d*x^4+c)^(1/2),x)","-\frac{a \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}+\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, b}"," ",0,"1/b/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-1/8*a/b^2*sum(1/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
817,1,191,570,0.331000," ","int(1/(b*x^4+a)/(d*x^4+c)^(1/2),x)","\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}}{8 b \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}"," ",0,"1/8/b*sum(1/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
818,1,288,605,0.306000," ","int(1/x^4/(b*x^4+a)/(d*x^4+c)^(1/2),x)","-\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}}{8 a \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}+\frac{-\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, c}-\frac{\sqrt{d \,x^{4}+c}}{3 c \,x^{3}}}{a}"," ",0,"1/a*(-1/3/c*(d*x^4+c)^(1/2)/x^3-1/3/c*d/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-1/8/a*sum(1/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
819,1,292,736,0.344000," ","int(x^6/(b*x^4+a)/(d*x^4+c)^(1/2),x)","-\frac{a \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}+\frac{i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{c}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, b \sqrt{d}}"," ",0,"I/b*c^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)/d^(1/2)*(EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-EllipticE((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-1/8*a/b^2*sum(1/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
820,1,191,583,0.249000," ","int(x^2/(b*x^4+a)/(d*x^4+c)^(1/2),x)","\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}}{8 b \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}"," ",0,"1/8/b*sum(1/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
821,1,310,763,0.254000," ","int(1/x^2/(b*x^4+a)/(d*x^4+c)^(1/2),x)","-\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}}{8 a \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}+\frac{\frac{i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{d}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, \sqrt{c}}-\frac{\sqrt{d \,x^{4}+c}}{c x}}{a}"," ",0,"-1/8/a*sum(1/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))+1/a*(-1/c*(d*x^4+c)^(1/2)/x+I/c^(1/2)*d^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*(EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-EllipticE((I/c^(1/2)*d^(1/2))^(1/2)*x,I)))","C"
822,1,923,155,0.247000," ","int(x^15/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","\frac{a^{3} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{4}}+\frac{a^{3} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{4}}+\frac{\sqrt{d \,x^{4}+c}\, x^{4}}{6 b^{2} d}-\frac{3 a^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{4}}-\frac{3 a^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{4}}-\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) b^{4}}+\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) b^{4}}-\frac{\sqrt{d \,x^{4}+c}\, a}{b^{3} d}-\frac{\sqrt{d \,x^{4}+c}\, c}{3 b^{2} d^{2}}"," ",0,"1/6/b^2*(d*x^4+c)^(1/2)/d*x^4-1/3/b^2*(d*x^4+c)^(1/2)/d^2*c-1/b^3*a/d*(d*x^4+c)^(1/2)-3/4*a^2/b^4/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-3/4*a^2/b^4/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/8*a^2/b^4*(-a*b)^(1/2)/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8*a^3/b^4*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+1/8*a^2/b^4*(-a*b)^(1/2)/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8*a^3/b^4*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
823,1,876,103,0.190000," ","int(x^11/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{a^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{a^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{a \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) b^{3}}-\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) b^{3}}+\frac{\sqrt{d \,x^{4}+c}}{2 b^{2} d}"," ",0,"1/2*(d*x^4+c)^(1/2)/b^2/d+1/2*a/b^3/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+1/2*a/b^3/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/8*a/b^3*(-a*b)^(1/2)/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8*a^2/b^3*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/8*a/b^3*(-a*b)^(1/2)/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8*a^2/b^3*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
824,1,851,83,0.197000," ","int(x^7/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","\frac{a d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, b^{2}}-\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) b^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) b^{2}}"," ",0,"-1/4/b^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/4/b^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/8/b^2*(-a*b)^(1/2)/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8*a/b^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+1/8/b^2*(-a*b)^(1/2)/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8*a/b^2*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
825,1,541,71,0.206000," ","int(x^3/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) a b}-\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) a b}"," ",0,"1/8*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/8*(-a*b)^(1/2)/a/b/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8/b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))","B"
826,1,880,108,0.272000," ","int(1/x/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","\frac{d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-\frac{a d -b c}{b}}\, a^{2}}-\frac{\ln \left(\frac{2 c +2 \sqrt{d \,x^{4}+c}\, \sqrt{c}}{x^{2}}\right)}{2 a^{2} \sqrt{c}}-\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) a^{2}}+\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) a^{2}}"," ",0,"1/4/a^2/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+1/4/a^2/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/8/a^2*(-a*b)^(1/2)/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8/a*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+1/8/a^2*(-a*b)^(1/2)/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8/a*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/2/a^2/c^(1/2)*ln((2*c+2*(d*x^4+c)^(1/2)*c^(1/2))/x^2)","B"
827,1,938,157,0.277000," ","int(1/x^5/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{b d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-\frac{a d -b c}{b}}\, a^{3}}+\frac{d \ln \left(\frac{2 c +2 \sqrt{d \,x^{4}+c}\, \sqrt{c}}{x^{2}}\right)}{4 a^{2} c^{\frac{3}{2}}}+\frac{b \ln \left(\frac{2 c +2 \sqrt{d \,x^{4}+c}\, \sqrt{c}}{x^{2}}\right)}{a^{3} \sqrt{c}}+\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) a^{3}}-\frac{\sqrt{-a b}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) a^{3}}-\frac{\sqrt{d \,x^{4}+c}}{4 a^{2} c \,x^{4}}"," ",0,"-1/4/a^2/c/x^4*(d*x^4+c)^(1/2)+1/4/a^2*d/c^(3/2)*ln((2*c+2*(d*x^4+c)^(1/2)*c^(1/2))/x^2)-1/2/a^3*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/2/a^3*b/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/8/a^3*b*(-a*b)^(1/2)/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8/a^2*b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/8/a^3*b*(-a*b)^(1/2)/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8/a^2*b*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+b/a^3/c^(1/2)*ln((2*c+2*(d*x^4+c)^(1/2)*c^(1/2))/x^2)","B"
828,1,953,163,0.273000," ","int(x^13/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{5 a^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}+\frac{5 a^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{\sqrt{-a b}\, a^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{4}}+\frac{\sqrt{-a b}\, a^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{4}}+\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) b^{3}}+\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a^{2}}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) b^{3}}+\frac{\sqrt{d \,x^{4}+c}\, x^{2}}{4 b^{2} d}-\frac{a \ln \left(\sqrt{d}\, x^{2}+\sqrt{d \,x^{4}+c}\right)}{b^{3} \sqrt{d}}-\frac{c \ln \left(\sqrt{d}\, x^{2}+\sqrt{d \,x^{4}+c}\right)}{4 b^{2} d^{\frac{3}{2}}}"," ",0,"1/4/b^2*x^2/d*(d*x^4+c)^(1/2)-1/4/b^2*c/d^(3/2)*ln(d^(1/2)*x^2+(d*x^4+c)^(1/2))-1/b^3*a*ln(d^(1/2)*x^2+(d*x^4+c)^(1/2))/d^(1/2)+5/8*a^2/b^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-5/8*a^2/b^3/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/8*a^2/b^3/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8*a^2/b^4*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/8*a^2/b^3/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8*a^2/b^4*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))","B"
829,1,893,117,0.238000," ","int(x^9/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","\frac{3 a \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{3}}-\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) b^{2}}-\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, a}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) b^{2}}+\frac{\ln \left(\sqrt{d}\, x^{2}+\sqrt{d \,x^{4}+c}\right)}{2 b^{2} \sqrt{d}}"," ",0,"1/2/b^2*ln(d^(1/2)*x^2+(d*x^4+c)^(1/2))/d^(1/2)-3/8*a/b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+3/8*a/b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/8*a/b^2/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8*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^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/8*a/b^2/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8*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^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))","B"
830,1,861,77,0.240000," ","int(x^5/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, b}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, b^{2}}+\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) b}+\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) b}"," ",0,"1/8/b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/8/b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/8/b/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8/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^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/8/b/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8/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^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))","B"
831,1,867,88,0.194000," ","int(x/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","\frac{\sqrt{-a b}\, d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) a}-\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) a}"," ",0,"-1/8/a/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8/b/a*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/8/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-1/8/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/8/a/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8/b/a*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))","B"
832,1,885,129,0.269000," ","int(1/x^3/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","\frac{3 b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{2}}+\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) a^{2}}+\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) a^{2}}-\frac{\sqrt{d \,x^{4}+c}}{2 a^{2} c \,x^{2}}"," ",0,"-1/2/a^2/x^2*(d*x^4+c)^(1/2)/c-3/8/a^2*b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))+3/8/a^2*b/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/8/a^2*b/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8/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^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))+1/8/a^2*b/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8/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^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))","B"
833,1,923,184,0.246000," ","int(1/x^7/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{5 b^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}-\frac{\sqrt{-a b}}{b}}\right)}{8 \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^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x^{2}+\frac{\sqrt{-a b}}{b}}\right)}{8 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a^{3}}-\frac{\sqrt{\left(x^{2}-\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{8 \left(a d -b c \right) \left(x^{2}-\frac{\sqrt{-a b}}{b}\right) a^{3}}-\frac{\sqrt{\left(x^{2}+\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, b^{2}}{8 \left(a d -b c \right) \left(x^{2}+\frac{\sqrt{-a b}}{b}\right) a^{3}}+\frac{\sqrt{d \,x^{4}+c}\, b}{a^{3} c \,x^{2}}-\frac{\sqrt{d \,x^{4}+c}\, \left(-2 d \,x^{4}+c \right)}{6 a^{2} c^{2} x^{6}}"," ",0,"b/a^3/x^2*(d*x^4+c)^(1/2)/c+5/8/a^3*b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))-5/8/a^3*b^2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/6/a^2*(d*x^4+c)^(1/2)*(-2*d*x^4+c)/x^6/c^2-1/8/a^3*b^2/(a*d-b*c)/(x^2-(-a*b)^(1/2)/b)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/8/a^3*b*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x^2-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2-(-a*b)^(1/2)/b))-1/8/a^3*b^2/(a*d-b*c)/(x^2+(-a*b)^(1/2)/b)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/8/a^3*b*(-a*b)^(1/2)*d/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x^2+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x^2+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x^2+(-a*b)^(1/2)/b))","B"
834,1,604,942,0.311000," ","int(x^8/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","\frac{\left(-\frac{\sqrt{d \,x^{4}+c}\, b x}{4 \left(a d -b c \right) \left(b \,x^{4}+a \right) a}-\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{4 \left(a d -b c \right) \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\left(-5 a d +3 b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{32 a b \left(a d -b c \right) \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}\right) a^{2}}{b^{2}}-\frac{a \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{4 b^{3} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}+\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, b^{2}}"," ",0,"1/b^2/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-1/4*a/b^3*sum(1/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))+a^2/b^2*(-1/4/a*b/(a*d-b*c)*x*(d*x^4+c)^(1/2)/(b*x^4+a)-1/4*d/(a*d-b*c)/a/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-1/32/b/a*sum((-5*a*d+3*b*c)/(a*d-b*c)/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a)))","C"
835,1,530,859,0.255000," ","int(x^4/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{\left(-\frac{\sqrt{d \,x^{4}+c}\, b x}{4 \left(a d -b c \right) \left(b \,x^{4}+a \right) a}-\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{4 \left(a d -b c \right) \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\left(-5 a d +3 b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{32 a b \left(a d -b c \right) \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}\right) a}{b}+\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}"," ",0,"1/8/b^2*sum(1/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))-a/b*(-1/4/(a*d-b*c)*(d*x^4+c)^(1/2)/(b*x^4+a)/a*b*x-1/4*d/(a*d-b*c)/a/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-1/32/b/a*sum((-5*a*d+3*b*c)/(a*d-b*c)/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a)))","C"
836,1,333,930,0.253000," ","int(1/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{\sqrt{d \,x^{4}+c}\, b x}{4 \left(a d -b c \right) \left(b \,x^{4}+a \right) a}-\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{4 \left(a d -b c \right) \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\left(-5 a d +3 b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{32 a b \left(a d -b c \right) \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}"," ",0,"-1/4/(a*d-b*c)*(d*x^4+c)^(1/2)/(b*x^4+a)/a*b*x-1/4*d/(a*d-b*c)/a/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-1/32/b/a*sum((-5*a*d+3*b*c)/(a*d-b*c)/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
837,1,626,987,0.247000," ","int(1/x^4/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{\left(-\frac{\sqrt{d \,x^{4}+c}\, b x}{4 \left(a d -b c \right) \left(b \,x^{4}+a \right) a}-\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{4 \left(a d -b c \right) \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\left(-5 a d +3 b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{32 a b \left(a d -b c \right) \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}\right) b}{a}-\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}}{8 a^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3}}+\frac{-\frac{\sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, c}-\frac{\sqrt{d \,x^{4}+c}}{3 c \,x^{3}}}{a^{2}}"," ",0,"1/a^2*(-1/3/c*(d*x^4+c)^(1/2)/x^3-1/3/c*d/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-1/8/a^2*sum(1/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))-1/a*b*(-1/4/(a*d-b*c)*(d*x^4+c)^(1/2)/(b*x^4+a)/a*b*x-1/4*d/(a*d-b*c)/a/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-1/32/b/a*sum((-5*a*d+3*b*c)/(a*d-b*c)/_alpha^3*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a)))","C"
838,1,556,1090,0.359000," ","int(x^6/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{\left(-\frac{\sqrt{d \,x^{4}+c}\, b \,x^{3}}{4 \left(a d -b c \right) \left(b \,x^{4}+a \right) a}+\frac{i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{c}\, \sqrt{d}}{4 \left(a d -b c \right) \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\left(-3 a d +b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{32 a b \left(a d -b c \right) \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}\right) a}{b}+\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}}{8 b^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}"," ",0,"1/8/b^2*sum(1/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))-a/b*(-1/4/a*b/(a*d-b*c)*x^3*(d*x^4+c)^(1/2)/(b*x^4+a)+1/4*I*d^(1/2)/(a*d-b*c)/a*c^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*(EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-EllipticE((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-1/32/b/a*sum((-3*a*d+b*c)/(a*d-b*c)/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a)))","C"
839,1,359,1088,0.247000," ","int(x^2/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{\sqrt{d \,x^{4}+c}\, b \,x^{3}}{4 \left(a d -b c \right) \left(b \,x^{4}+a \right) a}+\frac{i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{c}\, \sqrt{d}}{4 \left(a d -b c \right) \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\left(-3 a d +b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{32 a b \left(a d -b c \right) \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}"," ",0,"-1/4/(a*d-b*c)*(d*x^4+c)^(1/2)/(b*x^4+a)/a*b*x^3+1/4*I*d^(1/2)/(a*d-b*c)/a*c^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*(EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-EllipticE((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-1/32/b/a*sum((-3*a*d+b*c)/(a*d-b*c)/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))","C"
840,1,674,1165,0.230000," ","int(1/x^2/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","-\frac{\left(-\frac{\sqrt{d \,x^{4}+c}\, b \,x^{3}}{4 \left(a d -b c \right) \left(b \,x^{4}+a \right) a}+\frac{i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{c}\, \sqrt{d}}{4 \left(a d -b c \right) \sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\left(-3 a d +b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}\right)}{32 a b \left(a d -b c \right) \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}\right) b}{a}-\frac{\frac{2 \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{3} b \EllipticPi \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , \frac{i \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} b \sqrt{c}}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{\sqrt{c}}}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}}\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, a}-\frac{\arctanh \left(\frac{2 \RootOf \left(b \,\textit{\_Z}^{4}+a \right)^{2} d \,x^{2}+2 c}{2 \sqrt{\frac{-a d +b c}{b}}\, \sqrt{d \,x^{4}+c}}\right)}{\sqrt{\frac{-a d +b c}{b}}}}{8 a^{2} \RootOf \left(b \,\textit{\_Z}^{4}+a \right)}+\frac{\frac{i \sqrt{-\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{\sqrt{c}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, x , i\right)\right) \sqrt{d}}{\sqrt{\frac{i \sqrt{d}}{\sqrt{c}}}\, \sqrt{d \,x^{4}+c}\, \sqrt{c}}-\frac{\sqrt{d \,x^{4}+c}}{c x}}{a^{2}}"," ",0,"-1/8/a^2*sum(1/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a))+1/a^2*(-(d*x^4+c)^(1/2)/c/x+I/c^(1/2)*d^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*(EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-EllipticE((I/c^(1/2)*d^(1/2))^(1/2)*x,I)))-1/a*b*(-1/4/(a*d-b*c)*(d*x^4+c)^(1/2)/(b*x^4+a)/a*b*x^3+1/4*I*d^(1/2)/(a*d-b*c)/a*c^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2)*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*(EllipticF((I/c^(1/2)*d^(1/2))^(1/2)*x,I)-EllipticE((I/c^(1/2)*d^(1/2))^(1/2)*x,I))-1/32/b/a*sum((-3*a*d+b*c)/(a*d-b*c)/_alpha*(-1/((-a*d+b*c)/b)^(1/2)*arctanh(1/2*(2*_alpha^2*d*x^2+2*c)/((-a*d+b*c)/b)^(1/2)/(d*x^4+c)^(1/2))+2/(I/c^(1/2)*d^(1/2))^(1/2)*_alpha^3*b/a*(-I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)*(I/c^(1/2)*d^(1/2)*x^2+1)^(1/2)/(d*x^4+c)^(1/2)*EllipticPi((I/c^(1/2)*d^(1/2))^(1/2)*x,I*_alpha^2/a*b*c^(1/2)/d^(1/2),(-I/c^(1/2)*d^(1/2))^(1/2)/(I/c^(1/2)*d^(1/2))^(1/2))),_alpha=RootOf(_Z^4*b+a)))","C"
841,0,0,188,0.561000," ","int((e*x)^m*(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","\int \frac{\left(b \,x^{4}+a \right)^{2} \left(e x \right)^{m}}{\sqrt{d \,x^{4}+c}}\, dx"," ",0,"int((e*x)^m*(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","F"
842,0,0,113,0.413000," ","int((e*x)^m*(b*x^4+a)/(d*x^4+c)^(1/2),x)","\int \frac{\left(b \,x^{4}+a \right) \left(e x \right)^{m}}{\sqrt{d \,x^{4}+c}}\, dx"," ",0,"int((e*x)^m*(b*x^4+a)/(d*x^4+c)^(1/2),x)","F"
843,0,0,60,0.419000," ","int((e*x)^m/(d*x^4+c)^(1/2),x)","\int \frac{\left(e x \right)^{m}}{\sqrt{d \,x^{4}+c}}\, dx"," ",0,"int((e*x)^m/(d*x^4+c)^(1/2),x)","F"
844,0,0,71,0.584000," ","int((e*x)^m/(b*x^4+a)/(d*x^4+c)^(1/2),x)","\int \frac{\left(e x \right)^{m}}{\left(b \,x^{4}+a \right) \sqrt{d \,x^{4}+c}}\, dx"," ",0,"int((e*x)^m/(b*x^4+a)/(d*x^4+c)^(1/2),x)","F"
845,0,0,71,0.548000," ","int((e*x)^m/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","\int \frac{\left(e x \right)^{m}}{\left(b \,x^{4}+a \right)^{2} \sqrt{d \,x^{4}+c}}\, dx"," ",0,"int((e*x)^m/(b*x^4+a)^2/(d*x^4+c)^(1/2),x)","F"
846,0,0,71,0.648000," ","int((e*x)^m/(b*x^4+a)^3/(d*x^4+c)^(1/2),x)","\int \frac{\left(e x \right)^{m}}{\left(b \,x^{4}+a \right)^{3} \sqrt{d \,x^{4}+c}}\, dx"," ",0,"int((e*x)^m/(b*x^4+a)^3/(d*x^4+c)^(1/2),x)","F"
847,0,0,182,0.552000," ","int((e*x)^m*(b*x^4+a)^2/(d*x^4+c)^(3/2),x)","\int \frac{\left(b \,x^{4}+a \right)^{2} \left(e x \right)^{m}}{\left(d \,x^{4}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x)^m*(b*x^4+a)^2/(d*x^4+c)^(3/2),x)","F"
848,0,0,118,0.421000," ","int((e*x)^m*(b*x^4+a)/(d*x^4+c)^(3/2),x)","\int \frac{\left(b \,x^{4}+a \right) \left(e x \right)^{m}}{\left(d \,x^{4}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x)^m*(b*x^4+a)/(d*x^4+c)^(3/2),x)","F"
849,0,0,63,0.398000," ","int((e*x)^m/(d*x^4+c)^(3/2),x)","\int \frac{\left(e x \right)^{m}}{\left(d \,x^{4}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x)^m/(d*x^4+c)^(3/2),x)","F"
850,0,0,74,0.659000," ","int((e*x)^m/(b*x^4+a)/(d*x^4+c)^(3/2),x)","\int \frac{\left(e x \right)^{m}}{\left(b \,x^{4}+a \right) \left(d \,x^{4}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x)^m/(b*x^4+a)/(d*x^4+c)^(3/2),x)","F"
851,0,0,74,0.610000," ","int((e*x)^m/(b*x^4+a)^2/(d*x^4+c)^(3/2),x)","\int \frac{\left(e x \right)^{m}}{\left(b \,x^{4}+a \right)^{2} \left(d \,x^{4}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x)^m/(b*x^4+a)^2/(d*x^4+c)^(3/2),x)","F"
852,0,0,74,0.617000," ","int((e*x)^m/(b*x^4+a)^3/(d*x^4+c)^(3/2),x)","\int \frac{\left(e x \right)^{m}}{\left(b \,x^{4}+a \right)^{3} \left(d \,x^{4}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x)^m/(b*x^4+a)^3/(d*x^4+c)^(3/2),x)","F"
853,0,0,84,0.634000," ","int(x^17/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{x^{17}}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^17/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
854,0,0,58,0.601000," ","int(x^11/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{x^{11}}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^11/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
855,0,0,39,0.572000," ","int(x^5/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{x^{5}}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^5/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
856,0,0,65,0.631000," ","int(1/x/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}\, x}\, dx"," ",0,"int(1/x/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
857,0,0,93,0.725000," ","int(1/x^7/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}\, x^{7}}\, dx"," ",0,"int(1/x^7/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
858,0,0,99,0.921000," ","int(x^14/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{x^{14}}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^14/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
859,0,0,71,0.610000," ","int(x^8/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{x^{8}}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^8/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
860,0,0,42,0.605000," ","int(x^2/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{x^{2}}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^2/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
861,0,0,64,0.644000," ","int(1/x^4/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}\, x^{4}}\, dx"," ",0,"int(1/x^4/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
862,0,0,95,0.658000," ","int(1/x^10/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}\, x^{10}}\, dx"," ",0,"int(1/x^10/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
863,0,0,52,0.700000," ","int(x^4/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{x^{4}}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^4/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
864,0,0,52,0.589000," ","int(x^3/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{x^{3}}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^3/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
865,0,0,52,0.670000," ","int(x/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{x}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
866,0,0,49,0.621000," ","int(1/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(1/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
867,0,0,52,0.629000," ","int(1/x^2/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}\, x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
868,0,0,52,0.659000," ","int(1/x^3/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}\, x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
869,0,0,52,0.601000," ","int(1/x^5/(b*x^6+a)/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right) \sqrt{d \,x^{6}+c}\, x^{5}}\, dx"," ",0,"int(1/x^5/(b*x^6+a)/(d*x^6+c)^(1/2),x)","F"
870,0,0,103,0.454000," ","int(x^17/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{x^{17}}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^17/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
871,0,0,83,0.632000," ","int(x^11/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{x^{11}}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^11/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
872,0,0,71,0.619000," ","int(x^5/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{x^{5}}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^5/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
873,0,0,108,0.775000," ","int(1/x/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}\, x}\, dx"," ",0,"int(1/x/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
874,0,0,157,0.559000," ","int(1/x^7/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}\, x^{7}}\, dx"," ",0,"int(1/x^7/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
875,0,0,117,0.627000," ","int(x^14/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{x^{14}}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^14/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
876,0,0,77,0.656000," ","int(x^8/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{x^{8}}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^8/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
877,0,0,88,0.605000," ","int(x^2/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{x^{2}}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^2/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
878,0,0,129,0.483000," ","int(1/x^4/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}\, x^{4}}\, dx"," ",0,"int(1/x^4/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
879,0,0,184,0.448000," ","int(1/x^10/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}\, x^{10}}\, dx"," ",0,"int(1/x^10/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
880,0,0,52,0.627000," ","int(x^4/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{x^{4}}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^4/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
881,0,0,52,0.641000," ","int(x^3/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{x^{3}}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x^3/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
882,0,0,52,0.600000," ","int(x/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{x}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(x/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
883,0,0,49,0.642000," ","int(1/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}}\, dx"," ",0,"int(1/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
884,0,0,52,0.458000," ","int(1/x^2/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}\, x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
885,0,0,52,0.465000," ","int(1/x^3/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}\, x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
886,0,0,52,0.461000," ","int(1/x^5/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{6}+a \right)^{2} \sqrt{d \,x^{6}+c}\, x^{5}}\, dx"," ",0,"int(1/x^5/(b*x^6+a)^2/(d*x^6+c)^(1/2),x)","F"
887,0,0,84,0.593000," ","int(x^23/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{23}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^23/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
888,0,0,58,0.642000," ","int(x^15/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{15}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^15/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
889,0,0,39,0.625000," ","int(x^7/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{7}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^7/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
890,0,0,65,0.683000," ","int(1/x/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}\, x}\, dx"," ",0,"int(1/x/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
891,0,0,93,0.637000," ","int(1/x^9/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}\, x^{9}}\, dx"," ",0,"int(1/x^9/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
892,0,0,99,0.581000," ","int(x^19/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{19}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^19/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
893,0,0,71,0.596000," ","int(x^11/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{11}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^11/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
894,0,0,42,0.616000," ","int(x^3/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{3}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^3/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
895,0,0,64,0.664000," ","int(1/x^5/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}\, x^{5}}\, dx"," ",0,"int(1/x^5/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
896,0,0,95,0.662000," ","int(1/x^13/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}\, x^{13}}\, dx"," ",0,"int(1/x^13/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
897,0,0,826,0.640000," ","int(x^9/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{9}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^9/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
898,0,0,714,0.660000," ","int(x/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
899,0,0,849,0.642000," ","int(1/x^7/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}\, x^{7}}\, dx"," ",0,"int(1/x^7/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
900,0,0,977,0.739000," ","int(x^13/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{13}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^13/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
901,0,0,720,0.732000," ","int(x^5/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{5}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^5/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
902,0,0,1000,0.648000," ","int(1/x^3/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}\, x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
903,0,0,52,0.609000," ","int(x^4/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{4}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^4/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
904,0,0,52,0.594000," ","int(x^2/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{x^{2}}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^2/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
905,0,0,49,0.656000," ","int(1/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(1/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
906,0,0,52,0.640000," ","int(1/x^2/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}\, x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
907,0,0,52,0.638000," ","int(1/x^4/(b*x^8+a)/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right) \sqrt{d \,x^{8}+c}\, x^{4}}\, dx"," ",0,"int(1/x^4/(b*x^8+a)/(d*x^8+c)^(1/2),x)","F"
908,0,0,103,0.469000," ","int(x^23/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{23}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^23/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
909,0,0,83,0.594000," ","int(x^15/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{15}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^15/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
910,0,0,71,0.603000," ","int(x^7/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{7}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^7/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
911,0,0,108,0.799000," ","int(1/x/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}\, x}\, dx"," ",0,"int(1/x/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
912,0,0,157,0.658000," ","int(1/x^9/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}\, x^{9}}\, dx"," ",0,"int(1/x^9/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
913,0,0,117,0.647000," ","int(x^19/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{19}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^19/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
914,0,0,77,0.642000," ","int(x^11/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{11}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^11/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
915,0,0,88,0.601000," ","int(x^3/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{3}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^3/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
916,0,0,129,0.439000," ","int(1/x^5/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}\, x^{5}}\, dx"," ",0,"int(1/x^5/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
917,0,0,184,0.455000," ","int(1/x^13/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}\, x^{13}}\, dx"," ",0,"int(1/x^13/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
918,0,0,895,0.638000," ","int(x^9/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{9}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^9/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
919,0,0,966,0.608000," ","int(x/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
920,0,0,1021,0.464000," ","int(1/x^7/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}\, x^{7}}\, dx"," ",0,"int(1/x^7/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
921,0,0,1132,0.644000," ","int(x^13/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{13}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^13/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
922,0,0,1130,0.614000," ","int(x^5/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{5}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^5/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
923,0,0,1207,0.474000," ","int(1/x^3/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}\, x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
924,0,0,52,0.591000," ","int(x^4/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{4}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^4/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
925,0,0,52,0.641000," ","int(x^2/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{x^{2}}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(x^2/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
926,0,0,49,0.651000," ","int(1/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}}\, dx"," ",0,"int(1/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
927,0,0,52,0.447000," ","int(1/x^2/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}\, x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
928,0,0,52,0.460000," ","int(1/x^4/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","\int \frac{1}{\left(b \,x^{8}+a \right)^{2} \sqrt{d \,x^{8}+c}\, x^{4}}\, dx"," ",0,"int(1/x^4/(b*x^8+a)^2/(d*x^8+c)^(1/2),x)","F"
929,1,162,103,0.057000," ","int((a+b/x^2)*x^5*(c+d/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(8 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \,c^{\frac{3}{2}} x^{3}+3 a \,d^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-6 b c \,d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+3 \sqrt{c \,x^{2}+d}\, a \sqrt{c}\, d^{2} x -6 \sqrt{c \,x^{2}+d}\, b \,c^{\frac{3}{2}} d x -6 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \sqrt{c}\, d x +12 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b \,c^{\frac{3}{2}} x \right) x}{48 \sqrt{c \,x^{2}+d}\, c^{\frac{5}{2}}}"," ",0,"1/48*((c*x^2+d)/x^2)^(1/2)*x*(8*c^(3/2)*(c*x^2+d)^(3/2)*x^3*a-6*c^(1/2)*(c*x^2+d)^(3/2)*x*a*d+12*c^(3/2)*(c*x^2+d)^(3/2)*x*b+3*c^(1/2)*(c*x^2+d)^(1/2)*x*a*d^2-6*c^(3/2)*(c*x^2+d)^(1/2)*x*b*d+3*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*a*d^3-6*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*b*c*d^2)/(c*x^2+d)^(1/2)/c^(5/2)","A"
930,1,122,74,0.055000," ","int((a+b/x^2)*x^3*(c+d/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(-a \,d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+4 b c d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-\sqrt{c \,x^{2}+d}\, a \sqrt{c}\, d x +4 \sqrt{c \,x^{2}+d}\, b \,c^{\frac{3}{2}} x +2 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \sqrt{c}\, x \right) x}{8 \sqrt{c \,x^{2}+d}\, c^{\frac{3}{2}}}"," ",0,"1/8*((c*x^2+d)/x^2)^(1/2)*x*(2*(c*x^2+d)^(3/2)*c^(1/2)*x*a-(c*x^2+d)^(1/2)*c^(1/2)*x*a*d+4*(c*x^2+d)^(1/2)*c^(3/2)*x*b-ln(c^(1/2)*x+(c*x^2+d)^(1/2))*a*d^2+4*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*b*c*d)/(c*x^2+d)^(1/2)/c^(3/2)","A"
931,1,129,68,0.056000," ","int((a+b/x^2)*x*(c+d/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(-a \,d^{2} x \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-2 b c d x \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-\sqrt{c \,x^{2}+d}\, a \sqrt{c}\, d \,x^{2}-2 \sqrt{c \,x^{2}+d}\, b \,c^{\frac{3}{2}} x^{2}+2 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b \sqrt{c}\right)}{2 \sqrt{c \,x^{2}+d}\, \sqrt{c}\, d}"," ",0,"-1/2*((c*x^2+d)/x^2)^(1/2)*(-(c*x^2+d)^(1/2)*c^(1/2)*x^2*a*d-2*(c*x^2+d)^(1/2)*c^(3/2)*x^2*b+2*(c*x^2+d)^(3/2)*c^(1/2)*b-ln(c^(1/2)*x+(c*x^2+d)^(1/2))*x*a*d^2-2*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*x*b*c*d)/(c*x^2+d)^(1/2)/d/c^(1/2)","A"
932,1,109,47,0.055000," ","int((a+b/x^2)*(c+d/x^2)^(1/2)/x,x)","-\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(-3 a c d \,x^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-3 \sqrt{c \,x^{2}+d}\, a \,c^{\frac{3}{2}} x^{4}+3 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \sqrt{c}\, x^{2}+\left(c \,x^{2}+d \right)^{\frac{3}{2}} b \sqrt{c}\right)}{3 \sqrt{c \,x^{2}+d}\, \sqrt{c}\, d \,x^{2}}"," ",0,"-1/3*((c*x^2+d)/x^2)^(1/2)/x^2*(-3*(c*x^2+d)^(1/2)*c^(3/2)*x^4*a+3*(c*x^2+d)^(3/2)*c^(1/2)*x^2*a-3*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*x^3*a*c*d+(c*x^2+d)^(3/2)*b*c^(1/2))/(c*x^2+d)^(1/2)/d/c^(1/2)","B"
933,1,48,38,0.046000," ","int((a+b/x^2)*(c+d/x^2)^(1/2)/x^3,x)","-\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(5 a d \,x^{2}-2 b c \,x^{2}+3 b d \right) \left(c \,x^{2}+d \right)}{15 d^{2} x^{4}}"," ",0,"-1/15*((c*x^2+d)/x^2)^(1/2)*(5*a*d*x^2-2*b*c*x^2+3*b*d)*(c*x^2+d)/d^2/x^4","A"
934,1,70,62,0.046000," ","int((a+b/x^2)*(c+d/x^2)^(1/2)/x^5,x)","\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(14 a c d \,x^{4}-8 b \,c^{2} x^{4}-21 a \,d^{2} x^{2}+12 b c d \,x^{2}-15 b \,d^{2}\right) \left(c \,x^{2}+d \right)}{105 d^{3} x^{6}}"," ",0,"1/105*((c*x^2+d)/x^2)^(1/2)*(14*a*c*d*x^4-8*b*c^2*x^4-21*a*d^2*x^2+12*b*c*d*x^2-15*b*d^2)*(c*x^2+d)/d^3/x^6","A"
935,1,94,88,0.048000," ","int((a+b/x^2)*(c+d/x^2)^(1/2)/x^7,x)","-\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(24 a \,c^{2} d \,x^{6}-16 b \,c^{3} x^{6}-36 a c \,d^{2} x^{4}+24 b \,c^{2} d \,x^{4}+45 a \,d^{3} x^{2}-30 b c \,d^{2} x^{2}+35 b \,d^{3}\right) \left(c \,x^{2}+d \right)}{315 d^{4} x^{8}}"," ",0,"-1/315*((c*x^2+d)/x^2)^(1/2)*(24*a*c^2*d*x^6-16*b*c^3*x^6-36*a*c*d^2*x^4+24*b*c^2*d*x^4+45*a*d^3*x^2-30*b*c*d^2*x^2+35*b*d^3)*(c*x^2+d)/d^4/x^8","A"
936,1,118,114,0.048000," ","int((a+b/x^2)*(c+d/x^2)^(1/2)/x^9,x)","\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(176 a \,c^{3} d \,x^{8}-128 b \,c^{4} x^{8}-264 a \,c^{2} d^{2} x^{6}+192 b \,c^{3} d \,x^{6}+330 a c \,d^{3} x^{4}-240 b \,c^{2} d^{2} x^{4}-385 a \,d^{4} x^{2}+280 b c \,d^{3} x^{2}-315 b \,d^{4}\right) \left(c \,x^{2}+d \right)}{3465 d^{5} x^{10}}"," ",0,"1/3465*((c*x^2+d)/x^2)^(1/2)*(176*a*c^3*d*x^8-128*b*c^4*x^8-264*a*c^2*d^2*x^6+192*b*c^3*d*x^6+330*a*c*d^3*x^4-240*b*c^2*d^2*x^4-385*a*d^4*x^2+280*b*c*d^3*x^2-315*b*d^4)*(c*x^2+d)/d^5/x^10","A"
937,1,113,130,0.054000," ","int((a+b/x^2)*x^10*(c+d/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(315 a \,x^{8} c^{4}-280 a \,c^{3} d \,x^{6}+385 b \,c^{4} x^{6}+240 a \,c^{2} d^{2} x^{4}-330 b \,c^{3} d \,x^{4}-192 a c \,d^{3} x^{2}+264 b \,c^{2} d^{2} x^{2}+128 a \,d^{4}-176 b c \,d^{3}\right) \left(c \,x^{2}+d \right) x}{3465 c^{5}}"," ",0,"1/3465*((c*x^2+d)/x^2)^(1/2)*x*(315*a*c^4*x^8-280*a*c^3*d*x^6+385*b*c^4*x^6+240*a*c^2*d^2*x^4-330*b*c^3*d*x^4-192*a*c*d^3*x^2+264*b*c^2*d^2*x^2+128*a*d^4-176*b*c*d^3)*(c*x^2+d)/c^5","A"
938,1,89,101,0.047000," ","int((a+b/x^2)*x^8*(c+d/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(35 a \,x^{6} c^{3}-30 a \,c^{2} d \,x^{4}+45 b \,c^{3} x^{4}+24 a c \,d^{2} x^{2}-36 b \,c^{2} d \,x^{2}-16 a \,d^{3}+24 b c \,d^{2}\right) \left(c \,x^{2}+d \right) x}{315 c^{4}}"," ",0,"1/315*((c*x^2+d)/x^2)^(1/2)*x*(35*a*c^3*x^6-30*a*c^2*d*x^4+45*b*c^3*x^4+24*a*c*d^2*x^2-36*b*c^2*d*x^2-16*a*d^3+24*b*c*d^2)*(c*x^2+d)/c^4","A"
939,1,65,72,0.058000," ","int((a+b/x^2)*x^6*(c+d/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(15 a \,x^{4} c^{2}-12 a c d \,x^{2}+21 b \,c^{2} x^{2}+8 a \,d^{2}-14 b c d \right) \left(c \,x^{2}+d \right) x}{105 c^{3}}"," ",0,"1/105*((c*x^2+d)/x^2)^(1/2)*x*(15*a*c^2*x^4-12*a*c*d*x^2+21*b*c^2*x^2+8*a*d^2-14*b*c*d)*(c*x^2+d)/c^3","A"
940,1,43,45,0.050000," ","int((a+b/x^2)*x^4*(c+d/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(3 a \,x^{2} c -2 a d +5 b c \right) \left(c \,x^{2}+d \right) x}{15 c^{2}}"," ",0,"1/15*((c*x^2+d)/x^2)^(1/2)*x*(3*a*c*x^2-2*a*d+5*b*c)*(c*x^2+d)/c^2","A"
941,1,83,54,0.056000," ","int((a+b/x^2)*x^2*(c+d/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(3 b c \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-3 \sqrt{c \,x^{2}+d}\, b c -\left(c \,x^{2}+d \right)^{\frac{3}{2}} a \right) x}{3 \sqrt{c \,x^{2}+d}\, c}"," ",0,"-1/3*((c*x^2+d)/x^2)^(1/2)*x*(3*d^(1/2)*ln(2*(d^(1/2)*(c*x^2+d)^(1/2)+d)/x)*b*c-a*(c*x^2+d)^(3/2)-3*(c*x^2+d)^(1/2)*b*c)/(c*x^2+d)^(1/2)/c","A"
942,1,135,71,0.053000," ","int((a+b/x^2)*(c+d/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(2 a \,d^{\frac{3}{2}} x^{2} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+b c \sqrt{d}\, x^{2} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-2 \sqrt{c \,x^{2}+d}\, a d \,x^{2}-\sqrt{c \,x^{2}+d}\, b c \,x^{2}+\left(c \,x^{2}+d \right)^{\frac{3}{2}} b \right)}{2 \sqrt{c \,x^{2}+d}\, d x}"," ",0,"-1/2*((c*x^2+d)/x^2)^(1/2)/x*(2*d^(3/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^2*a+d^(1/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^2*b*c-2*(c*x^2+d)^(1/2)*x^2*a*d-(c*x^2+d)^(1/2)*x^2*b*c+(c*x^2+d)^(3/2)*b)/(c*x^2+d)^(1/2)/d","A"
943,1,175,75,0.059000," ","int((a+b/x^2)*(c+d/x^2)^(1/2)/x^2,x)","-\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(4 a c \,d^{\frac{3}{2}} x^{4} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-b \,c^{2} \sqrt{d}\, x^{4} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-4 \sqrt{c \,x^{2}+d}\, a c d \,x^{4}+\sqrt{c \,x^{2}+d}\, b \,c^{2} x^{4}+4 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a d \,x^{2}-\left(c \,x^{2}+d \right)^{\frac{3}{2}} b c \,x^{2}+2 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b d \right)}{8 \sqrt{c \,x^{2}+d}\, d^{2} x^{3}}"," ",0,"-1/8*((c*x^2+d)/x^2)^(1/2)/x^3*(4*d^(3/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^4*a*c-d^(1/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^4*b*c^2-4*(c*x^2+d)^(1/2)*x^4*a*c*d+(c*x^2+d)^(1/2)*x^4*b*c^2+4*(c*x^2+d)^(3/2)*x^2*a*d-(c*x^2+d)^(3/2)*x^2*b*c+2*(c*x^2+d)^(3/2)*b*d)/(c*x^2+d)^(1/2)/d^2","B"
944,1,220,103,0.059000," ","int((a+b/x^2)*(c+d/x^2)^(1/2)/x^4,x)","\frac{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(6 a \,c^{2} d^{\frac{3}{2}} x^{6} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-3 b \,c^{3} \sqrt{d}\, x^{6} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-6 \sqrt{c \,x^{2}+d}\, a \,c^{2} d \,x^{6}+3 \sqrt{c \,x^{2}+d}\, b \,c^{3} x^{6}+6 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a c d \,x^{4}-3 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b \,c^{2} x^{4}-12 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \,d^{2} x^{2}+6 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b c d \,x^{2}-8 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b \,d^{2}\right)}{48 \sqrt{c \,x^{2}+d}\, d^{3} x^{5}}"," ",0,"1/48*((c*x^2+d)/x^2)^(1/2)/x^5*(6*d^(3/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^6*a*c^2-3*d^(1/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^6*b*c^3-6*(c*x^2+d)^(1/2)*x^6*a*c^2*d+3*(c*x^2+d)^(1/2)*x^6*b*c^3+6*(c*x^2+d)^(3/2)*x^4*a*c*d-3*(c*x^2+d)^(3/2)*x^4*b*c^2-12*(c*x^2+d)^(3/2)*x^2*a*d^2+6*(c*x^2+d)^(3/2)*x^2*b*c*d-8*(c*x^2+d)^(3/2)*b*d^2)/(c*x^2+d)^(1/2)/d^3","B"
945,1,162,103,0.060000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)*x^5,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(-3 a \,d^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+18 b c \,d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-3 \sqrt{c \,x^{2}+d}\, a \sqrt{c}\, d^{2} x +18 \sqrt{c \,x^{2}+d}\, b \,c^{\frac{3}{2}} d x -2 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \sqrt{c}\, d x +12 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b \,c^{\frac{3}{2}} x +8 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a \sqrt{c}\, x \right) x^{3}}{48 \left(c \,x^{2}+d \right)^{\frac{3}{2}} c^{\frac{3}{2}}}"," ",0,"1/48*((c*x^2+d)/x^2)^(3/2)*x^3*(8*c^(1/2)*(c*x^2+d)^(5/2)*x*a-2*(c*x^2+d)^(3/2)*a*c^(1/2)*d*x+12*(c*x^2+d)^(3/2)*b*c^(3/2)*x-3*(c*x^2+d)^(1/2)*a*c^(1/2)*d^2*x+18*(c*x^2+d)^(1/2)*b*c^(3/2)*d*x-3*a*d^3*ln(c^(1/2)*x+(c*x^2+d)^(1/2))+18*b*c*d^2*ln(c^(1/2)*x+(c*x^2+d)^(1/2)))/(c*x^2+d)^(3/2)/c^(3/2)","A"
946,1,174,95,0.055000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)*x^3,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(3 a \,d^{3} x \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+12 b c \,d^{2} x \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+3 \sqrt{c \,x^{2}+d}\, a \sqrt{c}\, d^{2} x^{2}+12 \sqrt{c \,x^{2}+d}\, b \,c^{\frac{3}{2}} d \,x^{2}+2 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \sqrt{c}\, d \,x^{2}+8 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b \,c^{\frac{3}{2}} x^{2}-8 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b \sqrt{c}\right) x^{2}}{8 \left(c \,x^{2}+d \right)^{\frac{3}{2}} \sqrt{c}\, d}"," ",0,"1/8*((c*x^2+d)/x^2)^(3/2)*x^2*(8*c^(3/2)*(c*x^2+d)^(3/2)*x^2*b+12*c^(3/2)*(c*x^2+d)^(1/2)*x^2*b*d+2*c^(1/2)*(c*x^2+d)^(3/2)*x^2*a*d-8*c^(1/2)*(c*x^2+d)^(5/2)*b+3*c^(1/2)*(c*x^2+d)^(1/2)*x^2*a*d^2+3*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*x*a*d^3+12*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*x*b*c*d^2)/(c*x^2+d)^(3/2)/d/c^(1/2)","A"
947,1,216,90,0.063000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)*x,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(9 a c \,d^{3} x^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+6 b \,c^{2} d^{2} x^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+9 \sqrt{c \,x^{2}+d}\, a \,c^{\frac{3}{2}} d^{2} x^{4}+6 \sqrt{c \,x^{2}+d}\, b \,c^{\frac{5}{2}} d \,x^{4}+6 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \,c^{\frac{3}{2}} d \,x^{4}+4 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b \,c^{\frac{5}{2}} x^{4}-6 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a \sqrt{c}\, d \,x^{2}-4 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b \,c^{\frac{3}{2}} x^{2}-2 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b \sqrt{c}\, d \right)}{6 \left(c \,x^{2}+d \right)^{\frac{3}{2}} \sqrt{c}\, d^{2}}"," ",0,"1/6*((c*x^2+d)/x^2)^(3/2)*(4*c^(5/2)*(c*x^2+d)^(3/2)*x^4*b+6*c^(5/2)*(c*x^2+d)^(1/2)*x^4*b*d+6*c^(3/2)*(c*x^2+d)^(3/2)*x^4*a*d-4*c^(3/2)*(c*x^2+d)^(5/2)*x^2*b+9*c^(3/2)*(c*x^2+d)^(1/2)*x^4*a*d^2-6*c^(1/2)*(c*x^2+d)^(5/2)*x^2*a*d+9*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*x^3*a*c*d^3+6*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*x^3*b*c^2*d^2-2*c^(1/2)*(c*x^2+d)^(5/2)*b*d)/(c*x^2+d)^(3/2)/d^2/c^(1/2)","B"
948,1,153,60,0.066000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)/x,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(15 a \,c^{2} d^{2} x^{5} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+15 \sqrt{c \,x^{2}+d}\, a \,c^{\frac{5}{2}} d \,x^{6}+10 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \,c^{\frac{5}{2}} x^{6}-10 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a \,c^{\frac{3}{2}} x^{4}-5 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a \sqrt{c}\, d \,x^{2}-3 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b \sqrt{c}\, d \right)}{15 \left(c \,x^{2}+d \right)^{\frac{3}{2}} \sqrt{c}\, d^{2} x^{2}}"," ",0,"1/15*((c*x^2+d)/x^2)^(3/2)*(10*c^(5/2)*(c*x^2+d)^(3/2)*x^6*a+15*c^(5/2)*(c*x^2+d)^(1/2)*x^6*a*d-10*c^(3/2)*(c*x^2+d)^(5/2)*x^4*a+15*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*x^5*a*c^2*d^2-5*(c*x^2+d)^(5/2)*a*c^(1/2)*d*x^2-3*(c*x^2+d)^(5/2)*b*c^(1/2)*d)/x^2/(c*x^2+d)^(3/2)/d^2/c^(1/2)","B"
949,1,48,38,0.049000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)/x^3,x)","-\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(7 a d \,x^{2}-2 b c \,x^{2}+5 b d \right) \left(c \,x^{2}+d \right)}{35 d^{2} x^{4}}"," ",0,"-1/35*((c*x^2+d)/x^2)^(3/2)*(7*a*d*x^2-2*b*c*x^2+5*b*d)*(c*x^2+d)/d^2/x^4","A"
950,1,70,62,0.049000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)/x^5,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(18 a c d \,x^{4}-8 b \,c^{2} x^{4}-45 a \,d^{2} x^{2}+20 b c d \,x^{2}-35 b \,d^{2}\right) \left(c \,x^{2}+d \right)}{315 d^{3} x^{6}}"," ",0,"1/315*((c*x^2+d)/x^2)^(3/2)*(18*a*c*d*x^4-8*b*c^2*x^4-45*a*d^2*x^2+20*b*c*d*x^2-35*b*d^2)*(c*x^2+d)/d^3/x^6","A"
951,1,94,88,0.053000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)/x^7,x)","-\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(88 a \,c^{2} d \,x^{6}-48 b \,c^{3} x^{6}-220 a c \,d^{2} x^{4}+120 b \,c^{2} d \,x^{4}+385 a \,d^{3} x^{2}-210 b c \,d^{2} x^{2}+315 b \,d^{3}\right) \left(c \,x^{2}+d \right)}{3465 d^{4} x^{8}}"," ",0,"-1/3465*((c*x^2+d)/x^2)^(3/2)*(88*a*c^2*d*x^6-48*b*c^3*x^6-220*a*c*d^2*x^4+120*b*c^2*d*x^4+385*a*d^3*x^2-210*b*c*d^2*x^2+315*b*d^3)*(c*x^2+d)/d^4/x^8","A"
952,1,118,114,0.052000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)/x^9,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(208 a \,c^{3} d \,x^{8}-128 b \,c^{4} x^{8}-520 a \,c^{2} d^{2} x^{6}+320 b \,c^{3} d \,x^{6}+910 a c \,d^{3} x^{4}-560 b \,c^{2} d^{2} x^{4}-1365 a \,d^{4} x^{2}+840 b c \,d^{3} x^{2}-1155 b \,d^{4}\right) \left(c \,x^{2}+d \right)}{15015 d^{5} x^{10}}"," ",0,"1/15015*((c*x^2+d)/x^2)^(3/2)*(208*a*c^3*d*x^8-128*b*c^4*x^8-520*a*c^2*d^2*x^6+320*b*c^3*d*x^6+910*a*c*d^3*x^4-560*b*c^2*d^2*x^4-1365*a*d^4*x^2+840*b*c*d^3*x^2-1155*b*d^4)*(c*x^2+d)/d^5/x^10","A"
953,1,115,130,0.049000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)*x^12,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(1155 a \,x^{8} c^{4}-840 a \,c^{3} d \,x^{6}+1365 b \,c^{4} x^{6}+560 a \,c^{2} d^{2} x^{4}-910 b \,c^{3} d \,x^{4}-320 a c \,d^{3} x^{2}+520 b \,c^{2} d^{2} x^{2}+128 a \,d^{4}-208 b c \,d^{3}\right) \left(c \,x^{2}+d \right) x^{3}}{15015 c^{5}}"," ",0,"1/15015*((c*x^2+d)/x^2)^(3/2)*x^3*(1155*a*c^4*x^8-840*a*c^3*d*x^6+1365*b*c^4*x^6+560*a*c^2*d^2*x^4-910*b*c^3*d*x^4-320*a*c*d^3*x^2+520*b*c^2*d^2*x^2+128*a*d^4-208*b*c*d^3)*(c*x^2+d)/c^5","A"
954,1,91,101,0.051000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)*x^10,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(315 a \,x^{6} c^{3}-210 a \,c^{2} d \,x^{4}+385 b \,c^{3} x^{4}+120 a c \,d^{2} x^{2}-220 b \,c^{2} d \,x^{2}-48 a \,d^{3}+88 b c \,d^{2}\right) \left(c \,x^{2}+d \right) x^{3}}{3465 c^{4}}"," ",0,"1/3465*((c*x^2+d)/x^2)^(3/2)*x^3*(315*a*c^3*x^6-210*a*c^2*d*x^4+385*b*c^3*x^4+120*a*c*d^2*x^2-220*b*c^2*d*x^2-48*a*d^3+88*b*c*d^2)*(c*x^2+d)/c^4","A"
955,1,67,72,0.055000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)*x^8,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(35 a \,x^{4} c^{2}-20 a c d \,x^{2}+45 b \,c^{2} x^{2}+8 a \,d^{2}-18 b c d \right) \left(c \,x^{2}+d \right) x^{3}}{315 c^{3}}"," ",0,"1/315*((c*x^2+d)/x^2)^(3/2)*x^3*(35*a*c^2*x^4-20*a*c*d*x^2+45*b*c^2*x^2+8*a*d^2-18*b*c*d)*(c*x^2+d)/c^3","A"
956,1,45,45,0.044000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)*x^6,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(5 a \,x^{2} c -2 a d +7 b c \right) \left(c \,x^{2}+d \right) x^{3}}{35 c^{2}}"," ",0,"1/35*((c*x^2+d)/x^2)^(3/2)*x^3*(5*a*c*x^2-2*a*d+7*b*c)*(c*x^2+d)/c^2","A"
957,1,99,70,0.059000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)*x^4,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(-15 b c \,d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+15 \sqrt{c \,x^{2}+d}\, b c d +5 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b c +3 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a \right) x^{3}}{15 \left(c \,x^{2}+d \right)^{\frac{3}{2}} c}"," ",0,"1/15*((c*x^2+d)/x^2)^(3/2)*x^3*(3*a*(c*x^2+d)^(5/2)+5*(c*x^2+d)^(3/2)*b*c-15*d^(3/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*b*c+15*(c*x^2+d)^(1/2)*b*c*d)/(c*x^2+d)^(3/2)/c","A"
958,1,170,101,0.061000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)*x^2,x)","-\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(6 a \,d^{\frac{5}{2}} x^{2} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+9 b c \,d^{\frac{3}{2}} x^{2} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-6 \sqrt{c \,x^{2}+d}\, a \,d^{2} x^{2}-9 \sqrt{c \,x^{2}+d}\, b c d \,x^{2}-2 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a d \,x^{2}-3 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b c \,x^{2}+3 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b \right) x}{6 \left(c \,x^{2}+d \right)^{\frac{3}{2}} d}"," ",0,"-1/6*((c*x^2+d)/x^2)^(3/2)*x*(-2*(c*x^2+d)^(3/2)*a*d*x^2-3*(c*x^2+d)^(3/2)*b*c*x^2+6*d^(5/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^2*a+9*d^(3/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^2*b*c+3*(c*x^2+d)^(5/2)*b-6*(c*x^2+d)^(1/2)*x^2*a*d^2-9*(c*x^2+d)^(1/2)*x^2*b*c*d)/(c*x^2+d)^(3/2)/d","A"
959,1,213,94,0.058000," ","int((a+b/x^2)*(c+d/x^2)^(3/2),x)","-\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(12 a c \,d^{\frac{5}{2}} x^{4} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+3 b \,c^{2} d^{\frac{3}{2}} x^{4} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-12 \sqrt{c \,x^{2}+d}\, a c \,d^{2} x^{4}-3 \sqrt{c \,x^{2}+d}\, b \,c^{2} d \,x^{4}-4 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a c d \,x^{4}-\left(c \,x^{2}+d \right)^{\frac{3}{2}} b \,c^{2} x^{4}+4 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a d \,x^{2}+\left(c \,x^{2}+d \right)^{\frac{5}{2}} b c \,x^{2}+2 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b d \right)}{8 \left(c \,x^{2}+d \right)^{\frac{3}{2}} d^{2} x}"," ",0,"-1/8*((c*x^2+d)/x^2)^(3/2)/x*(12*d^(5/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^4*a*c+3*d^(3/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^4*b*c^2-4*(c*x^2+d)^(3/2)*a*c*d*x^4-(c*x^2+d)^(3/2)*b*c^2*x^4+4*(c*x^2+d)^(5/2)*x^2*a*d+(c*x^2+d)^(5/2)*x^2*b*c-12*(c*x^2+d)^(1/2)*x^4*a*c*d^2-3*(c*x^2+d)^(1/2)*x^4*b*c^2*d+2*(c*x^2+d)^(5/2)*b*d)/(c*x^2+d)^(3/2)/d^2","B"
960,1,259,103,0.066000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)/x^2,x)","-\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(18 a \,c^{2} d^{\frac{5}{2}} x^{6} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-3 b \,c^{3} d^{\frac{3}{2}} x^{6} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-18 \sqrt{c \,x^{2}+d}\, a \,c^{2} d^{2} x^{6}+3 \sqrt{c \,x^{2}+d}\, b \,c^{3} d \,x^{6}-6 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \,c^{2} d \,x^{6}+\left(c \,x^{2}+d \right)^{\frac{3}{2}} b \,c^{3} x^{6}+6 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a c d \,x^{4}-\left(c \,x^{2}+d \right)^{\frac{5}{2}} b \,c^{2} x^{4}+12 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a \,d^{2} x^{2}-2 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b c d \,x^{2}+8 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b \,d^{2}\right)}{48 \left(c \,x^{2}+d \right)^{\frac{3}{2}} d^{3} x^{3}}"," ",0,"-1/48*((c*x^2+d)/x^2)^(3/2)/x^3*(18*d^(5/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^6*a*c^2-3*d^(3/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^6*b*c^3-6*(c*x^2+d)^(3/2)*x^6*a*c^2*d+(c*x^2+d)^(3/2)*x^6*b*c^3+6*(c*x^2+d)^(5/2)*x^4*a*c*d-(c*x^2+d)^(5/2)*x^4*b*c^2-18*(c*x^2+d)^(1/2)*x^6*a*c^2*d^2+3*(c*x^2+d)^(1/2)*x^6*b*c^3*d+12*(c*x^2+d)^(5/2)*x^2*a*d^2-2*(c*x^2+d)^(5/2)*x^2*b*c*d+8*(c*x^2+d)^(5/2)*b*d^2)/(c*x^2+d)^(3/2)/d^3","B"
961,1,302,135,0.073000," ","int((a+b/x^2)*(c+d/x^2)^(3/2)/x^4,x)","\frac{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} \left(24 a \,c^{3} d^{\frac{5}{2}} x^{8} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-9 b \,c^{4} d^{\frac{3}{2}} x^{8} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-24 \sqrt{c \,x^{2}+d}\, a \,c^{3} d^{2} x^{8}+9 \sqrt{c \,x^{2}+d}\, b \,c^{4} d \,x^{8}-8 \left(c \,x^{2}+d \right)^{\frac{3}{2}} a \,c^{3} d \,x^{8}+3 \left(c \,x^{2}+d \right)^{\frac{3}{2}} b \,c^{4} x^{8}+8 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a \,c^{2} d \,x^{6}-3 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b \,c^{3} x^{6}+16 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a c \,d^{2} x^{4}-6 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b \,c^{2} d \,x^{4}-64 \left(c \,x^{2}+d \right)^{\frac{5}{2}} a \,d^{3} x^{2}+24 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b c \,d^{2} x^{2}-48 \left(c \,x^{2}+d \right)^{\frac{5}{2}} b \,d^{3}\right)}{384 \left(c \,x^{2}+d \right)^{\frac{3}{2}} d^{4} x^{5}}"," ",0,"1/384*((c*x^2+d)/x^2)^(3/2)/x^5*(24*d^(5/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^8*a*c^3-9*d^(3/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^8*b*c^4-8*(c*x^2+d)^(3/2)*x^8*a*c^3*d+3*(c*x^2+d)^(3/2)*x^8*b*c^4+8*(c*x^2+d)^(5/2)*x^6*a*c^2*d-3*(c*x^2+d)^(5/2)*x^6*b*c^3-24*(c*x^2+d)^(1/2)*x^8*a*c^3*d^2+9*(c*x^2+d)^(1/2)*x^8*b*c^4*d+16*(c*x^2+d)^(5/2)*x^4*a*c*d^2-6*(c*x^2+d)^(5/2)*x^4*b*c^2*d-64*(c*x^2+d)^(5/2)*x^2*a*d^3+24*(c*x^2+d)^(5/2)*x^2*b*c*d^2-48*(c*x^2+d)^(5/2)*b*d^3)/(c*x^2+d)^(3/2)/d^4","B"
962,1,129,74,0.059000," ","int((a+b/x^2)*x^3/(c+d/x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+d}\, \left(2 \sqrt{c \,x^{2}+d}\, a \,c^{\frac{5}{2}} x^{3}+3 a c \,d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-4 b \,c^{2} d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-3 \sqrt{c \,x^{2}+d}\, a \,c^{\frac{3}{2}} d x +4 \sqrt{c \,x^{2}+d}\, b \,c^{\frac{5}{2}} x \right)}{8 \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, c^{\frac{7}{2}} x}"," ",0,"1/8*(c*x^2+d)^(1/2)*(2*(c*x^2+d)^(1/2)*c^(5/2)*x^3*a-3*(c*x^2+d)^(1/2)*c^(3/2)*x*a*d+4*(c*x^2+d)^(1/2)*c^(5/2)*x*b+3*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*a*c*d^2-4*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*b*c^2*d)/((c*x^2+d)/x^2)^(1/2)/x/c^(7/2)","A"
963,1,90,47,0.052000," ","int((a+b/x^2)*x/(c+d/x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+d}\, \left(-a c d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+2 b \,c^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+\sqrt{c \,x^{2}+d}\, a \,c^{\frac{3}{2}} x \right)}{2 \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, c^{\frac{5}{2}} x}"," ",0,"1/2*(c*x^2+d)^(1/2)*(c^(3/2)*(c*x^2+d)^(1/2)*x*a+2*b*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*c^2-ln(c^(1/2)*x+(c*x^2+d)^(1/2))*a*c*d)/((c*x^2+d)/x^2)^(1/2)/x/c^(5/2)","A"
964,1,70,35,0.054000," ","int((a+b/x^2)/x/(c+d/x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+d}\, \left(-a d x \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)+\sqrt{c \,x^{2}+d}\, b \sqrt{c}\right)}{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \sqrt{c}\, d \,x^{2}}"," ",0,"-(c*x^2+d)^(1/2)*(-a*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*d*x+b*(c*x^2+d)^(1/2)*c^(1/2))/((c*x^2+d)/x^2)^(1/2)/x^2/c^(1/2)/d","A"
965,1,47,37,0.049000," ","int((a+b/x^2)/x^3/(c+d/x^2)^(1/2),x)","-\frac{\left(3 a d \,x^{2}-2 b c \,x^{2}+b d \right) \left(c \,x^{2}+d \right)}{3 \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, d^{2} x^{4}}"," ",0,"-1/3*(3*a*d*x^2-2*b*c*x^2+b*d)*(c*x^2+d)/((c*x^2+d)/x^2)^(1/2)/d^2/x^4","A"
966,1,70,62,0.047000," ","int((a+b/x^2)/x^5/(c+d/x^2)^(1/2),x)","\frac{\left(10 a c d \,x^{4}-8 b \,c^{2} x^{4}-5 a \,d^{2} x^{2}+4 b c d \,x^{2}-3 b \,d^{2}\right) \left(c \,x^{2}+d \right)}{15 \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, d^{3} x^{6}}"," ",0,"1/15*(10*a*c*d*x^4-8*b*c^2*x^4-5*a*d^2*x^2+4*b*c*d*x^2-3*b*d^2)*(c*x^2+d)/((c*x^2+d)/x^2)^(1/2)/d^3/x^6","A"
967,1,94,87,0.047000," ","int((a+b/x^2)/x^7/(c+d/x^2)^(1/2),x)","-\frac{\left(56 a \,c^{2} d \,x^{6}-48 b \,c^{3} x^{6}-28 a c \,d^{2} x^{4}+24 b \,c^{2} d \,x^{4}+21 a \,d^{3} x^{2}-18 b c \,d^{2} x^{2}+15 b \,d^{3}\right) \left(c \,x^{2}+d \right)}{105 \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, d^{4} x^{8}}"," ",0,"-1/105*(56*a*c^2*d*x^6-48*b*c^3*x^6-28*a*c*d^2*x^4+24*b*c^2*d*x^4+21*a*d^3*x^2-18*b*c*d^2*x^2+15*b*d^3)*(c*x^2+d)/((c*x^2+d)/x^2)^(1/2)/d^4/x^8","A"
968,1,67,70,0.052000," ","int((a+b/x^2)*x^4/(c+d/x^2)^(1/2),x)","\frac{\left(3 a \,x^{4} c^{2}-4 a c d \,x^{2}+5 b \,c^{2} x^{2}+8 a \,d^{2}-10 b c d \right) \left(c \,x^{2}+d \right)}{15 \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, c^{3} x}"," ",0,"1/15/x*(3*a*c^2*x^4-4*a*c*d*x^2+5*b*c^2*x^2+8*a*d^2-10*b*c*d)*(c*x^2+d)/((c*x^2+d)/x^2)^(1/2)/c^3","A"
969,1,44,43,0.044000," ","int((a+b/x^2)*x^2/(c+d/x^2)^(1/2),x)","\frac{\left(a \,x^{2} c -2 a d +3 b c \right) \left(c \,x^{2}+d \right)}{3 \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, c^{2} x}"," ",0,"1/3/x*(a*c*x^2-2*a*d+3*b*c)*(c*x^2+d)/((c*x^2+d)/x^2)^(1/2)/c^2","A"
970,1,73,39,0.051000," ","int((a+b/x^2)/(c+d/x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+d}\, \left(-b c \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+\sqrt{c \,x^{2}+d}\, a \sqrt{d}\right)}{\sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, c \sqrt{d}\, x}"," ",0,"(c*x^2+d)^(1/2)*(a*(c*x^2+d)^(1/2)*d^(1/2)-b*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*c)/((c*x^2+d)/x^2)^(1/2)/x/c/d^(1/2)","A"
971,1,105,49,0.057000," ","int((a+b/x^2)/x^2/(c+d/x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+d}\, \left(2 a \,d^{2} x^{2} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-b c d \,x^{2} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+\sqrt{c \,x^{2}+d}\, b \,d^{\frac{3}{2}}\right)}{2 \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, d^{\frac{5}{2}} x^{3}}"," ",0,"-1/2*(c*x^2+d)^(1/2)*(2*a*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^2*d^2-ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^2*b*c*d+(c*x^2+d)^(1/2)*d^(3/2)*b)/((c*x^2+d)/x^2)^(1/2)/x^3/d^(5/2)","B"
972,1,146,77,0.063000," ","int((a+b/x^2)/x^4/(c+d/x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+d}\, \left(-4 a c \,d^{2} x^{4} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+3 b \,c^{2} d \,x^{4} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+4 \sqrt{c \,x^{2}+d}\, a \,d^{\frac{5}{2}} x^{2}-3 \sqrt{c \,x^{2}+d}\, b c \,d^{\frac{3}{2}} x^{2}+2 \sqrt{c \,x^{2}+d}\, b \,d^{\frac{5}{2}}\right)}{8 \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, d^{\frac{7}{2}} x^{5}}"," ",0,"-1/8*(c*x^2+d)^(1/2)*(-4*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^4*a*c*d^2+3*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^4*b*c^2*d+4*(c*x^2+d)^(1/2)*d^(5/2)*x^2*a-3*(c*x^2+d)^(1/2)*d^(3/2)*x^2*b*c+2*(c*x^2+d)^(1/2)*d^(5/2)*b)/((c*x^2+d)/x^2)^(1/2)/x^5/d^(7/2)","A"
973,1,140,98,0.060000," ","int((a+b/x^2)*x^3/(c+d/x^2)^(3/2),x)","\frac{\left(c \,x^{2}+d \right) \left(2 a \,c^{\frac{7}{2}} x^{5}-5 a \,c^{\frac{5}{2}} d \,x^{3}+4 b \,c^{\frac{7}{2}} x^{3}-15 a \,c^{\frac{3}{2}} d^{2} x +12 b \,c^{\frac{5}{2}} d x +15 \sqrt{c \,x^{2}+d}\, a c \,d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-12 \sqrt{c \,x^{2}+d}\, b \,c^{2} d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)\right)}{8 \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} c^{\frac{9}{2}} x^{3}}"," ",0,"1/8*(c*x^2+d)*(2*c^(7/2)*x^5*a-5*c^(5/2)*x^3*a*d+4*c^(7/2)*x^3*b-15*c^(3/2)*x*a*d^2+12*c^(5/2)*x*b*d+15*(c*x^2+d)^(1/2)*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*a*c*d^2-12*(c*x^2+d)^(1/2)*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*b*c^2*d)/((c*x^2+d)/x^2)^(3/2)/x^3/c^(9/2)","A"
974,1,115,70,0.058000," ","int((a+b/x^2)*x/(c+d/x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+d \right) \left(-a \,c^{\frac{5}{2}} x^{3}-3 a \,c^{\frac{3}{2}} d x +2 b \,c^{\frac{5}{2}} x +3 \sqrt{c \,x^{2}+d}\, a c d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)-2 \sqrt{c \,x^{2}+d}\, b \,c^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)\right)}{2 \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} c^{\frac{7}{2}} x^{3}}"," ",0,"-1/2*(c*x^2+d)*(-c^(5/2)*x^3*a-3*c^(3/2)*x*a*d+2*c^(5/2)*x*b+3*(c*x^2+d)^(1/2)*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*a*c*d-2*(c*x^2+d)^(1/2)*ln(c^(1/2)*x+(c*x^2+d)^(1/2))*b*c^2)/((c*x^2+d)/x^2)^(3/2)/x^3/c^(7/2)","A"
975,1,75,44,0.058000," ","int((a+b/x^2)/(c+d/x^2)^(3/2)/x,x)","\frac{\left(c \,x^{2}+d \right) \left(-a \,c^{\frac{3}{2}} d x +b \,c^{\frac{5}{2}} x +\sqrt{c \,x^{2}+d}\, a c d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+d}\right)\right)}{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} c^{\frac{5}{2}} d \,x^{3}}"," ",0,"(c*x^2+d)*(-a*c^(3/2)*d*x+b*c^(5/2)*x+(c*x^2+d)^(1/2)*a*c*d*ln(c^(1/2)*x+(c*x^2+d)^(1/2)))/((c*x^2+d)/x^2)^(3/2)/x^3/c^(5/2)/d","A"
976,1,46,37,0.052000," ","int((a+b/x^2)/(c+d/x^2)^(3/2)/x^3,x)","\frac{\left(a d \,x^{2}-2 b c \,x^{2}-b d \right) \left(c \,x^{2}+d \right)}{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} d^{2} x^{4}}"," ",0,"(a*d*x^2-2*b*c*x^2-b*d)*(c*x^2+d)/((c*x^2+d)/x^2)^(3/2)/d^2/x^4","A"
977,1,69,60,0.050000," ","int((a+b/x^2)/(c+d/x^2)^(3/2)/x^5,x)","-\frac{\left(6 a c d \,x^{4}-8 b \,c^{2} x^{4}+3 a \,d^{2} x^{2}-4 b c d \,x^{2}+b \,d^{2}\right) \left(c \,x^{2}+d \right)}{3 \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} d^{3} x^{6}}"," ",0,"-1/3*(6*a*c*d*x^4-8*b*c^2*x^4+3*a*d^2*x^2-4*b*c*d*x^2+b*d^2)*(c*x^2+d)/((c*x^2+d)/x^2)^(3/2)/d^3/x^6","A"
978,1,94,88,0.053000," ","int((a+b/x^2)/(c+d/x^2)^(3/2)/x^7,x)","\frac{\left(40 a \,c^{2} d \,x^{6}-48 b \,c^{3} x^{6}+20 a c \,d^{2} x^{4}-24 b \,c^{2} d \,x^{4}-5 a \,d^{3} x^{2}+6 b c \,d^{2} x^{2}-3 b \,d^{3}\right) \left(c \,x^{2}+d \right)}{15 \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} d^{4} x^{8}}"," ",0,"1/15*(40*a*c^2*d*x^6-48*b*c^3*x^6+20*a*c*d^2*x^4-24*b*c^2*d*x^4-5*a*d^3*x^2+6*b*c*d^2*x^2-3*b*d^3)*(c*x^2+d)/((c*x^2+d)/x^2)^(3/2)/d^4/x^8","A"
979,1,118,112,0.054000," ","int((a+b/x^2)/(c+d/x^2)^(3/2)/x^9,x)","-\frac{\left(112 a \,c^{3} d \,x^{8}-128 b \,c^{4} x^{8}+56 a \,c^{2} d^{2} x^{6}-64 b \,c^{3} d \,x^{6}-14 a c \,d^{3} x^{4}+16 b \,c^{2} d^{2} x^{4}+7 a \,d^{4} x^{2}-8 b c \,d^{3} x^{2}+5 b \,d^{4}\right) \left(c \,x^{2}+d \right)}{35 \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} d^{5} x^{10}}"," ",0,"-1/35*(112*a*c^3*d*x^8-128*b*c^4*x^8+56*a*c^2*d^2*x^6-64*b*c^3*d*x^6-14*a*c*d^3*x^4+16*b*c^2*d^2*x^4+7*a*d^4*x^2-8*b*c*d^3*x^2+5*b*d^4)*(c*x^2+d)/((c*x^2+d)/x^2)^(3/2)/d^5/x^10","A"
980,1,91,95,0.055000," ","int((a+b/x^2)*x^4/(c+d/x^2)^(3/2),x)","\frac{\left(3 a \,x^{6} c^{3}-6 a \,c^{2} d \,x^{4}+5 b \,c^{3} x^{4}+24 a c \,d^{2} x^{2}-20 b \,c^{2} d \,x^{2}+48 a \,d^{3}-40 b c \,d^{2}\right) \left(c \,x^{2}+d \right)}{15 \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} c^{4} x^{3}}"," ",0,"1/15*(3*a*c^3*x^6-6*a*c^2*d*x^4+5*b*c^3*x^4+24*a*c*d^2*x^2-20*b*c^2*d*x^2+48*a*d^3-40*b*c*d^2)*(c*x^2+d)/((c*x^2+d)/x^2)^(3/2)/x^3/c^4","A"
981,1,66,67,0.061000," ","int((a+b/x^2)*x^2/(c+d/x^2)^(3/2),x)","\frac{\left(a \,x^{4} c^{2}-4 a c d \,x^{2}+3 b \,c^{2} x^{2}-8 a \,d^{2}+6 b c d \right) \left(c \,x^{2}+d \right)}{3 \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} c^{3} x^{3}}"," ",0,"1/3*(a*c^2*x^4-4*a*c*d*x^2+3*b*c^2*x^2-8*a*d^2+6*b*c*d)*(c*x^2+d)/((c*x^2+d)/x^2)^(3/2)/c^3/x^3","A"
982,1,43,41,0.044000," ","int((a+b/x^2)/(c+d/x^2)^(3/2),x)","\frac{\left(a \,x^{2} c +2 a d -b c \right) \left(c \,x^{2}+d \right)}{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} c^{2} x^{3}}"," ",0,"(a*c*x^2+2*a*d-b*c)*(c*x^2+d)/((c*x^2+d)/x^2)^(3/2)/x^3/c^2","A"
983,1,79,51,0.059000," ","int((a+b/x^2)/(c+d/x^2)^(3/2)/x^2,x)","-\frac{\left(c \,x^{2}+d \right) \left(\sqrt{c \,x^{2}+d}\, b c d \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+a \,d^{\frac{5}{2}}-b c \,d^{\frac{3}{2}}\right)}{\left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} c \,d^{\frac{5}{2}} x^{3}}"," ",0,"-(c*x^2+d)*((c*x^2+d)^(1/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*b*c*d+a*d^(5/2)-d^(3/2)*b*c)/((c*x^2+d)/x^2)^(3/2)/x^3/c/d^(5/2)","A"
984,1,132,76,0.059000," ","int((a+b/x^2)/(c+d/x^2)^(3/2)/x^4,x)","\frac{\left(c \,x^{2}+d \right) \left(-2 \sqrt{c \,x^{2}+d}\, a \,d^{2} x^{2} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+3 \sqrt{c \,x^{2}+d}\, b c d \,x^{2} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)+2 a \,d^{\frac{5}{2}} x^{2}-3 b c \,d^{\frac{3}{2}} x^{2}-b \,d^{\frac{5}{2}}\right)}{2 \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} d^{\frac{7}{2}} x^{5}}"," ",0,"1/2*(c*x^2+d)*(2*d^(5/2)*x^2*a-3*d^(3/2)*x^2*b*c-2*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*(c*x^2+d)^(1/2)*x^2*a*d^2+3*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*(c*x^2+d)^(1/2)*x^2*b*c*d-d^(5/2)*b)/((c*x^2+d)/x^2)^(3/2)/x^5/d^(7/2)","A"
985,1,157,103,0.063000," ","int((a+b/x^2)/(c+d/x^2)^(3/2)/x^6,x)","\frac{\left(c \,x^{2}+d \right) \left(12 \sqrt{c \,x^{2}+d}\, a c \,d^{2} x^{4} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-15 \sqrt{c \,x^{2}+d}\, b \,c^{2} d \,x^{4} \ln \left(\frac{2 d +2 \sqrt{c \,x^{2}+d}\, \sqrt{d}}{x}\right)-12 a c \,d^{\frac{5}{2}} x^{4}+15 b \,c^{2} d^{\frac{3}{2}} x^{4}-4 a \,d^{\frac{7}{2}} x^{2}+5 b c \,d^{\frac{5}{2}} x^{2}-2 b \,d^{\frac{7}{2}}\right)}{8 \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} d^{\frac{9}{2}} x^{7}}"," ",0,"1/8*(c*x^2+d)*(12*(c*x^2+d)^(1/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^4*a*c*d^2-15*(c*x^2+d)^(1/2)*ln(2*(d+(c*x^2+d)^(1/2)*d^(1/2))/x)*x^4*b*c^2*d-12*d^(5/2)*x^4*a*c+15*d^(3/2)*x^4*b*c^2-4*d^(7/2)*x^2*a+5*d^(5/2)*x^2*b*c-2*d^(7/2)*b)/((c*x^2+d)/x^2)^(3/2)/x^7/d^(9/2)","A"
986,0,0,97,0.347000," ","int((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^m,x)","\int \left(e x \right)^{m} \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^m,x)","F"
987,0,0,78,0.190000," ","int((a+b/x^2)^p*(c+d/x^2)^q*x^4,x)","\int x^{4} \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q*x^4,x)","F"
988,0,0,98,0.178000," ","int((a+b/x^2)^p*(c+d/x^2)^q*x^3,x)","\int x^{3} \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q*x^3,x)","F"
989,0,0,78,0.179000," ","int((a+b/x^2)^p*(c+d/x^2)^q*x^2,x)","\int x^{2} \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q*x^2,x)","F"
990,0,0,96,0.186000," ","int((a+b/x^2)^p*(c+d/x^2)^q*x,x)","\int x \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q*x,x)","F"
991,0,0,75,0.043000," ","int((a+b/x^2)^p*(c+d/x^2)^q,x)","\int \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q,x)","F"
992,0,0,95,0.212000," ","int((a+b/x^2)^p*(c+d/x^2)^q/x,x)","\int \frac{\left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}}{x}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q/x,x)","F"
993,0,0,78,0.214000," ","int((a+b/x^2)^p*(c+d/x^2)^q/x^2,x)","\int \frac{\left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}}{x^{2}}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q/x^2,x)","F"
994,0,0,85,0.190000," ","int((a+b/x^2)^p*(c+d/x^2)^q/x^3,x)","\int \frac{\left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}}{x^{3}}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q/x^3,x)","F"
995,0,0,78,0.196000," ","int((a+b/x^2)^p*(c+d/x^2)^q/x^4,x)","\int \frac{\left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}}{x^{4}}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q/x^4,x)","F"
996,0,0,83,0.076000," ","int((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(5/2),x)","\int \left(e x \right)^{\frac{5}{2}} \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(5/2),x)","F"
997,0,0,83,0.078000," ","int((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(3/2),x)","\int \left(e x \right)^{\frac{3}{2}} \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(3/2),x)","F"
998,0,0,83,0.083000," ","int((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(1/2),x)","\int \sqrt{e x}\, \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(1/2),x)","F"
999,0,0,83,0.076000," ","int((a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(1/2),x)","\int \frac{\left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}}{\sqrt{e x}}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(1/2),x)","F"
1000,0,0,83,0.076000," ","int((a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(3/2),x)","\int \frac{\left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}}{\left(e x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(3/2),x)","F"
1001,0,0,83,0.082000," ","int((a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(5/2),x)","\int \frac{\left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}}{\left(e x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(5/2),x)","F"
1002,1,75,83,0.054000," ","int(x^(5/2)*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2),x)","-\frac{\sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(-48 \sqrt{x -1}\, x^{\frac{7}{2}}+8 \sqrt{x -1}\, x^{\frac{5}{2}}+10 \sqrt{x -1}\, x^{\frac{3}{2}}+15 \ln \left(\sqrt{x}+\sqrt{x -1}\right)+15 \sqrt{x -1}\, \sqrt{x}\right)}{192 \sqrt{x -1}}"," ",0,"-1/192*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(-48*x^(7/2)*(x-1)^(1/2)+8*x^(5/2)*(x-1)^(1/2)+10*x^(3/2)*(x-1)^(1/2)+15*(x-1)^(1/2)*x^(1/2)+15*ln(x^(1/2)+(x-1)^(1/2)))/(x-1)^(1/2)","A"
1003,1,65,64,0.049000," ","int(x^(3/2)*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2),x)","-\frac{\sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(-8 \sqrt{x -1}\, x^{\frac{5}{2}}+2 \sqrt{x -1}\, x^{\frac{3}{2}}+3 \ln \left(\sqrt{x}+\sqrt{x -1}\right)+3 \sqrt{x -1}\, \sqrt{x}\right)}{24 \sqrt{x -1}}"," ",0,"-1/24*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(-8*(x-1)^(1/2)*x^(5/2)+2*(x-1)^(1/2)*x^(3/2)+3*(x-1)^(1/2)*x^(1/2)+3*ln(x^(1/2)+(x-1)^(1/2)))/(x-1)^(1/2)","A"
1004,1,52,45,0.047000," ","int(x^(1/2)*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2),x)","-\frac{\sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(-2 \sqrt{x -1}\, x^{\frac{3}{2}}+\ln \left(\sqrt{x}+\sqrt{x -1}\right)+\sqrt{x -1}\, \sqrt{x}\right)}{4 \sqrt{x -1}}"," ",0,"-1/4*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(-2*(x-1)^(1/2)*x^(3/2)+(x-1)^(1/2)*x^(1/2)+ln(x^(1/2)+(x-1)^(1/2)))/(x-1)^(1/2)","A"
1005,1,72,25,0.050000," ","int((x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)/x^(1/2),x)","-\frac{\sqrt{\left(\sqrt{x}-1\right) \left(\sqrt{x}+1\right)}\, \ln \left(\sqrt{x}+\sqrt{x -1}\right)}{\sqrt{\sqrt{x}+1}\, \sqrt{\sqrt{x}-1}}+\sqrt{\sqrt{x}-1}\, \left(\sqrt{x}+1\right)^{\frac{3}{2}}-\sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}"," ",0,"(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(3/2)-(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)-((x^(1/2)-1)*(x^(1/2)+1))^(1/2)/(x^(1/2)+1)^(1/2)/(x^(1/2)-1)^(1/2)*ln(x^(1/2)+(x-1)^(1/2))","B"
1006,1,47,45,0.054000," ","int((x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)/x^(3/2),x)","\frac{2 \sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(\sqrt{x}\, \ln \left(\sqrt{x}+\sqrt{x -1}\right)-\sqrt{x -1}\right)}{\sqrt{x -1}\, \sqrt{x}}"," ",0,"2*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(ln(x^(1/2)+(x-1)^(1/2))*x^(1/2)-(x-1)^(1/2))/(x-1)^(1/2)/x^(1/2)","A"
1007,1,23,19,0.052000," ","int((x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)/x^(5/2),x)","\frac{2 \sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(x -1\right)}{3 x^{\frac{3}{2}}}"," ",0,"2/3*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(x-1)/x^(3/2)","A"
1008,1,28,39,0.052000," ","int((x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)/x^(7/2),x)","\frac{2 \sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(x -1\right) \left(2 x +3\right)}{15 x^{\frac{5}{2}}}"," ",0,"2/15*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(x-1)*(2*x+3)/x^(5/2)","A"
1009,1,33,58,0.054000," ","int((x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)/x^(9/2),x)","\frac{2 \sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(x -1\right) \left(8 x^{2}+12 x +15\right)}{105 x^{\frac{7}{2}}}"," ",0,"2/105*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(x-1)*(8*x^2+12*x+15)/x^(7/2)","A"
1010,1,38,77,0.061000," ","int((x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)/x^(11/2),x)","\frac{2 \sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(x -1\right) \left(16 x^{3}+24 x^{2}+30 x +35\right)}{315 x^{\frac{9}{2}}}"," ",0,"2/315*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(x-1)*(16*x^3+24*x^2+30*x+35)/x^(9/2)","A"
1011,1,65,64,0.058000," ","int(x^(5/2)/(x^(1/2)-1)^(1/2)/(x^(1/2)+1)^(1/2),x)","\frac{\sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(8 \sqrt{x -1}\, x^{\frac{5}{2}}+10 \sqrt{x -1}\, x^{\frac{3}{2}}+15 \ln \left(\sqrt{x}+\sqrt{x -1}\right)+15 \sqrt{x -1}\, \sqrt{x}\right)}{24 \sqrt{x -1}}"," ",0,"1/24*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(8*(x-1)^(1/2)*x^(5/2)+10*(x-1)^(1/2)*x^(3/2)+15*(x-1)^(1/2)*x^(1/2)+15*ln(x^(1/2)+(x-1)^(1/2)))/(x-1)^(1/2)","A"
1012,1,55,45,0.063000," ","int(x^(3/2)/(x^(1/2)-1)^(1/2)/(x^(1/2)+1)^(1/2),x)","\frac{\sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(2 \sqrt{x -1}\, x^{\frac{3}{2}}+3 \ln \left(\sqrt{x}+\sqrt{x -1}\right)+3 \sqrt{x -1}\, \sqrt{x}\right)}{4 \sqrt{x -1}}"," ",0,"1/4*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(2*(x-1)^(1/2)*x^(3/2)+3*(x-1)^(1/2)*x^(1/2)+3*ln(x^(1/2)+(x-1)^(1/2)))/(x-1)^(1/2)","A"
1013,1,41,23,0.061000," ","int(x^(1/2)/(x^(1/2)-1)^(1/2)/(x^(1/2)+1)^(1/2),x)","\frac{\sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(\ln \left(\sqrt{x}+\sqrt{x -1}\right)+\sqrt{x -1}\, \sqrt{x}\right)}{\sqrt{x -1}}"," ",0,"(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*((x-1)^(1/2)*x^(1/2)+ln(x^(1/2)+(x-1)^(1/2)))/(x-1)^(1/2)","A"
1014,1,40,6,0.049000," ","int(1/x^(1/2)/(x^(1/2)-1)^(1/2)/(x^(1/2)+1)^(1/2),x)","\frac{2 \sqrt{\left(\sqrt{x}-1\right) \left(\sqrt{x}+1\right)}\, \ln \left(\sqrt{x}+\sqrt{x -1}\right)}{\sqrt{\sqrt{x}+1}\, \sqrt{\sqrt{x}-1}}"," ",0,"2*((x^(1/2)-1)*(x^(1/2)+1))^(1/2)/(x^(1/2)+1)^(1/2)/(x^(1/2)-1)^(1/2)*ln(x^(1/2)+(x-1)^(1/2))","B"
1015,1,20,19,0.056000," ","int(1/x^(3/2)/(x^(1/2)-1)^(1/2)/(x^(1/2)+1)^(1/2),x)","\frac{2 \sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}}{\sqrt{x}}"," ",0,"2*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)/x^(1/2)","A"
1016,1,25,39,0.058000," ","int(1/x^(5/2)/(x^(1/2)-1)^(1/2)/(x^(1/2)+1)^(1/2),x)","\frac{2 \sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(2 x +1\right)}{3 x^{\frac{3}{2}}}"," ",0,"2/3*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(2*x+1)/x^(3/2)","A"
1017,1,30,58,0.064000," ","int(1/x^(7/2)/(x^(1/2)-1)^(1/2)/(x^(1/2)+1)^(1/2),x)","\frac{2 \sqrt{\sqrt{x}-1}\, \sqrt{\sqrt{x}+1}\, \left(8 x^{2}+4 x +3\right)}{15 x^{\frac{5}{2}}}"," ",0,"2/15*(x^(1/2)-1)^(1/2)*(x^(1/2)+1)^(1/2)*(8*x^2+4*x+3)/x^(5/2)","A"
1018,0,0,74,0.993000," ","int(x^2*(b*x^n-a)^p*(b*x^n+a)^p,x)","\int x^{2} \left(b \,x^{n}+a \right)^{p} \left(b \,x^{n}-a \right)^{p}\, dx"," ",0,"int(x^2*(b*x^n-a)^p*(b*x^n+a)^p,x)","F"
1019,0,0,70,1.074000," ","int(x*(b*x^n-a)^p*(b*x^n+a)^p,x)","\int x \left(b \,x^{n}+a \right)^{p} \left(b \,x^{n}-a \right)^{p}\, dx"," ",0,"int(x*(b*x^n-a)^p*(b*x^n+a)^p,x)","F"
1020,0,0,71,0.953000," ","int((b*x^n-a)^p*(b*x^n+a)^p,x)","\int \left(b \,x^{n}+a \right)^{p} \left(b \,x^{n}-a \right)^{p}\, dx"," ",0,"int((b*x^n-a)^p*(b*x^n+a)^p,x)","F"
1021,0,0,72,1.758000," ","int((b*x^n-a)^p*(b*x^n+a)^p/x,x)","\int \frac{\left(b \,x^{n}+a \right)^{p} \left(b \,x^{n}-a \right)^{p}}{x}\, dx"," ",0,"int((b*x^n-a)^p*(b*x^n+a)^p/x,x)","F"
1022,0,0,74,1.006000," ","int((b*x^n-a)^p*(b*x^n+a)^p/x^2,x)","\int \frac{\left(b \,x^{n}+a \right)^{p} \left(b \,x^{n}-a \right)^{p}}{x^{2}}\, dx"," ",0,"int((b*x^n-a)^p*(b*x^n+a)^p/x^2,x)","F"
1023,1,36,13,0.052000," ","int((x^6+1)/x/(-x^6+1),x)","\ln \left(x \right)-\frac{\ln \left(x -1\right)}{3}-\frac{\ln \left(x +1\right)}{3}-\frac{\ln \left(x^{2}-x +1\right)}{3}-\frac{\ln \left(x^{2}+x +1\right)}{3}"," ",0,"-1/3*ln(x-1)-1/3*ln(x^2+x+1)-1/3*ln(x+1)+ln(x)-1/3*ln(x^2-x+1)","B"
1024,0,0,22,0.674000," ","int((e*x)^m*(b*x^n+a)^p*(a*(m+1)+b*(n*p+m+n+1)*x^n),x)","\int \left(\left(n p +m +n +1\right) b \,x^{n}+\left(m +1\right) a \right) \left(e x \right)^{m} \left(b \,x^{n}+a \right)^{p}\, dx"," ",0,"int((e*x)^m*(b*x^n+a)^p*(a*(m+1)+b*(n*p+m+n+1)*x^n),x)","F"
1025,0,0,118,1.018000," ","int((e*x)^m/(b*x^n+a)/(d*x^n+c),x)","\int \frac{\left(e x \right)^{m}}{\left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right)}\, dx"," ",0,"int((e*x)^m/(b*x^n+a)/(d*x^n+c),x)","F"
1026,0,0,89,0.938000," ","int(x^2/(b*x^n+a)/(d*x^n+c),x)","\int \frac{x^{2}}{\left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right)}\, dx"," ",0,"int(x^2/(b*x^n+a)/(d*x^n+c),x)","F"
1027,0,0,89,0.956000," ","int(x/(b*x^n+a)/(d*x^n+c),x)","\int \frac{x}{\left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right)}\, dx"," ",0,"int(x/(b*x^n+a)/(d*x^n+c),x)","F"
1028,0,0,76,0.042000," ","int(1/(b*x^n+a)/(d*x^n+c),x)","\int \frac{1}{\left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right)}\, dx"," ",0,"int(1/(b*x^n+a)/(d*x^n+c),x)","F"
1029,1,69,63,0.099000," ","int(1/x/(b*x^n+a)/(d*x^n+c),x)","\frac{b \ln \left(b \,x^{n}+a \right)}{\left(a d -b c \right) a n}-\frac{d \ln \left(d \,x^{n}+c \right)}{\left(a d -b c \right) c n}+\frac{\ln \left(x^{n}\right)}{a c n}"," ",0,"-1/n/c*d/(a*d-b*c)*ln(d*x^n+c)+1/n/a*b/(a*d-b*c)*ln(b*x^n+a)+1/n/c/a*ln(x^n)","A"
1030,0,0,88,1.021000," ","int(1/x^2/(b*x^n+a)/(d*x^n+c),x)","\int \frac{1}{\left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right) x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^n+a)/(d*x^n+c),x)","F"
1031,0,0,89,1.001000," ","int(1/x^3/(b*x^n+a)/(d*x^n+c),x)","\int \frac{1}{\left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right) x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^n+a)/(d*x^n+c),x)","F"
1032,0,0,179,1.016000," ","int((e*x)^m/(b*x^n+a)^2/(d*x^n+c),x)","\int \frac{\left(e x \right)^{m}}{\left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right)}\, dx"," ",0,"int((e*x)^m/(b*x^n+a)^2/(d*x^n+c),x)","F"
1033,0,0,142,0.970000," ","int(x^2/(b*x^n+a)^2/(d*x^n+c),x)","\int \frac{x^{2}}{\left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right)}\, dx"," ",0,"int(x^2/(b*x^n+a)^2/(d*x^n+c),x)","F"
1034,0,0,143,0.970000," ","int(x/(b*x^n+a)^2/(d*x^n+c),x)","\int \frac{x}{\left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right)}\, dx"," ",0,"int(x/(b*x^n+a)^2/(d*x^n+c),x)","F"
1035,0,0,126,0.050000," ","int(1/(b*x^n+a)^2/(d*x^n+c),x)","\int \frac{1}{\left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right)}\, dx"," ",0,"int(1/(b*x^n+a)^2/(d*x^n+c),x)","F"
1036,1,131,101,0.105000," ","int(1/x/(b*x^n+a)^2/(d*x^n+c),x)","\frac{2 b d \ln \left(b \,x^{n}+a \right)}{\left(a d -b c \right)^{2} a n}-\frac{b^{2} c \ln \left(b \,x^{n}+a \right)}{\left(a d -b c \right)^{2} a^{2} n}-\frac{d^{2} \ln \left(d \,x^{n}+c \right)}{\left(a d -b c \right)^{2} c n}-\frac{b}{\left(a d -b c \right) \left(b \,x^{n}+a \right) a n}+\frac{\ln \left(x^{n}\right)}{a^{2} c n}"," ",0,"-1/n/(a*d-b*c)^2/c*d^2*ln(d*x^n+c)-1/n/a*b/(a*d-b*c)/(b*x^n+a)+2/n*b/(a*d-b*c)^2/a*ln(b*x^n+a)*d-1/n*b^2/(a*d-b*c)^2/a^2*ln(b*x^n+a)*c+1/n/c/a^2*ln(x^n)","A"
1037,0,0,140,1.024000," ","int(1/x^2/(b*x^n+a)^2/(d*x^n+c),x)","\int \frac{1}{\left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right) x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^n+a)^2/(d*x^n+c),x)","F"
1038,0,0,139,1.289000," ","int(1/x^3/(b*x^n+a)^2/(d*x^n+c),x)","\int \frac{1}{\left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right) x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^n+a)^2/(d*x^n+c),x)","F"
1039,1,284,124,0.082000," ","int(x^(2*n-1)*(b*x^n+a)^3/(d*x^n+c),x)","-\frac{a^{3} c \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{2} n}+\frac{a^{3} {\mathrm e}^{n \ln \left(x \right)}}{d n}+\frac{3 a^{2} b \,c^{2} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{3} n}-\frac{3 a^{2} b c \,{\mathrm e}^{n \ln \left(x \right)}}{d^{2} n}+\frac{3 a^{2} b \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 d n}-\frac{3 a \,b^{2} c^{3} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{4} n}+\frac{3 a \,b^{2} c^{2} {\mathrm e}^{n \ln \left(x \right)}}{d^{3} n}-\frac{3 a \,b^{2} c \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 d^{2} n}+\frac{a \,b^{2} {\mathrm e}^{3 n \ln \left(x \right)}}{d n}+\frac{b^{3} c^{4} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{5} n}-\frac{b^{3} c^{3} {\mathrm e}^{n \ln \left(x \right)}}{d^{4} n}+\frac{b^{3} c^{2} {\mathrm e}^{2 n \ln \left(x \right)}}{2 d^{3} n}-\frac{b^{3} c \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 d^{2} n}+\frac{b^{3} {\mathrm e}^{4 n \ln \left(x \right)}}{4 d n}"," ",0,"1/d/n*exp(n*ln(x))*a^3-3/d^2/n*exp(n*ln(x))*a^2*b*c+3/d^3/n*exp(n*ln(x))*a*b^2*c^2-1/d^4/n*exp(n*ln(x))*b^3*c^3+1/4*b^3/d/n*exp(n*ln(x))^4+3/2*b/d/n*exp(n*ln(x))^2*a^2-3/2*b^2/d^2/n*exp(n*ln(x))^2*a*c+1/2*b^3/d^3/n*exp(n*ln(x))^2*c^2+b^2/d/n*exp(n*ln(x))^3*a-1/3*b^3/d^2/n*exp(n*ln(x))^3*c-c/d^2/n*ln(d*exp(n*ln(x))+c)*a^3+3*c^2/d^3/n*ln(d*exp(n*ln(x))+c)*a^2*b-3*c^3/d^4/n*ln(d*exp(n*ln(x))+c)*a*b^2+c^4/d^5/n*ln(d*exp(n*ln(x))+c)*b^3","B"
1040,1,173,86,0.077000," ","int(x^(2*n-1)*(b*x^n+a)^2/(d*x^n+c),x)","-\frac{a^{2} c \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{2} n}+\frac{a^{2} {\mathrm e}^{n \ln \left(x \right)}}{d n}+\frac{2 a b \,c^{2} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{3} n}-\frac{2 a b c \,{\mathrm e}^{n \ln \left(x \right)}}{d^{2} n}+\frac{a b \,{\mathrm e}^{2 n \ln \left(x \right)}}{d n}-\frac{b^{2} c^{3} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{4} n}+\frac{b^{2} c^{2} {\mathrm e}^{n \ln \left(x \right)}}{d^{3} n}-\frac{b^{2} c \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 d^{2} n}+\frac{b^{2} {\mathrm e}^{3 n \ln \left(x \right)}}{3 d n}"," ",0,"1/d/n*exp(n*ln(x))*a^2-2/d^2/n*exp(n*ln(x))*a*b*c+1/d^3/n*exp(n*ln(x))*b^2*c^2+1/3*b^2/d/n*exp(n*ln(x))^3+b/d/n*exp(n*ln(x))^2*a-1/2*b^2/d^2/n*exp(n*ln(x))^2*c-c/d^2/n*ln(d*exp(n*ln(x))+c)*a^2+2*c^2/d^3/n*ln(d*exp(n*ln(x))+c)*a*b-c^3/d^4/n*ln(d*exp(n*ln(x))+c)*b^2","A"
1041,1,87,58,0.071000," ","int(x^(2*n-1)*(b*x^n+a)/(d*x^n+c),x)","-\frac{a c \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{2} n}+\frac{a \,{\mathrm e}^{n \ln \left(x \right)}}{d n}+\frac{b \,c^{2} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{3} n}-\frac{b c \,{\mathrm e}^{n \ln \left(x \right)}}{d^{2} n}+\frac{b \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 d n}"," ",0,"1/d/n*exp(n*ln(x))*a-1/d^2/n*exp(n*ln(x))*b*c+1/2*b/d/n*exp(n*ln(x))^2-c/d^2/n*ln(d*exp(n*ln(x))+c)*a+c^2/d^3/n*ln(d*exp(n*ln(x))+c)*b","A"
1042,1,59,54,0.070000," ","int(x^(2*n-1)/(b*x^n+a)/(d*x^n+c),x)","\frac{a \ln \left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right)}{\left(a d -b c \right) b n}-\frac{c \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{\left(a d -b c \right) d n}"," ",0,"a/(a*d-b*c)/b/n*ln(b*exp(n*ln(x))+a)-c/d/n/(a*d-b*c)*ln(d*exp(n*ln(x))+c)","A"
1043,1,109,75,0.092000," ","int(x^(2*n-1)/(b*x^n+a)^2/(d*x^n+c),x)","\frac{c \ln \left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) n}-\frac{c \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) n}+\frac{{\mathrm e}^{n \ln \left(x \right)}}{\left(a d -b c \right) \left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right) n}"," ",0,"1/(a*d-b*c)/n*exp(n*ln(x))/(b*exp(n*ln(x))+a)+c/n/(a^2*d^2-2*a*b*c*d+b^2*c^2)*ln(b*exp(n*ln(x))+a)-c/n/(a^2*d^2-2*a*b*c*d+b^2*c^2)*ln(d*exp(n*ln(x))+c)","A"
1044,1,203,103,0.112000," ","int(x^(2*n-1)/(b*x^n+a)^3/(d*x^n+c),x)","\frac{c d \ln \left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right)}{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) n}-\frac{c d \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) n}+\frac{-\frac{b c \,{\mathrm e}^{n \ln \left(x \right)}}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) n}+\frac{\left(-a b d -b^{2} c \right) a}{2 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b^{2} n}}{\left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right)^{2}}"," ",0,"(-b*c/(a^2*d^2-2*a*b*c*d+b^2*c^2)/n*exp(n*ln(x))+1/2*a*(-a*b*d-b^2*c)/(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^2/n)/(b*exp(n*ln(x))+a)^2+c*d/n/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*ln(b*exp(n*ln(x))+a)-c*d/n/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*ln(d*exp(n*ln(x))+c)","A"
1045,1,342,150,0.070000," ","int(x^(3*n-1)*(b*x^n+a)^3/(d*x^n+c),x)","\frac{a^{3} c^{2} \ln \left(x^{n}+\frac{c}{d}\right)}{d^{3} n}-\frac{a^{3} c \,x^{n}}{d^{2} n}+\frac{a^{3} x^{2 n}}{2 d n}-\frac{3 a^{2} b \,c^{3} \ln \left(x^{n}+\frac{c}{d}\right)}{d^{4} n}+\frac{3 a^{2} b \,c^{2} x^{n}}{d^{3} n}-\frac{3 a^{2} b c \,x^{2 n}}{2 d^{2} n}+\frac{a^{2} b \,x^{3 n}}{d n}+\frac{3 a \,b^{2} c^{4} \ln \left(x^{n}+\frac{c}{d}\right)}{d^{5} n}-\frac{3 a \,b^{2} c^{3} x^{n}}{d^{4} n}+\frac{3 a \,b^{2} c^{2} x^{2 n}}{2 d^{3} n}-\frac{a \,b^{2} c \,x^{3 n}}{d^{2} n}+\frac{3 a \,b^{2} x^{4 n}}{4 d n}-\frac{b^{3} c^{5} \ln \left(x^{n}+\frac{c}{d}\right)}{d^{6} n}+\frac{b^{3} c^{4} x^{n}}{d^{5} n}-\frac{b^{3} c^{3} x^{2 n}}{2 d^{4} n}+\frac{b^{3} c^{2} x^{3 n}}{3 d^{3} n}-\frac{b^{3} c \,x^{4 n}}{4 d^{2} n}+\frac{b^{3} x^{5 n}}{5 d n}"," ",0,"1/5*b^3/d/n*(x^n)^5+3/4*b^2/d/n*(x^n)^4*a-1/4*b^3/d^2/n*(x^n)^4*c+b/d/n*(x^n)^3*a^2-b^2/d^2/n*(x^n)^3*a*c+1/3*b^3/d^3/n*(x^n)^3*c^2+1/2/d/n*(x^n)^2*a^3-3/2/d^2/n*(x^n)^2*a^2*b*c+3/2/d^3/n*(x^n)^2*a*b^2*c^2-1/2/d^4/n*(x^n)^2*b^3*c^3-c/d^2/n*x^n*a^3+3*c^2/d^3/n*x^n*a^2*b-3*c^3/d^4/n*x^n*a*b^2+c^4/d^5/n*x^n*b^3+c^2/d^3/n*ln(x^n+c/d)*a^3-3*c^3/d^4/n*ln(x^n+c/d)*a^2*b+3*c^4/d^5/n*ln(x^n+c/d)*a*b^2-c^5/d^6/n*ln(x^n+c/d)*b^3","B"
1046,1,236,112,0.072000," ","int(x^(3*n-1)*(b*x^n+a)^2/(d*x^n+c),x)","\frac{a^{2} c^{2} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{3} n}-\frac{a^{2} c \,{\mathrm e}^{n \ln \left(x \right)}}{d^{2} n}+\frac{a^{2} {\mathrm e}^{2 n \ln \left(x \right)}}{2 d n}-\frac{2 a b \,c^{3} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{4} n}+\frac{2 a b \,c^{2} {\mathrm e}^{n \ln \left(x \right)}}{d^{3} n}-\frac{a b c \,{\mathrm e}^{2 n \ln \left(x \right)}}{d^{2} n}+\frac{2 a b \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 d n}+\frac{b^{2} c^{4} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{5} n}-\frac{b^{2} c^{3} {\mathrm e}^{n \ln \left(x \right)}}{d^{4} n}+\frac{b^{2} c^{2} {\mathrm e}^{2 n \ln \left(x \right)}}{2 d^{3} n}-\frac{b^{2} c \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 d^{2} n}+\frac{b^{2} {\mathrm e}^{4 n \ln \left(x \right)}}{4 d n}"," ",0,"1/4*b^2/d/n*exp(n*ln(x))^4+1/2/d/n*exp(n*ln(x))^2*a^2-1/d^2/n*exp(n*ln(x))^2*a*b*c+1/2/d^3/n*exp(n*ln(x))^2*b^2*c^2+2/3*b/d/n*exp(n*ln(x))^3*a-1/3*b^2/d^2/n*exp(n*ln(x))^3*c-c/d^2/n*exp(n*ln(x))*a^2+2*c^2/d^3/n*exp(n*ln(x))*a*b-c^3/d^4/n*exp(n*ln(x))*b^2+c^2/d^3/n*ln(d*exp(n*ln(x))+c)*a^2-2*c^3/d^4/n*ln(d*exp(n*ln(x))+c)*a*b+c^4/d^5/n*ln(d*exp(n*ln(x))+c)*b^2","B"
1047,1,125,82,0.072000," ","int(x^(3*n-1)*(b*x^n+a)/(d*x^n+c),x)","\frac{a \,c^{2} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{3} n}-\frac{a c \,{\mathrm e}^{n \ln \left(x \right)}}{d^{2} n}+\frac{a \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 d n}-\frac{b \,c^{3} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{d^{4} n}+\frac{b \,c^{2} {\mathrm e}^{n \ln \left(x \right)}}{d^{3} n}-\frac{b c \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 d^{2} n}+\frac{b \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 d n}"," ",0,"1/3*b/d/n*exp(n*ln(x))^3+1/2/d/n*exp(n*ln(x))^2*a-1/2/d^2/n*exp(n*ln(x))^2*b*c-c/d^2/n*exp(n*ln(x))*a+c^2/d^3/n*exp(n*ln(x))*b+c^2/d^3/n*ln(d*exp(n*ln(x))+c)*a-c^3/d^4/n*ln(d*exp(n*ln(x))+c)*b","A"
1048,1,78,71,0.096000," ","int(x^(3*n-1)/(b*x^n+a)/(d*x^n+c),x)","-\frac{a^{2} \ln \left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right)}{\left(a d -b c \right) b^{2} n}+\frac{c^{2} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{\left(a d -b c \right) d^{2} n}+\frac{{\mathrm e}^{n \ln \left(x \right)}}{b d n}"," ",0,"1/b/d/n*exp(n*ln(x))+c^2/d^2/n/(a*d-b*c)*ln(d*exp(n*ln(x))+c)-a^2/(a*d-b*c)/b^2/n*ln(b*exp(n*ln(x))+a)","A"
1049,1,163,95,0.080000," ","int(x^(3*n-1)/(b*x^n+a)^2/(d*x^n+c),x)","\frac{a^{2} d \ln \left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b^{2} n}-\frac{2 a c \ln \left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b n}+\frac{c^{2} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d n}+\frac{a^{2}}{\left(a d -b c \right) \left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right) b^{2} n}"," ",0,"a^2/(a*d-b*c)/b^2/n/(b*exp(n*ln(x))+a)+c^2/d/n/(a^2*d^2-2*a*b*c*d+b^2*c^2)*ln(d*exp(n*ln(x))+c)+a^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^2/n*ln(b*exp(n*ln(x))+a)*d-2*a/(a^2*d^2-2*a*b*c*d+b^2*c^2)/b/n*ln(b*exp(n*ln(x))+a)*c","A"
1050,1,214,118,0.121000," ","int(x^(3*n-1)/(b*x^n+a)^3/(d*x^n+c),x)","-\frac{c^{2} \ln \left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right)}{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) n}+\frac{c^{2} \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) n}+\frac{\frac{\left(-a d +2 b c \right) a \,{\mathrm e}^{n \ln \left(x \right)}}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b n}+\frac{\left(-a d +3 b c \right) a^{2}}{2 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b^{2} n}}{\left(b \,{\mathrm e}^{n \ln \left(x \right)}+a \right)^{2}}"," ",0,"((-a*d+2*b*c)*a/n/b/(a^2*d^2-2*a*b*c*d+b^2*c^2)*exp(n*ln(x))+1/2*a^2*(-a*d+3*b*c)/(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^2/n)/(b*exp(n*ln(x))+a)^2+c^2/n/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*ln(d*exp(n*ln(x))+c)-c^2/n/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*ln(b*exp(n*ln(x))+a)","A"
1051,1,155,12,0.040000," ","int(x^13*(c*x+b)^13*(2*c*x+b),x)","\frac{1}{14} c^{14} x^{28}+b \,c^{13} x^{27}+\frac{13}{2} b^{2} c^{12} x^{26}+26 b^{3} c^{11} x^{25}+\frac{143}{2} b^{4} c^{10} x^{24}+143 b^{5} c^{9} x^{23}+\frac{429}{2} b^{6} c^{8} x^{22}+\frac{1716}{7} b^{7} c^{7} x^{21}+\frac{429}{2} b^{8} c^{6} x^{20}+143 b^{9} c^{5} x^{19}+\frac{143}{2} b^{10} c^{4} x^{18}+26 b^{11} c^{3} x^{17}+\frac{13}{2} b^{12} c^{2} x^{16}+b^{13} c \,x^{15}+\frac{1}{14} b^{14} x^{14}"," ",0,"1/14*c^14*x^28+b*c^13*x^27+13/2*b^2*c^12*x^26+26*b^3*c^11*x^25+143/2*b^4*c^10*x^24+143*b^5*c^9*x^23+429/2*b^6*c^8*x^22+1716/7*b^7*c^7*x^21+429/2*b^8*c^6*x^20+143*b^9*c^5*x^19+143/2*b^10*c^4*x^18+26*b^11*c^3*x^17+13/2*b^12*c^2*x^16+b^13*c*x^15+1/14*b^14*x^14","B"
1052,1,157,14,0.038000," ","int(x^27*(c*x^2+b)^13*(2*c*x^2+b),x)","\frac{1}{28} c^{14} x^{56}+\frac{1}{2} b \,c^{13} x^{54}+\frac{13}{4} b^{2} c^{12} x^{52}+13 b^{3} c^{11} x^{50}+\frac{143}{4} b^{4} c^{10} x^{48}+\frac{143}{2} b^{5} c^{9} x^{46}+\frac{429}{4} b^{6} c^{8} x^{44}+\frac{858}{7} b^{7} c^{7} x^{42}+\frac{429}{4} b^{8} c^{6} x^{40}+\frac{143}{2} b^{9} c^{5} x^{38}+\frac{143}{4} b^{10} c^{4} x^{36}+13 b^{11} c^{3} x^{34}+\frac{13}{4} b^{12} c^{2} x^{32}+\frac{1}{2} b^{13} c \,x^{30}+\frac{1}{28} b^{14} x^{28}"," ",0,"1/28*c^14*x^56+1/2*b*c^13*x^54+13/4*b^2*c^12*x^52+13*b^3*c^11*x^50+143/4*b^4*c^10*x^48+143/2*b^5*c^9*x^46+429/4*b^6*c^8*x^44+858/7*b^7*c^7*x^42+429/4*b^8*c^6*x^40+143/2*b^9*c^5*x^38+143/4*b^10*c^4*x^36+13*b^11*c^3*x^34+13/4*b^12*c^2*x^32+1/2*b^13*c*x^30+1/28*b^14*x^28","B"
1053,1,157,14,0.038000," ","int(x^41*(c*x^3+b)^13*(2*c*x^3+b),x)","\frac{1}{42} c^{14} x^{84}+\frac{1}{3} b \,c^{13} x^{81}+\frac{13}{6} b^{2} c^{12} x^{78}+\frac{26}{3} b^{3} c^{11} x^{75}+\frac{143}{6} b^{4} c^{10} x^{72}+\frac{143}{3} b^{5} c^{9} x^{69}+\frac{143}{2} b^{6} c^{8} x^{66}+\frac{572}{7} b^{7} c^{7} x^{63}+\frac{143}{2} b^{8} c^{6} x^{60}+\frac{143}{3} b^{9} c^{5} x^{57}+\frac{143}{6} b^{10} c^{4} x^{54}+\frac{26}{3} b^{11} c^{3} x^{51}+\frac{13}{6} b^{12} c^{2} x^{48}+\frac{1}{3} b^{13} c \,x^{45}+\frac{1}{42} b^{14} x^{42}"," ",0,"1/42*c^14*x^84+1/3*b*c^13*x^81+13/6*b^2*c^12*x^78+26/3*b^3*c^11*x^75+143/6*b^4*c^10*x^72+143/3*b^5*c^9*x^69+143/2*b^6*c^8*x^66+572/7*b^7*c^7*x^63+143/2*b^8*c^6*x^60+143/3*b^9*c^5*x^57+143/6*b^10*c^4*x^54+26/3*b^11*c^3*x^51+13/6*b^12*c^2*x^48+1/3*b^13*c*x^45+1/42*b^14*x^42","B"
1054,1,230,19,0.079000," ","int(x^(-1+14*n)*(b+c*x^n)^13*(b+2*c*x^n),x)","\frac{b^{14} x^{14 n}}{14 n}+\frac{b^{13} c \,x^{15 n}}{n}+\frac{13 b^{12} c^{2} x^{16 n}}{2 n}+\frac{26 b^{11} c^{3} x^{17 n}}{n}+\frac{143 b^{10} c^{4} x^{18 n}}{2 n}+\frac{143 b^{9} c^{5} x^{19 n}}{n}+\frac{429 b^{8} c^{6} x^{20 n}}{2 n}+\frac{1716 b^{7} c^{7} x^{21 n}}{7 n}+\frac{429 b^{6} c^{8} x^{22 n}}{2 n}+\frac{143 b^{5} c^{9} x^{23 n}}{n}+\frac{143 b^{4} c^{10} x^{24 n}}{2 n}+\frac{26 b^{3} c^{11} x^{25 n}}{n}+\frac{13 b^{2} c^{12} x^{26 n}}{2 n}+\frac{b \,c^{13} x^{27 n}}{n}+\frac{c^{14} x^{28 n}}{14 n}"," ",0,"1/14*c^14/n*(x^n)^28+b*c^13/n*(x^n)^27+13/2*b^2*c^12/n*(x^n)^26+26*b^3*c^11/n*(x^n)^25+143/2*b^4*c^10/n*(x^n)^24+143*b^5*c^9/n*(x^n)^23+429/2*b^6*c^8/n*(x^n)^22+1716/7*b^7*c^7/n*(x^n)^21+429/2*b^8*c^6/n*(x^n)^20+143*b^9*c^5/n*(x^n)^19+143/2*b^10*c^4/n*(x^n)^18+26*b^11*c^3/n*(x^n)^17+13/2*b^12*c^2/n*(x^n)^16+b^13*c/n*(x^n)^15+1/14*b^14/n*(x^n)^14","B"
1055,0,0,13,0.675000," ","int(x^(m-1)*(b*x^n+a)^(p-1)*(a*m+b*(n*p+m)*x^n),x)","\int \left(a m +\left(n p +m \right) b \,x^{n}\right) x^{m -1} \left(b \,x^{n}+a \right)^{p -1}\, dx"," ",0,"int(x^(m-1)*(b*x^n+a)^(p-1)*(a*m+b*(n*p+m)*x^n),x)","F"
1056,1,9,8,0.042000," ","int((2*c*x+b)/x/(c*x+b),x)","\ln \left(\left(c x +b \right) x \right)"," ",0,"ln(x*(c*x+b))","A"
1057,1,14,13,0.053000," ","int((2*c*x^2+b)/x/(c*x^2+b),x)","\ln \left(x \right)+\frac{\ln \left(c \,x^{2}+b \right)}{2}"," ",0,"ln(x)+1/2*ln(c*x^2+b)","A"
1058,1,14,13,0.048000," ","int((2*c*x^3+b)/x/(c*x^3+b),x)","\ln \left(x \right)+\frac{\ln \left(c \,x^{3}+b \right)}{3}"," ",0,"ln(x)+1/3*ln(c*x^3+b)","A"
1059,1,17,15,0.047000," ","int((b+2*c*x^n)/x/(b+c*x^n),x)","\frac{\ln \left(\left(c \,x^{n}+b \right) x^{n}\right)}{n}"," ",0,"1/n*ln(x^n*(b+c*x^n))","A"
1060,1,177,12,0.061000," ","int((2*c*x+b)/x^8/(c*x+b)^8,x)","\frac{c^{7}}{7 \left(c x +b \right)^{7} b^{7}}+\frac{c^{7}}{\left(c x +b \right)^{6} b^{8}}+\frac{4 c^{7}}{\left(c x +b \right)^{5} b^{9}}+\frac{12 c^{7}}{\left(c x +b \right)^{4} b^{10}}+\frac{30 c^{7}}{\left(c x +b \right)^{3} b^{11}}+\frac{66 c^{7}}{\left(c x +b \right)^{2} b^{12}}+\frac{132 c^{7}}{\left(c x +b \right) b^{13}}-\frac{132 c^{6}}{b^{13} x}+\frac{66 c^{5}}{b^{12} x^{2}}-\frac{30 c^{4}}{b^{11} x^{3}}+\frac{12 c^{3}}{b^{10} x^{4}}-\frac{4 c^{2}}{b^{9} x^{5}}+\frac{c}{b^{8} x^{6}}-\frac{1}{7 b^{7} x^{7}}"," ",0,"132/b^13*c^7/(c*x+b)+66/b^12*c^7/(c*x+b)^2+30/b^11*c^7/(c*x+b)^3+12/b^10*c^7/(c*x+b)^4+4/b^9*c^7/(c*x+b)^5+c^7/b^8/(c*x+b)^6+1/7*c^7/b^7/(c*x+b)^7-1/7/b^7/x^7-132/b^13*c^6/x+66/b^12*c^5/x^2-30/b^11*c^4/x^3+12/b^10*c^3/x^4-4/b^9*c^2/x^5+1/b^8*c/x^6","B"
1061,1,197,14,0.063000," ","int((2*c*x^2+b)/x^15/(c*x^2+b)^8,x)","-\frac{\left(-\frac{b^{6}}{7 \left(c \,x^{2}+b \right)^{7} c}-\frac{b^{5}}{\left(c \,x^{2}+b \right)^{6} c}-\frac{4 b^{4}}{\left(c \,x^{2}+b \right)^{5} c}-\frac{12 b^{3}}{\left(c \,x^{2}+b \right)^{4} c}-\frac{30 b^{2}}{\left(c \,x^{2}+b \right)^{3} c}-\frac{66 b}{\left(c \,x^{2}+b \right)^{2} c}-\frac{132}{\left(c \,x^{2}+b \right) c}\right) c^{8}}{2 b^{13}}-\frac{66 c^{6}}{b^{13} x^{2}}+\frac{33 c^{5}}{b^{12} x^{4}}-\frac{15 c^{4}}{b^{11} x^{6}}+\frac{6 c^{3}}{b^{10} x^{8}}-\frac{2 c^{2}}{b^{9} x^{10}}+\frac{c}{2 b^{8} x^{12}}-\frac{1}{14 b^{7} x^{14}}"," ",0,"-1/2*c^8/b^13*(-4*b^4/c/(c*x^2+b)^5-66*b/c/(c*x^2+b)^2-1/7*b^6/c/(c*x^2+b)^7-b^5/c/(c*x^2+b)^6-12*b^3/c/(c*x^2+b)^4-132/c/(c*x^2+b)-30*b^2/c/(c*x^2+b)^3)-1/14/b^7/x^14-66/b^13*c^6/x^2+33/b^12*c^5/x^4-15/b^11*c^4/x^6+6/b^10*c^3/x^8-2/b^9*c^2/x^10+1/2/b^8*c/x^12","B"
1062,1,197,14,0.062000," ","int((2*c*x^3+b)/x^22/(c*x^3+b)^8,x)","-\frac{\left(-\frac{b^{6}}{7 \left(c \,x^{3}+b \right)^{7} c}-\frac{b^{5}}{\left(c \,x^{3}+b \right)^{6} c}-\frac{4 b^{4}}{\left(c \,x^{3}+b \right)^{5} c}-\frac{12 b^{3}}{\left(c \,x^{3}+b \right)^{4} c}-\frac{30 b^{2}}{\left(c \,x^{3}+b \right)^{3} c}-\frac{66 b}{\left(c \,x^{3}+b \right)^{2} c}-\frac{132}{\left(c \,x^{3}+b \right) c}\right) c^{8}}{3 b^{13}}-\frac{44 c^{6}}{b^{13} x^{3}}+\frac{22 c^{5}}{b^{12} x^{6}}-\frac{10 c^{4}}{b^{11} x^{9}}+\frac{4 c^{3}}{b^{10} x^{12}}-\frac{4 c^{2}}{3 b^{9} x^{15}}+\frac{c}{3 b^{8} x^{18}}-\frac{1}{21 b^{7} x^{21}}"," ",0,"-1/3*c^8/b^13*(-4*b^4/c/(c*x^3+b)^5-66*b/c/(c*x^3+b)^2-1/7*b^6/c/(c*x^3+b)^7-b^5/c/(c*x^3+b)^6-12*b^3/c/(c*x^3+b)^4-132/c/(c*x^3+b)-30*b^2/c/(c*x^3+b)^3)-1/21/b^7/x^21-44/b^13*c^6/x^3+22/b^12*c^5/x^6-10/b^11*c^4/x^9+4/b^10*c^3/x^12-4/3/b^9*c^2/x^15+1/3/b^8*c/x^18","B"
1063,1,203,21,0.098000," ","int(x^(-1-7*n)*(b+2*c*x^n)/(c*x^n+b)^8,x)","-\frac{x^{-7 n}}{7 b^{7} n}+\frac{c \,x^{-6 n}}{b^{8} n}-\frac{4 c^{2} x^{-5 n}}{b^{9} n}+\frac{12 c^{3} x^{-4 n}}{b^{10} n}-\frac{30 c^{4} x^{-3 n}}{b^{11} n}+\frac{66 c^{5} x^{-2 n}}{b^{12} n}+\frac{\left(9009 b^{5} c \,x^{n}+20020 b^{4} c^{2} x^{2 n}+24024 b^{3} c^{3} x^{3 n}+16380 b^{2} c^{4} x^{4 n}+6006 b \,c^{5} x^{5 n}+924 c^{6} x^{6 n}+1716 b^{6}\right) c^{7}}{7 \left(c \,x^{n}+b \right)^{7} b^{13} n}-\frac{132 c^{6} x^{-n}}{b^{13} n}"," ",0,"-132/b^13*c^6/n/(x^n)+66/b^12*c^5/n/(x^n)^2-30/b^11*c^4/n/(x^n)^3+12/b^10*c^3/n/(x^n)^4-4/b^9*c^2/n/(x^n)^5+1/b^8*c/n/(x^n)^6-1/7/b^7/n/(x^n)^7+1/7*c^7*(924*(x^n)^6*c^6+6006*b*c^5*(x^n)^5+16380*b^2*c^4*(x^n)^4+24024*b^3*c^3*(x^n)^3+20020*b^4*c^2*(x^n)^2+9009*b^5*c*x^n+1716*b^6)/b^13/n/(c*x^n+b)^7","B"
1064,1,86,37,1.147000," ","int(x^31*(x^16+1)^(1/2)/(-x^16+1),x)","\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{x^{16} \RootOf \left(\textit{\_Z}^{2}-2\right)+3 \RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{x^{16}+1}}{\left(x -1\right) \left(x +1\right) \left(x^{2}+1\right) \left(x^{4}+1\right) \left(x^{8}+1\right)}\right)}{16}-\frac{\left(x^{16}+4\right) \sqrt{x^{16}+1}}{24}"," ",0,"-1/24*(x^16+4)*(x^16+1)^(1/2)+1/16*RootOf(_Z^2-2)*ln(-(RootOf(_Z^2-2)*x^16+4*(x^16+1)^(1/2)+3*RootOf(_Z^2-2))/(x-1)/(x+1)/(x^2+1)/(x^4+1)/(x^8+1))","C"
1065,1,143,69,0.102000," ","int((c+d/x)^(1/2)/x/(a+b/x)^(1/2),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \sqrt{\frac{c x +d}{x}}\, \left(-\sqrt{b d}\, c \ln \left(\frac{2 a c x +a d +b c +2 \sqrt{\left(c x +d \right) \left(a x +b \right)}\, \sqrt{a c}}{2 \sqrt{a c}}\right)+\sqrt{a c}\, d \ln \left(\frac{a d x +b c x +2 b d +2 \sqrt{b d}\, \sqrt{\left(c x +d \right) \left(a x +b \right)}}{x}\right)\right) x}{\sqrt{\left(c x +d \right) \left(a x +b \right)}\, \sqrt{b d}\, \sqrt{a c}}"," ",0,"-((a*x+b)/x)^(1/2)*x*((c*x+d)/x)^(1/2)*(ln((a*d*x+b*c*x+2*(b*d)^(1/2)*((c*x+d)*(a*x+b))^(1/2)+2*b*d)/x)*d*(a*c)^(1/2)-ln(1/2*(2*a*c*x+2*((c*x+d)*(a*x+b))^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*c*(b*d)^(1/2))/((c*x+d)*(a*x+b))^(1/2)/(b*d)^(1/2)/(a*c)^(1/2)","B"
1066,0,0,214,1.016000," ","int(x^(2*n-1)*(b*x^n+a)^(5/2)/(d*x^n+c)^(1/2),x)","\int \frac{\left(b \,x^{n}+a \right)^{\frac{5}{2}} x^{2 n -1}}{\sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(2*n-1)*(b*x^n+a)^(5/2)/(d*x^n+c)^(1/2),x)","F"
1067,0,0,167,0.961000," ","int(x^(2*n-1)*(b*x^n+a)^(3/2)/(d*x^n+c)^(1/2),x)","\int \frac{\left(b \,x^{n}+a \right)^{\frac{3}{2}} x^{2 n -1}}{\sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(2*n-1)*(b*x^n+a)^(3/2)/(d*x^n+c)^(1/2),x)","F"
1068,0,0,120,1.012000," ","int(x^(2*n-1)*(b*x^n+a)^(1/2)/(d*x^n+c)^(1/2),x)","\int \frac{\sqrt{b \,x^{n}+a}\, x^{2 n -1}}{\sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(2*n-1)*(b*x^n+a)^(1/2)/(d*x^n+c)^(1/2),x)","F"
1069,0,0,73,0.974000," ","int(x^(2*n-1)/(b*x^n+a)^(1/2)/(d*x^n+c)^(1/2),x)","\int \frac{x^{2 n -1}}{\sqrt{b \,x^{n}+a}\, \sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(2*n-1)/(b*x^n+a)^(1/2)/(d*x^n+c)^(1/2),x)","F"
1070,0,0,75,0.947000," ","int(x^(2*n-1)/(b*x^n+a)^(3/2)/(d*x^n+c)^(1/2),x)","\int \frac{x^{2 n -1}}{\left(b \,x^{n}+a \right)^{\frac{3}{2}} \sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(2*n-1)/(b*x^n+a)^(3/2)/(d*x^n+c)^(1/2),x)","F"
1071,0,0,83,0.918000," ","int(x^(2*n-1)/(b*x^n+a)^(5/2)/(d*x^n+c)^(1/2),x)","\int \frac{x^{2 n -1}}{\left(b \,x^{n}+a \right)^{\frac{5}{2}} \sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(2*n-1)/(b*x^n+a)^(5/2)/(d*x^n+c)^(1/2),x)","F"
1072,0,0,314,0.965000," ","int(x^(3*n-1)*(b*x^n+a)^(5/2)/(d*x^n+c)^(1/2),x)","\int \frac{\left(b \,x^{n}+a \right)^{\frac{5}{2}} x^{3 n -1}}{\sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(3*n-1)*(b*x^n+a)^(5/2)/(d*x^n+c)^(1/2),x)","F"
1073,0,0,253,0.934000," ","int(x^(3*n-1)*(b*x^n+a)^(3/2)/(d*x^n+c)^(1/2),x)","\int \frac{\left(b \,x^{n}+a \right)^{\frac{3}{2}} x^{3 n -1}}{\sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(3*n-1)*(b*x^n+a)^(3/2)/(d*x^n+c)^(1/2),x)","F"
1074,0,0,189,0.993000," ","int(x^(3*n-1)*(b*x^n+a)^(1/2)/(d*x^n+c)^(1/2),x)","\int \frac{\sqrt{b \,x^{n}+a}\, x^{3 n -1}}{\sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(3*n-1)*(b*x^n+a)^(1/2)/(d*x^n+c)^(1/2),x)","F"
1075,0,0,124,0.997000," ","int(x^(3*n-1)/(b*x^n+a)^(1/2)/(d*x^n+c)^(1/2),x)","\int \frac{x^{3 n -1}}{\sqrt{b \,x^{n}+a}\, \sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(3*n-1)/(b*x^n+a)^(1/2)/(d*x^n+c)^(1/2),x)","F"
1076,0,0,113,1.003000," ","int(x^(3*n-1)/(b*x^n+a)^(3/2)/(d*x^n+c)^(1/2),x)","\int \frac{x^{3 n -1}}{\left(b \,x^{n}+a \right)^{\frac{3}{2}} \sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(3*n-1)/(b*x^n+a)^(3/2)/(d*x^n+c)^(1/2),x)","F"
1077,0,0,123,1.091000," ","int(x^(3*n-1)/(b*x^n+a)^(5/2)/(d*x^n+c)^(1/2),x)","\int \frac{x^{3 n -1}}{\left(b \,x^{n}+a \right)^{\frac{5}{2}} \sqrt{d \,x^{n}+c}}\, dx"," ",0,"int(x^(3*n-1)/(b*x^n+a)^(5/2)/(d*x^n+c)^(1/2),x)","F"
1078,1,21,20,0.046000," ","int(x^p*(c*x+b)^p*(2*c*x+b),x)","\frac{x^{p +1} \left(c x +b \right)^{p +1}}{p +1}"," ",0,"x^(p+1)*(c*x+b)^(p+1)/(p+1)","A"
1079,1,26,25,0.044000," ","int(x^(2*p+1)*(c*x^2+b)^p*(2*c*x^2+b),x)","\frac{x^{2 p +2} \left(c \,x^{2}+b \right)^{p +1}}{2 p +2}"," ",0,"1/2*x^(2*p+2)*(c*x^2+b)^(p+1)/(p+1)","A"
1080,1,26,25,0.045000," ","int(x^(2+3*p)*(c*x^3+b)^p*(2*c*x^3+b),x)","\frac{x^{3 p +3} \left(c \,x^{3}+b \right)^{p +1}}{3 p +3}"," ",0,"1/3*x^(3+3*p)*(c*x^3+b)^(p+1)/(p+1)","A"
1081,0,0,27,0.688000," ","int(x^(-1+n*(p+1))*(c*x^n+b)^p*(b+2*c*x^n),x)","\int \left(2 c \,x^{n}+b \right) x^{\left(p +1\right) n -1} \left(c \,x^{n}+b \right)^{p}\, dx"," ",0,"int(x^(-1+n*(p+1))*(c*x^n+b)^p*(b+2*c*x^n),x)","F"